Ultrasound contrast agents (UCAs) are used in a clinical setting to enhance the backscattered signal from the blood pool to estimate perfusion and blood flow. The UCAs consist of encapsulated microbubbles, measuring 1-10 µm in diameter. Acoustic characterization of UCAs is generally carried out from an ensemble of bubbles. The measured signal is a complicated summation of all signals from the individual microbubbles. Hence, characterization of a single bubble from acoustic measurements is complex.

In this study, 583 optical observations of freely flowing, oscillating, individual microbubbles from an experimental UCA were analyzed. The excursions during ultrasound exposure were observed through a micro-

According to Oxford Advanced Learner's Dictionary of Current English [START_REF] Hornby | Oxford Advanced Learner's Dictionary of Current English[END_REF], popular science can be defined as organized knowledge suited to the taste or the education level of the general public. Since boiling water, opening soda bottles, and producing froth when pouring beer is probably "to the taste of the general public", observing and investigating bubble behavior can be considered as popular science.

One of the first to organize his knowledge on this science was Leonardo da Vinci. Not only did he have a theory on oversaturation of water [START_REF] Richter | The Notebooks of Leonardo da Vinci[END_REF]:

"Moreover the elements repel or attract each other, for one sees water expelling air from itself, and fire entering as heat under the bottom of a boiler and afterwards escaping in the bubbles on the surface of the boiling water."

He was also the first to describe the concept of surface tension [START_REF] Richter | The Notebooks of Leonardo da Vinci[END_REF]: i i "proefschrift041" -2004/7/6 -18:01 -page 16 -#20

i i i i i i [1, 1]
MEDICAL BUBBLES AND PHOTOGRAPHY "The centre of a particular sphere of water is that which is formed in the tiniest particles of dew, which is often seen in perfect roundness upon the leaves of plants where it falls; it is of such lightness that it does not flatten out on the spot where it rests, and it is almost supported by the surrounding air, so that it does not itself exert any pressure, or form any foundation; and because of this its surface is drawn towards its centre with equal force and they become magnets one of another, with the result that each drop necessarily becomes perfectly spherical, forming its centre in the middle, equidistant from each point of its gravity, it always places itself in the middle between opposite parts of equal weight."

Leonardo da Vinci had theories on acoustics, too:

"I say that the sound of the echo is reflected to the ear after it has struck, just as the images of objects striking the mirrors are reflected into the eyes. And as the image falls from the object into the mirror to the eye at equal angles, so sound will also strike and rebound at equal angles as it passes from the first percussion in the hollow and travels out to meet the ear."

As such, we may state that Leonardo da Vinci had already depicted the ingredients needed for contrast echography five hundred years ago. Roughly two centuries after his death, Sir Isaac Newton did some gravity-related experiments with encapsulated bubbles [START_REF] Newton | Philosophiae Naturalis Principia Mathematica. 3rd[END_REF][START_REF] Newton | The Principia: mathematical principles of natural philosophy[END_REF]:

"From the top of St. Paul's Cathedral in London in June 1710, glass balls were dropped simultaneously in pairs, one full of quicksilver, the other full of air; and in falling they described a space of 220 London feet."

Not until the work of Daniel Bernoulli [START_REF] Bernoulli | sive de viribus et motibus fluidorum commentarii[END_REF] it was understood that negative pressure can be produced within a liquid. According to De Jong's summary of historical technical aspects of cavitation [START_REF] De Jong | Acoustic properties of ultrasound contrast agents[END_REF], Euler & d'Alembert debated the consequences of negative pressures in the early eighteenth century. According to Euler, they would ultimately cause a rupture of the liquid, d'Alembert refused to accept this view.

Because of the Industrial Revolution, Euler's view was supported by evidence. As steam turbines became more powerful, the rotation speed of ship-screw propellers increased dramatically. With the increased rotation i i "proefschrift041" -2004/7/6 -18:01 -page 17 -#21 i i i i i i SOUND AND BUBBLES [1,1] speed, an "extraordinarily rapid" kind of erosion of the propellers was observed [START_REF] Silberrad | Propeller erosion[END_REF]. Silberrad showed pictures of ship-screws and described the seriousness of this problem:

"These have been photographed from specimens cut from the first set of propellers of the Mauretania, and exhibited at the recent Anglo-Japanese Exhibition. These original propellers had three loose blades, and an over-all diameter of about 17 ft. The metal, it will be seen, is eaten away to the depth of in some cases more than 2 in. The financial aspect of the question was thus very serious. Propellers of the alloys in question cost anywhere between 130l. to 180l. a ton and have a scrap value of less than half that amount, while the rapidity of the wear was such that in the case of the Mauretania and Lusitania they would, had no remedy been found, have required replacing every few months, at a cost of some thousands of pounds, since each propeller weighed about 20 tons."

As for the cause of the erosion, Silberrad stated:

"Further, it will be noted that the area attacked is, as has already been stated, near the hub. This was of large size, and it seems probable that there was a certain centrifugal action causing a reduction of pressure, and this region of reduced pressure was marked by the erosion. Here Dr. Silberrad considers that cavitation might occur, and, in consequence, water broken by intervening evacuated spaces with no air present."

The word cavitation for the formation of cavities due to negative pressures has been attributed to Froude according to an article by Thornycroft & Barnaby on torpedo-boat destroyers, written in 1895 [START_REF] Thornycroft | Torpedo-boat destroyers[END_REF].

In 1917, Lord Rayleigh published a masterpiece on cavitation [START_REF] Rayleigh | On the pressure development in a liquid during the collapse of a spherical cavity[END_REF], starting with: "When reading O. Reynolds's description of the sound emitted by water in a kettle as it comes to the boil, and their explanation as due to the partial or complete collapse of bubbles as they rise through cooler water, I proposed to myself a further consideration of the problem thus presented; but I had not gone far when I learned from Sir C. Parsons that he also was interested in the same question in connexion with cavitation behind i i "proefschrift041" -2004/7/6 -18:01 -page 18 -#22

i i i i i i [1, 1]
MEDICAL BUBBLES AND PHOTOGRAPHY screw-propellers, and that at his instigation Mr. S. Cook, on the basis of an investigation by Besant, had calculated the pressure developed when the collapse is suddenly arrested by the impact against a rigid concentric obstacle. During the collapse the fluid is regarded as incompressible.

In the present note I have given a simpler derivation of Besant's results, and have extended the calculation to find the pressure in the interior of the fluid during the collapse. It appears that before the cavity is closed these pressures may rise very high in the fluid near the inner boundary."

The equations presented are still applicable today. Cavitation with a mechanical origin is called hydraulic cavitation. de Haller experimented in a laboratory environment with hydraulic cavitation on turbines [START_REF] De Haller | Untersuchungen über die durch Kavitation hergerufenen Korrosionen[END_REF]. A more recent study on hydraulic cavitation involves snapping shrimp: predator shrimp that kill their prey by producing cavitation bubbles that collapse near their victims [START_REF] Versluis | How snapping shrimp snap: through cavitating bubbles[END_REF]. Light is emitted from the collapsing cavities, a phenomenon dubbed shrimpoluminescence [START_REF] Lohse | Snapping shrimp make flashing bubbles[END_REF].

Sound waves can create negative pressures, too, resulting into acoustic cavitation. To learn more about this subject, we have to look into the science of inaudible sound: ultrasonics.

In "Some Background History of Ultrasonics", written in 1948, Klein called ultrasonography, or: superaudible acoustics, "a by-product of the two world wars" [START_REF] Klein | Some background history of ultrasonics[END_REF]:

"To trace the progress of ultrasonics from its beginning, it is necessary to recall the years [1914][1915][1916][1917][1918] and Professor Paul Langevin who founded this subject. In 1915, the U-boat menace threatened the Allies. A Russian engineer named Chilowski submitted an idea for submarine detection to the French Government. The latter invited Langevin, then Director of the School of Physics and Chemistry in Paris, to evaluate it. Chilowski's proposal was to excite a cylindrical, mica condenser by a high frequency singing arc (Poulson Arc) operated at about 100 kc. This device was intended to be a generator of an ultrasonic beam for detecting submerged objects. The idea of locating underwater obstacles by means of sound echoes had been previously suggested by L.F. Richardson, in England. In 1912, following the Titanic disaster, he proposed to set a high frequency hydraulic whistle at the focus of a mirror and use the beam for locating submerged i i "proefschrift041" -2004/7/6 -18:01 -page 19 -#23 i i i i i i SOUND AND BUBBLES [1,1] navigational hazards. Sir Charles Parsons, the inventor of the vapor turbine, became interested in this device and built one in accordance to Richardson's ideas. This apparatus was found unsuitable for the job of searching underwater obstacles, but the idea was not lost."

(...)
"By making use of the piezoelectric effects of quartz, Langevin introduced the modern piston transducer. He became acquainted with piezoelectric phenomena while a student at the laboratory of the Curie brothers. Perhaps the most outstanding advance made by Langevin in this field was his theoretical calculation and experimental verification of the fact that a thin sheet of quartz sandwiched between two steel plates constituted an electromechanical resonant system."

(...)
"Various aspects of the piezoelectric piston transducer were investigated by Langevin and his co-workers, among whom were a number of British and American scientists. They observed many biological and physical effects of the ultrasonic beam. For example, they noted in their laboratory tank that small fish were killed as they swam into the intense portion of the ultrasonic beam. Also, they saw incipient cavitation in the water when the sound source was active and felt painful effects upon the hand when struck in front of the beam."

This is the first mentioning of acoustic cavitation. But the cavities themselves produced sound waves as well. Bragg related the sound of drops falling into water to cavities [START_REF] Bragg | The World of Sound[END_REF]:

"When photographs are taken from below the surface, it becomes clear that an air cavity is often formed."

(...)
"Now it appears that the note which we hear is the resonant note of this cavity, probably given out when the cavity has closed over i i "proefschrift041" -2004/7/6 -18:01 -page 20 -#24

i i i i i i [1, 1]
MEDICAL BUBBLES AND PHOTOGRAPHY at the top and burst again. My friend Richard Paget has actually measured these cavities in various cases and then made models of them in plasticine. Blowing across the top of the model cavity, he finds that its note is practically the same as that the drop makes when it falls. The note is very high, and has a frequency of two to three thousand vibrations a second."

In 1933, Minnaert presented his theory for the sounds created by bubbles in water [START_REF] Minnaert | On musical air bubbles and the sound of running water[END_REF]:

"We will suppose that the bubbles give a sound because they pulsate in closing. Periodically the bubble expands and contracts, the surrounding water being the inert mass which is set in vibration, while the elasticity is due to the air of the bubble. A formula for the frequency of such pulsations may be derived in a quite elementary way."

Thus, he formulated a theory on the resonance frequency of bubbles.

Noltingk & Neppiras were the first to formulate an equation to describe the behavior of gas filled and empty cavities in a sound field [START_REF] Noltingk | Cavitation produced by ultrasonics[END_REF]. Many more would follow. An excellent overview on the historic development of physical models of the interaction of bubbles with acoustics was written by De Jong [START_REF] De Jong | Acoustic properties of ultrasound contrast agents[END_REF].

In 1954, not long after the introduction of clinical ultrasound [START_REF] Wild | The use of ultrasonic pulses for the measurement of biologic tissues and the detection of tissue density changes[END_REF][START_REF] Wild | Use of high-frequency ultrasonic waves for detecting changes of texture in living tissues[END_REF], Fox & Herzfeld hypothesized that cavitation bubbles grow from gas nuclei encapsulated by organic skins. Because of the skins, these nuclei would not be subjected to diffusive processes [START_REF] Fox | Gas bubbles with organic skins as cavitation nuclei[END_REF]. This hypothesis could also be read as follows: If gas bubbles encapsulated by an elastic shell are insonified, they may still act as cavitation nuclei.

Fourteen years later, Gramiak et al. experimented with saline to create in vivo air bubbles [START_REF] Gramiak | Echocardiography of the aortic root[END_REF][START_REF] Gramiak | Ultrasound cardiography: contrast studies in anatomy and function[END_REF]. These rapidly diffusing air bubbles generated a characteristic response to ultrasound, such that perfused vessels would appear "brighter" on echographic images. This new diagnostic technique was called ultrasound contrast imaging.

Since then, a range of agents consisting of "medical bubbles" have been developed [START_REF] De Jong | Acoustic properties of ultrasound contrast agents[END_REF][START_REF] De Jong | Characteristics of contrast agents and 2D imaging[END_REF][START_REF] De Jong | New ultrasound contrast agents and technological innovations[END_REF][START_REF] Frinking | Ultrasound Contrast Agents: acoustic characterization and diagnostic imaging[END_REF]. Most of the ultrasound contrast agents (UCAs) that are currently used in clinical diagnostics contain slowly diffusing gas microbubbles encapsulated by highly elastic shells, to prevent them from dissolving too quickly during application. After intravascular injection of an agent into the circulation, microbubbles will pass the site of interest 20 i i "proefschrift041" -2004/7/6 -18:01 -page 21 -#25 [1,2] which is insonified by the clinician. Upon insonification, the microbubbles will generate a characteristic response, which is detected by the ultrasound scanner used. The resulting echographic image can then be interpreted by the clinician. The encapsulated gas bubbles generally used in diagnostic ultrasound contrast studies vary in diameter from 1 to 10 µm. They have resonance periods in the microsecond range. If released, the gas dissolves in several to several hundreds of milliseconds.

i i i i i i HISTORICAL NOTE
Most studies on microbubble behavior have been based on the acoustic response from an ensemble of bubbles. With high-speed photography fast enough to surpass the bubble resonance periods, the observation of individual microbubble behavior has become possible.

A historical note on high-speed photography

We may define high-speed photography as the capturing of events that are more rapid than the human brain can process, approximately 1 /15 th of a second.

According to Endelman [START_REF] Endelman | A brief history of high speed photography 1851-1930[END_REF], the beginning of high-speed photography "might be considered to be William Henry Fox Talbot's experiment in 1851. He attached a page of the London Times newspaper to a wheel, which was rotated in front of his wet plate camera in a darkened room. As the wheel rotated, Talbot exposed a few square inches of the newspaper page for about 1 /2,000 th of a second, using spark illumination from Leyden jars. This experiment resulted in a readable image." In 1858, Thomas Skaife claimed to have captured a photograph of a mortar shell in flight [START_REF] Skaife | A feat in photography[END_REF]. The excerpt of the newspaper is shown in Figure 1.1.

The first multi-frame recording was done by Muybridge in 1878. He captured a sequence of 12 photographs of a trotting horse, shown in Figure 1.2. Exposure times were 2 ms and interframe times 40 ms. Over the next years photographic technology rapidly improved, stimulated by the development of cinematography. Roughly thirty years after Muybridge's experiments, the first motion picture to embody a plot (The Great Train Robbery) was shown to the public [START_REF] Collins | The Story of America in Pictures[END_REF].

Early applications of high-speed photography were mainly in ballistics, but also in fluid dynamics. The Mach brothers and Sir Boys published sharp photographs of flying bullets at the end of the nineteenth century [START_REF] Boys | On electric spark photographs; or, photography of flying bullets, etc., by the light of the electric spark[END_REF][START_REF] Mach | Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorgänge[END_REF][START_REF] Mach | Über die in Pola und Meppen angestellten ballistisch-photographischen Versuche[END_REF][START_REF] Mach | Weitere ballistisch-photographische Versuche[END_REF]. In 1887 and 1904, photographs of rough and i i "proefschrift041" -2004/7/6 -18:01 -page 22 -#26

i i i i i i [1, 2]
MEDICAL BUBBLES AND PHOTOGRAPHY smooth spheres falling into water were published [START_REF] Worthington | Impact with a liquid surface studied by the aid of instantaneous photography[END_REF][START_REF] Worthington | Impact with a liquid surface studied by the aid of instantaneous photography[END_REF]. An elaborate overview of the development of high-speed photography in the nineteenth and twentieth century is given by Fuller & Rendell [START_REF] Fuller | The development of high speed photography[END_REF]. Nowadays, high-speed cameras capable of taking multiple frames are equipped with either beam splitters that divide an image over several recording devices, or a rotating mirror sweeping the image over numerous recording devices. Although recording speeds of 200 million frames per second can be reached with the former camera type, the total number of frames available is currently 16. With the latter technology, recording speeds of 25 million frames per second can be reached, whereas the total number of frames is virtually unlimited.

High-speed photography of medical bubbles

Over the past years various studies were performed involving visualization of medical bubbles during ultrasound irradiation. Klibanov et al. [START_REF] Klibanov | Direct video-microscopic observation of the dynamic effects of medical ultrasound on ultrasound contrast microspheres[END_REF] observed oscillations of UCA bubbles attached to a Petri dish with a 30 frames per second camera. Dayton et al. [34,[START_REF] Dayton | Optical and acoustical observations of the effects of ultrasound on contrast agents[END_REF] combined acoustical observations of UCA and optical observations with a 600 frames per sec-i i "proefschrift041" -2004/7/6 -18:01 -page 24 -#28

i i i i i i [1, 3]
MEDICAL BUBBLES AND PHOTOGRAPHY ond camera. They observed gas release and bubble destruction. Takeuchi [START_REF] Takeuchi | Pulsed stroboscopic visualizer to synchronously monitor the microballoon under insonification[END_REF]178] used TV-frame synchronous illumination and insonification to observe microballoon breakage. Because of the low frame rates of the cameras mentioned, the instance of shell breakage and the behavior of a bubble within an ultrasound cycle could not be observed. Kuribayashi et al. [START_REF] Kuribayashi | A high-magnification and high-speed system for the observation of microbubbles under ultrasound exposure[END_REF] observed changes in UCA bubble diameters within one cycle of ultrasound, at frame rates up to 10 MHz and 50× magnification. They concluded that the imaging frame rate and magnification were not sufficient for studying the details of UCA bubble behavior. De Jong et al. [START_REF] De Jong | Optical imaging of contrast agent microbubbles in an ultrasound field with a 100-MHz camera[END_REF] carried out a preliminary study on this subject. They proposed a method to visualize the oscillations of bubbles using a microscope and a fast framing camera operating at a 4 MHz frame rate. Furthermore, they compared radius-time curves, derived from two-dimensional bubble pictures, to a theoretical model. Morgan et al. [START_REF] Morgan | Experimental and theoretical analysis of individual contrast agent behavior[END_REF] used a 100 megaframes per second camera in streak mode to predict bubble-oscillating behavior. More recently, May et al. [START_REF] May | Dynamics and fragmentation of thickshelled microbubbles[END_REF] performed high-speed optical experiments on microbubbles with an outer lipid layer, an oil layer, and a gas core. Such microbubbles may have a future application in local drug delivery.

In our laboratory at Erasmus MC, we captured images of insonified encapsulated microbubbles at higher frame rates than the ultrasonic frequencies transmitted. We made use of a fast framing camera with a beam splitter, capturing 8 frames at a 3 MHZ frame rate, and of the Brandaris-128 rotating mirror camera system, capturing 128 frames at frame rates around 13 MHz. The microbubbles observed have been applied for diagnostic purposes, and have potential therapeutic applications. The potential clinical applications of insonifying medical bubbles have been explored, based on high-speed optical observations, combined with bubblesound theory.

An example of our results is shown in Figure 1.3, which shows a sequence of microscopic image frames of a freely flowing contrast agent microbubble. The frames were taken during one cycle of ultrasound insonification, with a center frequency of 500 kHz. The peak negative acoustic pressure at the region of interest was 0.85 MPa. Each frame corresponds to a 45 × 27 µm 2 area. The exposure time of each frame was 10 ns. Inter frame times were 0.33 µs, except for the time between frames e and f, which was 0.66 µs. The sequence shows an expanding medical bubble of 5.3 µm (a) and 17.6 µm (b), and its maximal expansion of 22.9 µm (c). After contracting to 20.2 µm (d), a violent effect is visible (e). The microbubble had been pushed to the lower left side of the frame, apparently by a water i i "proefschrift041" -2004/7/6 -18:01 -page 25 -#29 [1,4] jet that was projected through the microbubble at high speed, causing it to act as a microsyringe. A subframe shows the negative of the region of interest. Finally the deformed microbubble reoccurred as an asymmetric shape (f). Jetting behavior may find an application in drug delivery. Chapter 3 reviews the mechanism of the coalescence (merging) of microbubbles. The mechanism is based on computations and on observations from high-speed camera images. Some potential medical applications are addressed.

i i i i i i HIGH-SPEED PHOTOGRAPHY OF MEDICAL BUBBLES
Chapter 4 presents optical evidence of coalescing behavior of released gas bubbles. With these observations, the theory on expanding bubble coalescence can be validated.

Chapter 5 shows simulations of the diffusive behavior of gas microbubbles. Their applicability for diagnostic pressure measurements is discussed.

Chapter 6 reveals optical evidence for the dissolving behavior of gas bubbles simulated in Chapter 5. The release of gas from an encapsulated bubble is studied.

Chapter 7 gives an overview of types of behavior of microbubbles when insonified at high acoustic pressures. The potential clinical applications of these types of behavior are discussed.

Chapter 8 discusses general considerations and future prospects of medical bubbles.

i i "proefschrift041" -2004/7/6 -18:01 -page 28 -#32

i i i i i i [2, 1] IMAGES OF MICROBUBBLES
scope. Images were recorded with a high frame rate camera operating at 3 MHz. Microbubbles on these images were measured off-line and maximal excursions were determined. A technique is described to determine the diameters of the bubbles observed. We compared the maximal excursions of microbubbles of the same initial size in an ultrasound field with a 500 kHz center frequency at acoustic amplitudes ranging from 0.06 MPa to 0.85 MPa.

It was concluded that maximal excursions of identical bubbles can differ by 150% at low acoustic pressures (mechanical index or MI < 0.2). At a high acoustic pressure (MI = 1.2) an image sequence was recorded on which a bubble collapsed, while an apparently identical bubble survived.

Introduction

The detection of perfusion and blood flow is of great clinical interest, but technically challenging, because blood reflects ultrasound poorly. Reflections from blood can be increased by administering gaseous bubbles, due to their high echogenicity. Microbubble-based ultrasound contrast agents (UCAs) make blood better detectable in B-mode and Doppler mode imaging [4,[START_REF] Burns | Intravenous contrast agent for ultrasound Doppler: In vivo measurement of small tumor vessel doseresponse[END_REF][START_REF] De Jong | Ultrasound contrast imaging: principles and applications[END_REF]. A wide variety of contrast agents is commercially available or under clinical trial and development [4]. De Jong & Ten Cate [START_REF] De Jong | New ultrasound contrast agents and technological innovations[END_REF] gave an overview of clinical applications and technological innovations of ultrasound contrast agents. A review of current and near future detection procedures of UCAs was written in [START_REF] De Jong | Detection procedures of ultrasound contrast agents[END_REF].

Most of the commercially available UCAs consist of encapsulated microbubbles of low solubility gas, measuring 1-10 µm in diameter. They are sufficiently stable to pass into the systemic circulation following injection into a peripheral vein. Nowadays, new generations of UCA are under investigation to further improve the scattering from blood and to ameliorate its detection in the presence of surrounding tissue. In addition to UCA design and development, increased interest is directed to the development of more sensitive ultrasound equipment to visualize UCA. Consequently, contrast echocardiography has become a rapidly evolving field encompassing a family of technologies and practices for the noninvasive assessment of cardiac structure and function. Recent developments in engineering of microbubbles and in adapted imaging systems such as triggered modality in combination with imaging techniques such as power Doppler, pulse inversion and power modulation imaging are facilitating simultaneous as-INTRODUCTION [2,1] sessment of myocardial function and perfusion [4,[START_REF] De Jong | Contrast-specific imaging methods[END_REF]. Despite these new imaging techniques, myocardial contrast echocardiography has to overcome several problems if it is to be able to quantify myocardial blood flow. These limitations can be surmounted with a better understanding of the behavior of a single microbubble in an ultrasound field. As a matter of fact, the interactions of microbubbles with an ultrasound beam are complex. When a microbubble is exposed to an oscillating acoustic signal, it undergoes alternate expansions and contractions, equal and symmetrical at low acoustic powers, i.e., mechanical index (MI) < 0.1. The mechanical index is defined as

MI = p - ac f , ( 2.1)
where p - ac is the peak rarefactional acoustic pressure normalized by 1 MPa and f is the center frequency of the ultrasound normalized by 1 MHz. As the acoustic power increases, more complex nonlinear interactions occur. This oscillating behavior is associated with the production of harmonic signals. At still higher powers, highly nonlinear behavior is associated with complex bubble behavior, which can be revealed by phenomena like bubble rupture, fragmentation, and merging.

An improved understanding of contrast bubble properties and behavior under the influence of ultrasound may lead to more sophisticated detection techniques. Until now, mostly ultrasonic measurements supported by theoretical models were adopted to elucidate and quantify the interaction between ultrasound beam and contrast gas bubbles [START_REF] De Jong | Absorption and scatter of encapsulated gas filled microspheres: theoretical considerations and some measurements[END_REF][START_REF] De Jong | Ultrasound scattering properties of Albunex microspheres[END_REF][START_REF] Church | The effects of an elastic solid surface layer on the radial pulsations of gas bubbles[END_REF][START_REF] Hoff | Acoustic properties of ultrasonic contrast agents[END_REF][START_REF] Frinking | Acoustic modeling of shell-encapsulated gas bubbles[END_REF]. The experiments were mostly performed on an ensemble of gas bubbles with certainly a range of different sizes and possibly different shell parameters. Therefore, these studies express a bulk response of a majority of bubbles. Hence, the behavior and contribution of individual bubbles becomes difficult to predict. To make more thorough investigations on individual bubble response to ultrasound excitation, and by that develop new detection techniques, optical visualization of oscillating bubbles represents an attractive alternative. Over the past years various studies were performed involving visualization of gas bubbles during ultrasound irradiation. Klibanov et al. [START_REF] Klibanov | Direct video-microscopic observation of the dynamic effects of medical ultrasound on ultrasound contrast microspheres[END_REF] observed oscillations of UCA bubbles attached to a Petri dish with a 30 frames per second camera. Dayton et al. [34,[START_REF] Dayton | Optical and acoustical observations of the effects of ultrasound on contrast agents[END_REF] combined acoustical observations of UCA and optical observations with a 600 frames per second camera. They observed gas release and bubble destruction. Takeuchi [START_REF] Takeuchi | Pulsed stroboscopic visualizer to synchronously monitor the microballoon under insonification[END_REF]178] used TV-frame synchronous illumination i i "proefschrift041" -2004/7/6 -18:01 -page 30 -#34

i i i i i i [2, 2]
IMAGES OF MICROBUBBLES and insonification to observe microballoon breakage. Because of the low frame rates of the cameras mentioned, the instance of shell breakage and the behavior of a bubble within an ultrasound cycle could not be observed. Kuribayashi et al. [START_REF] Kuribayashi | A high-magnification and high-speed system for the observation of microbubbles under ultrasound exposure[END_REF] observed changes in UCA bubble diameters within one cycle of ultrasound, at frame rates up to 10 MHz and 50× magnification. They concluded that the imaging frame rate and magnification were not sufficient for studying the details of UCA bubble behavior. De Jong et al. [START_REF] De Jong | Optical imaging of contrast agent microbubbles in an ultrasound field with a 100-MHz camera[END_REF] carried out a preliminary study on this subject. They proposed a method to visualize the oscillations of bubbles using a microscope and a fast framing camera operating at a 4 MHz frame rate. Furthermore, they compared radius-time curves, derived from two-dimensional bubble pictures, to a theoretical model. Morgan et al. [START_REF] Morgan | Experimental and theoretical analysis of individual contrast agent behavior[END_REF] used a 100 megaframes per second camera in streak mode to predict bubble-oscillating behavior.

In this study, 583 optical observations of freely flowing, oscillating, individual microbubbles from an experimental UCA were analyzed. The excursions during ultrasound exposure were observed through a microscope. Images were recorded with a high frame rate camera operating at 3 MHz. Microbubbles on these images were measured off-line and maximal excursions were determined. A technique is described to precisely determine the diameters of the bubbles observed. We compared the maximal excursions of microbubbles of the same initial size in an ultrasound field with a 500 kHz frequency at acoustic amplitudes ranging from 0.06 MPa to 0.85 MPa. Furthermore, examples are shown of two-dimensional observations, revealing bubble-collapse and bubbles merging. In addition, the results are compared to theory.

Optical imaging theory and simulations

The optical system was studied to determine the relation between observed bubble sizes and true bubble sizes. To measure a bubble from an optical image, it has to be segmented from the background of the image. The measurement depends on the characteristics of the optical system and on the segmentation technique applied. In this section a segmentation technique is applied to simulated images to estimate the precision of our optical system.

An optical image of a radially symmetric flat object in focus, observed through a microscope, can be expressed as the following illumination in-i i "proefschrift041" -2004/7/6 -18:01 -page 31 -#35

i i i i i i
IMAGING THEORY AND SIMULATIONS [2,2] tensity function:

G(r ) = ∞ -∞ PSF(r -γ) F (γ) dγ + ε(r ) , (2.2)
where r is the coordinate in the image plane, γ is the coordinate in the object plane, G is the intensity of the image observed, PSF is the point-spread function of the optical imaging system, F represents the illumination intensity of the object, and ε is a one-dimensional additive noise function [1,[START_REF] Jain | Fundamentals of Digital Image Processing[END_REF]. The PSF, derived from geometrical optics, is given by [198,[START_REF] Lee | Review of image-blur models in a photographic system using the priciples of optics[END_REF]:

PSF(r ) = 2 J 1 (a r ) a r 2 , a = 2π NA λ , ( 2.3)
where J 1 is the first-order Bessel function of the first kind, NA is the numerical aperture of the objective lens, * and λ is the wavelength of the light. The PSF of our optical system was computed for NA = 1.25 and λ = 500 nm. The resolution R of an optical system is defined by the Rayleigh criterion [START_REF] Rayleigh | Investigations in optics, with special reference to the spectroscope[END_REF] PSF

1 2 R = 0 , ( 2.4)
which holds for

R = 1.22 λ NA .
(2.5)

To simulate the imaging in focus, we defined five differently sized circularly symmetric objects F : the Heaviside function

H (r ) = 1 , r ≥ 0 0 , r < 0 , ( 2.6)
and four disks with diameters τ of 1 µm, 0.5 µm, 0.2 µm, and 0.1 µm, respectively. τ i corresponds to the true diameter of disk i. By applying (2.2) to F and assuming ε = 0, simulated images G were obtained [Figure 2.1].

To obtain the true object diameters from the obtained images, the objects i i "proefschrift041" -2004/7/6 -18:01 -page 32 -#36 had to be segmented. A common method to discriminate objects from the background in optical images is to segment the image into:

i i i i i i [2, 2] IMAGES OF MICROBUBBLES PSF(r) F(r) G(r) ξ(r)
ξ(r ) = 1 , G(r ) ≤ θ 0 , G(r ) > θ , ( 2.7)
where ξ represents the segmented image and θ is the gray-level used as a threshold value; (2.7) segments objects that are lighter than the background. This segmentation technique is called gray-level window-slicing [START_REF] Jain | Fundamentals of Digital Image Processing[END_REF]. Window-slicing was applied to the images G in Figure 2.1. A threshold value θ = 0.5 was used for segmentation, corresponding to a threshold level halfway between imaged object intensity G = 1 and background G = 0. The segmented values ξ are plotted as a function of lateral distance r . We define ζ i as the diameter of a segmented object in image i. We show in Table 2 a threshold of 50% between object intensity and background under conditions similar to those of our optical system. For disks in the size range 50 nm ≤ τ ≤ 2 µm, simulated images G(r ) were calculated. The previously described 50% threshold θ = 0.5 was applied for segmentation. The resulting measured diameters ζ were plotted as a function of τ [Figure 2.2]. For τ > 0.35 µm, the measured object diameter was equal to the true object diameter (ζ = τ). Thus, true object diameters larger than 0.35 µm can be determined from one-dimensional, gray-scaled, monochromic optical images with a 50% threshold between object intensity and image background. For objects smaller than 0.35 µm, the measured diameters deviate from the true diameters and approach half of the resolution R of the optical system.

We investigated the influence of the threshold value on the measured diameters. Figure 2.3 shows the measured diameter ζ as a function of applied threshold θ for three differently sized disks. The slopes of the curves are determined by the PSF. For thresholds 0.3 ≤ θ ≤ 0.7, measured diameter ζ equals true diameter τ ± 0.1 µm, which means that flat object diameters can be determined with 0.1 µm precision. The effects of defocusing have been mathematically described by [START_REF] Stokseth | Properties of a defocused optical system[END_REF][START_REF] Gibson | Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy[END_REF][START_REF] Rönneberg | Eignung von Fokusverfahren für Beobachtung und Vermessung von Mikrostrukturen[END_REF][START_REF] Dey | Modélisation et étude de la formation de l'image d'un objet 3D translucide[END_REF]. When an object is large compared to the PSF, only the slope of the edge is changed by defocusing. Hence, the threshold θ = 0.5 is still applicable [START_REF] Groen | A comparison of different focus functions for use in autofocus algorithms[END_REF]. A three-dimensional object can be considered as a stack of infinitely thin two-dimensional layers [1,[START_REF] Preza | Regularized linear method for reconstruction of three-dimensional microscopic objects from optical sections[END_REF][START_REF] Hiraoka | The use of a charge-coupled device for quantitative optical micoscropy of biological structures[END_REF]. When three-dimensional objects are imaged through a microscope, the image projected onto the charge coupled device (CCD) element consists of contributions from all layers. A sphere is considered in focus when the middle layer of the sphere is in the focal plane [START_REF] Dey | Modélisation et étude de la formation de l'image d'un objet 3D translucide[END_REF][START_REF] Hiraoka | The use of a charge-coupled device for quantitative optical micoscropy of biological structures[END_REF] have to be considered as part of the optical system [START_REF] Kam | Computational adaptive optics for live three-dimensional biological imaging[END_REF]. Hence, images from an axial shift above the focal plane are not necessarily identical to the images from the same shift below the focal plane.

Experimental setup

An overview of the experimental setup for taking pictures of oscillating contrast agent microbubbles is shown in Figure 2 (Membrana GmbH, Wuppertal, Germany) was fixed in the focal area of the transducer, through which contrast agent was flowing. Because the wall of the capillary tube had been impregnated with water and because the tube was much smaller in diameter than the acoustic wavelenght, it was not expected to interfere with the ultrasound transmitted. Without contrast agent inserted, we did not observe reflections from the tube. Underneath the capillary tube either a 5 mm or a 7 mm optic fiber was fixed, that was mounted to a modified Xenon flash source. This light source was triggered by a PM 5716 pulse/delay generator (Koninklijke Philips Electronics N.V., Eindhoven, The Netherlands).

The container was positioned beneath a BH-2 microscope (Olympus Optical Co., Ltd., Tokyo, Japan) with an SPlan 100 oil immersion objective lens (Olympus Optical Co., Ltd.) with numerical aperture NA = 1.25. Because we did not use oil but water between the objective lens and the capillary tube, the numerical aperture was reduced to

NA w =   ¨B 1.3 n w ¨B 1.5 n oil   ¨B 1.25 NA = 1.1 , (2.8)
where NA w is the reduced numerical aperture, n w is the refraction index of water, and n oil is the refraction index of oil. Because the reduced numerical aperture is much higher than 0.6, our optical system still could be considered a high-NA imaging system [START_REF] Flagello | Theory of high-NA imaging in homogeneous thin films[END_REF]. For focusing and calibration purposes, a WAT-902HS CCD camera (Watec Co., Ltd., Yamagata, Japan) was fitted to the eye-piece of the microscope. Focusing was done manualy at the middle of the cellulose tube. Because the tube was wide compared to the contrast microbubbles measured, its upper half was considered a flat surface between contrast microbubbles and object lens, not causing aberrations but theoretically lowering the dynamic range of the images. The optical observations were recorded with an Imacon 468 fast framing camera (DRS Hadland, Ltd., Tring, UK), capable of recording eight twodimensional frames at 100 MHz. In all observations, the first frame was taken a few microseconds before ultrasound waves reached the contrast agent. The other seven frames were taken during ultrasound insonification, with 330 ns interframe time for 500 kHz ultrasound, spanning a full ultrasound cycle. Frame exposure times ranged from 10 ns to 70 ns. A photograph of the optical observation part of the setup is shown in Figure 2.6.

We investigated an experimental UCA (supplied by Bracco Research SA, Geneva, Switzerland). It consists of phospholipid-encapsulated gas bubbles ranging in diameter from 1 to 6 µm with a median of 2 µm. The acous- tic behavior of a very similar contrast agent was modeled and described in [START_REF] Gorce | Influence of bubble size distribution on the echogenicity of ultrasound contrast agents: A study of SonoVue TM[END_REF]. In this article we make use of the parameters from this model. The UCA bubbles were insonified by 500 kHz ultrasound at peak rarefactional acoustic pressures between 0.06 and 0.85 MPa. Acoustic pressures applied were measured with a calibrated MH28-10 hydrophone (FORCE Technology, Brøndby, Denmark) in a separate water tank. Figure 2.7 displays the acoustic signal measured at the transducer focus, after transmitting 10 cycles of ultrasound at 210 kPa peak rarefactional pressure. It is assumed the in-situ acoustic signal is comparable to the signal measured. † Undiluted UCA (5ml of a 0.9% sodium chloride dilution, added to a 25 mg UCA vial) was inserted through the capillary tube using either a syringe pressed by hand or a hose operated by a gravity fed or pumped infusion.

Furthermore, we did observations of diluted Quantison TM (Upperton Limited, Nottingham, UK) UCA, freely flowing underneath a glass coverslip.

The measuring of the numerous experimental UCA microbubbles was done with a partly automated method, using a MATLAB R (The MathWorks, Inc., Natick, MA) program. From previously recorded images, bubbles were selected for off-line measurement. These bubbles were selected only if they were visibly sharp, both before ultrasound arrival and in maximal expansion phase. Around each bubble to be measured, a rectangular region of interest was selected manually, which was much larger than the bubble [ particular region of interest. If the resulting image did not appear to have a continuous circular shape, the measurement would not be taken into account. Individual circular areas were selected manually to be measured. Segmented points outside a selected circular area were removed automatically and the area inside the circular area was filled automatically [Figure 2.8(d)]. The bubble cross-section area A was measured by summation of all points of the circular area [198,[START_REF] Matérn | Precision of area estimation: a numerical study[END_REF]. Bubble diameters D were calculated with the equation

D = 2 A π .
(2.10)

Results

Object size measurements

To perform measurements on flat, circular objects, a test grid was built (DIMES/TU Delft, Delft, The Netherlands). It consists of differently sized transparent triacontakaidigons (32-sided polygons) on a dark background, each specified by the diameter of the biggest circle fitting inside the triacontakaidigon. From measurements of a 228.0 cycles/mm grid on a negative 1951 USAF glass slide resolution target (Edmund Industrial Optics, Barrington, NJ) [START_REF] Postema | Real-time optical imaging of individual microbubbles in an ultrasonic field[END_REF] it was appreciated that identical transparent and dark objects were measured the same width. Hence, the results of measurements of transparent triacontakaidigons on a dark background are expected to be the same as those of measurements of dark triacontakaidigons on a transparent background. We studied if the threshold θ = 0.5 is still applicable if a sphere is slightly out of visual focus. Figure 2.10 shows four images of a 5 µm glass microsphere (Structure Probe, Inc., West Chester, PA), recorded with a CCD camera through our optical system. was between focal plane and objective lens, as demonstrated in the next two figures. Figure 2.11 shows optical images of highly stable Quantison TM (Upperton Limited) UCA microbubbles placed underneath a glass coverslip and shifted through the visual focus of our optical system. Each frame corresponds to a 43 × 32 µm 2 area. 12 displays a collection of randomly taken pictures of freely flowing, ultrasound insonified, experimental UCA microbubbles. Figure 2.12(a) and (f) contain bubbles with a bright center, which are considered to be out of focus, and some sharp bubbles in the lower part of the frames. Figure 2.12(b), (c), (d), and (e) contain both sharp and fuzzy, unsharp bubbles that are comparable in size. Bubbles that were clearly out of focus were not taken into account in this study.

We quantified the errors caused by our optical recording system and our segmentation procedure [171]. The precision of the bubble diameter measurement is dependant of axial focus deviation of the bubble, light intensity, uniformity of illumination, CCD channel, multichannel plate amplification, and choice of region of interest. Because the choice of the region of interest is directly related to the threshold to be used, we do not have to consider this error separately. As we demonstrated with the two-i i "proefschrift041" -2004/7/6 -18:01 -page 43 -#47

i i i i i i RESULTS [2, 4]
Cross-section (µm) dimensional simulations, a slightly changed threshold value from the 50% level between object and background intensity will not cause a systematic error. Because we only measured bubbles that were in visual focus, and we found no error from spheres that were slightly out of focus, the error caused by defocusing is considered negligible for our measurements.

The random error, caused by light intensity, uniformity of illumination, CCD channel, and multichannel plate amplification, was calculated from 184 separate measurements of bubble diameters from 21 different bubbles on image sequences of freely flowing experimental UCA and freely flowing gas bubbles. The bubbles were in visual focus. They were not insonified with ultrasound. Their diameters ranged from 1.4 µm to 28 µm. The gain of each CCD was varied, as was the exposure time, resulting in different illumination per frame. In each frame, the same region of interest was selected. For each bubble, the mean diameter was calculated.

The largest and the smallest diameter measured were used to calculate the maximal deviation from the mean diameter due to random error. The maximal deviations are plotted in [Figure 2.13] as a function of the mean bubble diameter measurements. The figure shows that the values of the random error do not exceed 9% of the mean diameter.

Insonified UCA measurements

In this study, 583 results of initial diameter and maximal diameter measurements of insonified bubbles, selected from 1320 events, were subjected to an exhaustive analysis. Peak rarefactional acoustic pressures applied to these bubbles ranged from 0.06 MPa to 0.85 MPa. Bubble diameters were measured, using the 50% threshold between darkest foreground and median background, as described in the previous section. Therefore, the range of sizes studied is mainly located in the acoustic Rayleigh scattering zone. This is clearly shown in Figure 2.14, in which the maximal bubble expansion increases for larger bubbles, especially at the lowest acoustic pressure applied. At higher pressures, the slope of increase in bubble expansion as a function of initial diameter is steeper. This demonstrates that bubbles at these pressures undergo strong nonlinear oscillations. In addition, we can appreciate for all acoustic pressures applied that bubbles with the same initial diameter can oscillate differently, leading to different maximal expansions. This phenomenon is more pronounced at higher acoustic pressures. At MI = 0.15, 15 microbubbles in the range 2.8 µm to 3.2 µm reached maximal diameters between 3.2 µm and 7.6 µm. This corresponds to a maximal difference in excursion of Ψ = 151%. At MI = 0.25 we observed 25 microbubbles in the range 1.8 µm to 2.2 µm expand to maximal diameters between 2.5 µm and 8.8 µm, corresponding to Ψ = 340%.

To further explore these large differences in maximal expansion, we investigated the bubble response at high MI. An example of this investiga- Figure 2.16 summarizes the results of 39 bubbles selected from ten events, recorded at an MI of 0.93. Figure 2.16 displays the relative bubble excursion as a function of the initial diameter. Identical markers indicate bubbles from the same sequence. In each first frame of the image sequences, bubbles of apparently the same size could be observed. Hence, for these bubbles, all conditions such as illumination, gain, and ultrasound field were kept unchanged, and the previously calculated random errors do not apply. We clearly notice that bubbles recorded from the same events (e.g., those indicated by ' * ') oscillate differently. All these bubbles had initial diameters approaching 2.6 µm, whereas their maximal diameters range from 5.0 µm to 7.6 µm, corresponding to relative expansions of 91% to 185% (Ψ = 94%). Differences in oscillation or behavior of bubbles with similar initial sizes are also demonstrated in the optical images shown in Figure 2.17, which demonstrates bubble expansion and collapse at MI = 1.2. Each frame corresponds to a 88 × 58 µm 2 area. In the i i "proefschrift041" -2004/7/6 -18:01 -page 47 -#51 first frame, taken before ultrasound arrival, no bubbles were visible. We presume that the bubbles were too small (i.e. below the optical resolution R) to be detected. From Figure 2.17(b), (c), (d), and (e), the bubbles oscillate and appear to have similar sizes. Both bubbles expanded to 17.0 µm in Figure 2.17(d). In Figure 2.17(f), where the contraction phase of the ultrasonic wave starts, one bubble clearly collapsed while the other bubble continues contracting. In the last two frames, contraction is maximal, so both bubbles were no longer visible. Initial diameter (µm) Relative excursion (%) At acoustic pressures corresponding to MI > 0.5, not only the phenomenon of bubbles violently collapsing [143], but also the phenomenon of bubbles coalescing was observed [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF]. Figure 2.18 was recorded during insonification at MI = 0.93. In each 88×58 µm 2 frame, a 21×22 µm 2 region of interest is highlighted. In Figure 2.18(a) three sharp microbubbles can be discriminated, of which two seem to stick together. In Figure 2.18(b) there are only two separate expanding bubbles left. these two bubbles attaching. In Figure 2.18(d) the lower left bubble appears to merge into the upper right bubble. The remaining bubble appears to have an oval shape in Figure 2.18(e), but a round shape in the remaining frames. Such asymmetric oscillations were regularly observed at high acoustic pressures. Mean relative bubble excursion is plotted as a function of acoustic pressure in Figure 2.19, from 134 bubbles with diameters between 1.8 µm and 2.2 µm. Standard deviations of the data were calculated for each acoustic pressure. The plotted theoretical curves were calculated numerically for a 2 µm bubble and based on the parameters of the constant thickness model [START_REF] Gorce | Influence of bubble size distribution on the echogenicity of ultrasound contrast agents: A study of SonoVue TM[END_REF]. The models used are based on a modified RPNNP equation, named after its developers Rayleigh, Plesset, Noltingk, Neppiras, and Poritsky [START_REF] De Jong | Higher harmonics of vibrating gas-filled microspheres. Part one: simulations[END_REF], and a modified Herring equation [START_REF] Morgan | Experimental and theoretical evaluation of microbubble behavior: Effect of transmitted phase and bubble size[END_REF]. We refer to these models as model A and model B, respectively. At acoustic pressures below 0.4 MPa, model B comes closest in describing the mean expansion, although there is clearly no fit. For higher acoustic pressures, model B predicts values much higher than the measured ones.

i i i i i i RESULTS [2, 4]

Discussion and conclusions

This was the first optical investigation of a large UCA data set using a 500 kHz transducer. The errors caused by our optical system and segmentation process are within 9% of the mean bubble sizes measured for median UCA bubble diameters larger than 1.4 µm.

The initial diameters of the bubbles shown in Figure 2 normally distributed. This is attributed to the lack of expansion of bubbles smaller than 2 µm at lower pressures and to the rupturing and coalescing behavior of larger bubbles at higher pressures. Because only bubbles with measurable maxima were plotted, these two groups were excluded. We checked the representativity of the bubbles analyzed for the whole agent by comparing the optically determined size distribution of our bubbles with published data of a SonoVue TM (Bracco Research SA, Geneva, Switzerland) distribution measured with a Coulter instrument [START_REF] Schneider | BR1: A new ultrasonographic contrast agent based on sulfur hexafluoride-filled microbubbles[END_REF]. The median diameter of 2 µm is confirmed by these measurements, but bubbles over 4 µm are hardly observed in the optical data. Only bubbles showing expansion were measured. We conclude that our optical observations are representative in the diameter range 1 µm to 4 µm.

Because the image exposure times are low relative to the interframe times, the measured maxima do not have to correspond to the true maximal bubble expansions. In worst case, if the bubble expands according to i i "proefschrift041" -2004/7/6 -18:01 -page 51 -#55

i i i i i i
DISCUSSION AND CONCLUSIONS [2,5] a sine, the maximal growth measured can be off the true value by half an interframing interval, which equals a twelfth of an expansion cycle, giving a measured excursion of 100% × cos( 2π /12) = 87% of the true excursion.

Because the bubbles in the experiments shown in Figure 2.15 are closer to each other than 1% of the acoustic wavelength, acoustic differences due to location are negligible in this situation.

Although big bubbles that are out of optical focus might cause differences in bubble oscillating behavior, we did not take such effects into account. ‡ From the above results, it is concluded that identical bubbles can have different oscillating behavior. The differences in the oscillation maxima observed might be explained by differences in elastic properties of individual bubbles. The same stages of coalescence described for colliding bubbles could be distinctly observed with expanding contrast agent microbubbles. Flattening of the opposing bubble surfaces occurs if and only if the bubble system has a Weber number greater than 0.5. In our results, Weber numbers are relatively high because of the rapid bubble expansions, with a maximal radius increase at a rate of several m /s.

The film drainage was computed for immobile (rigid) bubble surfaces resulting in a laminar flow, and for mobile (free) bubbles surfaces resulting in a plug flow. The observed coalescence times appeared to be at least three times shorter than the times produced by laminar flow. In conclusion, we suspect that during expansion the lipid shell is so dilute that the contrast agent microbubble coalescence times are comparable to those of free gas bubbles.

Introduction

Ultrasound contrast agent (UCA) is a suspension of encapsulated gas bubbles. The bubbles have diameters ranging from 1 to 10 µm. They oscillate upon insonification, generating a characteristic acoustic response. UCAs are widely used in medical diagnostics [START_REF] Burns | Intravenous contrast agent for ultrasound Doppler: In vivo measurement of small tumor vessel doseresponse[END_REF][START_REF]Ultrasound Contrast Agents. Basic principles and clinical applications[END_REF].

Observing ultrasound insonified UCA with a high-speed camera is a promising method for analyzing microbubble oscillation and destruction behavior [178,[START_REF] De Jong | Optical imaging of contrast agent microbubbles in an ultrasound field with a 100-MHz camera[END_REF][START_REF] Chomas | Threshold of fragmentation for ultrasonic contrast[END_REF][START_REF] Kudo | Study on mechanism of cell damage caused by microbubbles exposed to ultrasound[END_REF][START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF]. Expanding UCA microbubble coalescence, observed with a high-speed camera during one cycle of ultrasound, has been previously reported by us [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF].

To understand microbubble coalescence, one needs to comprehend the drainage of the liquid separating the bubble surfaces. Reynolds [START_REF] Reynolds | On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil[END_REF] noted that the viscosity of a liquid can be determined by pressing two flat plates together, squeezing the liquid out, and measuring the drainage velocity. Thus, he formulated an equation for the drainage velocity of a fluid between rigid surfaces. General theories on the coalescence of colliding bubbles and droplets that are based on liquid film drainage, were put forward by Marrucci [START_REF] Marrucci | A theory of coalescence[END_REF], Dimitrov & Ivanov [START_REF] Dimitrov | Hydrodynamics of thin liquid films. On the rate of thinning of microscopic films with deformable interfaces[END_REF], Ivanov et al. [START_REF] Ivanov | Generalized equations of thin films hydrodynamics and their application to the calculations of the thinning rate of films with non-deformed surfaces[END_REF], Lin & Slattery [START_REF] Lin | Thinning of a liquid film as a small drop or bubble approaches a fluid-fluid interface[END_REF], Chesters & Hofman [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF], Duineveld [START_REF] Duineveld | Bouncing and coalescence of two bubbles in water[END_REF], and Klaseboer et al. [START_REF] Klaseboer | Film drainage between colliding drops at constant approach velocity: experiments and modeling[END_REF]. Literature overviews on film drainage and bubble coalescence were given by Kralchevsky et al. [START_REF] Kralchevsky | Thin liquid film physics[END_REF], Narsimhan & Ruckenstein [START_REF] Narsimhan | Structure, drainage, and coalescence of foams and concentrated emulsions[END_REF], and i i "proefschrift041" -2004/7/6 -18:01 -page 55 -#59

i i i i i i THEORY [3, 2]
Dhainaut [START_REF] Dhainaut | Literature study on observations and experiments on coalescence and breakup of bubbles and drops[END_REF].

Theories on droplet coalescence find applications in fuel ignition research and aerosol studies, whereas the research on bubble coalescence focuses on thin film physics and foam stability [START_REF] Kralchevsky | Thin liquid film physics[END_REF][START_REF] Narsimhan | Structure, drainage, and coalescence of foams and concentrated emulsions[END_REF]. This paper explores ultrasound-induced coalescence of microbubbles. Controlled coalescence will have potential applications in the clinical field.

Theories on bubble coalescence are generally based on the collision of unencapsulated bubbles or droplets, approaching each other at constant velocity. The following stages are discriminated in the process [START_REF] Dhainaut | Literature study on observations and experiments on coalescence and breakup of bubbles and drops[END_REF]. When two bubbles approach collision, the adjacent bubble surfaces will flatten, trapping liquid in between. The liquid drains, until the separation reaches a critical thickness that lies between 10 nm and 200 nm. An instability mechanism will cause the rupture of the separation and the formation of a coalesced bubble. We define bubble coalescence as the process of the fusing of two or more bubbles into a single bubble. The process begins with the flattening of the bubble surfaces and is considered finished when the resulting bubble has a spherical shape.

In this Chapter, we give a description of the coalescence of expanding microbubbles, based on optical observations and theoretical modeling. First, we present theories for expanding bubble coalescence, based on film drainage theory. Then, we present experimental results, obtained by recording optical images of insonified UCA. Finally, theories and results are compared and discussed.

Theory

During expansion, microbubbles may come into contact with bubbles nearby, resulting in coalescence or bounce. We discriminate the following stages in the coalescence mechanism, optically observed in Figure 3.1 and schematically represented in Figure 3.2. First, two bubbles approach collision while expanding (Figure 3.2a). Prior to contact, there may be a flattening of the adjacent bubble surfaces, trapping liquid in between (Figure 3.1a, Figure 3.2b). This trapped liquid drains (Figure 3.1b, Figure 3.2c) until the separation reaches a critical thickness (Figure 3.2d). An instability mechanism (Figure 3.2d, magnified) results in rupture of the separation (Figure 3.2e) and the formation of a merged bubble (Figure 3.1c). After coalescence the resulting bubble will have an ellipsoidal shape (Figure 3.1d, Figure 3.2f). Owing to surface tension, it will relax into a spherical shape. When the contact time is less than the time needed for film drainage, the bubbles bounce off each other [START_REF] Chaudhari | Coalescence of gas bubbles in liquids[END_REF].

Flattening of the interface

Flattening of the opposing bubble surfaces occurs if and only if the bubble system has a Weber number We > 0.5 [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF]. The Weber number for a fluid containing two bubbles with radii R 1 and R 2 , respectively, is given by the inertial force relative to the surface tension force: where u is the relative approach velocity of the bubble walls, * ρ is the fluid density, σ is the surface tension, and R m is the mean bubble radius for which holds:

We = ρu 2 σ R m , ( 3
2 R m = 1 R 1 + 1 R 2 . ( 3.2)
In our results, Weber numbers are relatively high because of the rapid bubble expansions, with maximal radius increases of several m s -1 . If the Weber number is lower than 0.5, bubble coalescence will always occur, without flattening of the adjacent surfaces prior to contact [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF]. In our observations, Weber numbers are up to 10. In the high-Weber number * For bubbles with a constant center-to-center distance,

u = Ṙ1 + Ṙ2 .
i i i i i i [3, 2] ULTRASOUND-INDUCED COALESCENCE h R 1 R 2 R f p 0 p 2 p 1 p f Figure 3.3: Schematic overview of variables used.
regimens, coalescence is determined by a second step, after flattening: film drainage.

Film drainage

We investigate microbubble coalescence by computing the film drainage for immobile (rigid) bubble surfaces resulting in a laminar flow, and for mobile (free) bubbles surfaces resulting in a plug flow.

Let us consider two bubbles with radii R 1 and R 2 , and internal pressures p 1 and p 2 , respectively, assumed spherical everywhere with the exception of a flattened interface that separates them through a liquid film of thickness h (cf. Figure 3.3). The drainage rate of the liquid film depends on the difference (p+Π) between the film pressure p f and the liquid ambient pressure p 0 . We estimate the pressure in the film by the mean of pressures p 1 and p 2 , since the parallel film surfaces lead to equal pressure differences towards both bubbles:

p + Π = p f -p 0 = 1 2 p 1 + p 2 -p 0 = = σ 1 R 1 + 1 R 2 ≡ p LY , ( 3.3)
"proefschrift041" -2004/7/6 -18:01 -page 59 -#63

i i i i i i THEORY [3, 2]
where p LY is the Laplace-Young film pressure [START_REF] Isenberg | The science of soap films and soap bubbles[END_REF], σ is the surface tension, and Π is the disjoining pressure that slows down film thinning in the range 0.1 µm > h > 0.01 µm until the film ruptures [START_REF] Marrucci | A theory of coalescence[END_REF][START_REF] Chaudhari | Coalescence of gas bubbles in liquids[END_REF]5]. For the estimates we are going to make, we neglect Π, knowing that we will underestimate drainage times only for h < 0.1 µm. Therefore, we take p equal to the Laplace-Young pressure for the films observed. As such, the pressure gradient determining the drainage velocity is independent of the ambient pressure. We choose a coordinate system such that the film is symmetric around the plane z = 0 and that its boundaries are located at z = ± h 2 . Then the radial velocity of the liquid in the film is a combination of a plug flow driven by the motion of the interfaces, and a laminar velocity profile (analogous to Poiseuille flow) driven by the radial pressure gradient [START_REF] Klaseboer | Film drainage between colliding drops at constant approach velocity: experiments and modeling[END_REF][START_REF] Young | A Brief Introduction to Fluid Mechanics[END_REF].

We will study two cases: the first for bubbles with immobile interfaces, and the second for bubbles with mobile interfaces.

Immobile interfaces

If the bubble surfaces consist of a high concentration of surfactant, on our working scales the interfaces are to be considered immobile [START_REF] Lin | Thinning of a liquid film as a small drop or bubble approaches a solid plane[END_REF][START_REF] Lin | Thinning of a liquid film as a small drop or bubble approaches a fluid-fluid interface[END_REF][START_REF] Chen | Effects of London-van der Waals forces on the thinning of a dimpled liquid film as a small drop or bubble approaches a horizontal solid plane[END_REF]]. In the case of immobile interfaces, the interfacial tangential velocity is zero, so the plug flow contribution is zero [START_REF] Klaseboer | Film drainage between colliding drops at constant approach velocity: experiments and modeling[END_REF].

The film drainage velocity for rigid radial surfaces (disks) is given by the Reynolds equation [START_REF] Reynolds | On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil[END_REF]:

- dh dt = 2 p h 3 3 η R 2 f , (3.4)
where η is the viscosity of the liquid, and R f is the radius of the film surface.

The drainage time, τ d , between the initial film thickness h i and the critical film thickness h c can be determined by integration of eq. (3.4):

h c h i - dh h 3 = τ d 0 2 p 3 η R 2 f dt . (3.5)
By taking p and R f constant over time, we obtain

τ d = 3 η R 2 f 4 p h 2 c 1 - h 2 c h 2 i . ( 3
τ d ≈ 3 η R 2 f 4 p h 2 c . (3.7)

Mobile interfaces

If the bubble surfaces consist of a low concentration of surfactant, which is less than (on the order of) 10 -4 M, the interfaces are to be considered mobile [2]. In the case of mobile interfaces, the Poiseuille contribution to the drainage flow becomes negligible [START_REF] Klaseboer | Film drainage between colliding drops at constant approach velocity: experiments and modeling[END_REF]. The film drainage velocity for free radial surfaces is given by the equation [START_REF] Dimitrov | Hydrodynamics of thin liquid films. On the rate of thinning of microscopic films with deformable interfaces[END_REF]:

- dh dt = 2 p h 3 η R 2 f . ( 3.8)
Similarly to the immobile case, making the same assumptions with regards to p, R f , and h c , the drainage time can be approximated by

τ d ≈ η R 2 f 4 p h 2 c . (3.9)
Film rupture

Sharma & Ruckenstein described film instability as a combination of surface waves and thermal perturbations [START_REF] Sharma | Critical thickness and lifetimes of foams and emulsions: role of surface wave-induced thinning[END_REF]. For thermal perturbations of a gas bubble in the micrometer range, the initial perturbation will be on the order of kT σ , where k is Boltzmann's constant, and T is the absolute temperature, in our situation approximately 300 K. Hence, the initial thermal perturbation is lower than 1 nm.

Films gradually thin to a critical thickness at which it either ruptures due to a local instability or at which it converts to an equilibrium thickness. Aksoy measured these thicknesses for water, dependant of surfactant concentration [2]. For water films with a surfactant concentration below 10 -4 M, critical film thicknesses are between 150 and 170 nm, whereas for surfactant concentrations above 10 -3 M, critical thicknesses are between 20 and 70 nm. i i "proefschrift041" -2004/7/6 -18:01 -page 61 -#65 [3,4] 3 Experimental setup

i i i i i i EXPERIMENTAL SETUP
Our experimental setup for imaging insonified contrast bubbles is as previously described in [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF] We investigated coalescence events of an experimental UCA (Bracco Research SA, Geneva, Switzerland). These bubbles are covered with a monolayer phospholipid shell and range in diameter from 1 to 6 µm with a median of 2 µm. Undiluted UCA (5 ml of a 0.9% NaCl dilution, added to a 25 mg vial) was inserted through a cellulose capillary tube using either a syringe pressed by hand or a gravity fed or pumped infusion. This tube was positioned in the acoustic focus area. Since the capillary tube slightly moved within the acoustic focus area between experiments, the exact phase of the ultrasound wave in an image frame is not known. We performed 482 experiments at high acoustic amplitudes with the experimental UCA. We recorded 133 optical image sequences where microbubble coalescence was observed. Bubble sizes and distances were measured manually or by using a segmentation method described by Postema et al. [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF].

Results

The observed phenomena are classified as follows: coalescence, bounce, multiple coalescence, and combined coalescence and fragmentation. ). The remaining bubble, with a diameter of 5.0 µm, is separated from microbubble 1, which is seen to have expanded to 3.8 µm, with a center-to-center distance d 0 = 4.8 µm. The center of bubble 1 has shifted slightly to the upper right. The thickness of the liquid film, separating the bubble shells is approximately h = 1.1 µm, and the film radius is larger than 1.7 µm. In Figure 3.4(i)c the liquid film appears to have drained while the bubbles expanded, but, a separation is still visible. This boundary appears to have disappeared in Figure 3.4(i)d, † leaving a pear-shaped bubble that turns ellipsoidal (Figure 3.4(i)e) when contracting. Figure 3.4(i)f,g,h shows that the coalesced bubble expands uniformly. It takes between 0.33 µs and 0.66 µs for the film in Figure 3. In the remaining frames the bubbles expand and contract, but coalescence does not occur.

Multiple coalescence

Figure 3.4(iii) shows an example of multiple coalescence. In Figure 3.4(iii)b an agglomerate of 8 touching microbubbles can be seen. Microbubbles 1 and 3 appear to be slightly above the focal plane [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF]. As the bubbles expand, they coalesce into one heart-shaped bubble and one ellipsoidal bubble (Figure 3.4(iii)c,d). In the contraction phase, the heart-shaped bubble takes on an ellipsoidal shape (Figure 3.4(iii)e).

Combined coalescence and fragmentation

We observed repeated coalescence and fragmentation behavior in twelve events. Figure 3.4(iv) demonstrates the fragmentation, coalescence, and re-fragmentation of a microbubble.

Discussion

If we take η = 0.001 Pa s,

σ = 0.072 N m -1 , p = σ 1 R 1 + 1 R 2 , h c = 0.15 µm [2]
, and substitute the parameters R 1 = 6.2 µm, R 2 = 9.0 µm, and R f = 4.8 µm obtained from Figure 3.4(ii), we find a film drainage time τ d = 39 µs for immobile interfaces and τ d = 13 µs for mobile interfaces. Within 1 µs, the film can only drain to a minimum thickness h m = 0.94 µm. This is consistent with the absence of coalescence in Figure 3.4(ii).

If we substitute the parameters R 1 = 1.9 µm, R 2 = 2.5 µm, and R f = 1.7 µm obtained from Figure 3.4(i), we find a film drainage time τ d = 1.4 µs for immobile interfaces and τ d = 0.48 µs for mobile interfaces. Drainage theory of a thin film mobile interfaces is sufficient to account for the rapid coalescence in Figure 3.4(i), whereas drainage theory of a thin film with immobile interfaces is insufficient to account the observed coalescence.

The results presented in Figure 3.1 and Figure 3.4 show that the bubbles have expanded to more than ten-fold their initial surface areas before coalescing. As the UCA shell consists of a lipid monolayer, this layer is very dilute by the time of coalescence. Therefore, we may assume that the shell hardly influences the film instability mechanism, which confirms that the interfaces may be assumed mobile. We demonstrated previously with high-speed optical images that the UCA microbubbles used may expand to several times their original sizes, particularly at high acoustic pressures [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF].

One of the effects of secondary radiation forces is that they lead to mutual attraction of similar-sized bubbles over multiple cycles. This may account for the translations observed in Figure 3.4.

The most unstable situations occur when a bubble is contracting and decelerating [START_REF] Plesset | On the stability of the spherical shape of a vapor cavity in a liquid[END_REF][START_REF] Brennen | Fission of collapsing cavitation bubbles[END_REF]. Moreover, the forming of a re-entrant jet from a collapsing bubble has been related to the bubble shattering into fragments when the jet impacts the other side of the bubble surface. An optical image sequence of jet occurrence in a contrast microbubble was demonstrated by Postema et al. [143]. Apparently water was projected through the freely flowing microbubble. Although we clearly observed jets in two events, we did not observe fragmentation in the same events [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF].

Irregular shapes of oscillating bubbles, like those shown in Figure 3.4(iii) and (iv), were interpreted as modes of shape instability of a single bubble before [START_REF] Chomas | High speed optical experimental analysis of microbubble destruction, supported by theoretical development[END_REF][START_REF] Chomas | Optimization of microbubble destruction[END_REF][START_REF] May | Acoustic fragmentation of therapeutic contrast agents designed for localized drug delivery[END_REF][START_REF] May | Dynamics and fragmentation of thickshelled microbubbles[END_REF], but may also be accounted for by coalescence of bubbles or bubble fragments.

After coalescence, the resulting bubble will have different acoustic prop-"proefschrift041" -2004/7/6 -18:01 -page 65 -#69

i i i i i i CONCLUSIONS [3, 6]
erties than the original bubbles, especially if it is comparable to the size resonant with the ultrasonic driving. If small UCA microbubbles, having passed through the narrowest vessels, coalesce, they may be controlled to obtain resonant sizes. Especially for subharmonic imaging [START_REF] Shankar | Subharmonic backscattering from ultrasound contrast agents[END_REF], where twice the resonant bubble size is needed, and for tracking the diffusion of free gas bubbles with subharmonics, a promising technique in noninvasive blood pressure measurements [START_REF] Postema | Noninvasive microbubble-based pressure measurements: a simulation study[END_REF], controlled microbubble coalescence may be applicable.

Owing to secondary radiation forces, clusters of bubbles may be formed. By inducing coalescence of such groups of bubbles, and thus creating emboli, the perfusion of tumor vascularization may be reduced.

If coalescence of a lipid-shelled microbubble and a cell membrane can be induced, this will imply a promising technique in targeted drug delivery [START_REF] Van Wamel | Effects of diagnostic ultrasound parameters on molecular uptake and cell viability[END_REF][START_REF] Marmottant | Controlled vesicle deformation and lysis by single oscillating bubbles[END_REF].

Conclusions

Ultrasound-induced microbubble coalescence is the fusion of two or more microbubbles when subjected to an ultrasound field. Contrast agent microbubble coalescence has been observed frequently in an experimental setup. We showed that a coalescence mechanism for colliding bubbles also applies for expanding bubbles.

As adjacent bubbles expand, the following stages can be distinctly observed: flattening of the adjacent bubble surfaces prior to contact, drainage of the interposed liquid film toward a critical thickness, rupture of the liquid film, and formation of a single bubble. The time between flattening until coalescence was observed to take less than 1 µs for ultrasound contrast agent microbubbles in the micron diameter range.

Ultrasound-induced coalescence has potential clinical applications in harmonic imaging, noninvasive blood pressure measurements, and targeted drug delivery. crobubbles to ultrasound, in order to release gas, and photograph the coalescence of these free gas bubbles. As with colliding bubbles, bubble surface flattening is related to the Weber number. Calculated drainage times are comparable with observed coalescence times of released gas bubbles.

Introduction

When two gas bubbles collide or are driven into each other, coalescence into a single bubble may result. The following stages of bubble coalescence have been identified (cf. Free gas bubble coalescence after collision has been studied extensively [START_REF] Marrucci | A theory of coalescence[END_REF][START_REF] Dimitrov | Hydrodynamics of thin liquid films. On the rate of thinning of microscopic films with deformable interfaces[END_REF][START_REF] Ivanov | Generalized equations of thin films hydrodynamics and their application to the calculations of the thinning rate of films with non-deformed surfaces[END_REF][START_REF] Lin | Thinning of a liquid film as a small drop or bubble approaches a fluid-fluid interface[END_REF][START_REF] Chesters | Bubble coalescence in pure liquids[END_REF][START_REF] Duineveld | Bouncing and coalescence of two bubbles in water[END_REF]. With ultrasound contrast agents, microbubble coalescence has been observed during ultrasound insonification, when expanding microbubbles come into contact with adjacent bubbles [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF][START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]. With the aid of high-speed photography, we previously investigated the coalescence times of insonified soft-shelled microbubbles. We compared observed coalescence times to calculated film drainage times, based on the Reynolds equation [START_REF] Reynolds | On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil[END_REF]. We concluded that the bubbles behaved as if they had mobile interfaces like free gas bubbles [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]. However, to support this conclusion, we should investigate the validity of the Reynolds-like equations for expanding bubbles. In this study we do so, by subjecting rigidshelled contrast agent microbubbles to ultrasound, in order to release gas, and investigate the coalescence of these free gas bubbles. We compare these times to the Reynolds-like computations.

Theory

Flattening of the opposing bubble surfaces occurs if and only if the bubble system has a Weber number We > 0.5 [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF]. If We < 0.5, the bubbles will coalesce without the prior formation of an interposed film. The Weber number for a fluid containing two bubbles with radii R 1 and R 2 , respectively, is given by the inertial force relative to the surface tension force: We = ρu 2 / σ R m , where u is the relative approach velocity, ρ is the fluid density, σ is the surface tension, and R m is the mean bubble radius for which holds:

2

R m = 1 R 1 + 1 R 2 .
Because the radius and with it the approach velocity of oscillating bubbles change during a cycle, so does the Weber number. If the bubble surfaces are considered to be mobile, the liquid film drainage time τ d is approximated by [START_REF] Dimitrov | Hydrodynamics of thin liquid films. On the rate of thinning of microscopic films with deformable interfaces[END_REF]:

τ d ≈ η R 2 f 4 p h 2 c , ( 4.1)
where η is the viscosity of the fluid, R f is the film radius, h c is the critical film thickness, at which the film ruptures, p and is the pressure difference between film and surrounding fluid which is taken

p = σ 1 R 1 + 1 R 2 .
In our computations, we take η = 0.001 Pa s, ρ = 998 kg m -3 , σ = 0.072 N m -1 , and h c = 0.15 µm [2].

Experimental methods

Our experimental setups for taking pictures of insonified contrast bubbles were as described in [START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF]. A 200 µm capillary tube, through which contrast agent was flowing, was fixed in the focal area of a V389-SU 500 kHz or a V397-SU 2.25 MHz single-element transducer (Panametrics Inc., Waltham, MA). The optical observations of the insonified ultrasound contrast agent were recorded with the Brandaris-128 system, operating at speeds up to 15 MHz. The free gas bubbles were released from PB127 (POINT Biomedical Corporation, San Carlos, CA). PB127 consists of bilayered microspheres encapsulating nitrogen bubbles with a mean diameter of 4 µm. The outermost layer is albumin and the inner layer is composed of a biodegradable polymer. The content of a PB127 vial was resuspended in 5 ml of deionized water, and shaken gently for 20 seconds before further dilution. Diluted PB127 was inserted through the capillary tube using a syringe pressed by hand. It was insonified by 6 or 8 cycles of 500 kHz, or by 8 cycles of 1.7 MHz ultrasound at acoustic pressures corresponding to mechanical indices between 0.3 and 1.9.

Results and discussion

The same stages of coalescence described for colliding bubbles could be distinctly observed with expanding free gas microbubbles and soft-shelled microbubbles. Examples of soft-shelled microbubble coalescence were shown in [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF][START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF][START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF] and Chapter 3.

As with encapsulated bubbles, coalescence and bounce were regularly observed. For the interacting free gas microbubbles measured from the optical images, We < 30. We obtained 9 image sequences where free bubble coalescence times and the bubble dimensions could be measured. The times between flattening of the free bubble surfaces and coalescence are less than 0.3 µs, for expanded gas bubbles with diameters between 3 and 5 µm. During expansion, gas escapes from the 3 µm upper bubble [START_REF] Burns | Intravenous contrast agent for ultrasound Doppler: In vivo measurement of small tumor vessel doseresponse[END_REF][START_REF] Burns | Looking at and listening to breaking bubbles: a correlative optical acoustic study of some experimental polymer/air agents[END_REF][START_REF] Chaudhari | Coalescence of gas bubbles in liquids[END_REF][START_REF] Chen | Effects of London-van der Waals forces on the thinning of a dimpled liquid film as a small drop or bubble approaches a horizontal solid plane[END_REF]. The free gas is seen detached in frame 21. It expands [START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF][START_REF] Chin | Optical imaging of ultrasound contrast bubble motions at 25 million frames per second[END_REF][START_REF] Chiou | Clinical applications of contrast echocardiography[END_REF][START_REF] Chomas | High speed optical experimental analysis of microbubble destruction, supported by theoretical development[END_REF] and starts to contract [START_REF] Chomas | Optimization of microbubble destruction[END_REF]. Close to its minimum, the free gas bubble splits up into multiple fragments [START_REF] Chomas | Mechanisms of contrast agent destruction[END_REF]. During expansion, the fragments appear to have coalesced into two separate bubbles [START_REF] Chomas | Threshold of fragmentation for ultrasonic contrast[END_REF][START_REF] Church | The effects of an elastic solid surface layer on the radial pulsations of gas bubbles[END_REF]. These bubbles collide during expansion [START_REF] Collins | The Story of America in Pictures[END_REF]. The Weber number, calculated with the bubble wall displacement (29-30): u > 2 µm 0.1 µs , is greater than We > 20 0.5, which agrees with the flattening of the bubble surfaces. Computing equation (4.1) with R 1 = 3.9 µm, R 2 = 3.4 µm, and R f = 2.1 µm yields τ d = 1.1 µs. This long drainage time accounts for the observed bounce [START_REF] Collins | The Story of America in Pictures[END_REF][START_REF] Cook | Erosion by water-hammer[END_REF][START_REF] Dayton | Action of microbubbles when insonified: experimental evidence[END_REF]. Close to maximal contraction [START_REF] Dayton | Acoustic radiation force in vivo: a mechanism to assist targeting of microbubbles[END_REF], the two bubbles fragment (34). During expansion, the fragments are seen to coalesce (35-37) into two bubbles of perpendicular orientation. Again, these bubbles bounce [START_REF] Dayton | Optical and acoustical observations of the effects of ultrasound on contrast agents[END_REF][START_REF] Dey | Modélisation et étude de la formation de l'image d'un objet 3D translucide[END_REF], fragment [START_REF] Dhainaut | Literature study on observations and experiments on coalescence and breakup of bubbles and drops[END_REF], and coalesce into two bubbles perpendicular to their mother bubbles [START_REF] Marco | Experimental study on rising velocity of nitrogen bubbles in FC-72[END_REF]. This process repeats itself, until insonification ends [START_REF] Hiraoka | The use of a charge-coupled device for quantitative optical micoscropy of biological structures[END_REF]. The two remaining free gas bubbles still pulsate, and collide while doing so. These collisions may possibly be attributed to secondary radiation forces. In frame 82, the bubbles coalesce. This coalescence is induced by the pressure field exerted by the bubbles themselves. The remaining bubble has a maximum of 3.8 µm. It pulsates at 1.7 MHz. Hence, the pulsations may be attributed to reflections.

Conclusions

Expanding gas bubble coalescence has been observed with released gas.

As with colliding bubbles, bubble surface flattening is related to the Weber number. Calculated drainage times are comparable with the observed coalescence times of released gas bubbles.

Abstract

This paper describes a noninvasive method to measure local hydrostatic pressures in fluid filled cavities. The method is based on the disappearance time of a gas bubble, as the disappearance time is related to the hydrostatic pressure. When a bubble shrinks, its response to ultrasound changes. From this response, the disappearance time, and with it the hydrostatic pressure, can be determined. We investigated the applicability of the gases Ar, C 3 F 8 , Kr, N 2 , Ne, and SF 6 , based on their diffusive properties. For pressure measurements with a limited duration, e.g. 150 ms, Kr and Ar bubbles are most suitable, since they are most sensitive to pressure change. If there is also a limitation to bubble size, e.g. a maximum diameter of 6 µm, SF 6 is most suitable. We present improvements of a method that correlates the duration of the decay of the fundamental ultrasound response to the hydrostatic overpressure. We propose to correlate the duration until subharmonic occurrence in combination with its decay, to hydrostatic overpressure, since the subharmonic decays more rapidly than the fundamental response. For a dissolving Ar gas bubble with an initial diameter of 14 µm, the overpressure can be determined 4 times as precise from the decay of the subharmonic response as from the decay of the fundamental response. Overpressures as small as 11 mmHg may be discriminated with this method.

Introduction

Local pressure measurements in cavities are widely used in medical diagnostics. Local pressure measurements in the heart are generally done by catheterization, causing pain and risk of infection [START_REF] Sprung | Pulmonalarterienkatheter: Methodik und klinische Anwendung[END_REF]. We propose a renewed noninvasive method to measure pressure in cavities, based on the diffusion of free gas microbubbles and their interaction with ultrasound waves.

Epstein & Plesset [START_REF] Epstein | On the stability of gas bubbles in liquid-gas solutions[END_REF] and De Jong et al. [START_REF] De Jong | Principles and recent developments in ultrasound contrast agents[END_REF] demonstrated the relation between the disappearance time of gas bubbles and the hydrostatic pressure applied. Because the sizes of gas bubbles change as a function of the hydrostatic pressure, the acoustic properties of the bubbles are affected. Based on this finding, a relation between bubble disappearance time, its acoustic response, and ambient pressure can be established. Bouakaz et al. gave an overview of pressure measurement methods using this relation, and studied one in vitro [START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF]. Instead of free gas bubbles, they inserted ultrasound contrast agent in their setup. Hard-shelled ultrasound contrast agent can act as a vehicle to carry gas to a region of interest. Upon insonification at sufficient acoustic pressure, the gas is released. This process is called sonic cracking [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF]. Bouakaz et al. determined overpressures from the decay of the fundamental acoustic response from diffusing released air bubbles. Pressure differences of 50 mmHg could be distinguished theoretically and experimentally. In medical diagnostics a resolution lower than 50 mmHg is desirable. To improve the sensitivity of the measurement approach mentioned above, we investigated the use of different gases. Furthermore, we investigated subharmonics as a marker for half resonant bubble size, since the subharmonic response is more sensitive to bubble size change than the fundamental [START_REF] Palanchon | Subharmonic and ultraharmonic emissions for emboli detection and characterization[END_REF]. Shi et al. had suggested the use of subharmonics for noninvasive pressure measurements [START_REF] Shi | Pressure measurements using contrast microbubbles[END_REF]. They measured the scattering of encapsulated microbubbles over the pressure range 0-186 mmHg, and found a decrease of approximately 10 dB. It had previously been demonstrated theoretically that subharmonic generation from free gas bubbles and from ultrasound contrast agents requires a threshold insonifying pressure, which is minimal when microspheres are insonified at twice their resonance frequency [START_REF] Prosperetti | Application of the subharmonic threshold to the measurement of the damping of oscillating gas bubbles[END_REF][START_REF] Shankar | Subharmonic backscattering from ultrasound contrast agents[END_REF]. Palanchon et al. determined such thresholds with simulations and experiments for free microemboli [START_REF] Palanchon | Subharmonic and ultraharmonic emissions for emboli detection and characterization[END_REF].

Since subharmonics can be generated with the resonant bubble size corresponding to half the transmitted frequency, we propose to correlate the time until subharmonic occurrence, to the hydrostatic overpressure.

In this Chapter we present improvements of a previously published method that correlates the duration of the decay of the fundamental response to the hydrostatic overpressure [START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF]. To improve the method, we simulate the diffusive behavior of six gases, and suggest a qualitative measure for the applicability of a specific gas. We discuss the results with respect to boundary conditions and limitations, which hold for the ultimate in vivo situation. Furthermore, we simulate the scattering behavior of ultrasound-insonified diffusing gas bubbles. We investigate the sensitivity of the subharmonic response in comparison to the fundamental response.

Methods

Theoretical model

The change of gas bubble radius as a function of time, is given by [START_REF] De Jong | Principles and recent developments in ultrasound contrast agents[END_REF][START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF]:

dR dt = DL      C i C 0 -1 - 2 σ R p 0 - p ov p 0 1 + 4 σ 3 R p 0      1 R + 1 √ π D t , ( 5.1)
where

C i
C 0 is the ratio of the dissolved gas concentration to the saturation concentration (saturation ratio), D is the diffusion constant, L is the Ostwald coefficient, p 0 is the ambient pressure, p ov is the applied overpressure, R is the instantaneous bubble radius, t is the time starting (t = 0) when the bubble surface is exposed to the liquid surface, and σ is the "proefschrift041" -2004/7/6 -18:01 -page 78 -#82

i i i i i i [5, 3]
PRESSURE MEASUREMENTS: SIMULATIONS surface tension. Eq. (5.1) shows that the disappearance of gas bubbles in a liquid medium is highly influenced by gas diffusion parameters and applied overpressure, and that the disappearance time of gas bubbles is shorter when the liquid medium is under pressure. When a gas bubble dissolves into a liquid medium, its acoustic response changes with its radius. The oscillating behavior of a gas bubble in a liquid, subjected to a sound field with a low acoustic pressure, was derived by [START_REF] Morgan | Experimental and theoretical evaluation of microbubble behavior: Effect of transmitted phase and bubble size[END_REF]. The changes in oscillating behavior of the dissolving gas bubble lead to changes in scattering cross sections [START_REF] Hilgenfeldt | Sound scattering and localized heat deposition of pulse-driven microbubbles[END_REF], and thus, the scattering behavior of an insonified, diffusing gas bubble can be calculated, dependent of the applied overpressure.

Simulations

First, we investigate the diffusive behavior of six gases by simulations, and define a qualitative measure for the applicability of a specific gas. Then we explore the sensitivity of the subharmonic acoustic response from diffusing gas bubbles, in comparison to the fundamental response.

The disappearance of free gas bubbles was simulated at hydrostatic overpressures between 0 and 200 mmHg, with gases Ar, C 3 F 8 , Kr, N 2 , Ne, and SF 6 . For our computations we used MATLAB R (The MathWorks, Inc., Natick, MA) programs. The parameters used were published in [START_REF] De Jong | Higher harmonics of vibrating gas-filled microspheres. Part one: simulations[END_REF]. The diffusion constants and the Ostwald coefficients were used for gas diffusing in water at room temperature [START_REF] Wilhelm | Low-pressure solubility of gases in liquid water[END_REF][START_REF] King | Measurement of the diffusion coefficient of sulfur hexafluoride in water[END_REF][START_REF] Chomas | Mechanisms of contrast agent destruction[END_REF][START_REF] Lide | CRC Handbook of Chemistry and Physics[END_REF][START_REF] Mayer | Myocardial contrast agents: recent advances and future directions[END_REF]. Saturation ratios C i C 0 = 0 were used, indicating that the gases are not present in water. From the diffusion curves, we computed the times it takes for bubbles to diffuse until they reach half their initial diameters. Half-size times were computed for gas bubbles varying in diameters from 5 to 20 µm, at ambient pressure, and at 20 mmHg overpressure. When applying an overpressure, the halfsize time of a bubble is shorter than the half-size time at ambient pressure, t1 /2 . This difference in half-size times, ∆t1 /2 , is a qualitative measure for the applicability of a specific gas for the measurement of hydrostatic overpressures: The sensitivity of the bubble to pressure change improves when ∆t1 /2 increases.

Scattering cross-sections were calculated for the diffusing gas bubbles as a function of time [START_REF] Morgan | Experimental and theoretical evaluation of microbubble behavior: Effect of transmitted phase and bubble size[END_REF][START_REF] Hilgenfeldt | Sound scattering and localized heat deposition of pulse-driven microbubbles[END_REF][START_REF] De Jong | Higher harmonics of vibrating gas-filled microspheres. Part one: simulations[END_REF], after filtering the fundamental and subharmonic responses from the acoustic bubble responses using a bandpass filter. The acoustic frequencies simulated, ranged from 0.

Results and discussion

From our simulations it follows that diffusion duration, and with it ∆t1 /2 , increases with the initial bubble diameter D. However, bubble size is a limiting factor in the in vivo situation, as an encapsulated bubble may have to pass through narrow vessels before arriving in the cavity where the gas is released. The measurement duration is another limitation, especially for blood pressure measurements, since pressure changes occur within the cardiac cycle. A measurement of the systolic pressure in the left ventricle is limited to a duration of roughly 150 ms [6]. Table 5.1 gives an overview of values ∆t1 /2 , for different limitations. If the half-size time is limited to 150 ms, and there is no limit to the bubble size, Kr and Ar gas bubbles result in the highest ∆t1 /2 . If the bubble diameter is limited to 6 µm, and there is no limit to the measurement duration, C 3 F 8 and SF 6 bubbles result in the highest ∆t1 /2 . If both limitations are combined, SF 6 and N 2 bubbles result in the highest ∆t1 /2 . Hence, the applicability of a specific gas is mainly determined by the limitations that apply.

Shi et al. noted, that yet another limitation of our approach may lie in the fact that the disappearance times of the gas bubbles depend also on the gas content of the blood [START_REF] Shi | Pressure measurements using contrast microbubbles[END_REF]. We may overcome this limitation by choosing gases that are not present in the human body, and as such have a saturation ratio C i C 0 = 0. Figure 5.1 shows the fundamental and subharmonic scattered power of "proefschrift041" -2004/7/6 -18:01 -page 80 -#84 i i i i i i [5,4] PRESSURE MEASUREMENTS: SIMULATIONS a dissolving 14 µm Ar bubble, insonified at 1 and 2 MHz, respectively, as a function of time. The solid lines represent the situation at ambient pressure, the dashed at a 50 mmHg hydrostatic overpressure. The maximum of the fundamental is reached gradually, whereas the subharmonic has a rapid rise near double-resonant size. The subharmonic peaks decay with 40 dB in 8.2 ms, whereas the most rapid fundamental decay is only 20 dB in 15.2 ms. Hence, the subharmonic response is more sensitive to diameter change than the fundamental response, indeed. Since overpressures of 50 mmHg could be distinguished from the decay of the fundamental response [START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF], we estimate that the scattering may have a ±5 dB variation.

With this variation, we computed diffusion time differences ∆t d for the decays observed in Figure 5.1: ∆t d = 7.6 ms for the fundamental response, and ∆t d = 2.0 ms for the subharmonic response. In our simulations, these diffusion time differences correspond to hydrostatic overpressures of 45 and 11 mmHg, respectively. Hence, the overpressure can be determined 4 times as precisely from the decay of the subharmonic response as from the decay of the fundamental response.

As an improvement of noninvasive pressure measurements, we propose to correlate the duration until the subharmonic peak in combination with the subharmonic decay, to hydrostatic overpressure. Evidently, precise knowledge of the initial bubble size is of importance. This might be established by generating subharmonics around the initial bubble size too.

Controlled gas release from a single bubble is currently under investigation in vitro with an ultrafast framing camera system [START_REF] Chin | Optical imaging of ultrasound contrast bubble motions at 25 million frames per second[END_REF].

Conclusions

For pressure measurements with a limited duration, e.g. 150 ms, Kr and Ar bubbles are most suitable, since they are most sensitive to pressure change. If there is also a limitation to bubble size, e.g. a maximum diameter of 6 µm, SF 6 is most suitable.

When a diffusing gas bubble with known initial diameter is insonified, the duration until subharmonic occurrence in combination with its decay, is an indicator of the hydrostatic overpressure. The subharmonic decays more rapidly than the fundamental response. For a diffusing Ar gas bubble with an initial diameter of 14 µm, the overpressure can be determined 4 times as precisely from the decay of the subharmonic response as from the decay of the fundamental response. Overpressures as small i i "proefschrift041" -2004/7/6 -18:01 -page 81 -#85 as 11 mmHg may be discriminated with this method. Generating subharmonics may also be useful for verifying the initial bubble size.

i i i i i i CONCLUSIONS [5, 4]
Free gas bubbles can be delivered to cavities, and released by means of sonic cracking, which is currently under investigation. Ultrasound-induced Gas Release from Rigid-Shelled Microbubbles

Abstract

We investigated gas release from two rigid-shelled ultrasound contrast agents, by subjecting them to high-MI ultrasound and simultaneously capturing high-speed photographs. At an insonifying frequency of 1.7 MHz, a larger percentage of contrast bubbles is seen to crack than at 0.5 MHz. Most of the released gas bubbles have equilibrium diameters between 1.25 and 1.75 µm. Their disappearance was observed optically. Free gas bubbles have equilibrium diameters smaller than the bubbles from which they have been released.

Based on the manuscript Postema M, Bouakaz A, Versluis M, de Jong N. Ultrasoundinduced gas release from contrast agent microbubbles. 2004 submitted.

This work has been supported by the Technology Foundation STW (RKG.5104) and by the Interuniversity Cardiology Institute of the Netherlands. i i "proefschrift041" -2004/7/6 -18:01 -page 84 -#88

i i i i i i [6, 1]
ULTRASOUND-INDUCED GAS RELEASE

Introduction

Bubbles have been under investigation for medical imaging and drug delivery, but may also be of interest for noninvasive pressure measurements.

Bubbles have been under investigation for medical imaging and drug delivery, but may also be of interest for noninvasive pressure measurements.

The assessment of local blood pressure plays an important role in contemporary cardiology. Local cardiac pressure measurements are generally done by catheterization. This is an expensive procedure with a risk of infection [START_REF] Sprung | Pulmonalarterienkatheter: Methodik und klinische Anwendung[END_REF].

Since the 1970s, several noninvasive methods have been proposed for local blood pressure assessment, based on the acoustic properties of microbubbles under different hydrostatic pressure conditions.

The resonance frequency f r of a free gas bubble is related to its diameter D according to [START_REF] Tickner | Precision microbubbles for right side intracardiac pressure and flow measurements[END_REF]:

f r ≈ 6.5 m s -1 D . (6.1)
When subjected to a hydrostatic overpressure, a bubble will contract, and by that increase its resonance frequency. In [START_REF] Jr | A new noninvasive technique for cardiac pressure measurement: resonant scattering of ultrasound from bubbles[END_REF][START_REF] Tickner | Precision microbubbles for right side intracardiac pressure and flow measurements[END_REF][START_REF] Schlief | Ultrasonic manometry process in a fluid by means of microbubbles[END_REF] it was suggested to measure pressures from changes in resonance frequency of relatively big, and thus slowly dissolving, gas bubbles. The dissolving time of gas bubbles is related to the hydrostatic pressure as well [START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF]. Hence, another noninvasive method for blood pressure assessment would be the measurement of the acoustic response from a dissolving bubble population. Simulations of the dissolving behavior of gas bubbles have been presented in [START_REF] Kabalnov | Dissolution of multicomponent microbubbles in the bloodstream: 1. Theory[END_REF][START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF][START_REF] Chen | The disappearance of ultrasound contrast bubbles: observations of bubble dissolution and cavitation nucleation[END_REF][START_REF] Postema | Noninvasive microbubble-based pressure measurements: a simulation study[END_REF]. The precision of the pressure measurement might be increased by making use of the (sub)harmonic components of the acoustic signals [START_REF] Shi | Pressure dependence of subharmonic signals from contrast microbubbles[END_REF][START_REF] Postema | Noninvasive microbubble-based pressure measurements: a simulation study[END_REF].

For both noninvasive methods, free gas bubbles have to be delivered to a region of interest. Hard-shelled ultrasound contrast bubbles might act as the vehicles to deliver the gas. Upon insonification, the gas would then be released from their encapsulation and immediately be subjected to the local hydrostatic overpressure. The ultrasound-induced release of gas from an encapsulated microbubble is referred to as 'sonic cracking' [178]. Previous experiments demonstrated the feasibility of gas release from contrast agent microbubbles and the subsequent fading acoustic response from the dissolving released gas bubbles [START_REF] Takeuchi | Industrial use thermoplastic microballoon to mimic the contrast agents and its in-vitro behavior including released gas dynamics[END_REF][START_REF] Kabalnov | Dissolution of multicomponent microbubbles in the bloodstream: 2. Experiment[END_REF][START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF][START_REF] Chen | The disappearance of ultrasound contrast bubbles: observations of bubble dissolution and cavitation nucleation[END_REF]. In this study, we visualize the release and the dissolution of air bubbles after sonic cracking. Furthermore, we discuss if the sizes of the released gas bubbles are in agreement with previous measurements of acoustic decay times.

Experimental setup Overview

For the observations of gas release, we made use of the Brandaris-128 fast framing camera system [START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF]. The amplitude of the electrical signal

Optics

Underneath the capillary tube an optic fiber was mounted. This fiber was connected to an MVS-7010 Fiber Optic Strobe (PerkinElmer Optoelectronics, Salem, MA), and to a KLS-201 continuous fiber light source (Olympus KMI (KeyMed Ltd), Southend-on-Sea, UK).

The container was positioned beneath a customized BXFM microscopic system (Olympus Optical Co., Ltd., Tokyo, Japan) with a U-CA magnification changer (Olympus Optical Co., Ltd.), switched to 2× magnification and a LUMPlanFl 60× water immersion objective lens (Olympus Optical Co., Ltd.). For image control purposes, an LCL-902K CCD camera (Watec Co., Ltd., Yamagata, Japan) was mounted to the top of the microscope.

Camera

The optical observations were recorded with a Brandaris-128 (cf. Figure 6.1) fast framing camera system [START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF]. The Brandaris-128 captured sequences of 128 image frames at speeds up to 15 million frames per second. Typical frame sizes correspond to 89 × 68 µm 2 . In all observations, image frames were captured before, during, and after ultrasound insonification.

For the observations of gas dissolution, which is a relatively slow process compared to bubble oscillations, we made use of a data set recorded with a CR 2000 camera (Redlake MASD, LLC, San Diego, CA) that operated at a speed of two thousand frames per second. This camera had been installed on top of the microscope, as shown in Figure 6.1.

"proefschrift041" -2004/7/6 -18:01 -page 87 -#91

i i i i i i EXPERIMENTAL SETUP [6, 2]

Contrast agents

We investigated the ultrasound contrast agent Quantison TM (Upperton Limited). It consists of human serum albumin-encapsulated air bubbles with a mean diameter of 3.2 µm. Shell thicknesses are between 0.2 and 0.3 µm [START_REF] Frinking | Acoustic modeling of shell-encapsulated gas bubbles[END_REF]. The resonance frequency of the bulk agent is 4 MHz [START_REF] Frinking | Acoustic modeling of shell-encapsulated gas bubbles[END_REF]. The content of a Quantison TM vial was resuspended in 5 ml of Isoton R II (Beckman Coulter, Inc., Fullerton, CA), and shaken gently for 20 seconds before further dilution.

We also investigated PB127 (POINT Biomedical Corporation, San Carlos, CA), which is specified as follows: PB127 consists of bilayered microspheres encapsulating nitrogen bubbles with a mean diameter of 4 µm. The outermost layer is albumin and the inner layer is composed of a biodegradable polymer. The resonance frequency of PB127 lies between 6 and 7 MHz. The content of a PB127 vial was resuspended in 2 ml of deionized water, and shaken gently for 20 seconds before further dilution.

Ultrasound

The agents were insonified either by 6 or 8 cycles of 500 kHz ultrasound, or by 8 cycles of 1.7 MHz ultrasound. For both frequencies transmitted, peak acoustic pressures corresponded to mechanical indices in the range 0.3 < MI < 1.9. We refer to ultrasound transmission with mechanical indices greater than 0.8 as high-MI insonification. Acoustic pressures in this regimen are high enough to ensure gas release [START_REF] Burns | Looking at and listening to breaking bubbles: a correlative optical acoustic study of some experimental polymer/air agents[END_REF].

Acoustic pressures applied were measured with a calibrated MH28-10 hydrophone (FORCE Technology, Brøndby, Denmark) in a separate water tank (cf. Chapter 2).

Procedure

We recorded 533 image sequences with the Brandaris-128 system, and 55 sequences with the CR 2000 camera. For each event, the total number of contrast agent microbubbles visible in the frames were counted, and the number of contrast agent microbubbles from which gas was released. From the frames recorded after ultrasound insonification, the diameters of the released gas bubbles (if still present) or fragments thereof were measured, as well as the diameters of the contrast agent microbubbles from which they had escaped. Bubble diameters and distances were measured manually or by using an image processing method described in [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF] and Chapter 2.

3 Results

Quantison TM

An example of the sonic cracking of a Quantison TM bubble is shown in Figure 6.2. Frames numbering is from left to right, then from upper to lower. The camera system operated at a speed of 10 million frames per second. Gas is seen to escape from a 4.3 µm shelled Quantison TM bubble in the third frame. Apparently, the Quantison TM shell is too rigid to be seen expanded. The free gas expands to 12.3 µm in the eighth frame, after which it contracts. In the eleventh frame, the free gas bubble, which has been subjected to motion blur, appears to be detached from the encapsulated bubble. In the twelfth frame, the gas is hardly visible. Another example of gas release is given in Figure 6.3. The camera system operated at a speed of 3 million frames per second. In the second frame, gas escapes from a 3.7 µm bubble. The response of the released gas to ultrasound can be clearly appreciated. After expanding to a 8.0 µm maximum in frame three, it is seen detached and contracted in frames four and five. The encapsulated bubble clearly looks different than before cracking, as if there is no gas left inside the shell. A few microseconds after insonification, the left frame of Figure 6.4 was captured. The released gas bubble is visible to the upper left of the bubble from which we ULTRASOUND-INDUCED GAS RELEASE saw it escape. Its diameter is estimated to be less than 1 µm. One hundred ms later, the right frame was captured. Here, the released gas bubble has disappeared.

The dissolving process itself of the released gas bubbles was captured at 2000 frames per second. The upper images of Figure 6.5 show 8-bit photographs of three Quantison TM bubbles before ultrasound arrival. The lower images show the same photographs after gray-level window-slicing. After insonification, the Quantison TM bubbles have translated, and two fragments are visible in the second frame. The diameters of the fragments are less than 1 µm. These fragments slowly disappear, and are hardly visible in the last frame.

-0.5 ms 0.0 m s 0 .5 ms 1.0 m s 1 .5 ms After release (first three rows), the free gas bubbles interact, until one free gas bubble remains (last row).

PB127

An example of the sonic cracking of a PB127 bubble is shown in Figure 6.6.

Frames numbering is from left to right, then from upper to lower. The camera system operated at a speed of 9.4 million frames per second. Upon ultrasound arrival in the second frame, the bubbles start to contract. From frame four on, gas is released from two 7 µm PB127 bubbles. In frame eight, both gas bubbles have been detached from the shell. Starting with frame ten, gas release is again observed from the lower PB127 bubble. The released gas bubbles interact, and both fragmentation and coalescence occur several times between frames 21 and 47. After insonification had finished, one resulting free gas bubble remained, which was still seen to pulsate. The left frame of Figure 6.7 was captured after insonification. The free gas bubble is the lower bubble in the diamond-shaped bubble group. Its resting diameter is 4 µm. One hundred ms later, the right frame was captured. Here, the free gas bubble has disappeared.

Our results show that the sizes of the PB127 bubbles from which gas was released, are normally distributed. The mean diameter of these bubbles is 3.6 µm, with a standard deviation of 1.5 µm.

The size distribution of the released gas bubbles from PB127 is shown in Figure 6.8. For both frequencies, most released gas bubbles have equi-i i "proefschrift041" -2004/7/6 -18:01 -page 93 -#97 The size distribution of the released gas bubbles from PB127 is shown in Figure 6.8. For both frequencies, most released gas bubbles have final restng diameters between 1.25 and 1.75 µm.

i i i i i i RESULTS [ 6, 3] 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4

Overview

A quantitative overview of gas release is demonstrated in Figure 6.9. Typically, 10-15 contrast agent bubbles were visible in the field of view. For both agents, the percentage of released gas bubbles is greater at 1.7 MHz than at 0.5 MHz insonification.

Released gas bubbles have been observed to translate, to fragment, and to coalesce with other released bubbles. The contrast agent bubbles did not demonstrate these phenomena. Our measurements of resting sizes of released gas bubbles include fragments of released gas bubbles and coalesced bubbles. Bubbles that did not show gas release upon insonification, have been observed to crack during a subsequent ultrasonic burst.

After sonic cracking, contrast bubbles of both agents can stay acoustically active. Gas remainder has been observed inside the shells from sonically cracked bubbles, which was released by a subsequent ultrasonic burst.

Discussion and conclusions

We can only speculate on why certain bubbles crack while others stay intact. Tiny flaws in the shells may account for this observation. Such flaws are apparently formed or widened during ultrasound insonification, causing the bubble to crack during a subsequent ultrasonic burst.

The difference in average cracking percentage observed at 0.5 MHz and 1.7 MHz, may lie in the proximity of the resonance frequency of the agent to the insonifying frequency. The resonance frequency of Quantison TM , i.e. 4 MHz, is closest to 1.7 MHz, indeed. So is the resonance frequency of The phenomenon of bubbles translating during an ultrasonic cycle has only been observed with free gas bubbles. We attribute this behavior to the small size of the free gas bubbles during contraction, and the lack thereof with the hard-shelled contrast agent bubbles. When in contraction phase, free gas bubbles have a very small translating mass, as it is equivalent to half the mass of the displaced fluid [START_REF] Leighton | The Acoustic Bubble[END_REF]. Because of impulse conservation, such small bubbles can translate further than the relatively big encapsulated bubbles.

The acoustic response from an ensemble of Quantison TM microbubbles disappears between 15 and 30 ms after transmission of a high-MI ultrasonic burst [START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF], whereas the disappearance time of the fundamental acoustic response of an ensemble of PB127 microbubbles lies between 50 and 100 ms after transmission of a high-amplitude ultrasonic burst [START_REF] Burns | Looking at and listening to breaking bubbles: a correlative optical acoustic study of some experimental polymer/air agents[END_REF]. Figure 6.10 demonstrates simulations of the dissolution of nitrogen mi-"proefschrift041" -2004/7/6 -18:01 -page 96 -#100

i i i i i i [6, 4]
ULTRASOUND-INDUCED GAS RELEASE crobubbles with diameters between 0.5 and 4.5 µm into saturated water at ambient pressure. Since most released gas bubbles have equilibrium diameters between 1.25 and 1.75 µm, they will disappear within 15 ms. The longer decay times measured in Quantison TM [START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF] and PB127 [START_REF] Burns | Looking at and listening to breaking bubbles: a correlative optical acoustic study of some experimental polymer/air agents[END_REF] must be attributed to the relatively small number of large released gas bubbles around 4 µm. These large bubbles might be formed by coalescence of released gas bubbles or fragments [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF].

For noninvasive pressure measurements, the influence of applying hydrostatic overpressures on the occurrence of sonic cracking will have to be investigated. Furthermore, the influence of pulse length and pulse repetition are of great practical interest. i i "proefschrift041" -2004/7/6 -18:01 -page 98 -#102

i i i i i i [7, 1]
MICROBUBBLE PHENOMENA: OVERVIEW oscillation mode. Remarkable are our observations of jetting through contrast agent microbubbles. The pressure at the tip of a jet is high enough to penetrate any human cell. Hence, liquid jets may act as remote-controlled microsyringes, delivering a drug to a region of interest. Encapsulated microbubbles have (potential) clinical applications in both diagnostics and therapeutics.

Introduction

Blood does not reflect ultrasound well, but its response may be enhanced by gas microbubbles of a few micrometers in diameter that are introduced into the blood pool [START_REF]Ultrasound Contrast Agents. Basic principles and clinical applications[END_REF]. These microbubbles oscillate upon insonification, and generate as such a characteristic acoustic response.

An ultrasound contrast agent (UCA) is a liquid containing gas microbubbles that are encapsulated by a shell. UCAs are widely used in clinical diagnostic imaging [4,[START_REF]Ultrasound Contrast Agents. Basic principles and clinical applications[END_REF]. The intravascular use of UCA enhances the quantification of perfusion and blood flow [START_REF] Klibanov | Targeted delivery of gas-filled microspheres, contrast agents for ultrasound imaging[END_REF][START_REF] Wei | Blood flow and perfusion measurements: background and clinical utility[END_REF], and lowers the detectability threshold of tumor and tissue vascularization, using conventional Doppler instruments [START_REF] Burns | Intravenous contrast agent for ultrasound Doppler: In vivo measurement of small tumor vessel doseresponse[END_REF]. An overview of UCA detection procedures in ultrasound imaging has been presented by De Jong et al. [START_REF] De Jong | Detection procedures of ultrasound contrast agents[END_REF], and an overview of UCA imaging innovations has been put forward by Chiou et al. [START_REF] Chiou | Clinical applications of contrast echocardiography[END_REF].

To understand encapsulated microbubble behavior better in order to develop or enhance applications in diagnostics and therapeutics, UCA microbubbles have been subjected to high-speed photography. Postema et al. [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF] gave an overview of publications on high-speed optical observations of insonified UCA.

Observations of dynamic UCA microbubble behavior have resulted in new insights and novel approaches in diagnostics and therapeutics: The nonlinear behavior of oscillating bubbles has led to the development of contrast harmonic imaging [START_REF] Schrope | Second harmonic ultrasonic blood perfusion measurement[END_REF][START_REF] De Jong | Higher harmonics of vibrating gas-filled microspheres. Part one: simulations[END_REF][START_REF] De Jong | Contrast harmonic imaging[END_REF][START_REF] Bouakaz | Improved contrast to tissue ratio at higher harmonics[END_REF][START_REF] Bouakaz | Super harmonic imaging: a new imaging technique for improved contrast detection[END_REF], whereas observations of bubble destruction have led to the development of high-MI imaging techniques [START_REF] Uhlendorf | Nonlinear acoustical response of coated microbubbles in diagnostic ultrasound[END_REF][START_REF] Frinking | A new ultrasound contrast imaging approach based on the combination of multiple imaging pulses and a separate release burst[END_REF].

Targeted UCA delivery is based on microbubbles with ligands attached to them [START_REF] Klibanov | Targeted delivery of gas-filled microspheres, contrast agents for ultrasound imaging[END_REF][START_REF] Unger | Thrombus-specific contrast agents for imaging and thrombolysis[END_REF]. These bubbles circulate through vessels and accumulate at a target tissue, thereby marking the target in ultrasound images. Klibanov [START_REF] Klibanov | Targeted delivery of gas-filled microspheres, contrast agents for ultrasound imaging[END_REF] put forward the idea that targeted microbubbles may be applied for selective delivery to the areas where selective enhancement of the action of ultrasound would be required, and if such a bubble would INTRODUCTION [START_REF] Bernoulli | sive de viribus et motibus fluidorum commentarii[END_REF]1] contain plasmid DNA, enzyme, or another therapeutic agent, it might be released at the site of interest during insonification. Another means of targeting was suggested by Dayton et al. [START_REF] Dayton | Optical and acoustical dynamics of microbubble contrast agents inside neutrophils[END_REF]. They provided optical verification that microbubbles oscillate differently when inside neutrophils in response to insonification, and emit acoustic signals that are distinct from free microbubbles. Thus, microbubbles within neutrophils might be detected, providing a potential method to image activated neutrophils as they accumulate at sites of inflammation. Recently, Unger et al. [START_REF] Unger | Therapeutic applications of microbubbles[END_REF] gave an overview of the therapeutic applications of UCA microbubbles. They presented experimental results using UCAs for thrombolysis, drug delivery, and gene delivery. Other recent advances in local drug and gene delivery include the in vivo delivery of a virus vector, attached to albumin microbubbles [START_REF] Shohet | Echocardiographic destruction of albumin microbubbles directs gene delivery to the myocardium[END_REF], the in vitro and in vivo transfection of endothelial cells with plasmid DNA mixed with UCA [START_REF] Taniyama | Local delivery of plasmid DNA into rat carotid artery using ultrasound[END_REF], and the accelerated cellular drug uptake in vitro when UCA microbubbles are present [START_REF] Van Wamel | Effects of diagnostic ultrasound parameters on molecular uptake and cell viability[END_REF]. Tachibana et al. [START_REF] Tachibana | Induction of cell-membrane porosity by ultrasound[END_REF] subjected cells in the presence of a photosensitive drug to continuous ultrasound, and noticed surface pores on the cells. Inducing porosities in cells with ultrasound, generally referred to as sonoporation, has potential applications in (tumor) cell lysis and selective delivery of drugs and genes into cells. Independently, it was demonstrated that moderate microbubble oscillations are sufficient to achieve rupture of lipid membranes, in a regimen in which the bubble dynamics can be accurately controlled [START_REF] Marmottant | Controlled vesicle deformation and lysis by single oscillating bubbles[END_REF]. This might enable the transport of drugs through the cell membrane.

At high acoustic amplitudes, destructive effects of UCA microbubbles have been observed, such as hemorrhaging [START_REF] Skyba | Direct in vivo visualization of intravascular destruction of microbubbles by ultrasound and its local effects on tissue[END_REF][START_REF] Maruvada | Optical monitoring of ultrasound interaction with blood vessels in transparent fish after injection with contrast agents[END_REF], and lysis [START_REF] Van Wamel | Effects of diagnostic ultrasound parameters on molecular uptake and cell viability[END_REF]. Kudo et al. [START_REF] Kudo | Study on mechanism of cell damage caused by microbubbles exposed to ultrasound[END_REF] performed an in vitro study on bovine arterial cell damage by ultrasound in combination with microbubbles. They found that the locations of damaged cells were similar to the locations where violent bubble collapse was observed, suggesting that bubble collapse is responsible for cell membrane damage.

In this Chapter, we present an overview of dynamic encapsulated microbubble behavior observed at high acoustic amplitudes. The mechanisms for each type of behavior, found in literature on free (not encapsulated) gas bubbles, acoustics, and cavitation, are correlated to our highspeed optical observations. Furthermore, we address the potential clinical applications of the phenomena.

Previously, some UCA microbubble destruction phenomena were categorized by Chomas et al. [START_REF] Chomas | Mechanisms of contrast agent destruction[END_REF] and Postema et al. [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF]. From our optical i i "proefschrift041" -2004/7/6 -18:01 -page 100 -#104

i i i i i i [7, 1]
MICROBUBBLE PHENOMENA: OVERVIEW observations, we discriminate the following categories: oscillation, translation, coalescence, fragmentation, sonic cracking, and jetting.

In the following subsections, we give a brief overview of these phenomena, and an explanation of their occurrence. Most theories on bubble behavior were validated for big, free (not encapsulated) microbubbles.

Oscillation

When a microbubble is exposed to an oscillating acoustic signal, it undergoes alternate expansions and contractions with the same amplitude and duration at low driving pressures [START_REF] Strasberg | Gas bubbles as sources of sound in liquids[END_REF]. This regimen of pulsation amplitudes has been referred to as moderate [START_REF] Vokurka | Comparison of Rayleigh's, Herring's, and Gilmore's models of gas bubbles[END_REF]. Bubble activity which may occur at relatively low-amplitude pressures has been denoted as stable cavitation [START_REF] Miller | Theoretical investigation of the response of gas-filled micropores and cavitation nuclei to ultrasound[END_REF]. As the driving pressure increases, more complex nonlinear interactions occur: greater bubble expansion amplitude than contraction amplitude, and relatively slow expansion followed by rapid contraction (collapse). This behavior has been referred to as violent [START_REF] Vokurka | Comparison of Rayleigh's, Herring's, and Gilmore's models of gas bubbles[END_REF] or inertial (or transient) cavitation [START_REF] Miller | Theoretical investigation of the response of gas-filled micropores and cavitation nuclei to ultrasound[END_REF][START_REF] Flynn | Transient pulsations of small gas bubbles in water[END_REF]3]. It has been associated with the production of harmonic signals [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF].

The transition from the moderate to the violent regimen is rather abrupt: For any driving pressure, there exists a transitional equilibrium microbubble radius R tr 0 , above which microbubbles pulsate like inertial cavities [START_REF] Flynn | Cavitation dynamics. II. Free pulsations and models for cavitation bubbles[END_REF][START_REF] Flynn | Transient pulsations of small gas bubbles in water[END_REF][START_REF] Hilgenfeldt | Analysis of Rayleigh-Plesset dynamics for sonoluminescing bubbles[END_REF]. This transition is referred to as the cavitation threshold. A bubble is judged to have grown into an inertial cavity when its maximum radius is greater than approximately twice its equilibrium radius [START_REF] Flynn | Cavitation dynamics. II. Free pulsations and models for cavitation bubbles[END_REF][START_REF] Flynn | Transient pulsations of small gas bubbles in water[END_REF].

A number of models for computing radius-time curves of insonified gas bubbles has been developed. These models differ both in complexity and in the range of acoustic amplitudes for which they can be used [START_REF] Vokurka | Comparison of Rayleigh's, Herring's, and Gilmore's models of gas bubbles[END_REF].

To model the behavior of UCA microbubbles, the presence of an encapsulation around the gas core has to be accounted for. Hence, we have to introduce parameters that describe the dynamic behavior of the shell.

Presently, two models have been used for modeling UCA microbubble oscillations. De Jong et al. [START_REF] De Jong | Higher harmonics of vibrating gas-filled microspheres. Part one: simulations[END_REF] used a modified RPNNP equation, named after its developers Rayleigh, Plesset, Neppiras, Noltingk, and Poritsky. They accounted for the presence of a shell by introducing a shell stiffness and a shell friction parameter. Morgan et al. [START_REF] Morgan | Experimental and theoretical evaluation of microbubble behavior: Effect of transmitted phase and bubble size[END_REF] used a modified Herring equation. They introduced the shell properties thickness, elasticity modulus, and viscosity. Both models are consistent with optical observations at low driving pressures [START_REF] De Jong | Optical imaging of contrast agent microbubbles in an ultrasound field with a 100-MHz camera[END_REF][START_REF] Morgan | Experimental and theoretical evaluation of microbubble behavior: Effect of transmitted phase and bubble size[END_REF][START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF]. Currently, models on UCA microbubble INTRODUCTION [START_REF] Bernoulli | sive de viribus et motibus fluidorum commentarii[END_REF]1] oscillating behavior at high driving pressures have been under investigation [START_REF] Stride | On the destruction of microbubble ultrasound contrast agents[END_REF].

Translation

Translations of UCA microbubbles in the direction of the sound field and towards each other have been frequently observed with high-speed cameras [START_REF] Dayton | Action of microbubbles when insonified: experimental evidence[END_REF][START_REF] Dayton | A preliminary evaluation of the effects of primary and secondary radiation forces on acoustic contrast agents[END_REF][START_REF] Dayton | Acoustic radiation force in vivo: a mechanism to assist targeting of microbubbles[END_REF]35,[START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]. Microbubble translation in the direction of the sound field has been attributed to a primary radiation force resulting from a pressure gradient across the bubble surface. The translation is maximal in contraction phase [START_REF] Reddy | Coupled dynamics of translation and collapse of acoustically driven microbubbles[END_REF]. It was demonstrated that the velocity v of a gas bubble in a steady fluid subjected to an ultrasound field can be calculated from the following ordinary differential equation [START_REF] Magnaudet | The motion of high-Reynolds-number bubbles in inhomogeneous flows[END_REF][START_REF] Rensen | Spiraling bubbles: how acoustic and hydrodynamic forces compete[END_REF][START_REF] De Vries | Induced bubble shape oscillations and their impact on the rise velocity[END_REF][START_REF] Lohse | Controlling bubbles[END_REF]:

F = F rad + F d + F a = d dt (ρ g V b v) ≈ 0 , ( 7.1)
where F rad is the primary radiation force, F d is the drag force, F a is the added mass force, ρ g is the density of the gas, and V b is the volume of the bubble.

In a steady flow, averaging over one acoustic cycle, the added mass force for small accelerations is given by [START_REF] Rensen | Spiraling bubbles: how acoustic and hydrodynamic forces compete[END_REF]:

F a = -ρ C m V b v , ( 7.2)
where ρ is the density of the surrounding fluid, C m is the added mass coefficient, which is 1 /2 for a sphere, whatever the Reynolds number [START_REF] Magnaudet | The motion of high-Reynolds-number bubbles in inhomogeneous flows[END_REF], and V b ≈ 4π 3 R 3 0 , in which R 0 is the ambient bubble radius. Averaging over one acoustic cycle, the primary radiation force is given by [START_REF] Dayton | A preliminary evaluation of the effects of primary and secondary radiation forces on acoustic contrast agents[END_REF][START_REF] Tortoli | On the interaction between ultrasound and contrast agents during Doppler investigations[END_REF]:

F rad = p - ac 2 R 0 ρ c f δ t f r f   f r f 2 -1   2 + δ t f r f 2 , ( 7.3)
where c is the speed of sound, p - ac is the peak rarefactional acoustic pressure, δ t is the dimensionless total damping coefficient [START_REF] Medwin | Counting bubbles acoustically: a review[END_REF], and f r is the bubble resonant frequency [START_REF] Medwin | Counting bubbles acoustically: a review[END_REF]. The drag force is given by [START_REF] Magnaudet | The motion of high-Reynolds-number bubbles in inhomogeneous flows[END_REF][START_REF] Tortoli | On the interaction between ultrasound and contrast agents during Doppler investigations[END_REF]: is the drag coefficient of a contaminated system [START_REF] Marco | Experimental study on rising velocity of nitrogen bubbles in FC-72[END_REF], such as a contrast agent.

F d = - π η 4 C d Re R 0 v(t) , (7.4) 101 i
The microbubble translations towards each other have been attributed to secondary radiation forces: oscillating bubbles generate spatially varying pressure fields. If two bubbles are either both below or both above the resonant size, this results in attraction. However, if one bubble is below and the other is above the resonant size, they oscillate out of phase [START_REF] Pain | The physics of vibrations and waves[END_REF][START_REF] Leighton | The Acoustic Bubble[END_REF][START_REF] Reddy | Coupled dynamics of translation and collapse of acoustically driven microbubbles[END_REF], causing the bubbles to recede from each other. The mean approach velocity v a of two identical bubbles is given by [START_REF] Dayton | A preliminary evaluation of the effects of primary and secondary radiation forces on acoustic contrast agents[END_REF]:

v a = - 2π f p - ac 2 27 η ρ κ 2 R 5 0 d 2 0 , ( 7.6)
where d 0 is the distance between the centers of the two bubbles, and κ is the compressibility of the bubble

κ = 1 ρ ∂ρ ∂p , ( 7.7)
in which ∂ρ ∂p is the partial derivative of the density with respect to the pressure.

Coalescence

Ultrasound-induced microbubble coalescence is the fusion of two or more microbubbles. As adjacent bubbles expand, the pressure in the film between them increases, resulting in a deformation (flattening) of the bubble surfaces. The continuing bubble expansion causes drainage of the interposed film. This thinning continues until a critical thickness around 0.1 µm is reached, at which the Van der Waals attractive forces result in film rupture and the coalescence of the bubbles [START_REF] Duineveld | Bouncing and coalescence of two bubbles in water[END_REF]. Thinning and rupture of thin liquid films have been described by Sheludko [START_REF] Sheludko | Thin liquid films[END_REF], Kralchevsky et al. [START_REF] Kralchevsky | Thin liquid film physics[END_REF], and Narsimhan & Ruckenstein [START_REF] Narsimhan | Structure, drainage, and coalescence of foams and concentrated emulsions[END_REF].

Flattening of the adjacent bubble surfaces occurs if and only if the bubble system has a Weber number We > 0.5 [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF]. The Weber number for a INTRODUCTION [START_REF] Bernoulli | sive de viribus et motibus fluidorum commentarii[END_REF]1] fluid containing two bubbles with radii R 1 and R 2 , respectively, is given by the inertial force relative to the surface tension force:

We = ρu 2 σ R m , ( 7.8)
where u is the relative approach velocity of the bubble walls, ρ is the fluid density, σ is the surface tension, and R m is the mean bubble radius for which holds:

2

R m = 1 R 1 + 1 R 2 .
In our results, Weber numbers are relatively high because of the rapid bubble expansions, with maximal radius increases of several m s -1 . If the Weber number is lower than 0.5, bubble coalescence will always occur, without flattening of the adjacent surfaces prior to contact [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF].

In a separate paper, we investigated the coalescence mechanism of microbubbles, based on high-speed optical observations of insonified UCA [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF] (cf. Chapter 3). We investigated the mechanism of film drainage by comparing the observed coalescence times with calculated film drainage times for mobile interfaces and immobile interfaces (7.9). The drainage time τ d of an interposed film with immobile interfaces until a critical thickness h c is given by:

τ d = 3 η R 2 f R m 8 σ h 2 c , ( 7.9)
where R f is the film radius, and R m is the mean bubble radius. The drainage time of a film with mobile interfaces is three times as low.

The calculated drainage times for immobile interfaces prove too long to be compatible with the observations. Stated differently, if the film between bubbles thinned by eq. (7.9) alone during the observed time span, it would only reach a minimum thickness that is much larger than that needed to induce film rupture. Hence, a mechanism for film rupture might be at work that overrules the drainage. We investigated if shape instabilities of the bubble can cause local corrugations that bridge the film and rupture it, before thinning of the whole film [START_REF] Postema | Ultrasound-induced microbubble coalescence by parametric instability[END_REF]. Although small perturbations on the bubble surface may grow tremendously, a phenomenon known as parametric instability, sufficiently large perturbations to bridge the liquid film cannot be formed within the times observed.

Bounce is the process where bubbles approach and flatten, but do not coalesce [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]. This behavior has been attributed to the drainage given in eq. (7.9) taking more time than the expansion phase.

Fragmentation

Fragmentation is the fission of a bubble into smaller bubbles [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF]. Although acoustical observations have been associated with microbubble destruction [START_REF] Shi | Destruction of contrast microbubbles and the association with inertial cavitation[END_REF], fragmentation of UCA microbubbles was first visualized with high-speed cameras in 2001 [START_REF] Chomas | Mechanisms of contrast agent destruction[END_REF][START_REF] Postema | Real-time optical imaging of individual microbubbles in an ultrasonic field[END_REF]. In the same year, Brennen [START_REF] Brennen | Fission of collapsing cavitation bubbles[END_REF] computed the number of fragments for a cavitation bubble distorted by spherical harmonics. He demonstrated that, for any positive

Γ = ρ R 2 R σ , ( 7.10)
where R denotes the second time derivative of R, there must be a mode n for which the spherical harmonic distortion has a maximum. This mode depends on Γ as

n = 1 3 7 + 3Γ - 2 3 . ( 7.11)
The number of fragments N is estimated N ≈ n 3 . Chomas et al. [START_REF] Chomas | Threshold of fragmentation for ultrasonic contrast[END_REF] showed that fragmentation occurs around peak contraction, when the bubble collapse is driven by inertial forces, since the inward acceleration continues to increase as the bubble approaches its minimum radius and suddenly changes sign as the bubble begins a rebound. They suggest that if the energy that is transferred during collapse is not sufficiently dissipated during one ultrasonic cycle, the bubble will become unstable and fragment.

Longuet-Higgins [START_REF] Ms | The crushing of air cavities in a liquid[END_REF] related the intrinsic energy of a bubble fragment population with a size distribution P (R) to the initial intrinsic energy of the mother-bubble with equilibrium radius R 0 :

E * = ∞ 0 R R 0 2 P (R) dR , ( 7.12)
where E * is the intrinsic energy ratio, and R is the radius of a fragment. For bubble fragments of equal sizes,

E * = R 0 R = 3 √ N . (7.13)
Longuet-Higgins [START_REF] Ms | The crushing of air cavities in a liquid[END_REF] also presented an elegant method to compute the size distribution of bubbles generated by "shattering a single air cavity".

INTRODUCTION [7, 1]

Sonic cracking

Sonic cracking is the ultrasound-induced formation of a shell defect causing gas to escape from UCA microbubbles. It has been observed with rigidshelled UCA microbubbles [34,178,[START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF]. The physical mechanism behind sonic cracking is yet not known. Tiny flaws in the shells may account for the fact that certain bubbles crack while others stay intact [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF].

Jetting

When a bubble rapidly contracts (collapses) near a boundary, this collapse will be asymmetrical. A high-speed liquid jet may form which projects through the bubble towards the boundary [3], pulling a slight volume of the bubble content along. This remarkable phenomenon is called jetting. The jetting phenomenon for cavitation bubbles was described by Philipp & Lauterborn [START_REF] Philipp | Cavitation erosion by single laser-produced bubbles[END_REF] and depicted by Ory (cf. Figure 7.1): The asymmetric collapse causes the velocity of the upper bubble wall to exceed the velocity of the lower wall in order to conserve the impulse of the bubble/fluid system. Consequently, the fluid volume above the bubble is accelerated and focused during collapse, leading to the formation of a liquid jet directed towards the boundary. This jet hits the lower bubble wall, causing a funnel-shaped protrusion and finally impacts on the boundary.

Jets have regularly been observed with cavitation bubbles [START_REF] Lauterborn | [END_REF][START_REF] Philipp | Cavitation erosion by single laser-produced bubbles[END_REF]. An illustrative enlargement of a high-speed photograph of a cavitation jet in the millimeter range was published by Lauterborn & Ohl [START_REF] Lauterborn | Cavitation bubble dynamics[END_REF]. Ohl & Ory [START_REF] Ohl | Aspherical bubble collapse -comparison with simulations[END_REF] calculated the shapes of asymmetrically collapsing bubbles. Their results are consistent with photographs of a collapsing cavitation bubble developing a jet. Kodama & Takayama [START_REF] Kodama | Dynamic behavior of bubbles during extracorporeal shock-wave lithotripsy[END_REF] studied the impact of jets on gelatin surfaces. They found that the radius of the jet R j is approximately related to the radius of the bubble on the verge of collapsing R c as: [START_REF] Kodama | Dynamic behavior of bubbles during extracorporeal shock-wave lithotripsy[END_REF][START_REF] Ohl | Shock-wave-induced jetting of micron-size bubbles[END_REF] R

j R c ≈ 0.1 . (7.14)
The length of the jet l j , defined as the full travel path of the propelled liquid, is approximately related to R c as [START_REF] Ohl | Shock-wave-induced jetting of micron-size bubbles[END_REF]: From these two ratios the amount of liquid within the jet, V j , is estimated [START_REF] Ohl | Shock-wave-induced jetting of micron-size bubbles[END_REF]:

l j R c ≈ 3 . ( 7
V j ≈ 0.1 R 3 c . (7.16)
The impact of a jet on a surface generates a high-pressure region. The pressure in this region happens similarly to the water-hammer pressure effect [START_REF] Cook | Erosion by water-hammer[END_REF]. For a perfectly plastic impact, the water-hammer pressure of a cavitation jet was estimated by de Haller [START_REF] De Haller | Untersuchungen über die durch Kavitation hergerufenen Korrosionen[END_REF] and Ohl & Ory [START_REF] Ohl | Aspherical bubble collapse -comparison with simulations[END_REF]:

p wh ≈ 1 2 ρ c v j , ( 7.17)
where p wh is the water-hammer pressure, v j is the jet velocity, ρ is the fluid density, and c is the speed of sound.

The damage caused by a jet can be estimated by comparing the waterhammer pressure to the maximum stress the impact surface can withstand INTRODUCTION [START_REF] Bernoulli | sive de viribus et motibus fluidorum commentarii[END_REF]1] before rupture. The maximum stress τ max is given by:

τ max = E ε r , (7.18)
where E is the elastic (Young's) modulus of the material, and ε r is the relative deformation of the surface before rupture.

Clinical applications

UCA microbubble oscillating behavior is the basis of most diagnostic imaging techniques [4,[START_REF]Ultrasound Contrast Agents. Basic principles and clinical applications[END_REF]. Since oscillating microbubbles provide a means to discriminate blood from tissue, they are applicable in perfusion and flow imaging, and tumor detection [START_REF] Burns | Intravenous contrast agent for ultrasound Doppler: In vivo measurement of small tumor vessel doseresponse[END_REF][START_REF] Wei | Quantification of myocardial blood flow with ultrasound-induced destruction of microbubbles administered as a constant venous infusion[END_REF][START_REF] Wei | Blood flow and perfusion measurements: background and clinical utility[END_REF]. Medical applications of the manipulation of the movement of UCA microbubbles by means of acoustic energy will be primarily in directing UCA toward cells [35].

If small UCA microbubbles, having passed through the narrowest vessels, coalesce, they may be controlled to obtain resonant sizes. Especially for subharmonic imaging [START_REF] Shankar | Subharmonic backscattering from ultrasound contrast agents[END_REF], where twice the resonant bubble size is needed, and for tracking the diffusion of free gas bubbles with subharmonics, a promising technique in noninvasive blood pressure measurements [START_REF] Postema | Noninvasive microbubble-based pressure measurements: a simulation study[END_REF], controlled microbubble coalescence may be applicable. If coalescence of a lipid-shelled microbubble and a cell membrane can be induced, this will imply a promising technique in targeted drug delivery.

Bouncing behavior of UCA microbubbles has got no potential medical application yet.

UCA microbubble fragmentation has been associated with violent effects, such as cell membrane permeabilization and lysis. The reason for this may lie in the fact that fragmenting bubbles produce shock-waves. Because of the strong acoustic signal generated, fragmentation finds applications in high-MI imaging. The applicability of microbubble fragmentation for local drug delivery is fully dependent of the presence of a shell after fragmentation. If the shell is absent after fragmentation, the fragments will behave as released gas bubbles. Thus, the potential therapeutic applications will then be identical to those for sonic cracking.

Sonic cracking may find applications in drug delivery, if the released bubble content has therapeutic properties [START_REF] Frinking | Effect of ultrasound on the release of micro-encapsulated drugs[END_REF]. Frinking et al. [START_REF] Frinking | A new ultrasound contrast imaging approach based on the combination of multiple imaging pulses and a separate release burst[END_REF] suggested a technique they called release burst imaging: Upon transmission of a high-MI ultrasound burst, there will be a strong scattering response "proefschrift041" -2004/7/6 -18:01 -page 108 -#112

i i i i i i [7, 2]
MICROBUBBLE PHENOMENA: OVERVIEW from the released gas bubbles. The free gas will rapidly dissolve, and with it the strong scattering response will fade away. Wei et al. [START_REF] Wei | Quantification of myocardial blood flow with ultrasound-induced destruction of microbubbles administered as a constant venous infusion[END_REF] proposed that the acoustical measurement of the reappearance of UCA microbubbles may provide a means for determining tissue perfusion in any organ accessible to ultrasound.

The diffusion rate of a gas bubble with a certain size is known for every hydrostatic pressure. By making use of the changing acoustic properties of the dissolving gas bubbles, hydrostatic pressures may be determined in a minimally invasive clinical setting [START_REF] Bouakaz | Noninvasive pressure measurement using microbubble contrast agent and wavelet transforms[END_REF][START_REF] Postema | Noninvasive microbubble-based pressure measurements: a simulation study[END_REF].

It has been speculated that jets may be formed when UCA microbubbles in the bloodstream are insonified with high enough acoustic pressures. These jets would be directed towards a boundary like a cell or a capillary wall with adjacent cells. As such, jets might function as microsyringes [START_REF] Miller | Gene transfection and drug delivery[END_REF][START_REF] Ohl | Shock-wave-induced jetting of micron-size bubbles[END_REF], if they could penetrate cells. The maximum extension measured in human cells is less than 50% (ε r < 0.5) [START_REF] Lendon | Atherosclerotic plaque caps are locally weakened when macrophages density is increased[END_REF]. Therefore, we may assume that for any human cell or cell part, ε r 1. Elastic moduli of human cells were measured E 7.3 kPa for endothelial cells [START_REF] Mathur | Atomic force and total internal reflection fluorescence microscopy for the study of force transmission in endothelial cells[END_REF], and E 12 kPa for fibroblasts [START_REF] Rotsch | Dimensional and mechanical dynamics of active and stable edges in motile fibroblasts investigated by using atomic force microscopy[END_REF]: less than half the elastic modulus of murine skeletal muscle cells (E ≈ 24 kPa) [START_REF] Mathur | Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy[END_REF]. Rabbit cardiac cells are among the stiffest, with E ≈ 100 kPa [START_REF] Mathur | Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy[END_REF]. It is safe to assume that even for the stiffest human cell E 200 kPa. Combining both assumptions in eq. (7.18) gives τ max 200 kPa. If the water-hammer pressure of a jet exceeds this stress, the jet will be able to penetrate any human cell.

The porosities observed on cell-membranes by Tachibana et al. [START_REF] Tachibana | Induction of cell-membrane porosity by ultrasound[END_REF] may well be attributed to jets. Probably, particles that were present in the photosensitive drug acted as cavitation nuclei, whereas the cell-membranes acted as the boundaries towards which the jets were directed.

Experimental setup Overview

For the high-speed observations, we made use of the Brandaris-128 system [START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF] and an Imacon 468 fast framing camera. An overview of this experimental setup is shown in Figure 7.2. A computer controlled the triggering of a waveform generator, a Xenon flash source, and the cameras.

The electrical signal was generated by an AWG 520 arbitrary waveform generator (Tektronix, Inc., Beaverton, OR), or by an LW 420A arbitrary waveform generator (LeCroy Corp., Chestnut Ridge, NY). The signal was adjusted by two variable 355C/D attenuators (Hewlett Packard Company, Palo Alto, CA) in series, and an A-500 60 dB linear power amplifier (ENI technology, Inc., Rochester, NY). It was converted to ultrasound by a V389-SU 500 kHz, or by a V397-SU 2.25 MHz single-element transducer (Panametrics Inc., Waltham, MA), both spherically focused at 7.5 cm. The transducers were mounted in a Perspex container at an angle of 45 • relative to the top of the container. This container was filled with saturated water. A 200 µm cellulose Cuprophan R capillary tube (Membrana GmbH, Wuppertal, Germany) was fixed in the focal area of the transducer, through which contrast agent was flowing. Because the capillary tube was watersoaked and much smaller in diameter than the acoustic wavelenght, it was not expected to interfere with the ultrasound transmitted. Without contrast agent inserted, we did not observe reflections from the tube.

Optics

Underneath the capillary tube an optic fiber was mounted. This fiber was connected to an MVS-7010 Fiber Optic Strobe (PerkinElmer Optoelectronics, Salem, MA), and to a KLS-201 continuous fiber light source (Olympus KMI (KeyMed Ltd), Southend-on-Sea, UK). The pulsed light source was trig- scope. Focusing was done manually at the middle of the cellulose tube.

Because the tube was wide compared to the contrast microbubbles measured, its upper half was considered a flat surface between contrast microbubbles and object lens, not causing aberrations but lowering the dynamic range of the images.

Camera

The optical observations were recorded with a Brandaris-128 fast framing camera system [START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF].

Contrast agents

We investigated the ultrasound contrast agent Quantison TM (Upperton Limited). It consists of human serum albumin-encapsulated air bubbles with a mean diameter of 3.2 µm. Shell thicknesses are between 0.2 and 0.3 µm [START_REF] Frinking | Acoustic modeling of shell-encapsulated gas bubbles[END_REF]. The content of a Quantison TM vial was resuspended in 5 ml of Isoton R II (Beckman Coulter, Inc., Fullerton, CA), and shaken gently for 20 seconds before further dilution. The agent was inserted through the capillary tube using a syringe pressed by hand.

We also investigated an experimental UCA (supplied by Bracco Research SA, Geneva, Switzerland). It consists of phospholipid-encapsulated gas bubbles ranging in diameter from 1 to 6 µm with a median of 2 µm. The acoustic behavior of a very similar contrast agent was modeled and described in [START_REF] Gorce | Influence of bubble size distribution on the echogenicity of ultrasound contrast agents: A study of SonoVue TM[END_REF]. Undiluted UCA (5ml of a 0.9% sodium chloride dilution, added to a 25 mg UCA vial) was inserted through the capillary tube using either a syringe pressed by hand or a hose operated by a gravity fed or pumped infusion.

Ultrasound

For the experiments with the Brandaris-128 camera system, the UCA bubbles were insonified by 8 cycles of 1.7 MHz ultrasound at a peak rarefactional acoustic pressure of 2 MPa, corresponding to a mechanical index of MI = 1.5. For the experiments with the Imacon 468 camera, the UCA bubbles were insonified by 10 cycles of 500 kHz ultrasound at peak rarefactional acoustic pressures between 0.66 and 0.85 MPa, corresponding to mechanical indices in the range 0.9 < MI < 1.2. The mechanical index is defined as MI = p - ac / f , where p - ac is the peak rarefactional acoustic pressure normalized by 1 MPa and f is the center frequency of the ultrasound normalized by 1 MHz.

Acoustic pressures applied were measured with a calibrated MH28-10 hydrophone (FORCE Technology, Brøndby, Denmark) in a separate water tank. An example of the acoustic signal measured at the transducer focus has been published in [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF]. The in-situ reverberant component due to the presence of the microscopic lens was observed to be less than -14 dB. Thus, it is assumed the in-situ acoustic signal is comparable to the signal measured.

Procedure

We recorded 277 image sequences with the Brandaris-128 system. We performed 527 experiments at high acoustic amplitudes with the Imacon 468 camera. Bubble sizes and distances were measured manually or by using a segmentation method described by Postema et al. [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF].

Results and discussion

The following types of ultrasound-induced UCA microbubble behavior have been distinctly observed and categorized: oscillation, translation, coalescence, fragmentation, sonic cracking, and jetting. Thus, the expansion and contraction of the bubbles are symmetric. We do not expect a violent collapse in this regimen, since the maximum bubble radius is less than twice its equilibrium radius. The oscillating amplitude is represented in the left frame of Figure 7.6(iii). The solid line represents the radius-period curve of a free gas bubble [START_REF] De Jong | Higher harmonics of vibrating gas-filled microspheres. Part one: simulations[END_REF]. Apparently, the UCA bubbles have comparable excursions to a free gas bubble. Figure 7.6(ii) and the right frame of Figure 7.6(iii) show a similar situation for a 1.5 µm strongly oscillating microbubble insonified at MI = 0.67. Again, the UCA bubble excursion is comparable to a free gas bubble. At the acoustic amplitude applied there may be some energy loss in the shell, causing increased thermal damping. Maximum size is reached in frame e with a bubble diameter of 10.0 µm, whereas minimum size is displayed in frame g with a bubble diameter of 0.57 µm. The bubble oscillates highly asymmetrically. We expect the microbubble to grow into an inertial cavity in this regimen, since the maximum bubble radius is much greater than its equilibrium radius. . (ei) The released gas is subjected to a primary radiation force. Each image frame corresponds to a 30 × 16 µm 2 area. Frames shown were selected from a sequence of 128 frames. The travel distance of the bubble center between (e) and (h) is 14 µm over 4 ultrasonic cycles.

Oscillation

Translation

been measured 14 µm over 4 periods (frames e-h). The resting diameter of the released bubble after insonification was 1.3 µm. The theoretical mean bubble displacement over time has been computed by integrating eq. ( 7.1) over 4 periods, taking c = 1480 m s -1 , ρ = 998 kg m -3 , R 0 = 0.65 µm, f = 1.7 MHz, f r = 5.3 MHz, δ t = 1.0, p ac (t) = [2 MPa] sin 2π f t, and η = 0.001 Pa s. The damping was computed using the parameters stated in Medwin [START_REF] Medwin | Counting bubbles acoustically: a review[END_REF] and De Jong [START_REF] De Jong | Acoustic properties of ultrasound contrast agents[END_REF]. The theoretical displacement is 18 µm. The measured displacement is lower than the theoretical value. At the acoustic pressure applied, the expansion phase is longer than the contraction phase, which may account for this difference.

Figure 7.8 shows 5 image frames of two 4 µm experimental UCA microbubbles, each captured after insonification by 10 cycles of 0. [START_REF] Bernoulli | sive de viribus et motibus fluidorum commentarii[END_REF]3] trasound (duration T p = 20 µs). Each image frame corresponds to a 30 × 20 µm 2 area. During every ultrasound burst the bubbles draw nearer to each other. For each center-to-center distance d 0 measured the mean approach velocity v a has been computed from eq. (7.6), taking κ = 5×10 -6 m 2 N -1 (Estimated from [START_REF] De Jong | Acoustic properties of ultrasound contrast agents[END_REF] and [START_REF] Dayton | A preliminary evaluation of the effects of primary and secondary radiation forces on acoustic contrast agents[END_REF]). By combining d 0 with v a , the theoretical distances ∆d th = v a T p have been computed. These were compared to the distance ∆d m measured from Figure 7.8. The results are summarized in Table 7.1. The measured values ∆d are consistent with theory. ported by a conservative estimate of the Weber number. Based on our analysis of the optical system [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF], we may assume that the optical resolution R 0.5 µm, and fragment diameters in Figure 7.9(i)b) < 0.5 µm. Even if the bubbles would expand linearly to the sizes observed in Figure 7.9(i)c, the approach velocity would still have to be u ≈ 2 ∆R m ∆t > 2.7 µm -0.5 µm 0.33 µs = 6.7 m s -1 . (

Coalescence

By taking ρ = 998 kg m 3 and σ = 0.072 N m -1 , we obtain a Weber number We > 0.8. As stated before, flattening of the adjacent bubble surfaces is expected to occur if We > 0.5. From eq. (7.9), it is expected that the drainage time of the film shown in Figure 7.9(i)c until a critical thickness h c = 0.15 µm is τ d = 0.3 µs, taking η = 0.001 Pa s and R f ≈ 2 3 R m [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]. However, Figure 7.9(i)d shows not only film drainage, but also continuing bubble expansion. For these bubble diameters of 4.6 µm, the interposed film would take 1.3 µs to drain. Still, 0.66 µs later the bubbles have coalesced, although the bubbles have continued to expand. This supports the theory that the expanded bubble surfaces may be considered mobile. 7.9(ii)a was captured prior to ultrasound arrival. In Figure 7.9(ii)b the bubble has broken up into 8 discernable fragments, suggesting a mode n = 3 √ 8 = 2 spherical harmonic instability. The fragments coalesce and form an ellipsoidal bubble in Figure 7.9(ii)e. Because the ellipsoidal shape can be discriminated, we may conclude that the second spherical harmonic mode is dominant. After collapse, the fragments in Figure 7.9(ii)f are too small to be counted, but in Figure 7.9(ii)g, captured while the fragments have begun to expand, 8 fragments can be discerned, which confirms the second mode instability.

Sonic cracking

Figure 7.9(iii) shows the sonic cracking of a 3 µm Quantison TM microbubble. Each frame corresponds to a 23 × 23 µm 2 area. In Figure 7.9(iii)d gas starts to escape from the bubble in the middle of the frame. It expands to approximately 8 µm in Figure 7.9(iii)g, and then begins to contract in Figure 7.9(iii)h.

Clearly, the gas bubble has been released from its rigid shell. However, in the image sequence, the pixel size (0.15 × 0.15 µm 2 ) corresponds in approximation to the shell thickness. Thus, even if the optical resolution were on the order of the shortest wavelength of the light, the presence of tiny flaws in the rigid shell would not have been detectable.

Jetting

We recorded two optical sequences showing jet development in UCA microbubbles [143], one of which is shown in Figure 7.10.

Influence of the capillary tube

Ishida et al. [START_REF] Ishida | Cavitation behavior near solid boundaries[END_REF] demonstrated with simulations and high-speed optical observations, that if the distance between the walls of their solid test vessel was greater than 5 times the maximum free-field expansion radius of a cavitation bubble, the bubble would remain spherical while expanding. In our setup, the diameter of the water-soaked capillary tube is approximately 20 times the largest microbubble radius measured. Thus, the phenomena described other than jetting cannot be attributed to the boundaries imposed by the capillary tube, since our imaging plane is at the center of the tube.

Conclusions

An overview of dynamic behavior of ultrasound insonified encapsulated microbubbles has been presented. The following types of behavior have been observed and categorized: oscillation, translation, coalescence, fragmentation, sonic cracking, and jetting. Oscillation is the expanding and contracting bubble response to an oscillating acoustic signal. At low acoustic amplitudes bubbles pulsate moderately, at high amplitudes their longer expansion phase is followed by a violent collapse. Microbubble translation has been associated with primary and secondary radiation forces. Our optical observations of translating bubbles are consistent with theory. Coalescence, the fusion of two or more bubbles, is mainly caused by the drainage of the liquid film separating expanding bubbles, whereas bounce -unsuccessful coalescence -is caused by the drainage taking longer than the expansion of the bubbles. Fragmentation is the fission of a bubble into smaller bubbles. The number of fragments has been related to the dominant spherical harmonic oscillation mode of a bubble. In our observations, the second spherical harmonic mode appears to be the dominant mode. Remarkable are our observations of jetting through encapsulated microbubbles. For an observed jet, we computed a volume of approximately 60 femtoliter, generating a pressure at the tip of the jet around 60 MPa. This is high enough to penetrate any human cell. Hence, liquid jets may act as microsyringes, delivering a drug to a region of interest. As a result of investigations based on acoustic imaging methods, the use of ultrasound contrast agents are becoming widespread in clinical diagnostics. Since the acoustic interrogation of an agent takes place on an ensemble of bubbles, however, the contribution of an individual contrast agent microbubble to the acoustic response cannot be predicted. Therefore, the development of more sophisticated detection techniques, and the research on therapeutic applications of ultrasound contrast agents have to be based on other investigation methods, such as high-speed optical imaging.

In this thesis, we made use of fast-framing camera systems to observe dynamic behavior of individual microbubbles subjected to ultrasound. Multiple frames were captured during a single ultrasonic cycle. Previous studies made use of (one-dimensional) streak images, or frames that covered multiple ultrasonic cycles. GENERAL CONSIDERATIONS Most of the observed phenomena described in this thesis occur within one ultrasonic cycle. The pictures on which these descriptions were based are asymmetric. Hence, the applicability of streak imaging and slowerthan-sound framing in predicting microbubble behavior is very limited.

To account for the presence of a shell encapsulating the gas microbubble, the physical properties shell stiffness and shell friction have been accounted for in models describing microbubble oscillation. These properties have been measured for ensembles of ultrasound contrast agent microbubbles. From our results, however, it is suggested that the shell properties may differ between individual bubbles, because optically identical bubbles reveal different oscillating behavior.

The presence of a shell appears to be less of interest for ultrasound contrast agent microbubble phenomena observed at high acoustic pressures: The physical mechanisms of microbubble coalescence, fragmentation, translation, and jetting are comparable to those of free gas bubbles in the millimeter range. Because of the fast-framing, we are the first to notice repeated coalescence and fragmentation. Irregular shapes of insonified bubbles were previously interpreted and published in literature as modes of shape instability of a single bubble. However, these shapes may also be accounted for by coalescence of bubbles or bubble fragments.

We investigated the influence of the lipid shell on the coalescence by computing the film drainage for immobile bubble surfaces resulting in a laminar flow, and for mobile bubbles surfaces resulting in a plug flow. The coalescence of lipid-encapsulated microbubbles appeared to be unimpeded by shells.

Previously, release of gas from encapsulated microbubbles had been assumed from acoustical measurements. We demonstrated such release from encapsulated microbubbles with a rigid albumin shell during insonification. After this so-called 'sonic cracking', the free gas dissolves in the surrounding fluid. Although the mechanism of sonic cracking is not yet fully understood, the release of gas from encapsulations may find an application in noninvasive pressure measurements.

Determining overpressures is feasible in vivo from the decay of the fundamental acoustic response from diffusing released air bubbles. Pressure differences of 50 mmHg can be distinguished. In medical diagnostics a resolution lower than 50 mmHg is desirable. To improve the sensitivity of the measurement approach mentioned above, gases other than air might be used. Furthermore, subharmonics may be utilized as a marker for half resonant bubble size, since the subharmonic response is more sensitive to 124 i i "proefschrift041" -2004/7/6 -18:01 -page 125 -#129 i i i i i i FUTURE PROSPECTS [START_REF] Bouakaz | Improved contrast to tissue ratio at higher harmonics[END_REF]2] bubble size change than the fundamental. The phenomena observed have potential clinical applications in imaging, pressure measurements, tumor detection, permeabilization, lysis, targeting, and drug delivery.

Future prospects

Now that we know which phenomena may occur, it is time to quantify them under different conditions. Fragmentation, jetting, and sonic cracking can only be effective mechanisms in drug delivery, if their occurrence can be predicted.

When developing new ultrasound imaging techniques based on the microbubble behavior observed at high acoustic amplitudes, individual bubble contributions to the bulk acoustic response of an agent should be known or at least be estimated.

After in vitro quantification, drug-coated microbubbles and microbubbles containing e.g. anaesthetic gases revealing the same destruction behavior may be developed and studied. For bubbles containing drugs in the gas phase, sonic cracking should be the mechanism to focus on. For drug-coated bubbles, jetting would be the ideal release mechanism, since it effectively deals with the question how to penetrate the cell membranes. However, in vitro observations of jetting contrast microbubbles have been very rare. Thus, ideal conditions for jetting near cells have to be found.

We have demonstrated, that noninvasive pressure measurements are theoretically feasible, if noble gas can be released from encapsulated microbubbles, and its dissolution traced by means of the subharmonic acoustic response. In order to develop this novel clinical method, the first step is to make rigid-shelled encapsulated bubbles containing a noble gas, of which the released gas after sonic cracking has a narrow size distribution.

Furthermore, it should be studied whether bubbles can be forced to cluster and coalesce when subjected to ultrasound, so that emboli are created inside tumors.

International symposia on ultrasound contrast agents are shifting their attention from imaging to targeting and drug delivery. As the applications of medical bubbles become more diverse, the demand for medical bubbles with diverse behavior will grow.

In the near future, medical bubbles will play an important role, not only in ultrasonic imaging, but also in therapy.

Samenvatting

Met geluid kun je kijken. Dat wil zeggen: als je geluid produceert, reflecteert en vervormt het, afhankelijk van het voorwerp dat in de weg staat, en aan de hand van het teruggekaatste geluid zijn eigenschappen van dit voorwerp af te leiden. Ook eigenschappen die met het blote oog niet zichtbaar zijn.

Hoe hoger het geluid is dat gebruikt wordt, des te gedetailleerder is de informatie van het reflecterende voorwerp. Geluid boven de menselijke gehoorgrens wordt ultrageluid genoemd.

In de dierenwereld maken vleermuizen en dolfijnen gebruik van ultrageluidtechnieken voor afstands-en snelheidsbepaling. Sonar en Parking Distance Control zijn alledaagse technieken die van deze dieren afgekeken zijn.

In de echografie wordt geluid uitgezonden het lichaam in. Het vervormde, teruggekaatste geluid wordt afgebeeld in een echogram. Op deze manier kan een afbeelding gemaakt worden van delen van het lichaam, zonder dat het opengesneden hoeft te worden.

Bloed is -in tegenstelling tot ander weefsel -geen goede reflector. Daardoor is het met conventionele echografietechnieken moeilijk om de doorbloeding van organen te bepalen.

Een oplossing van dit probleem is het inspuiten van microscopisch kleine gasbelletjes (microbellen) in de bloedbaan. Gasbellen zetten uit wanneer de omgevingsdruk wordt verlaagd en krimpen in wanneer de omgevingsdruk wordt verhoogd. Geluid bestaat uit drukgolven, die de omgevingsdruk laten fluctueren. Het aantal fluctuaties per tijdseenheid (de frequentie) bepaalt de toonhoogte van het geluid. Bij hoorbaar geluid fluctueert de omgevingsdruk een paar keer tot een paar duizend keer per seconde. Bij medisch ultrageluid fluctueert de omgevingsdruk honderdduizenden tot vele miljoenen keren per seconde. Microbellen in zo'n geluidsveld gaan alternerend uitzetten en inkrimpen, met frequenties van dezelfde orde als het geluidsveld. Dit gedrag heet oscilleren, oftewel slingeren. Iedere oscillerende bel zendt radieel een drukveld uit en gedraagt Dergelijke medische bellen worden gewoonlijk aangeduid met ultrageluid-contrastmiddelen. Ultrageluid-contrastmiddelen zijn voor klinischdiagnostische doeleinden zo populair, dat er diverse soorten commercieel verkrijgbaar zijn. De meeste bestaan uit belletjes van een paar micrometer (miljoenste meter) in diameter. Om te voorkomen dat de belletjes te snel oplossen bevatten de contrastbellen een gas dat veel langzamer dan lucht oplost en zitten er schilletjes om de bellen.

Omdat een enkele injectie met contrastmiddel bestaat uit miljarden microbellen, kunnen we met ultrageluidtechnieken alleen het groepsgedrag van microbellen meten. Voor de ontwikkeling van meer geavanceerde detectietechnieken en voor het onderzoek naar therapeutische toepassingen van microbellen is het van belang dat ook het gedrag van individuele microbellen vastgelegd en voorspeld kan worden. Daartoe kunnen optische technieken zoals hogesnelheidsfotografie gebruikt worden.

In deze studie werd gebruikgemaakt van hogesnelheidscamera's om het dynamisch gedrag van individuele microbellen onder invloed van ultrageluid waar te nemen. Binnen een enkele periode van een ultrageluidsgolf, maximaal 2 miljoenste seconde, werden zeven foto's gemaakt met sluitertijden tussen 10 en 70 miljardste seconde. In voorgaande studies werden één-dimensionale foto's gepubliceerd en foto's met sluitertijden langer dan de periode van de geluidsgolf. De verschijnselen die in deze studie beschreven worden, vinden meestal plaats binnen een enkele periode. Bovendien zijn de verschijnselen niet radieel symmetrisch. Daardoor zijn één-dimensionale fotografie en fotografie met "lange" sluitertijden beperkt qua voorspellend vermogen van belgedrag.

Aangezien contrastbellen een schilletje hebben, moet hiermee rekening gehouden worden bij de fysische beschrijving van het oscilleren. In bestaande modellen worden hiertoe de fysische grootheden schilstijfheid en schilfrictie gebruikt. Deze grootheden worden bepaald door metingen aan hoeveelheden contrastmiddel. Uit deze studie echter lijkt te volgen dat schileigenschappen van contrastbellen onderling kunnen verschillen, aangezien optisch identieke bellen verschillend slingergedrag vertonen.

De aanwezigheid van een schil blijkt minder van belang te zijn voor de verschijnselen die waargenomen worden bij contrastbellen in een ultrageluidsveld met een hoge akoestische amplitude: De fysische mechanis-i i "proefschrift041" -2004/7/6 -18:01 -page 129 -#133 i i i i i i SAMENVATTING men van microbelfusie, -fragmentatie, -translatie en -jetten zijn vergelijkbaar met de mechanismen voor vrije gasbellen (zonder schil) die duizend keer zo groot zijn. Door de hoge snelheid van de camera's is dit de eerste studie waarin zich herhalende microbelfusie en -fragmentatie zijn waargenomen. Onregelmatige vormen van bellen in een geluidsveld werden voorheen geïnterpreteerd en gepubliceerd als modes van vorminstabiliteit van een enkele bel. Deze vormen kunnen echter toegeschreven worden aan de fusie van bellen of belfragmenten.

Drainagetijden van de dunne vloeistoffilm die bellen van elkaar scheidt, werden berekend met de Reynolds-vergelijking. De berekende tijden voor bellen met een schilletje zijn te lang om overeen te komen met optische waarnemingen van fusie van microbellen met een vetschilletje. Deze observaties kunnen wel verklaard worden wanneer de schillen zich als mobiele oppervlakken gedragen. Hierdoor worden de theoretische drainagetijden een factor drie verkort. Deze theorie is geverifieerd met optische waarnemingen van fusie van vrije gasbellen.

Op grond van akoestische metingen werd er voorheen aangenomen dat gas uit contrastbellen kan ontsnappen. In deze studie is aangetoond dat we onder invloed van ultrageluid gas kunnen laten ontsnappen uit contrastbellen met een rigide albumineschil. Na dit zogeheten sonisch kraken lost het vrije gas op in de vloeistof. Hoewel het mechanisme achter sonisch kraken nog niet uitgewerkt is, kan het laten ontsnappen van gas uit schillen in de nabije toekomst een toepassing vinden in niet-invasieve drukmeting.

Het bepalen van overdruk is in principe in vivo mogelijk aan de hand van het verval van de grondtoon van een oplossende vrije gasbel. Drukverschillen van 50 millimeter kwikdruk kunnen worden onderscheiden. In de medische diagnostiek is een kleinere resolutie wenselijk. Om de gevoeligheid van bovengenoemde meetmethode te verbeteren, zouden andere gassen dan lucht kunnen worden gebruikt. Aangezien ondertonen gevoeliger zijn voor een verandering in de belgrootte dan grondtonen, kan bovendien gebruik gemaakt worden van ondertonen om de halve resonantiegrootte van een bel te markeren.

De waargenomen verschijnselen zijn mogelijk klinisch toepasbaar in ultrasone afbeelding, drukmeting, tumordetectie, doorbloedingsbepaling, lysis, targeting en gerichte medicijnbezorging.

Dit project wordt ondersteund door de stichting STW (RKG.5104). All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the author.

Typesetting system: L A T E X 2 ε Printed in The Netherlands by Universal Press, Veenendaal Cover design: Michiel Postema

Figure 1 . 1 :

 11 Figure 1.1: Thomas Skaife's claim in The Times, London, of May 29, 1858. Reprinted with permission.

Figure 1 . 2 :

 12 Figure 1.2: "Abe Edgington, owned by Leland Stanford; driven by C. Marvin, trotting at a 2:24 gait over the Palo Alto track, 15th June 1878." Reprinted with permission from Muybridge HE. The Horse in Motion 1878. In: Adolf Nichtenhauser history of motion picture collection ca. 1950. Collection number MS C 380 located in: Modern Manuscripts Collection, History of Medicine Division, National Library of Medicine, National Institutes of Health, Department of Health and Human Services, Bethesda, MD.

Figure 1 . 3 :Chapter 2

 132 Figure 1.3: Medical bubble acting as a microsyringe. c 2002 IEEE. Reprinted with permission from Postema M, Bouakaz A, de Jong N. IEEE Trans Ultrason, Ferroelect, Freq Contr 2002 49(3):cover.

Figure 2 . 1 :

 21 Figure 2.1: One-dimensional, differently sized objects F , convolved with the PSF, resulting in optical images G. Segmented objects ξ were obtained after applying the threshold θ = 0.5.

Figure 2 . 2 :

 22 Figure 2.2: Measured object diameter (ζ) versus true object diameter (τ) after segmentation using the threshold θ = 0.5.

Figure 2 . 3 :

 23 Figure 2.3: Measured object diameter (ζ) as a function of applied threshold (θ) for three different object diameters.

Figure 2 . 4 :

 24 Figure 2.4: Basic setup for taking UCA microbubble pictures.

Figure 2 . 5 :

 25 Figure 2.5: Front-side view of container.

Figure 2 . 6 :

 26 Figure 2.6: Optical observation part of the experimental setup.

1 2Figure 2 . 7 :

 127 Figure 2.7: Acoustic signal measured at the transducer focus.

Figure 2 . 8 :

 28 Figure 2.8: Semi-automated segmentation. Selection of region of interest (a) and (b), binary segmented image (c), segmented object (d).

  Figure 2.9(i) shows two 8-bit optical images of the test grid, recorded with the WAT-902HS CCD camera (Watec Co., Ltd.). The image size corresponds to a 43 × 32 µm 2 area. The median intensity φ inside triacontakaidigon 1 was φ = 187 and the median background value ψ was ψ = 28, giving a 50% threshold level of θ = 1 /2(φ + ψ) = 107.5. This threshold was applied to both images [Figure2.9(ii)]. From the measured areas, the respective diameters were calculated and corrected for the polygon shape. These values are summarized in Table2.2. Triacontakaidigon 11 was too small to be measured. For circles > 1 µm, measured values differ from specified values on the order of 1%.

Figure 2 . 9 :

 29 Figure 2.9: CCD images of 11 triacontakaidigons (i) on a calibration grid, (ii) segmented with a θ = 1 /2(φ + ψ) threshold.

Figure 2 .

 2 10(c) is in visual focus. Figure 2.10(b) and (d) were taken 2 µm proximal and 2 µm distal to the focus, respectively.

Figure 2 .

 2 10(a) was taken 4 µm proximal to focus. The same threshold, determined from the median background value and the darkest bubble wall values, was applied to all four of the images. From each binarysegmented image, the size of an enclosed area representing a sphere was measured. From this area the microsphere diameter was calculated. The diameters calculated from Figure2.10(b) and (c) were 5.01 µm; the diameter calculated from Figure2.10(d) was 4.95 µm. The diameter could not be calculated from Figure2.10(a), which was too far out of focus. Based on these measurements with calibration spheres, we assume that diameters from bubbles that were slightly out of focus could be correctly measured with the threshold used.Characteristic aberration was observed when a large part of the bubble i i "proefschrift041" -2004/7/6 -

Figure 2 .

 2 11(e) is in visual focus. The bubbles that were below the focal plane got fuzzy rims [Figure 2.11(g), (h), (i)], whereas bubbles largely above the focal plane got bright centers with optical interference patterns around them [Figure 2.11(a) and (b)]. Figure 2.

Figure 2 . 10 :

 210 Figure 2.10: Intensity cross-sections of a 5 µm glass calibration particle, 4 µm proximal to focus (a), 2 µm proximal to focus (b), in focus (c), and 2 µm distal to focus (d).

Figure 2 . 11 :

 211 Figure 2.11: Quantison TM contrast microbubbles above the focal plane of the optical system (a)-(d), shifted through visual focus (e), below the focal plane (f)-(i). Each frame corresponds to a 43 × 32 µm 2 area.

  Figure 2.14 summarizes the data from events at four different acoustic pressures, corresponding to mechanical indices of MI = 0.089, MI = 0.15, MI = 0.25, and MI = 0.39. Maximal diameters were plotted as a function of initial bubble diameters. As Figure 2.14 shows, the bubbles investigated had initial diameters ranging from 1 µm to 4 µm. We found no observations for initial diameters larger than 3 µm at MI = 0.25 [Figure 2.14(c)] and at MI = 0.39 [Figure 2.14(d)], in contrast to the observations at MI = 0.089 [Figure 2.14(a)]

Figure 2 . 12 :

 212 Figure 2.12: Randomly taken pictures of freely flowing, ultrasound insonified, experimental UCA. Bubbles with a bright center are considered to be out of focus (a), (f). Sharp and unsharp, fuzzy bubbles are comparable in size (b)-(e)

Figure 2 . 13 :

 213 Figure 2.13: Maximal deviation in bubble measurement due to random error caused by the optical system and the segmentation process, as a function of mean bubble diameter measurement.

Figure 2 .

 2 15(a) was taken before ultrasound arrival. The maximal difference in excursion is Ψ = 28%.

Figure 2 . 14 :

 214 Figure 2.14: Bubble expansion at four different acoustic pressures. MI = 0.089 (a), MI = 0.15 (b), MI = 0.25 (c), MI = 0.39 (d).

Figure 2 . 15 :

 215 Figure 2.15: Optical image sequence of three microbubbles with apparently the same initial diameters, insonified at MI = 0.93. Each frame corresponds to a 55 × 45 µm 2 area. Frame (a) was taken before ultrasound arrival. The microbubbles expanded to different maximal diameters (b)-(d).

Figure 2 . 16 :

 216 Figure 2.16: Relative excursion at MI = 0.93. 39 bubbles were selected from 10 image sequences. Identical markers indicate bubbles from the same image sequence.

Figure 2

 2

Figure 2 . 17 :Figure 2 . 18 :

 217218 Figure 2.17: Bubble expansion (b)-(e) and collapse (f) within one acoustic cycle at MI = 1.2.

  lipid shells were insonified at 0.5 MHz with acoustic amplitudes of 0.66-0.85 MPa.

Figure 3 . 1 :

 31 Figure 3.1: Optical images of stages of ultrasound-induced microbubble coalescence: flattening of contact surfaces (a), liquid film drainage (b), forming of a merged bubble (c), turning into an ellipsoidal bubble (d). Each frame in event (i) corresponds to a 21 × 21 µm 2 area. Each frame in events (ii)-(iv) corresponds to a 30 × 30 µm 2 area. Interframe times are 0.33 µs.

Figure 3 . 2 :

 32 Figure 3.2: Schematic representation of stages of expanding bubble coalescence: bubble collision (a), flattening of contact surfaces (b), liquid film drainage (c) until a critical thickness (d), film rupture (e), and formation of an ellipsoidal bubble (f).

  -2004/7/6 -18:01 -page 58 -#62

Figure 3 . 4 :

 34 Figure 3.4: Optical images of microbubble coalescence and spherical rebound (i), bounce (ii), multiple coalescence (iii), and repeated coalescence (iv). Each frame corresponds to a 30 × 30 µm 2 area. The frames in column a have been captured prior to ultrasound arrival. Interframe times are 0.33 µs.

Figure 3 .

 3 Figure 3.4(i) shows an example of coalescence.Figure 3.4(i)a shows three microbubbles with diameters (1) 2.5 µm, (2) 2.5 µm, and (3) 2.0 µm. After ultrasound arrival, microbubbles 2 and 3 have apparently coalesced (Figure 3.4(i)b). The remaining bubble, with a diameter of 5.0 µm, is separated from microbubble 1, which is seen to have expanded to 3.8 µm, with a center-to-center distance d 0 = 4.8 µm. The center of bubble 1 has shifted slightly to the upper right. The thickness of the liquid film, separating the bubble shells is approximately h = 1.1 µm, and the film radius is larger than 1.7 µm. In Figure3.4(i)c the liquid film appears to have drained while the bubbles expanded, but, a separation is still visible. This boundary appears to have disappeared in Figure3.4(i)d, † leaving a pear-shaped bubble that turns ellipsoidal (Figure3.4(i)e) when contracting. Figure3.4(i)f,g,h shows that the coalesced bubble expands uniformly. It takes between 0.33 µs and 0.66 µs for the film in Figure3.4(i)b to drain and rupture.

Figure 3 . 4 (

 34 Figure 3.4(i) shows an example of coalescence.Figure 3.4(i)a shows three microbubbles with diameters (1) 2.5 µm, (2) 2.5 µm, and (3) 2.0 µm. After ultrasound arrival, microbubbles 2 and 3 have apparently coalesced (Figure 3.4(i)b). The remaining bubble, with a diameter of 5.0 µm, is separated from microbubble 1, which is seen to have expanded to 3.8 µm, with a center-to-center distance d 0 = 4.8 µm. The center of bubble 1 has shifted slightly to the upper right. The thickness of the liquid film, separating the bubble shells is approximately h = 1.1 µm, and the film radius is larger than 1.7 µm. In Figure3.4(i)c the liquid film appears to have drained while the bubbles expanded, but, a separation is still visible. This boundary appears to have disappeared in Figure3.4(i)d, † leaving a pear-shaped bubble that turns ellipsoidal (Figure3.4(i)e) when contracting. Figure3.4(i)f,g,h shows that the coalesced bubble expands uniformly. It takes between 0.33 µs and 0.66 µs for the film in Figure3.4(i)b to drain and rupture.

Figure 3 . 4 (

 34 iv)a shows three microbubbles with diameters (1) 4.3 µm, (2) 2.6 µm, and (3) 2.8 µm. After ultrasound arrival, microbubbles 2 and 3 have translated towards microbubble 1 (Figure3.4(iv)b). From Figure3.4(iv)c, captured in contraction phase, it is appreciated that microbubble 1 has broken up into fragments. Three remaining fragments have started coalescing in Figure3.4(iv)d, and have obtained an irregular shape in Figure3.4(iv)e. The films separating the individual microbubbles have drained in Figure3.4(iv)f, while microbubble 2 appears to touch the coalescing structure. In Figure3.4(iv)g, the fragments of microbubble 1 have coalesced into one spherical bubble. Notice the translation of microbubble 2.

Figure 3 . 4 (

 34 iv)h shows that the coalesced bubble has re-fragmented in compression phase.

Abstract

  When gas bubbles collide, the following stages of bubble coalescence have been reported: flattening of the opposing bubble surfaces prior to contact, drainage of the interposed liquid film toward a critical minimal thickness, rupture of the liquid film, and formation of a single bubble. During insonification, expanding contrast agent microbubbles may collide with adjacent bubbles, resulting in coalescence or bounce. We previously investigated the coalescence times of insonified soft-shelled microbubbles, by comparing observed coalescence times to calculated film drainage times, based on the Reynolds equation.In this study, we investigate the validity of the Reynolds-like equations for expanding free bubbles, by subjecting rigid-shelled contrast agent mi-Based on the manuscript Postema M, Marmottant P, Lancée CT, Versluis M, Hilgenfeldt S, de Jong N. Ultrasound-induced coalescence of free gas microbubbles. Proc IEEE Ultrason Symp 2004 to be submitted.This work has been supported by the Technology Foundation STW (RKG.5104) and by the Interuniversity Cardiology Institute of the Netherlands.

Figure 4 . 1 :

 41 Figure 4.1: Schematic representation of colliding bubbles or droplets: approach (a-b), flattening of the interposed film (c), drainage to a critical thickness (d), film rupture (e), and formation of a single bubble (f).

Figure 4 . 1 )

 41 : flattening of the opposing bubble surfaces prior to contact, drainage of the interposed liquid film toward a critical minimal thickness, rupture of the liquid film, and formation of a single bubble. If the critical thickness is not reached during collision, the bubbles bounce off each other instead.

Figure 4 . 2 :

 42 Figure 4.2: Gas release from PB127 microbubbles, captured at 10 MHz. Each frame corresponds to a 23×23 µm 2 area. Spontaneous coalescence of free gas microbubbles takes place in frames 81-83.

Figure 4 .

 4 Figure 4.2 shows an example of gas release from a PB127 bubble. Each frame corresponds to a 23 × 23 µm 2 area. Four PB127 bubbles are in the field of view. After ultrasound arrival (frame 13) the bubbles contract.During expansion, gas escapes from the 3 µm upper bubble[START_REF] Burns | Intravenous contrast agent for ultrasound Doppler: In vivo measurement of small tumor vessel doseresponse[END_REF][START_REF] Burns | Looking at and listening to breaking bubbles: a correlative optical acoustic study of some experimental polymer/air agents[END_REF][START_REF] Chaudhari | Coalescence of gas bubbles in liquids[END_REF][START_REF] Chen | Effects of London-van der Waals forces on the thinning of a dimpled liquid film as a small drop or bubble approaches a horizontal solid plane[END_REF]. The free gas is seen detached in frame 21. It expands[START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF][START_REF] Chin | Optical imaging of ultrasound contrast bubble motions at 25 million frames per second[END_REF][START_REF] Chiou | Clinical applications of contrast echocardiography[END_REF][START_REF] Chomas | High speed optical experimental analysis of microbubble destruction, supported by theoretical development[END_REF] and starts to contract[START_REF] Chomas | Optimization of microbubble destruction[END_REF]. Close to its minimum, the free gas bubble splits up into multiple fragments[START_REF] Chomas | Mechanisms of contrast agent destruction[END_REF]. During expansion, the fragments appear to have coalesced into two separate bubbles[START_REF] Chomas | Threshold of fragmentation for ultrasonic contrast[END_REF][START_REF] Church | The effects of an elastic solid surface layer on the radial pulsations of gas bubbles[END_REF]. These bubbles collide during expansion[START_REF] Collins | The Story of America in Pictures[END_REF]. The Weber number, calculated with the bubble wall displacement[START_REF] Church | The effects of an elastic solid surface layer on the radial pulsations of gas bubbles[END_REF][START_REF] Collins | The Story of America in Pictures[END_REF]: u >

c

  2004 Elsevier B.V. Reprinted with permission from Postema M, Bouakaz A, de Jong N. Noninvasive microbubble-based pressure measurements: a simulation study. Ultrasonics 2004 42(1-9):759-762. This work has been supported by the Technology Foundation STW (RKG.5104) and by the Interuniversity Cardiology Institute of the Netherlands.

Figure 5 . 1 :

 51 Figure 5.1: Fundamental and subharmonic scattering cross-sections of a diffusing 14 µm Ar bubble, insonified at 1 and 2 MHz, respectively, as a function of time, when applying hydrostatic overpressures of 0 and 50 mmHg.

Figure 6 . 1 :

 61 Figure 6.1: Line drawings of the housing of the Brandaris-128 (left) and the CR 2000 camera (right).

  GAS RELEASEgenerated by an AWG 520 arbitrary waveform generator (Tektronix, Inc., Beaverton, OR) was adjusted by two variable 355C/D attenuators (Hewlett Packard Company, Palo Alto, CA) in series, and an A-500 60 dB linear power amplifier (ENI technology, Inc., Rochester, NY). The signal was converted to ultrasound by a V389-SU 500 kHz, or by a V397-SU 2.25 MHz single-element transducer (Panametrics Inc., Waltham, MA), both spherically focused at 7.5 cm. The transducer was mounted in a Perspex container at an angle of 45 • relative to the top of the container. This container was filled with saturated water. A 200 µm cellulose Cuprophan R capillary tube (Membrana GmbH, Wuppertal, Germany) was fixed in the focal area of the transducer, through which contrast agent was flowing.

Figure 6 . 2 :

 62 Figure 6.2: Gas release from a Quantison TM contrast microbubble at 0.5 MHz and MI = 1.1. Each frame corresponds to a 19 × 19 µm 2 area. Interframe times are 0.1 µs.

Figure 6 . 3 :

 63 Figure 6.3: Gas release from a Quantison TM contrast microbubble at 0.5 MHz and MI = 0.9. Each frame corresponds to a 13 × 13 µm 2 area. Interframe times are 0.33 µs.

Figure 6 . 4 :

 64 Figure 6.4: Dissolution of released gas. Each frame corresponds to a 13 × 13 µm 2 area. Time between recordings is 100 ms. The free gas bubble is visible to the upper left of the PB127 bubble in the left frame.

Figure 6 . 5 :Figure 6 . 6 :

 6566 Figure 6.5: Dissolution of released gas, captured at 2 kHz. Upper frames show raw CCD images, lower frames show segmented images. Each frame corresponds to a 10 × 10 µm 2 area. The released gas fragments (arrow) are less than 1 µm.

Figure 6 . 7 :

 67 Figure 6.7: Three PB127 bubbles and one released gas bubble (left). After 100 ms the released gas bubble has disappeared (right). Each frame corresponds to a 23 × 23 µm 2 area. Time between recordings is 100 ms.

Figure 6 . 8 :

 68 Figure 6.8: Size distribution of released gas from PB127. librium diameters between 1.25 and 1.75 µm.The size distribution of the released gas bubbles from PB127 is shown in Figure6.8. For both frequencies, most released gas bubbles have final restng diameters between 1.25 and 1.75 µm.

Figure 6 . 9 :

 69 Figure 6.9: Average number of cracked contrast agent bubbles for MI> 0.8.

Figure 6 . 10 :

 610 Figure 6.10: Dissolution of nitrogen microbubbles with diameters between 0.5 and 4.5 µm into saturated water at ambient pressure. PB127, i.e. 6 < f r < 7 MHz.The phenomenon of bubbles translating during an ultrasonic cycle has only been observed with free gas bubbles. We attribute this behavior to the small size of the free gas bubbles during contraction, and the lack thereof with the hard-shelled contrast agent bubbles. When in contraction phase, free gas bubbles have a very small translating mass, as it is equivalent to half the mass of the displaced fluid[START_REF] Leighton | The Acoustic Bubble[END_REF]. Because of impulse conservation, such small bubbles can translate further than the relatively big encapsulated bubbles.The acoustic response from an ensemble of Quantison TM microbubbles disappears between 15 and 30 ms after transmission of a high-MI ultrasonic burst[START_REF] Bouakaz | Noninvasive measurement of the hydrostatic pressure in a fluid-filled cavity based on the disappearance time of micrometer-sized free gas bubbles[END_REF], whereas the disappearance time of the fundamental acoustic response of an ensemble of PB127 microbubbles lies between 50 and 100 ms after transmission of a high-amplitude ultrasonic burst[START_REF] Burns | Looking at and listening to breaking bubbles: a correlative optical acoustic study of some experimental polymer/air agents[END_REF]. Figure6.10 demonstrates simulations of the dissolution of nitrogen mi-

  where η is the shear viscosity of the fluid, Re =

Figure 7 . 1 :

 71 Figure 7.1: Schematic evolution of jet development in a collapsing bubble near a boundary (below): bubble on the verge of collapse (a), asymmetric collapse (b), jet development (c), funnel-shaped protrusion (d).

Figure 7 . 2 :

 72 Figure 7.2: Basic setup of the high-speed photography system.

Figure 7 . 4 :

 74 Figure 7.4: Line drawing of the optical observation part of the Brandaris-128 system.

Figure 7 .

 7 Figure 7.6(i) shows an optical image sequence of two identical 6 µm moderately oscillating experimental UCA microbubbles freely flowing through a capillary tube. The frames have been taken during one cycle of ultrasound insonification, with a center frequency of 0.5 MHz and a mechanical index MI = 0.09. Inter-frame times for frames b to h are 0.33 µs. Each frame corresponds to a 88 × 58 µm 2 area. Frame a has been taken prior to ultrasound arrival. Maximal sizes are reached in frame d with bubble diameters of 7.6 µm, whereas minimal sizes are displayed in frame f with bubble diameters of 4.4 µm. Thus, the expansion and contraction of the bubbles are symmetric. We do not expect a violent collapse in this regimen, since the maximum bubble radius is less than twice its equilibrium radius. The oscillating amplitude is represented in the left frame of Figure7.6(iii). The solid line represents the radius-period curve of a free gas bubble[START_REF] De Jong | Higher harmonics of vibrating gas-filled microspheres. Part one: simulations[END_REF]. Apparently, the UCA bubbles have comparable excursions to a free gas bubble.Figure7.6(ii) and the right frame of Figure7.6(iii) show a similar situation for a 1.5 µm strongly oscillating microbubble insonified at MI = 0.67. Again, the UCA bubble excursion is comparable to a free gas bubble. At the acoustic amplitude applied there may be some energy loss in the shell, causing increased thermal damping. Maximum size is reached in frame e with a bubble diameter of 10.0 µm, whereas minimum size is displayed in frame g with a bubble diameter of 0.57 µm. The bubble oscillates highly asymmetrically. We expect the microbubble to grow into an inertial cavity

Figure 7 . 6 :

 76 Figure 7.6: Oscillating experimental UCA microbubbles. Both respective image sequences span one ultrasonic cycle. Frames a have been captured prior to ultrasound arrival. Inter-frame times for frames b to h are 0.33 µs. Each frame corresponds to a 88 × 58 µm 2 area. (i) Two6 µm bubbles moderately oscillating (MI = 0.09). (ii) A 1.5 µm bubble strongly oscillating (MI = 0.67). (iii) Radius-period plots of both events. The solid line represents an oscillating free gas bubble.

Figure 7 .Figure 7 . 7 :

 777 Figure 7.7 shows a high-speed optical image sequence of Quantison TM insonified by 8 cycles of 1.7 MHz ultrasound with a mechanical index MI = 1.5. The ultrasound travels from the lower side of the frames to the upper side. Frame times are indicated in ns. Each frame corresponds to a 30 × 16 µm 2 area. In Figure 7.7(b,c,d) gas escapes from a 4 µm bubble. This free gas bubble expands and contracts, and translates towards the upper side of the frames. The displacement of the free gas bubble center has

Figure 7 .Figure 7 . 8 :

 778 Figure 7.9(i) shows an example of microbubble coalescence. The first frame has been captured prior to ultrasound arrival. In Figure7.9(i)b), the main bubble with an initial diameter of 4 µm has split up, into several fragments with diameters below or around optical resolution, and these fragments have started to coalesce upon expansion. As the resulting two bubbles have expanded to mean diameters of approximately 2.7 µm, shown in Figure7.9(i)c), the flattening of the adjacent bubble surfaces is clearly visible. After the bubbles have expanded further to mean diameters of 4.6 µm, as demonstrated in Figure7.9(i)d, the interposed film has drained to a critical thickness to rupture (Figure7.9(i)e), which has resulted in the formation of a single bubble (Figure7.9(i)f).The flattening of the adjacent bubble surfaces in Figure7.9(i)b) is sup-

Figure 7 . 9 :

 79 Figure 7.9: Experimental UCA microbubbles showing (i) coalescence, (ii) second mode spherical harmonic fragmentation, (iii) sonic cracking. Frames a have been captured prior to ultrasound arrival. Inter-frame times for frames b to h are 0.33 µs. Each image frame corresponds to a 23 × 23 µm 2 area.

FragmentationFigure 7 . 9 (

 79 Figure 7.9(ii) shows the repeated fragmentation, coalescence, and re-fragmentation of an experimental UCA microbubble with an initial diameter D = 6 µm. Each frame corresponds to a 23 × 23 µm 2 area. Figure7.9(ii)a was captured prior to ultrasound arrival. In Figure7.9(ii)b the bubble has broken up into 8 discernable fragments, suggesting a mode n =

Figure

  Figure 7.9(ii) shows the repeated fragmentation, coalescence, and re-fragmentation of an experimental UCA microbubble with an initial diameter D = 6 µm. Each frame corresponds to a 23 × 23 µm 2 area. Figure7.9(ii)a was captured prior to ultrasound arrival. In Figure7.9(ii)b the bubble has broken up into 8 discernable fragments, suggesting a mode n =

Figure 7 .

 7 10(a) shows a microbubble with a radius R c = 8.43 µm.

Figure 7 .Figure 7 . 10 :

 7710 Figure 7.10: Ultrasound-induced jet development in an experimental UCA microbubble (MI = 1.2). Each image frame corresponds to a 38 × 30 µm 2 area. Interframe time is 0.33 µs and exposure time is 10 ns. Taking ρ = 998 kg m -3 and c = 1480 m s -2 , the water-hammer pressure is around 60 MPa. Since p wh 200 kPa τ max , such a jet may penetrate any cell.

  als een geluidsbron. Dus wanneer microbellen ingespoten worden in de bloedbaan, zijn ze door hun karakteristieke respons op ultrageluid op te sporen. Hun aanwezigheid is een indicatie voor de doorbloeding van individuele vaten en hele organen.

Table 2 .

 2 1: True and segmented object diameter.

Table 2 .

 2

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	18:01 -page 42 -#46	i

2: Specified and measured diameters of triacontakaidigons.

  The optical images were recorded through a microscope at a frame rate of 3 million frames per second. Contrast agent microbubbles with monolayer Based on the manuscript Postema M, Marmottant P, Lancée CT, Hilgenfeldt S, de Jong N. Ultrasound-induced microbubble coalescence. Ultrasound Med Biol 2004 submitted. This work has been supported by the Technology Foundation STW (RKG.5104) and by the Interuniversity Cardiology Institute of the Netherlands.

	3 Ultrasound-induced Microbubble
	Coalescence

Abstract

When gas bubbles collide, the following stages of bubble coalescence have been reported: flattening of the opposing bubble surfaces prior to contact, drainage of the interposed liquid film toward a critical minimal thickness, rupture of the liquid film, and formation of a single bubble. For ultrasound contrast agents this phenomenon has not yet been studied. During insonification, expanding contrast agent microbubbles may come into contact with each other, resulting in coalescence or bounce. In this study, we give a description of the coalescence mechanism of insonified microbubbles, based on high-speed photography and theoretical modeling.

  and Chapter 2. In short: a V389-SU 500 kHz single-element transducer (Panametrics Inc., Waltham, MA) was mounted into a water-filled container, spherically focused at the focal plane of the optical system. The optical images were recorded through a microscope with an Imacon 468 fast framing camera (DRS Hadland, Ltd., Tring, UK), capable of taking 8 frames per experiment. It operated at a frame rate of 3 million frames per second, corresponding to interframe times of 0.33 µs. Exposure times ranged from 10 ns to 70 ns. The frames presented in this paper correspond to 30 × 30 µm 2 areas, except for Figure3.1(i). The first frame was typically captured prior to arrival of the ultrasound wave at the focal area. Seven frames were taken during ultrasound insonification, spanning a full ultrasound cycle of 2 µs. Contrast agent was insonified by 10 cycles of 0.5 MHz ultrasound with high acoustic amplitudes, in the range 0.66-0.85 MPa.

Table 5 .

 5

1: Half-size time differences for different limitations.

  The Brandaris-128 captured sequences of 128 image frames at an average speed of 13 million frames per second. Typical frame sizes correspond to 89 × 68 µm2 . In all observations, image frames were captured before, during, and after ultrasound insonification. A line

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		EXPERIMENTAL SETUP	[7, 2]
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Table 7 .

 7 2 gives an overview of potential clinical applications related to the encapsulated microbubble phenomena discussed. The phenomena have potential clinical applications in imaging, pressure measurements, tumor detection, permeabilization, lysis, targeting, and drug delivery.

	oscillation	translation	coalescence	fragmentation	sonic cracking	jetting
	imaging
	pressure measurements			?
	tumor detection
	permeabilization and lysis
	targeting
	drug delivery			?

Table 7 .

 7

	2: Potential clinical applications for encapsulated microbubble phenom-
	ena observed.
	121

NA = n * sin αwhere n * is the refraction index of the material between the object plane and the objective lens, and α is the maximum angle of incidence relative to the optical axis.

† In a separate experiment the in-situ reverberant component due to the presence of the microscopic lens was observed to be less than -14 dB, with a delay of 4 µs.

‡ A hidden bubble "2" generates a spatially varying far field pressure of[START_REF] Landau | Fluid Mechanics[END_REF]:p(r 2 ) = ρ 4π V2 (t) 1 r 2 ,where ρ is the fluid density, r 2 is the distance to the center of bubble 2, and V2 is the second time derivative of the volume of bubble 2. For bubbles in our size range, just outside the depth of field (±5 µm) the pressure may be of the order 50 kPa, which is less than 10% of the ultrasonic amplitude in our examples, and which cannot account for the large expansion differences in our optical observations.

† If the line of sight is not perpendicular to the film, but at a tilt, the projection of the film boundaries might be obfuscated.

Acknowledgments

We thank Martijn Frijlink for designing the calibration grid and Leo Bekkering for building part of the experimental setup.

Acknowledgments

We thank POINT Biomedical Corporation for supplying PB127.

Acknowledgments

We thank POINT Biomedical Corporation for supplying PB127, Upperton Limited for supplying Quantison TM , Leo Bekkering and Jan Honkoop for technical assistance, and Cees Pakvis for drawing Figure 6.1.

Acknowledgments

We thank Kees Slager for the data on cell elasticity, Emmanuel Ory (Laboratory of Applied Thermodynamics, Helsinki University of Technology) for computing Figure 7.1, Leo Bekkering and Elmer Koene for technical assistance, and Cees Pakvis for drawing Figures 7.3, 7.4, and 7.5.

This work has been supported by the Technology Foundation STW (RKG.5104) and by the Interuniversity Cardiology Institute of the Netherlands. "proefschrift041" -2004/7/6 -18:01 -page 29 -#33 i i i i i i * The numerical aperture is given by "proefschrift041" -2004/7/

Abstract

When encapsulated microbubbles are subjected to high-amplitude ultrasound, the following phenomena have been reported: oscillation, translation, coalescence, fragmentation, sonic cracking, and jetting.

In this Chapter, we explain these phenomena, based on theories that were validated for relatively big, free (not encapsulated) gas bubbles. These theories are compared with high-speed optical observations of insonified contrast agent microbubbles. Furthermore, the potential clinical applications of the bubble-ultrasound interaction are explored.

We conclude that most of the results obtained are consistent with free gas bubble theory. Similar to cavitation theory, the number of fragments after bubble fission is in agreement with the dominant spherical harmonic [