Mathieu Pernot
email: <mathieu.pernot@espci.fr

Jean-François Aubry

Mickaël Tanter

Jean-Louis Thomas

Mathias Fink

Jean-Fran Ois Aubry

Mathias Fink Loa

High power transcranial beam steering

Keywords: Brain, pathology, radiation effects, Brain Diseases, therapy, Computer Simulation, Computer-Aided Design, Equipment Design, Equipment Failure Analysis, Hot Temperature, Humans, Liver, pathology, radiation effects, Models, Biological, Radiometry, methods, Transducers, Ultrasonic Therapy, instrumentation, methods

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

The effects of High Intensity Focused Ultrasound (HIFU) in human and animal brains have been extensively investigated (Fry et al. 1955, , , , , ), and these [START_REF] Basauri | A simple method for production of trackless focal lesions with focused ultrasound: Statistical evaluation of the effects of irradiation on the central nervous system of the cat[END_REF][START_REF] Dunn | Ultrasonic threshold dosages for the mammalian central nerveous system[END_REF][START_REF] Robinson | An analysis of lesion development in the brain an in plastics by high-intensity focused ultrasound at low-Megahertz frequencies[END_REF][START_REF] Fry | A focused ultrasound system for tissue volume abalation in deep seated brain sites[END_REF][START_REF] Vykhodtseva | Pulse Duration and Peak intensity during focused ultrasound surgery: theoretical and experimental effects in rabbit brain in vivo[END_REF] studies have shown the feasibility of ultrasound brain therapy and surgery with the skull bone removed. However non invasive transskull therapy remains very limited due to the strong phase aberrations and absorption induced by the skull, as was first shown by Fry and Barger . To compensate for this distortion, Phillips . (1975) introduced the idea of phased array corrections to ultrasound diagnostic (1978) et al imaging through the skull. In 1996, Thomas and Fink proposed to use a time reversal mirror in therapeutic ultrasound. Prior to the treatment and taking advantage of the biopsy, which ensures that the tumor is malignant, one could put a hydrophone in the neighborhood of the tumor and record the signals relating this hydrophone to each element of the therapeutic array. Once the diagnosis has been confirmed and the hydrophone removed, one would have to emit the time reversed signals with amplitude compensation in order to correct for both phase and amplitude aberrations induced by the skull. They validated this technique experimentally at low amplitude levels,

showing a strong improvement of up to 10 dB in focus quality. In 1998, Hynynen have applied a similar phase conjugation technique et al. (equivalent to time reversal process for monochromatic signals) with a high intensity ultrasound system. Recently several studies have shown that this reliable and minimally invasive procedure could be replaced by a totally non-invasive method that uses MRI (Sun and ) or CT images ( , , ) to predict the aberrations that will be Hynynen in vitro necrosis at the geometrical center of the array with a beam steered from an implantable hydrophone located 1cm away. However, as explained in their article, the beamwidths of the elements were too tight to obtain a good beam focusing outside of the geometrical center and the array only permitted the restoration of the focus with enough power at the geometrical center. They concluded that a significant improvement in the steering range would occur by using much smaller elements. The present study demonstrates that a significant power at the focus and high precision focusing and steering capabilities can be obtained with a reasonable number of transducers.

In order to build an array that can correct for these aberrations, a number of design considerations such as the number of elements, the aperture and the frequency, have been previously discussed by . Based on different considerations on the beam Clement (2000) et al steering capabilities, we put our efforts to design a new prototype that used the great versatility of single-element technology. In close collaboration with Imasonic (Besan on, France) we have developed a new technology of high power elements with small diameter that can ç be distributed on any surface. Such a technology enables to control completely the shape and the size of the array active surface. Moreover the large bandwidth of this single-element technology enables to work between 0.7 and 1.1 MHz. All the single-elements are embedded in homemade moulds resulting in an easily upgradeable system. The number of elements results from several compromises: the energy must be distributed over a large area of the skull in order to reach the maximum antenna gain and avoid undesired skull heating, but at the same time the size of the transducers elements should be small compared to the correlation length of the skull in order to achieve a good correction of the skull aberrations. Moreover the steering capabilities of the array and the grating lobes are strongly related to the size and inter-element distance of the transducers. Finally the cost of the system increases with the number of transducers and has to be taken into consideration.

However, an important disadvantage of large phased arrays is the unwanted presence of grating lobes, and the need to reduce the grating lobes has been common to all therapeutic arrays reported to date ( , ).

Dupenloup

. 1996 et al Lockwood and Foster 1996 Goss et al , , have shown theoretically that the use of elements randomly distributed on a segment of a spherical . (1996) [START_REF] Gavrilov | A theoretical assessment of the relative performance of spherical phased arrays for ultrasound surgery[END_REF] surface may improve the performances of a phased array, particularly the focusing quality when the focus is moved electronically in the vicinity of the geometrical center.

In this study such a large sparse array is specially designed for transskull brain therapy. It is optimized both for correcting the skull aberrations and for its beam steering capabilities. The electronic conception of the multi-channel system represents an important progress since 200 high power emission boards and 100 independent reception boards are available for positioning and imaging before and during the heating sequence. The performance of several transducers distributions (hexagonal, annular and quasi-random distribution) has been investigated in order to minimize the grating lobes, and maximize the region in which the focus can be successfully moved. Based on the simulation, the array has been constructed and experimental results are shown. This new device presents very good performances in terms of aberration correction capabilities, electronic beam steering and power level. Finally these performances are experimentally demonstrated by thermally inducing precise lesions through human skulls in fresh liver and brain samples.

Array Design and specifications

A 900 kHz central frequency has been chosen for the array by considering several factors: the aperture of the array, the focal spot size, the absorption coefficient, the cavitation threshold and finally the electrical matching of the transducers (linked to ratio between the size of the transducer and the wavelength). On the one hand, at a lower frequency, the absorption coefficient of the brain is smaller and the necrosis threshold would be harder to reach. Moreover the cavitation will appear at lower amplitude since the cavitation threshold increases with frequency. On the other hand, a higher frequency could achieve a more localized focus, but above 1.3 MHz the absorption and the scattering loss of the skull increase rapidly (

), and the acoustic power at focus would not be sufficient. [START_REF] Fry | Acoustical properties of the human skull[END_REF] Moreover, at high frequency, the required steering capabilities would be incompatible with a reasonable number of transducers. Finally, contrary to classical HIFU transducers, the single elements technology developed in collaboration with Imasonic presents very good performances in terms of bandwidth since the cut frequencies at 6dB are 0.63 MHz and 1.17 MHz. Thus the transducers can be used either in monochromatic or pulse emission mode, for therapeutic or imaging purposes.

In order to optimize the number of transducers and their size, several considerations have been taken into account. The array must be able to focus at its geometric center, correcting the aberrations induced by the skull, so that the active element size has to be smaller than the correlation length of the skull, approximately 10 mm at 1MHz. This has been confirmed by , since they shown Clement (2000) et al that dividing their large 64 elements array in 500 elements (approximately 3 cm ) working at 650 kHz increased the intensity at focus by a 2 factor 1.5.

Moreover the array must be large enough and distribute energy evenly across the skull bone in order to avoid undesired skull heating.

A geometrical focus F 120 mm and an array diameter D 180 mm were chosen, minimizing as far as possible the F/D ratio. Finally, the

= =
number of transducers must also be sufficient to deliver therapeutic power level at focus. The acoustic power required in ablation operating regime is typically 1000 W.cm at 0.9 MHz, which corresponds to an overpressure of 54 bars at focus after propagation through the skull.

Acoustic field simulations

The performances of several transducers distributions such as quasi-random, annular and hexagonal patterns were investigated (Fig. 1 ). These specific distributions were chosen for their different degrees of symmetry. The first array consisted of 200 elements of 8 mm diameter, each distributed in a quasi random manner: a totally random distribution was modified so that the minimum distance between the center of any two neighboring elements was 10 mm. The second array was a standard axi-symmetrical array: the elements were regularly placed on concentric rings, each ring being shifted with respect to the others. Finally the hexagonal array was completely regular, and could be easily compared to others hexagonal patterns with any sparseness or hexagonal compact distribution. All the arrays have the same 52 sparseness, and should provide approximately the same acoustic power at focus. According to , a sparseness of % [START_REF] Gavrilov | A theoretical assessment of the relative performance of spherical phased arrays for ultrasound surgery[END_REF] 52 being within the limited 40 to 70 range, enabled beneficial effects of randomization.

% % %

For each array, the 3D acoustic field was calculated by using the impulse diffraction code PASS ( ). In 1 [START_REF] Cassereau | Computation of the impulse diffraction of any obstacle by impulse ray modelling Prediction of the signals distortions[END_REF] order to assess the performance of the different arrays, the acoustic fields were calculated when focusing at geometrical focus and when the focus was steered off-axis and along the beam axis. The fields were calculated in a 100 100 200 mm volume with a 0.25 mm step.

× ×

3

The intensity distributions in the focal plane for the hexagonal and quasi-random arrays are shown in . Grating lobes associated Fig. 2 with an aperiodic distribution (concentric shifted rings and quasi-random arrays) are 10 to 12dB less than those associated with the periodic hexagonal element spacing array. Actually, the concentric rings array and the quasi-random array have quite similar performance in the focal plane, the maximum grating lobe being lower than 20dB: 22,3dB for the concentric ring array and 21,4dB for the --quasi-random array. However the quasi-random array has better performance in the near field: on the beam axis the pressure amplitude of the quasi-random array was found to be 10dB lower than the one of the concentric rings array ( ). The reduction of the grating lobes Fig. 3 in the near field is a very important point to address, as the overheating of the skull surface located in the near field has to be avoided.

The increase of the grating lobes when the focus was electronically moved off-axis has also been investigated. The intensity distributions in the focal plane for the quasi-random array are shown in . On these simulations the focus is steered from 0 to 20 mm Fig. 4 off the beam axis. The intensity distribution was deemed acceptable if the maximum pressure in the grating lobes was at least 10 dB lower than the pressure at focus (a factor 10 in the corresponding intensities), which is an accepted level for safe delivery of treatment (Ebbini et ). The steering range was found to be very poor with the hexagonal distribution ( / 3mm), but quite good with the aperiodic 1991 al.

+distributions ( / 15 mm) as it is shown in . Moreover the peak pressure-squared value remains above 50 of its maximum value to + -Fig. 5 % a 15 mm steering radial distance and a 20 mm axial distance away from the geometric focus. Thus, treatment volumes of about 30 30

× ×
40 mm should be reached.

3

Consequently, the quasi-random distribution was definitively chosen as it gives the lowest level of grating lobes in the focal plane as well as in the near field and it presents very good steering capabilities.

Experiments and results

Array construction

Based on the simulation study a 200-elements array was constructed. The 200 high power piezocomposite transducers (8 mm diameter, 0.5 cm active area, Imasonic, Besan on, France) were mounted in a sealed spherically curved holder made of a mixture of Ureol 2 ç 6414B and Ureol 5075A (Vantico Ltd), with a 12 cm radius of curvature. This material was selected for its thermal, mechanical and acoustical properties. Each transducer element is individually matched to the 50 Ohms output impedance of the generator. The matching boxes are placed in a waterproof PVC box ( ). The coaxial lines from the matching boxes are connected to a 200-channels electronic Fig. 6 driving system. Each electronic channel is fully programmable and has its own emission and reception electronic board. 16 electrical Watts per channel ( / 40V, 50 Ohms) can be delivered. A computer is used to control the operation of the 200-channels electronic driving

+ - system.

Acoustic field measurements

The acoustic field was measured at low acoustic intensity (< 5 W.cm ) in a tank filled with degassed water. A 0.4 mm PVDF 2 bilaminar calibrated hydrophone (Golden Lipstick, SEA, Soquel, CA) was set at the array geometrical focus. The hydrophone was moved using a stepper-motor-controlled 3D positioning system (Newport). At each location of the hydrophone the measured signal was sent through an amplifier (SEA, Soquel, CA), and recorded by one of the reception channels of the electronic driving system. The scan position and the data acquisition were computer controlled.

A 900 kHz 30 cycles sinusoidal wave was emitted on each channel at low electrical power (0.04 W per channel) and 15 bars were measured at focus. The acoustic field was scanned in a 50 50 50 mm volume with a 0.5 mm step. The experimental fields shown in -Then a half human skull was placed between the array and the hydrophone as shown in , the skull-array distance was Fig. 8 approximately 4 cm, and the 2D map of the wavefront distortions induced by the skull was recorded. As shown in , the wavefront Fig. 9 was severely distorted by the skull. Some part of the skull induced an important phase distortion (the celerity can reach 3500 m.s ), 1 whereas other parts induced a huge absorption (up to 8 dB.mm ). But there is no obvious correlation between the region of high or low 1 attenuation and the region of large or small phase shift. In order to correct for both phase and amplitude aberrations a time reversal process combined with amplitude correction was performed. The signal coming from each transducer of the therapeutic array was recorded by the hydrophone. Then the signals were time-reversed, the amplitudes were adjusted to the same level and the signals were reemitted by the ultrasonic array. This procedure takes advantage of the reciprocity in order to use a sensor rather than an acoustical source at the focus. The resulting acoustic field was scanned in the focal plane. It is shown in and compared with the field obtained without any Fig. 10 aberration corrections. The uncorrected beam is strongly degraded by the skull. The focal spot is not at the desired location and is widely spread in comparison with the corrected one. After correcting the aberrations, the focus is located at exactly the desired position.

Moreover, an important point is that the pressure amplitude of the corrected beam (68 Bars) is 4.5 times higher at focus than the pressure amplitude of the uncorrected one (15 bars). Consequently, it results in a 20 times higher heat deposit and it shows the feasibility to induce lesions in the brain.

The time reversal process with amplitude compensation was repeated at several skull positions. The skull was moved step by step in regard to the system array hydrophone over a few centimeters. For each skull position, the acoustic field was scanned in the focal region.

+

For all locations, thanks to the adaptive focusing the grating lobes were lower than 20 dB, and the 6 dB dimension of focus remained -equal to 1.5 1.5 10.5 mm . The pressure at each focus was also measured and ranged from 52 to 75 bars.

× ×

3

Thermally induced lesions in fresh tissues with steering process

Lesions were induced in fresh degassed liver samples. The temperature of the degassed water was 25 C. A human skull and a sample °of fresh degassed cow liver were set between the array and the hydrophone. The hydrophone was implanted in the tissue sample at the geometrical focus of the array and a time reversal process combined with amplitude compensation was performed. Once the signals had been recorded, the hydrophone was removed. A continuous monochromatic wave with the phase and amplitude previously corrected was emitted on each of the 200 electronic channels. Two sonications were performed at the initial hydrophone location in the liver sample at the maximum power level for a duration of 5s with a waiting time of 10 s between shots. The lesion is about 2 mm in diameter and 8 mm in length. Then, the beam was electronically steered off-axis in order to focus at 8 others points located on a 1-cm side square centered on the geometrical focus. The targets were the four corners and the middle of each side of the square. Two 5s sonications were performed again at each focus, with a waiting time of 10s between each shot. The nine lesions are shown in . Due to the change in the liver Fig. 11.a color, the necroses are very well defined. They are located exactly at the desired position and the boundary between burned cells and other cells is very narrow.

In a second experiment a square-shaped necrosis was created in liver by focusing on 25 points inside of the square with a 2-mm spatial step between each target. Two sonications were performed at each focus for 5s with a waiting time of 10s between shots. As shown in Fig Finally, a fresh sheep brain was placed behind a half human skull so that the brain surface was located in the focal plane of the system.

The hydrophone was implanted in the brain at the geometrical focus of the array and a time reversal process was performed. The aberrations corrections were similar to those of section 4.2. Two sonications of 5 s duration were performed at the geometrical focus. Then the beam was electronically steered in order to focus on a cross centered on the geometrical focus. The beam was steered along a vertical and a horizontal 1cm line with a 0.2mm spatial step, and at each point two 5s sonications were performed. On the cross-shaped Fig. 12 necrosis is well defined although the color change in the brain is not as marked as in the liver.

Discussion and conclusion

A large therapeutic array using single-elements technology has been specially designed for transskull brain therapy. Its capabilities in terms of aperture, working frequency, electrical matching and electronic steering have been optimized. The experiments demonstrated that using a time reversal process with amplitude compensation, achieved with an implantable hydrophone, the aberrations induced by the skull are well corrected with this therapeutic device. A sharp focus was produced at the desired location, and the pressure reaches 4.5 times the pressure obtained with the uncorrected beam. The experiments were repeated at several skull positions and the focusing quality remained very good. Depending on the skull position, the pressure at focus ranged from 52 to 75 bars, which corresponds to an acoustic intensity of 900 to 1900 W.cm . This is within the range of intensities typically used in ablation operating regimes. The sonication duration can be 2 easily changed in order to induce a thermal dose independent of the skull position.

High power experiments on a large number of liver and brain samples have also demonstrated the therapeutic capabilities of ex-vivo the array. Lesions about 2 mm in diameter have been induced after correcting the ultrasound beam. The high precision steering capabilities of the array have also been demonstrated. Electronically steered focusing enables to coagulate tissues through a human skull in a volume of 30 30 40 mm around the geometrical focus as the acoustic intensity deposit for each individual focus was found to remain higher

× ×
The overheating induced on the skull outer table was checked in several locations on the outer table for a 10s sonication time at maximum power (1900 W.cm at focus) with a 50 duty cycle. A 2.5 C spatially averaged temperature increase was found from the 2 -% °initial 25 C temperature of the water tank. This temperature rise is acceptable ( ) especially if a water-cooling system °Ter [START_REF] Haar | HIFU Treatments: Dosimetric considerations[END_REF] is used to reduce the temperature at skin-bone interface.

Another important innovation of this system consists in its electronic driving channels that allow mixing therapeutic and imaging sequences. Each channel is fully programmable and has its own emission and reception electronic board. The transmit and receive sequences can be changed at a very high frame rate. Therefore it could be possible to image the region close to the focus with the therapeutic array and perform ultrasound based temperature estimation or elastography measurements.

Finally, the single element technology will enable to modify very easily this system by adding additional elements in the array. Thus the power delivered at the focus could be increased and the temperature rise at skin-bone interface could be decreased. This would make it possible to optimize the amplitude compensation technique and fully adjust the amplitude gain of each channel. Moreover the focal spot could be successfully moved in a larger region around the geometrical focus.

Ackowledgements:

We would like to thank Imasonic (Besan on, France) for their highly valued collaboration in developing the high power single-element ç technology. We wish also to thank Didier Cassereau for his help on the impulse diffraction software PASS.

Footnotes:

1 . http://www.loa.espci.fr/pass/ white lines correspond to 3dB and 6dB.

--

Fig. 8

Experimental setup for the time reversal process. On the left side: the needle hydrophone (PZT, 0.4 mm, SEA) used for the corrections of the skull aberrations. On the right side: the high power 200-elements ultrasonic array. The whole experiment is performed in degassed water.

  steer the beam electronically and heat the whole target spot by spot without moving the therapeutic array, Tanter . et al proposed in 1998 combining the time reversal process with a numerical back-propagation and steering algorithm, and demonstrated experimentally its feasibility at low intensities. Recently, used a similar steering technique at high power to achieve Clement (2002) et al.

2 - 1 -

 21 Considering the absorption of the brain (0.7 dB.cm .MHz ), the reflection and absorption induced by the skull (an average transmission 1 loss of 11 dB at 0.9 MHz), the overpressure has to reach 350 bars at focus in water without the skull. All the transducers of the array have been characterized individually. Each transducer was linked to its 50 Ohms electrical matching and the electrical to acoustical efficiency reached 50 . With a 16 W electrical power supply, each transducer could generate a monochromatic wave with amplitude of 1.8 bars at % 120 mm in water during 5 seconds. Therefore the array was composed of 200 elements.

  Fig. are very close to those obtained with the simulation. The 6dB dimension of the focus is 1.5 1.5 10.5 mm , and the grating 7.a and 7.b -× ×

.

  the necrosis is a well-defined square of 1.1cm side. The temperature increase has also been modeled by a diffusion type equation 11.b computed using the 3D finite-difference time-domain method. The thermal dose for changing temperature exposure was calculated by numerical integration ( ). It gives the time that would yield an equivalent thermal dose of 240 min at 43 C and Sapareto and Dewey 1984 °enabled the prediction of the necrosis size in good agreement with the measurements ( ). Fig 11.b

Fig. 1

 1 Fig. 1 (a) Hexagonal (b) annular and (c) quasi-random transducer distributions.

Fig. 2

 2 Fig. 2Pressure distribution in the focal plane for the hexagonal (left) and quasi-random (right) arrays. The pressure squared is in dB scale.

Fig. 3

 3 Fig. 3Maximum pressure squared (in dB scale) reached on the beam axis for the concentric ring and quasi random arrays.

Fig. 4

 4 Fig. 4 Intensity distribution in the focal plane for the quasi-random array, with the focus moved electonically at (a) 0 mm (b) 5mm (c) 10mm and (d) 15 mm in the y lateral direction.

Fig. 5

 5 Fig. 5 Maximum intensity of the grating lobes when the focus is steered from 0 to 20 mm off the beam axis. The values are normalized by the intensity of the main lobe. Solid line: quasi random array. Dotted line: annular array. Dash-dotted line: hexagonal array.

Fig. 6

 6 Fig. 6The 200-element sparse array prototype and the electronic system. The waterproof PVC cube contains the 200 electrical matching boxes. On the right: the quasi random distribution of transducers embedded in spherical shaped Ureol.

Fig. 7

 7 Fig. 7 (a) Experimental scan of the pressure squared for the quasi-random array in the focal plane (XY plane). This beam pattern was found to be in good agreement with the numerical simulation in . (b) Experimental scan of the pressure squared in the longitudinal XZ plane. The Fig. 4

Fig. 9 -

 9 Fig. 9 2D spatial map of the wavefront aberrations induced by the skull. Typically the celerity in the skull can reach 3500 m.s in some locations 1 and the absorption 8 dB.mm . The black dots represents the projection of the transducers positions. (a) The phase distortions ( s) (b) The 1 μ relative amplitude distortion.

Fig. 10

 10 Fig. 10 Experimental distribution of the intensity in the focal plane (a) without aberrations corrections and (b) with corrections. Black lines correspond to -3 dB, -6 dB and -9 dB.

Fig. 11

 11 Fig. 11Thermally induced lesions in fresh liver through a human skull. The target is located at depth Z 120 mm from the array. In both experiments = the aberration corrections were achieved at center by using an implanted hydrophone and the other impacts were achieved by tilting electronically the beam. a) Lesion size is about 2 mm in diameter for the center spot. The spatial step between each lesion is 5 mm. b) Square-shaped necrosis performed with 25 electronically steered focus (2mm spatial step). The thermal dose has been calculated for this experiment. The contour delimits the zone where the thermal dose is higher than 243 min. It predicts the size of the necrosis in good agreement with the real necrosis.

Fig. 12

 12 Fig. 12Thermally induced lesions in a sheep brain through a human skull. The target is located at depth Z 120 mm from the array. The aberration = corrections were achieved at center by using an implanted hydrophone and next impacts were achieved by tilting electronically the beam along a cross. On the vertical and the horizontal lines the step between each lesion was 0.2 mm. The white arrows point the extremity of the cross.

10

10

than 500 W.cm . Therefore in practice a whole tumor could be treated spot by spot without mechanically moving the system. 2 -

10

10

10

10

10

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Jean-François Aubry

Mathieu Pernot

Fabrice Marquet

Mickaël Tanter

Mathias Fink

J.-F Aubry

Transcostal high-intensity-focused ultrasound: ex vivo adaptive

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

The use of high intensity focused ultrasound (HIFU) as a non invasive method for treating tumours is rapidly increasing. The first successful clinical trials have been performed in the early 90s by placing the therapeutic probe in contact with the organ to be treated: in contact with the eye for the treatment of glaucoma [START_REF] Silverman | Therapeutic ultrasound for the treatment of glaucoma[END_REF] and in contact with the prostate using trans-rectal introduction for both benign prostate hyperplasia (BPH) [START_REF] Gelet | High-intensity focused ultrasound experimentation on human benign prostatic hypertrophy[END_REF], Madersbacher et al 1994[START_REF] Sanghvi | Noninvasive surgery of prostate tissue by high-intensity focused ultrasound[END_REF] and prostate cancer [START_REF] Madersbacher | Effect of high intensity focused ultrasound on human prostate cancer in-vivo[END_REF][START_REF] Gelet | Treatment of prostate cancer with transrectal focused ultrasound: Early clinical experience[END_REF]. These clinical treatments proved that it was possible to safely target tissues with ultrasound by inducing a rapid heating of the tissues located in the millimetric volume of the focal spot while leaving tissues on the propagation path relatively unaffected. The feasibility of using extracorporeal ultrasounds to treat tumours has been first demonstrated in organs such as the kidney (Valancien et al 1992) and the liver (terHaar et al 1998). Many extracorporeal clinical devices are now commercially available and can be divided in two groups: some rely on an ultrasonic monitoring using an echographic array inserted in the therapeutic probe (Wu et al 2004) and others rely on a magnetic resonance (MR) monitoring by inserting an MR compatible therapeutic probe in an MRI unit [START_REF] Hynynen | A clinical noninvasive MRI monitored ultrasound surgery method[END_REF][START_REF] Vimeux | Real-Time Control of Focused Ultrasound Heating Based on Rapid MR Thermometry[END_REF]. MR monitoring received FDA approval for clinical use in the treatment of uterine fibroids [START_REF] Chan | An image-guided high intensity focused ultrasound device for uterine fibroids treatment[END_REF], Tempany et al 2003, Stewart et al 2003) and research programs are currently conducting clinical trials for the treatment of breast tumours [START_REF] Gianfelice | MR Imaging-guided Focused Ultrasound Surgery of Breast Cancer: Correlation Between Dynamic Contrast-Enhanced MRI and Histopathologic Findings Breast[END_REF][START_REF] Furusawa | The Evolving Non-Surgical Ablation of Breast Cancer: MR Guided Focused Ultrasound[END_REF], liver tumours [START_REF] Okada | A Case of Hepatocellular Carcinoma Treated by MR-guided Focused Ultrasound Ablation with Respiratory Gating[END_REF][START_REF] Kopelman | Magnetic Resonance-guided Focused Ultrasound Surgery (MRgFUS): Ablation of Liver Tissue in a Porcine Model[END_REF], and bone metastases [START_REF] Catane | MR guided focused ultrasound surgery (MRgFUS) for the palliation of pain in patients with bone metastases -preliminary clinical experience[END_REF]. Wu et al (2004) reported a total of 1038 patients with solid tumours treated with extracorporeal HIFU ablation under ultrasonic monitoring. This study included primary and metastatic liver cancer, malignant bone tumour, breast cancer, soft tissue sarcoma, kidney cancer and pancreatic cancer. In the same report, solid benign tumours such as uterine myoma, benign breast tumour, and hepatic hemangioma have also been treated with HIFU thermal ablation. All these studies suggest that HIFU is a safe and feasible technique capable of complete tumour ablation. But in the case of liver, however, the presence of the rib cage is affecting the HIFU treatment planning: on the one hand, the rib cage acts as an aberrator that might affects the focusing [START_REF] Kennedy | The effects of absorbers such as ribs in the HIFU Beam-path on the focal profile 2nd[END_REF] and on the other hand, due to the high value of the absorption coefficient of the bone [START_REF] Goss | Ultrasonic absorption and attenuation in mammalian tissues[END_REF], the overheating on the ribs can be quite important. There are two ways for the ribs to damage the surrounding tissues: ribs absorb the ultrasonic energy because of their higher absorption coefficient than soft tissues and radiate heat to the surrounding tissues, and reflection of the therapeutic beam at the bone-tissue interface can induce undesired constructive interferences in the surrounding tissues. In vivo measurements of temperature elevation on pork ribs have been reported by [START_REF] Daum | In vivo demonstration of noninvasive thermal surgery of the liver and kidney using an ultrasonic phased array Ultrasound in[END_REF] thanks to MR temperature monitoring: temperature elevation during sonication was 5 times higher on the ribs than in the intercostal space. Damage to the skin during liver treatment has thus been reported (Wu et al 2004a, b, Kennedy et al 2004[START_REF] Li | Complications of high intensity focused ultrasound in patients with recurrent and metastatic abdominal tumors[END_REF]. [START_REF] Li | Complications of high intensity focused ultrasound in patients with recurrent and metastatic abdominal tumors[END_REF] reported skin burns for all of the 17 patients that were treated, most of which located on the skin directly in the pathway of ultrasound (ventral side) but in three cases skin burns were also located on the opposite side (dorsal side). Such dorsal skin burns might be explained by the fact that the ribs surrounding the chest have a high absorption coefficient and are also heating in the contra lateral side and by the fact that the acoustic pressure field might have exceeded the required dose for thermal ablation: focal peak intensities up to 5000W.cm -2 were reported with up to 30s continuous exposure. To overcome this problem, prior to the treatment, Wu et al (2004b) resected a portion of the ribs overlying the targeted region of the liver in order to provide an acoustic window: as a single-element therapeutic transducer was used in this study, it was indeed impossible to avoid ultrasonic reflection of the ribs by adaptive focusing. It has been proposed in the late 90s that the liver could be treated by using a phased array to sonicate between the ribs or bones (Mc-Gough et al 1996, Botros et al 1997, 1998) but it could not be experimentally tested at that time. [START_REF] Civale | The use of a segmented transducer for rib sparing in HIFU treatments[END_REF] recently lowered the temperature of the ribs during sonication by switching off up to three elements of a linearly segmented HIFU transducer made of 10 elements: a temperature rise of up to 1K was measured on the skin surface when all segments were active; this rise was reduced to approximately 0.2K when three segments were switched off. Even though no focal lesions were induced and the number of active elements was not sufficient for a clinical application, this study confirmed the proof of concept introduced by Mc-Gough et al (1996) and Botros et al (1997). Multi element phased arrays made of hundreds of elements have since been developed (Daum et al 1998[START_REF] Chapelon | New Piezoelectric Transducers for Therapeutic Ultrasound Ultrasound in[END_REF][START_REF] Pernot | High power transcranial beam steering for ultrasonic brain therapy[END_REF][START_REF] Ebbini | Dual-mode ultrasound phased arrays for image-guided surgery[END_REF][START_REF] Tanter | Compensating for bone interfaces and Respiratory motion in High Instensity Focused[END_REF] making it possible to focus through the intercostals space, as will be shown in this paper. In this study, a high power 200-element phased array is used to investigate the influence of the presence of ribs on HIFU treatment. In a first part the defocusing effect of the ribs will be experimentally measured in vitro and an adaptive focusing technique (time reversal) will be introduced in order to decrease this effect. Thanks to temperature measurements on the ribs it will be shown that the overheating of the rib cage can be dramatically reduced by time reversal techniques.

Materials and methods

Transducer

A quasi-random sparse array has been constructed in house. It has been made of 200 high power piezocomposite single elements, as seen on figure 1. The transducers have been mounted on a spherical surface (figure 1b) with a semi random distribution in order to minimize the side lobe level in the focal plane as well as the pressure level in the near field [START_REF] Pernot | High power transcranial beam steering for ultrasonic brain therapy[END_REF]. The 8mm diameter individual transducers were designed to support a maximum output intensity of more than 40 W/cm² during 5 seconds at a 1MHz central frequency. The system was driven by 200 fully programmable individual electronic channels with 120 emitting channels and 80 emitting and receiving channels (18W per channel with a 40 output impedance).

Experimental setup

A freshly excised pork rib cage(figure 2c) has been put in front of the array so that it was partially shadowing the beam(figure 2 a and b) as would be the case in vivo. The rib cage was kept intact, with flesh and skin. The whole experiment was immersed in degassed and deionised water. A PVDF hydrophone (Onda Corporation, 200µm active surface) was mounted on an automated 3D gantry system capable of motion in three orthogonal linear directions (Newport Motion controller MM4006). Pressure was recorded on the hydrophone for each position as a function of time by using one of the receive channels of our electronics, so that only 199 elements could be used to generate the pressure field. Once the position of the geometrical focus had been established, acoustic field measurements were made in the focal plane from -30mm to +30mm in both X and Y axis with a step size of 0.2mm in both axes. For each position, pressure was averaged over five sets of measurements before being stored in memory.

Temperature measurements

In order to investigate the thermal effect of the ultrasonic beam on the ribs, temperature measurements were made at various locations on the ribs and in the intercostal space with thin thermocouples (Ironconstantan, 40 µm diameter, PhysiTemp Corp). Thermocouples were inserted inside the tissues under the skin and muscles using a needle and after insertion the needle was removed so that the thermocouples were covered by a thin layer of tissues to avoid the effects of acoustic streaming and direct contact with water. Five thermocouples were inserted on the ribs, between the bone and the surrounding tissues and seven thermocouples were inserted in the intercostal space. Temperature rises were recorded on a PC board.

Simulations

2D finite difference simulations have been performed in order to better understand the way the acoustic beam is affected by the ribs. Simulations were performed with a finite differences software called Acel. Acel is a FDTD numerical code developed at the Laboratoire Ondes et Acoustique. In this paper, the 2D mixed Fluid -Solid wave equation has been used in order to take into account mode conversions at the bone water interfaces. A 2D image of the ribs has been extracted from a 3D CT scan of a human thorax and is displayed in figure 3b. From high resolution computed tomography (CT) images, a 2D portion of the chest wall has been extracted. As previously described in Aubry et al (2003), the porosity map () can be directly deduced from the raw CT data. Then, the acoustical properties of the ribs are determined using mixture laws in a biphasic medium (bone/water). The mass density is easily deduced from porosity by :   . (Williams 1992) According to Carter and Hayes (1977), in a first approximation, a linear relationship may be assumed between velocity mass density, so that a linear relationship can be assumed between velocity and porosity: For longitudinal waves: Simulations were conducted at a 1MHz central frequency. The corresponding wavelength was 1.5mm. The simulation grid was set to one tenth of a wavelength. In order to meet the stability criteria, the temporal step must meet the following inequality : r m ax ( ( )) 2

x t cr     (eq. 3)
where x is the spatial step of the grid. The temporal step was thus set to 0.0366 µs. The experimental setup was reproduced: an acoustic source was located at the geometrical focus of spherical array (120mm curvature). The propagation of an impulse (3 arches at 1 MHz central frequency) from the source to the array was simulated and the corresponding signals received by each element of the array were recorded. Even though the simulation was realised in 2D, the sizes of the receiver Spatial distribution of pressure was recorded regularly in order to reproduce a movie of the propagation of the beam through the ribs.

Results

Acoustic field of the beam

Once the geometrical focus of the array had been determined, the hydrophone was set to this position. Each element of the array emitted a narrow band signal (50 periods) and the corresponding signals were recorded by the hydrophone and stored in memory. These signals are displayed in figure 4 a. Using spatial reciprocity, they correspond to the set of signals that would have been received on the array of transducers if a small ultrasonic source located at the hydrophone position had been emitting a 50 periods signal. In order to evaluate the influence of the ribs, the normalized peak to peak amplitude of the signals is displayed in figure 4b. The amplitude received by each transducer is presented with a colour coding and displayed at the location of the transducer. One can see that even though the ribs were placed almost vertically, the pattern is not striped but quite complex due to the fact that the ribs are not perfectly linear and to reflection and diffraction effects between the ribs and the array. The shadowing effect of the ribs is confirmed by the simulations: an acoustic source was located at the geometrical centre of the array and emitted an impulse. Part of the wave front was reflected by the bone, so that the transmitted wave front was almost binarized: the amount of energy going through the ribs was almost negligible. The ratio between the amplitude of the waves propagating between the ribs (intercostals wave) and the waves propagating through the ribs (transcostal wave) was equal to 6.03 in the experiment and to 7.04 in the simulation. Two different focusing techniques have then been experimentally tested: spherical laws (no correction) and time reversal (Fink 1997, Fink et al 2003). Without any correction, the pressure field in the focal plane is affected by both inhomogeneous attenuation and phase distortion and three main effects are observed in figure 6: a mean 2 mm shift of the main lobe, a mean 1.25 mm spreading in the half width of the main lobe and up to 20 dB increase in the secondary lobe level. The wave front is thus slightly distorted when crossing the chest wall but is not dramatically defocused so that by increasing the total energy emitted by the array, it is possible to induce thermal ablation of the liver through the ribs (Wu et Then a time reversal experiment was conducted though the ribs: the wave front presented in figure 4a was time reversed and reemitted by the array. The pressure field was scanned by the hydrophone in the focal plane. Compared to the non-corrected beam, the position and the half width of the main lobe could be restored, as seen in figure 6. A cut of this 2D pressure distribution is plotted in the horizontal axis (X axis) in Figure 7a. These results show that time reversal is improving the focusing quality (1.73dB  1.26 dB) while slightly improving the pressure at the focal spot (Table 2). But the focusing quality is not the main concern when focusing though the rib cage: one also has to pay attention to the pressure level on the ribs that may cause a temperature elevation due to the high absorption of the bones and to induced side effects (Wu et al 2004a, b, Kennedy et al 2004[START_REF] Li | Complications of high intensity focused ultrasound in patients with recurrent and metastatic abdominal tumors[END_REF]

Temperature measurements

Temperature elevation has been measured on several locations over the outer rib surface at the bone location for 5s sonications performed with each focusing technique (1600W.cm -2 at focus in water without the ribs). The maximum emission amplitude was the same for all the experiments and a thermal lesion was obtained at the focus in ex vivo tissue samples. The pressure at the focus was approximatively the same for the time reversal experiment and the non corrected experiment (Table 2). A summary of the mean temperature elevation is given on Table 3.

Focusing technique

Discussion

Time reversal has been shown to be well suited for ribs sparing in liver treatment planning as it both improves the focusing quality and decreases the overheating of the ribs. Mathematically, it is the best adaptive technique to spare the ribs as it acts as a matched filter and maximises the ratio between the energy deposited at the target location and the total amount of energy emitted by the therapeutic array as demonstrated by [START_REF] Tanter | Time reversal and the inverse filter[END_REF]. Nevertheless, such a technique is invasive as it requires an acoustic source (or receiver) at focus. For clinical applications a non invasive approach would be needed. This should be feasible by using the therapeutic array in the receive mode in order to image the chest and localize ribs surface with the therapeutic array.

The ability of the array to image the ribs has been first validated on simulations. 29 transducers of 8mm in active diameter mounted on a spherical surface have been modelled. Pulse echo imaging sequences have been simulated with a reception beamforming and the corresponding image is displayed in figure 9a. It agrees with the original ribs geometry displayed in figure 9b. Transducers located in front of a rib bone can be identified. Instead of emitting a spherical wave (no correction) with the same phase and the same amplitude on each element of the array, one can thus set the amplitude to zero on the transducers located in front of the ribs. This has been done numerically and the result can be seen in figure 10: using this approach the ribs are not sonicated. However the energy ratio E r (eq. 5) is 13% lower than by using time reversal. Indeed time reversal also benefits from diffraction effects on the edge of the ribs. One can see on figure 9 that without any correction, reverberations occur between the costal walls and the transducer without contributing to energy deposition at the focus. On the contrary time reversal largely sonicates between the ribs: it is much more efficient in terms of energy saving and also in decreasing temperature elevation on the ribs. In order to optimize the energy ratio E r (eq. 4), it would also be possible to reproduce a time reversal operation instead of simply switching off some transducers: the propagation of a signal originated at the target location can be simulated with our numerical finite differences code in this simple model made of ovoid bones embedded in soft tissues. In that case, the location and size of each rib would be roughly provided by the echographic images (as the one presented in fig. 9a). This yields to non-invasive time reversal as the propagation from a virtual source located at the target position on the model is now computed instead of being measured experimentally as was the case in paragraph 3.1. This means that a stripped transducer might be an ingenious way to limit the overheating of the ribs [START_REF] Civale | The use of a segmented transducer for rib sparing in HIFU treatments[END_REF] but is not the optimal configuration.

It has been shown that time reversal acts as a spatial and temporal matched filter [START_REF] Tanter | Time reversal and the inverse filter[END_REF][START_REF] Tanter | Optimal focusing by spatio-temporal inverse filter : Part I[END_REF][START_REF] Tanter | Optimal focusing by spatio-temporal inverse filter : Part I[END_REF]. In other words, for a given acoustic energy emitted by the array, it optimizes the acoustic energy deposition at the focus. This property holds even if the medium is absorbing, so that the following energy ratio between the energy deposited at the target location and the total amount of energy emitted by the therapeutic array is always optimized when using time reversal:

R acoustical energy at focus E total em itted energy by therapeutic array  (eq. 4)

In the case of the ribs, this energy ratio has been measured to be 36 times higher with time reversal than without correction. Indeed time reversal naturally sonicates between the ribs in order to spare energy: -if a rib bone is placed between the hydrophone and a transducer, the wave front is strongly absorbed during the first step of the time reversal process, and the amplitude recorded on this transducer is small so that the time reversed signal will also have a low amplitude. In the way back to the target point, this part of the way front will cross a second time the absorbing area but as its amplitude is low it will induce a low temperature elevation. -On the contrary, if the wave front is not absorbed in its way to the transducer, lots of energy will be emitted in the way back, and will reach the target point with a good efficiency.

Time reversal is thus expected to minimize the temperature elevation on the rib surface. This is confirmed by the temperature measurements: a mean 0.3°C has been measured on the rib surface by using time reversal compared to more than 5°C without any correction as can be seen in table 3.

Another approach would consist in placing a set of virtual sources in the intercostals space in order to force the beam to go through these sources without sonicating on the ribs. Botros et al (1997,1998) proposed to use so called "hybrid virtual arrays" made of such sources. To do so, they propose to solve optimal synthesis of complex pressure in the virtual array plane while minimizing power deposition at critical points. The pseudo inversion is based on a weighting in order to favour either the sparing of the ribs or the focusing quality at focus. It would be up to the physician to play with the weighting in order to plan the treatment. As time reversal is a matched filter, by favouring the sparing of the ribs the hydrid virtual array method would end up with the solution of time reversal focusing presented in this paper, but if the physician is willing to increase even more the temperature rise at focus, he could use the hybrid method, with the risk of slightly increasing the temperature elevation on the ribs.

Conclusion

Time reversal seems to be the most suited technique investigated in this paper in order to focus through the rib cage for therapeutic applications. The focusing quality is indeed well restored while the temperature elevation on the rib surface is negligible (a mean 0.3°C). The temperature elevation on the surface of the ribs can also be non invasively reduced by turning off the transducers that are located in front of rib bones. As shown in this paper, the imaging capabilities of the multi-element phased array technology enable to image the outer ribs surface. The locations of the bones appear clearly. This process is currently implemented for clinical investigations using 200 emitting and receive electronic channels. Another extension of this work would be to couple this adaptive focusing technique to 3D real-time motion correction techniques in order to take into account the relatively large respiratory motion during treatment [START_REF] Pernot | 3D real time motion correction in High Intensity Focused Ultrasound therapy Ultras[END_REF]. The ability of transmit/receive HIFU arrays to solve transribs propagation and motion correction, the two main problems of liver treatments clearly emphasize the potential of such dual-mode arrays.

Aubry JF, Tanter M, Gerber J, Thomas JL, [START_REF] Tanter | Optimal focusing by spatio-temporal inverse filter : Part I[END_REF]

  200 elements sparse array prototype and the electronic system. (a) The waterproof plastic box contains the 200 electrical matching boxes. (b) Front view of the array: the transducers are mounted on a spherical surface. (c) High Power electronics (individual channels)

Figure 2 :

 2 Experimental setup: schematic diagram (a) and picture (b). Freshly excised ribs (c)

Figure 3 :

 3 2D raw data in Hounsfield units (a) and the corresponding 2D longitudinal speed of sound map in mm.µs -1 (b)

Figure 4 :

 4 Figure 4: Signals received at the geometrical focus (a) and corresponding amplitude distribution (b).

Figure 5 :

 5 Snapshots of the simulated wave front: an acoustic source was located at the geometrical centre of the array and was emitting an impulse.

  al 2004a, b, Kennedy et al 2004, Li et al 2007) without any correction.

Figure 6 :

 6 Two dimensional pressure field measured in the focal plane (dB scale): no correction (a) and time reversal (b).

Figure 7 :

 7 Pressure distribution (dB scale) obtained with time reversal (gray line) and with no correction (dotted line) in the focal plane (a: experiment and b: simulation) and along the beam axis (c: experiment).

Figure 8 Figure 8 :

 88 Figure 8 highlights the difference between both focusing techniques: snapshots of the propagation during treatment (continuous waves) are displayed without correction and with time reversal. Pressure fields are displayed in a dB scale. Pressure levels 40dB below the maximum pressure amplitude appear in black. The maximum pressure amplitude is the one obtained at the focus. (a) (b) (c)

Figure 9 :

 9 Figure 9: (a) pulse echo imaging sequence simulated with a 2D finite differences code (b) ribs configuration.

Figure 10 :

 10 Figure 10: snapshots of the propagation during treatment: (a) (b) and (c) using a binarised spherical wave

Table 1 :

 1 Pressure amplitude of the wave after propagation through the ribs cage, between the bones (intercostal waves) or through the bones (transcostal waves).

		Pressure Amplitude	Pressure Amplitude	Ratio
		Intercostal waves (A.U.)	Transcostal waves(A.U.)
	Experiments	5.89  42%,	0.98  52%	6.03
	Simulation	5.88  32%	0.83  41%	7.04

Table 2 :

 2 ). Relative

		Non-corrected	Time-reversal	Ratio
	Experiments	6.75	7.03	1.04
	Simulation	6.60	6.89	1.04

pressures amplitude at the focus (A. U.) The pressure is almost similar for the noncorrected treatment and the time-reversal focusing.

Table 3 :

 3 temperature elevation on the ribs

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