Nicolas Verrier

Daniel Alexandre

Michel Gross
email: michel.gross@univ-montp2.fr

Laser Doppler holographic microscopy in transmission: application to fish embryo imaging

Keywords: tering, particles; (300.6310) Spectroscopy, heterodyne

We have extended Laser Doppler holographic microscopy to transmission geometry. The technique is validated with living fish embryos imaged by a modified upright bio-microcope. By varying the frequency of the holographic reference beam, and the combination of frames used to calculate the hologram, multimodal imaging has been performed. Doppler images of the blood vessels for different Doppler shifts, images where the flow direction is coded in RGB colors or movies showing blood cells individual motion have been obtained as well. The ability to select the Fourier space zone that is used to calculate the signal, makes the method quantitative.

Introduction

Blood flow imaging techniques are widely used in biomedical studies, since they can assess physiological processes or can be used for early detection of disease [START_REF] Friedman | Ocular blood flow velocity in age-related macular degeneration[END_REF][START_REF] Pase | Cardiovascular disease risk and cerebral blood flow velocity[END_REF][START_REF] Kur | Cellular and physiological mechanisms underlying blood flow regulation in the retina and choroid in health and disease[END_REF]. However, many blood flow studies require, for imaging purposes, the use of a contrast agent, making the blood flow characterization invasive [START_REF] Sakurada | Measurement of local cerebral blood flow with iodo [14c] antipyrine[END_REF][START_REF] Kanno | A system for cerebral blood flow measurement using an h215o autoradiographic method and positron emission tomography[END_REF]. Scanning Doppler imaging techniques can be considered to alleviate this issue, but due to the scanning step, acquisition of an image is a time consuming process [START_REF] Yeh | Localized fluid flow measurements with an he-ne laser spectrometer[END_REF]. An overview of the main techniques has been proposed by J. D. Briers [START_REF] Briers | Laser doppler, speckle and related techniques for blood perfusion mapping and imaging[END_REF]. Among these, one can outline two ways of monitoring the blood flow: performing measurements either in spatial domain (speckle analysis) or in temporal domain (Doppler analysis). Blood flow monitoring has been demonstrated by Laser Speckle Contrast Analysis/Imaging (LASCA/LSCI) [START_REF] Briers | Laser speckle contrast analysis (lasca): a nonscanning, full-field technique for monitoring capillary blood flow[END_REF]. Here, spatial statistics of the dynamic speckle are used to obtain blood flow images [START_REF] Dunn | Laser speckle contrast imaging of cerebral blood flow[END_REF][START_REF] Briers | Laser speckle contrast imaging: theoretical and practical limitations[END_REF]. Improvement of the acquired constrast image have been achieved through exposure time optimization [START_REF] Yuan | Determination of optimal exposure time for imaging of blood flow changes with laser speckle contrast imaging[END_REF], or intensity fluctuation analysis [START_REF] Zeng | Laser speckle imaging based on intensity fluctuation modulation[END_REF] resulting in high quality perfusion images. However, these techniques are only limited to perfusion monitoring and do not allow to assess other quantities such as amplitude or phase contrasts.

Originally proposed by Gabor [START_REF] Gabor | A new microscopic principle[END_REF] as an optimization of electron microscopy, classical holography aims at recording, on a photo-sensitive material, the interference between a reference field and a diffracted object field. However, within the proposed common-path interferometric configuration, holographic imaging suffer from the so-called twin-image noise [START_REF] Gabor | Microscopy by reconstructed wave-fronts[END_REF]. In 1962, Leith and Upatnieks propose to introduce an off-axis reference field, which lead to a separation of the object and its twin image contribution in spatial frequencies domain [START_REF] Leith | Reconstructed wavefronts and communication theory[END_REF]. Development and democratization of high resolution CCD/CMOS sensors paid a major role in holographic imaging spreading out, making possible both digital recording and processing of holographic images [START_REF] Schnars | Direct recording of holograms by a ccd target and numerical reconstruction[END_REF]. Therefore, due to its intrinsic properties, digital holographic imaging is used in a wide variety of studies in fluid mechanics [START_REF] Lozano | Use of holography in particle image velocimetry measurements of a swirling flow[END_REF][START_REF] Pu | Four-dimensional dynamic flow measurement by holographic particle image velocimetry[END_REF][START_REF] Desse | Digital three-color holographic interferometry for flow analysis[END_REF][START_REF] Verrier | Digital in-line holography in thick optical systems: application to visualization in pipes[END_REF][START_REF] Verrier | Micropipe flow visualization using digital in-line holographic microscopy[END_REF], biomedical imaging and microscopy [START_REF] Charrière | Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba[END_REF][START_REF] Xu | Digital in-line holography for biological applications[END_REF][START_REF] Kemper | Digital holographic microscopy for live cell applications and technical inspection[END_REF][START_REF] Kim | Principles and techniques of digital holographic microscopy[END_REF][START_REF] Lee | Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications[END_REF], or mechanical inspection [START_REF] Picart | Some opportunities for vibration analysis with time averaging in digital fresnel holography[END_REF][START_REF] Leval | Full-field vibrometry with digital fresnel holography[END_REF][START_REF] Asundi | Time-averaged in-line digital holographic interferometry for vibration analysis[END_REF].

Further development led to the introduction of heterodyne digital holography [START_REF] Le Clerc | Numerical heterodyne holography with two-dimensional photodetector arrays[END_REF]. Here, the reference field is dynamically phase shifted with respect to the object field. Therefore, the recorded hologram is time modulated, thus enabling phase-shifted interferometric measurements [START_REF] Atlan | Accurate phase-shifting digital interferometry[END_REF]. Moreover, this data acquisition scheme as been demonstrated to be shot-noise limited [START_REF] Verpillat | Digital holography at shot noise level[END_REF][START_REF] Lesaffre | Noise and signal scaling factors in digital holography in weak illumination: relationship with shot noise[END_REF]. Temporal modulation feature of digital heterodyne holography can also be used to investigate dynamic phenomena, and being considered as a laser Doppler imaging technique [START_REF] Atlan | Laser doppler imaging, revisited[END_REF]. The ability of heterodyne digital holography to perform Doppler imaging has been demonstrated in various domains such as microfluidics [START_REF] Atlan | Laser doppler imaging of microflow[END_REF], vibration motion characterization [START_REF] Verpillat | Imaging velocities of a vibrating object by stroboscopic sideband holography[END_REF][START_REF] Verrier | Absolute measurement of small-amplitude vibrations by time-averaged heterodyne holography with a dual local oscillator[END_REF][START_REF] Verrier | Phase-resolved heterodyne holographic vibrometry with a strobe local oscillator[END_REF], in vivo vasculature assessment, without contrast agent [START_REF] Atlan | Frequency-domain wide-field laser doppler in vivo imaging[END_REF][START_REF] Atlan | Cortical blood flow assessment with frequency-domain laser doppler microscopy[END_REF][START_REF] Simonutti | Holographic laser doppler ophthalmoscopy[END_REF] and motion of biological objects [START_REF] Fang-Yen | Imaging voltagedependent cell motions with heterodyne mach-zehnder phase microscopy[END_REF][START_REF] Iwai | Doppler-spectrally encoded imaging of translational ob-jects[END_REF][START_REF] Joseph | A heterodyne mach-zehnder interferometer employing static and dynamic phase demodulation techniques for live-cell imaging[END_REF].

In this paper, we combine laser Doppler holography [START_REF] Atlan | Laser doppler imaging, revisited[END_REF] and transmission microscopy to analyze blood flow in fish embryos. We have adapted a laser Doppler holographic setup to a standard bio-microscope by carrying the two beams of the holographic interferometer (illumination of the object and reference), whose frequency offset is controlled, by optical fibers. Multimodal acquisition and analysis of the data is made by acting on the frequency offset of the two beams, and on the location of the Fourier space filtered zone. With the same set of data, we have imaged, with amplitude contrast, the whole fish embryo, or only the moving blood vessels. In that last case, we have obtained images where the flow direction is coded in RGB color. For large vessels, the dependance of the holographic signal with the frequency offset yields the Doppler frequency shift, and thus the flow velocity. For small vessels, individual Red Blood Cells (RBC) can be imaged, and movies showing the RBC motion are obtained. Our off-axis digital holography set-up is a Mach-Zehnder interferometer in which the recombining cube beam splitter is angularly tilted. To fit our set-up into regular upright microscope, the interferometer is split into an injection (a) and a recombination (b) part, which are connected together with optical fibers (Fig. 1).

Materials

Heterodyne holographic microscopy setup

The injection part (Fig. 1(a)) is mounted on a separate breadboard, and is used to build both object illumination (field E I ) and reference (or local oscillator (LO) E LO ) beams. Laser light is provided by a 785 nm, 80 mW Sanyo® DL7140-201S continuous mono-mode laser diode (angular frequency ω I ). Laser beam is split by a polarizing beam splitter (PBS), which in combination with the first half wave plate (HWP) allows to adjust the optical power in both reference and object arms of the interferometer. To enable phase shifting interferometry and frequency scanning of the holographic detection frequency, we control the frequency ω LO of the reference beam by using the heterodyne holography method [START_REF] Le Clerc | Numerical heterodyne holography with two-dimensional photodetector arrays[END_REF]. The reference arm is thus frequency shifted by using two acousto-optic modulators AOM1 and AOM2 (80 MHz AA electronics®), operating at ω 1 and ω 2 respectively, so that ω LO = ω I + ∆ω with ∆ω = ω 2 -ω 1 . Reference and object fields are finally injected into two mono-mode optical fibers (Thorlabs® P1-780A-FC-2 fiber patch).

Both reference (E LO ) and object illumination (E I ) fibers are brought to an upright microscope (Olympus® CX41) working in transmission configuration (Fig. 1(b)). The object is imaged by an Olympus DPlan microscope objective (MO: NA= 0.25, G=10, corrected at 160 mm). The illumination field (E I ) is scattered by the studied living object (the zebrafish embryo) yielding the object signal field (E). Signal (E) and reference field (E LO ) are combined together by a cube beam splitter (BS) that is angularly tilted thus introducing an off-axis angle in the interferometric arrangement. Interferences (i.e. E + e j∆ωt E LO ) between both fields are recorded on a 1360×1024 pixel (6.45 µm square pitch) 12-bits CCD camera (Jenoptik ProgRes MF®) operating at a framerate of ω S /(2π) ≤ 10 Hz. Recorded data are cropped to 1024 × 1024 and FFT (Fast Fourier Transform) are made on a 1024 × 1024 calculation grid. The CCD to MO distance is such that the effective MO enlargement factor is G ′ = 10.4 (instead of G = 10). In order to perfectly control the phase and frequency of the E LO reference beam, the CCD camera is triggered at frequency ω CCD , and the ω 1 , ω 2 and ω CCD signals are generated by digital synthesizers driven by a common 10 MHz clock.

Zebrafish (Danio rerio, wild type AB line) were maintained according to standard protocols [START_REF] Westerfield | The Zebrafish Book: a Guide for the Laboratory use of Zebrafish (Danio rerio)[END_REF]. Larvae were mounted on a standard glass slide under a 22 mm 1.5 round coverslip with a 0.5 mm thick caoutchouc ring as a spacer and sealant. They were embeded in a drop of cooling 1.5% low melting point agarose at 37 • C and oriented before gelation. The chamber was filled with 100 mg/l tricaine in filtered tank water and imaging was performed at room temperature. Blood vessels nomenclature is according to [START_REF] Isogai | The vascular anatomy of the developing zebrafish: an atlas of embryonic and early larval development[END_REF]. Due to motions within the sample (mainly the RBC motion within the embryo vasculature), the incident field E I (of wave vector k I ) that is scattered to wave vector k S (yielding E S ) undergoes a Doppler shift

Laser Doppler holography mode

ω S -ω I = q .v (1)
where v is the velocity of the scatterer and q = k Sk I the scattering vector (see Fig. 2(a)) and q.v the inner product of vectors q and v. As detection is made for all wave vectors k S within the MO collection cone, the frequency spectrum of the moving scatterers signal is broadened. One then gets two components: a sharp narrow peak from the photons that are not scattered (ballistic photons) or scattered by objects that do not move, and a broad pedestal from the photons that are scattered by moving objects and that are collected by MO. The width of the pedestal is proportional to the MO numerical aperture NA since |q| ∼ NA|k I |. With NA = 0.25, the Doppler broadening we observe here is much smaller (10 to 100 Hz) than the one (100 to 1000 Hz) observed in previous in vivo Doppler holographic experiments made in reflection configuration [START_REF] Simonutti | Holographic laser doppler ophthalmoscopy[END_REF][START_REF] Atlan | Frequency-domain wide-field laser doppler in vivo imaging[END_REF][START_REF] Atlan | Cortical blood flow assessment with frequency-domain laser doppler microscopy[END_REF][START_REF] Atlan | High-speed wave-mixing laser doppler imaging in vivo[END_REF], where |q| ∼ 2|k I |. Since our camera operates at ω S /(2π) = 10 Hz, the bandwidth of our holographic detection (±5 Hz around ω LO in not enough to acquire the moving scatterer Doppler signal. As in previous works, the frequency ω LO = ω I + ∆ω (with ∆ω = ω 1 -ω 2 ) is swept in order to acquire the whole Doppler signal and to analyze its spectrum.

Experimental results

Spatial filtering and reconstruction.

The reconstruction procedure is similar to the one used in previous works [START_REF] Warnasooriya | Imaging gold nanoparticles in living cell environments using heterodyne digital holographic microscopy[END_REF][START_REF] Verpillat | Dark-field digital holographic microscopy for 3d-tracking of gold nanoparticles[END_REF]. To illustrate reconstruction, let us consider 4 phase detection of the ballistic peak signal (no Doppler shift). We have thus adjusted ω 1 and ω 2 to have ∆ω = ω CCD /4, and calculated the demodulated hologram by:

H(x, y) = [I 0 (x, y) -I 2 (x, y)] + j [I 1 (x, y) -I 3 (x, y)] (2)
Figure 3(a) shows the holographic signal |H(x, y)| 2 displayed in log scale. To select the +1 holographic grating order by the Cuche et al. method [START_REF] Cuche | Spatial filtering for zero-order and twin-image elimination in digital off-axis holography[END_REF], we have performed the holographic reconstruction of the MO pupil by the Schnars et al. method [START_REF] Schnars | Direct recording of holograms by a ccd target and numerical reconstruction[END_REF] yielding H 1 (k x , k y ) with:

H 1 (k x , k y ) = FFT H(x, y) e j|k|(x 2 +y 2 )/2d ( 3
)
where FFT is the Fast Fourier transform operator, and e j|k|(x 2 +y 2 )/2d the phase factor that makes the pupil image sharp (see Fig. 3(b)). For a plane wave reference, the parameter d is equal to the MO pupil to CCD camera distance. Optimal spatial filtering is then made by cropping the MO pupil disk on its sharp circular edge, and by moving the cropped zone in the center of the Fourier space (see Fig. 3(c)) yielding H 2 (k x , k y ). The reconstructed hologram H 3 (x, y, z) is then calculated by the angular spectrum method that involves 2 FFT from FFT -1 [H 2 (k x , k y )]. We have thus:

H 3 (x, y, z) = FFT -1 H 2 (k x , k y ) e j(k 2 x +k 2 y )/2z (4)
where e j(k 2

x +k 2 y )/2z is the phase factor that describe the propagation of the field from the CCD plane z = 0 to the location z of the zebrafish image (via MO). In most cases, the embryo is in focus on the camera, and z = 0. Here, the selection of the +1 grating order is made by the crop, the compensation of the MO phase curvature by the e j|k|(x 2 +y 2 )/2d phase factor, and the compensation of the off axis tilt by the translation of the cropped zone.

We have calculated the so called instantaneous intensity signal The images show a side view of the zebrafish embryo. Due to the use of coherent light illumination, the image exhibits some speckle noise but anatomical details such as the notochord, somite boundaries and pigment cells are distinguished. In the corresponding movie Media 1, motion of blood can be barely seen in the caudal artery and vein but none is observe in the smaller capillaries.

Holographic Doppler images of the moving scatterers.

To select the moving scatterer signal that corresponds to the Doppler pedestal, we have swept the detection frequency shift ∆ω by step ω CCD , and calculated 2 phase holograms from the recorded data. We have thus:

∆ω = ω LO -ω I = mω CCD (5) H(x, y) = I 0 (x, y) -I 1 (x, y)
where m is integer. Note that H(x, y) is defined by Eq. 2 for 4 phase holograms, and by Eq. 5 for 2 phase holograms. We have kept the same notation (i.e. H(x, y)), because the reconstruction equations Eq. 3 and Eq. 4 are the same in both cases. We have calculated the 2 phase holographic detection efficiency (i.e. η for the field and |η| 2 for the intensity) as a function of the frequency ω S of the scattered field. This calculation is similar to the one done in previous works [START_REF] Atlan | Accurate phase-shifting digital interferometry[END_REF][START_REF] Verpillat | Digital holography at shot noise level[END_REF]. We get:

η(x) = 1 2T exp 1 ∑ k=0 (-1) k kT CCD +T exp /2 t=kT CCD -T exp /2 e j2πxt dt (6) = 1 2 sinc(πxT exp ) 1 -e j2πxT CCD
where T CCD = 2π/ω CCD is the frame time interval, and x = (ω S -ω LO )/2π the LO versus signal frequency offset. The efficiency η 2 is plotted on Fig. 4. As seen, the 2 phase detection selects scattered field components with x close to zero (i.e. with ω S ≃ ω LO ). Moreover, since |η| 2 is null for x = -20, -10, 0, 10, 20... Hz, the holographic detection efficiency |η| 2 remains null at the illumination frequency ω I , whatever the frequency shift ∆ω = mω CCD is. The ballistic peak (whose frequency is ω I ), which is much bigger than the Doppler pedestal, is thus not seen during the sweep. Figure 5 shows the Doppler average reconstructed holograms |H 3 (x, y)| 2 obtained with frequency shifts ∆ω/(2π) varying from 0 Hz (a) to 80 Hz (i) by step of 10 Hz. The recorded hologram H(x, y), and the reconstructed intensity hologram |H 3 (x, y)| 2 are calculated from successive sequence of 2 frames (I n and I n+1 ) within the sequence of N = 32 frames (with N = 0 to 30), the displayed signal |H 3 (x, y)| 2 corresponding to the average of |H 3 (x, y)| 2 over n. Since the ballistic peak is not seen, the contrast of the Fig. 5 images is reversed with respect to Fig. 3 (d), and vessels where blood flows are therefore seen in white on a black background. In image (a) caudal vein (A) and caudal artery (B,C) are seen as well as intersegmental vessels (D, E) and dorsal longitudinal anastomotic vessels. An abnormal shunt between caudal artery and vein in seen near arrow (C).

The reconstructed images (a) to (i) are displayed with the same Log scale for the average intensity |H 3 | 2 . One thus clearly see the decrease of the holographic signal with the frequency shift (ω LO -ω I )/(2π) that is expected. Figure 6 analyzes this decreases for the zones of the reconstructed image marked by arrows (A) to (F) in Fig. 5(a). All curves are calculated by applying on the holographic signal |H 3 | 2 a gaussian low pass filter (of 10 pixels width for curves A,B,C and F curves, and 4 pixels width for curves D and E), and by summing the filtered holographic signal over 8 × 8 pixels. On curve (A), which corresponds to the flow in caudal vein, the holographic signal decreases regularly with the frequency offset ∆ω. The same occurs in (B) and (C), but the decrease is slower showing faster velocities for the blood cells in the caudal artery.

In intersegmental vessels (curves D and E), the signal |H 3 | 2 is much lower than the one of larger artery and vein. The corresponding frequency spectrum (Fig. 6D andE) exhibit a decrease of the signal at ∆ω/(2π) = 40 and 80 Hz offset followed by an increase at 60 and 100 Hz. This might be related to the instrumental response of our holographic detection [START_REF] Atlan | Accurate phase-shifting digital interferometry[END_REF]. A fine analysis shows that the signal fluctuates a lot within each sequence of N frames, and from one sequence to the next, since the flowing blood cells can be visualized individually on the instantaneous intensity signal The RBCs individual motion in intersegmental vessels is clearly seen on Media 2 and Media 3. These two movies are very similar to those seen in reference [START_REF] Gao | In vivo imaging and quantitative analysis of zebrafish embryos by digital holographic microscopy[END_REF]. They can be used to measure the RBC velocity by Particule Image Velocimetry (PIV). The holographic experiment made in transmission configuration gives here a Doppler signal corresponding to single scattering events like in Dynamic Light Scattering (DLS) experiments. The Doppler shift is thus simply q.v where q = k Sk I . The illumination (or incident) wave vector k I is fixed by the geometry of the experimental setup. In transmission geometry, k I is parallel to u z (where u x , u y and u z are the unit vectors in the x, y and z directions). On the other hand, k S = (k x , k y , k z ) with |k S | = 2π/λ is measured by our holographic experiment. In the reconstruction procedure, the cropped and translated zone seen on Fig. 3(c It is then possible to select k S by spatial filtering in the Fourier space, and to reconstruct images corresponding to given intervals of k S . To illustrate this idea, we have selected three k S zones covering half of the Fourier space. These zones are oriented toward u ϕ=0 , u ϕ=2π/3 and u ϕ=4π/3 with u ϕ = cosϕ u x + sin ϕ u y . With the holographic signal H 2 (k x , k y ) of each zone, we have reconstructed a Red, Green or Blue colored image |H 3 (x, y, z)| 2 , and we have combined these three images to get RGB images sensitive to the direction of k S (and thus to the direction of q and v). One must notice here, that the wave vector of ballistic light remains parallel to u z yielding a bright peak near the center of the Fourier space (k x , k y ≃ 0). Although most of the ballistic light is removed in 2 phase holograms recorded without frequency offset, this peak still remains visible in that case as seen on Fig. 7(a). To fully eliminate the ballistic light, the center of the Fourier space (i.e. k x , k y ≃ 0) has thus been removed from the selected zones as shown on Figure 7(b) and (c). Figure 8(a) to (g) shows the RGB colored reconstructed image of the zebrafish sample obtained with the holographic data of Fig. 5(a) to (g). Without frequency offset (Fig. 8(a) with ∆ω = 0), the RGB colored reconstructed image is very similar to the black and white one (Fig. 5(a)), but with lower resolution, since half of the Fourier space information is used in the reconstruction. The images of Fig. 8 are obtained from a sequence of 32 images (i.e. with an acquisition time of 3.2 s). The reconstruction is made on GPU in less than one second for the 32 images. Since the detection shift ∆ω is null, the detection efficiency does not depend on the sign of the Doppler shift of the signal ω S -ω I . Detection is not sensitive to the sign of q.v, nor to the v direction (even if q direction is selected in the Fourier space). The colors in the reconstructed image of Fig. 8(a) are thus the same whatever the motion direction is. With increasing frequency shifts ∆ω, signal decreases but colors change, depending on the flow direction. On figure 8(d), with ∆ω = 30 Hz, caudal artery appears in cyan, while caudal vein, where blood flows in opposite direction, is seen in orange. The flow direction corresponds here to the Fig. 8 color wheel. This wheel corresponds to the colored image of the Fourier space filtered signal |H 2 (k x , k y )| 2 of Fig. 7(d) rotated by 180 • .

RGB holographic Doppler images yielding direction of motion.

To verify that the RGB colored images give a realistic information on the direction of the velocity v, we have recorded, with another embryo, holograms for both sign of the frequency offset ∆ω. Figure 8(h) and (i) shows the reconstructed RGB images obtained for ∆ω/(2π) = ±20 Hz. Here again, the colors of the reconstructed image depend on the flow direction, but the color coding is reversed for negative frequency offsets: ∆ω < 0. The correspondence of the motion direction with the color wheel is only valid for positive shifts ∆ω > 0.

Conclusion

In this paper, we have shown that an upright commercial bio-microscope can be transformed into a powerful holographic setup, by coupling the microscope to an heterodyne holographic [START_REF] Le Clerc | Numerical heterodyne holography with two-dimensional photodetector arrays[END_REF] breadboard with optical fibers. By controlling the frequency offset ∆ω of the reference beam, and by using different combinations of frames to calculate the hologram H, we have imaged a living zebrafish embryo under different modalities. With ∆ω = 0 and H = (I 0 -I 2 ) + j(I 1 -I 3 ), we have calculated the amplitude and the phase of the transmitted light. Although the phase can be qualitatively explored, we have not displayed phase images because the phase variation is too fast (the thickness of the embryo is hundreds of microns).

With ∆ω = mω CCD (where m = 0 is integer) and H = (I 0 -I 1 ), we have selected the signal whose Doppler shift ω S -ω I is close to ∆ω according to Eq. 4 and Fig. 4) and imaged the blood flow. With ∆ω = 0 and H = (I 0 -I 1 ), we have visualized individual moving bloods cells in intersegmental vessels, getting movies that show their instantaneous motion.

Since the scattering is moderate like in DLS (Dynamic Light Scattering) experiment, the Doppler shift is directly related to the scatterers (i.e. blood cells) velocity v by ω S -ω I = q.v with q = k Sk I . Since k I u z is known, and since k S can be selected in the Fourier space, the scatterers velocity v can be measured quantitatively by a proper choice of both the frequency offset ∆ω and the Fourier space selected zone. To illustrate one of the numerous possibilities of Doppler holography in transmission, we have imaged the blood cell motion direction in RGB colors.

In the present paper, we have not used the possibilities for numerical refocusing to image different z layers of our sample. This could be useful, since all blood vessels are not in the same z plane. For instance, in Fig. 5 and Fig. 8(a)-8(g), the caudal artery is roughly on focus, while the caudal vein is out of focus by about 100 µm. Refocusing could thus be used to reconstruct the embryo vascular system in 3D.

We intend to further improve the method by using a faster camera (to better analyze the motion of individual blood cells) and a higher numerical aperture objective (for better optical sectioning).

Fig. 1 .

 1 Fig. 1. Heterodyne digital holographic microscopy experimental arrangement (a) Injection part of the interferometer. HWP: half wave plate; PBS: polarizing beam splitter; AOM1, AOM2: acousto optic modulators (Bragg cells). (b) Classical upright microscope used for the off-axis recombinaison of reference and object beams. BS: cube beam splitter; CCD: CCD camera.

Fig. 2 .

 2 Fig. 2. Detection of zebrafish embryo blood flow in transmission geometry. (a) Illustration of the spectral broadening of light encountering moving scattering objects (here, red blood cells). (b) Principles of the spectral measurement by heterodyne digital holography.

Fig. 3 .

 3 Fig. 3. Spatial filtering and reconstruction principle. Holograms H(x, y) (a), H 1 (k x , k y ) (b), H 2 (k x , k y ) (c) and H 3 (x, y, z = 0) (d): see Media 1. The display is made in arbitrary Log scale for the average intensity |H X | 2 . This average is calculated made by making the reconstruction with I 0 ..I 3 , with I 1 ..I 4 ... and with I 28 ..I 31 , and by averaging the resulting |H X | 2 . Images (a) and (d) show a side view of a 6 days old zebrafish embryo. Ventral side in on the right and anterior is up.

|H 3 |

 3 2 by using data of successive sequences of 4 frames, i.e. by calculating |H 3 | 2 with I 0 ..I 3 , then with I 1 ..I 4 ... and to the end with I 28 ..I 31 ). The movie of the instantaneous intensity signal |H 3 | 2 (see Media 1) shows that the time varying components of |H 3 (t)| 2 are extremely low. We have then averaged |H 3 (t)| 2 over the sequence of n frames, getting |H 3 | 2 that is displayed on Fig. 3(d).

Fig. 4 .

 4 Fig. 4. Two phase detection efficiency |η| 2 as a function of the LO versus signal frequency offset: x. Calculation is made by Eq.6 with T CCD = 100 ms and T exp = 50 ms.

Fig. 5 .

 5 Fig. 5. Reconstructed hologram H 3 (x, y, z = 0) made for (ω LO -ω I )/(2π) = 0 Hz (a): see also Media 2, 10 Hz (b) ... to 80 Hz (i). Images (a) to (i) are displayed with the same Log scale for the average intensity |H 3 | 2 . The sample is the same as the one in Fig. 3.

Fig. 6 .

 6 Fig. 6. Dependance of the Doppler holographic signal |H 3 (x, y)| 2 with the frequency offset (ω LO -ω I )/(2π) for different location A to F of the reconstructed image of Fig. 3(a). Curves are drawn with linear (a) and logarithmic (b) scales.

  |H 3 (t)| 2 reconstructed with successive sequence of 2 frames. Movie Media 2 shows |H 3 (t)| 2 for the sequence of N = 32 frames recorded at 0 Hz (i.e. without frequency offset) that has been used to display |H 3 | 2 on Fig. 5(a). Movie Media 3 shows |H 3 (t)| 2 for a sequence of N = 96 frames that image the embryo shown in Fig. 8(h) and (i).

Fig. 7 .

 7 Fig. 7. Fourier space reconstructed hologram H 2 (k x , k y ) made without (a) and with (b,c) selection of the scattered wave vector k S . In (b) the selected zone is oriented toward u ϕ=0 . In (c), three zones oriented along u ϕ with ϕ = 0 (blue), 2π/3 (green) and 4π/3 (red) are selected. Display is made in arbitrary log scale for |H 2 | 2 . Frequency shift is (ω LO -ω I ) = 0 .

  ) and on Fig 7(a) is a map of the holographic signal as a function of k x and k y .

Figure 7 (

 7 b) shows the |H 2 (k x , k y )| 2 signal, filtered by the ϕ = 0 spatial filter, which corresponds to the blue image.

Figure 7 (

 7 c) shows the Fourier space RGB image of the |H 2 (k x , k y )| 2 signal obtained by combining the three colored images corresponding to the ϕ = 0, ϕ = 2π/3 and ϕ = 4π/3 filters.

Fig. 8 .

 8 Fig. 8. Colored reconstructed hologram H 3 (x, y, z = 0) made for (ω LO -ω I )/(2π) = 0 Hz (a), 10 Hz (b) ... to 60 Hz (g), and for -20 Hz (h) and + 20 Hz (i). Images (a) to (g) are made with same zebrafish sample and same viewpoint as Fig. 3 and Fig. 5. Images (h) to (i) correspond to another fish embryo. Images (a) to (g) (and (h) and (i)) are displayed with the same color RGB Log scale for the average intensity |H 3 | 2 . Media 3 corresponds to images (h) and (i).

Acknowledgments

We acknowledge OSEO-ISI Datadiag grant and ANR Blanc Simi 10 (n • 11 BS10 015 02) grant for funding, and Rémy Vialla for technical support.


Hayssam S O U E I D A N

V Fabienne W O N G J U N Ta I

Macha N I K O L S K I

Efficient mapping of short peptides on whole proteome database for biomarker discovery

Keywords: mapping, string matching, peptide, phage display

In vivo phage display can be used to simultaneously screen peptide repertoires for peptides presenting specificity for certain interaction and recognition sites, and thus enable biomarker identification. In this work we assume the hypothesis that certain small peptides mimic physiological interactions of proteins that contain a sub-sequence similar to these peptides. A possible solution then involves mapping of the peptide repertoire against the proteome of interest, which is computationally challenging. We formulate this problem as simultaneous matching of multiple patterns against multiple strings and propose an algorithmically efficient solution.

Introduction

The aim of this work is to streamline the biomarker discovery based on the hypothesis of mimed proteins in the context of selection of phage displayed peptides. Phage display is an in vitro or in vivo technique used to identify relevant protein interaction and recognition sites, first described in 1985 by Smith [START_REF] Smith | Filamentous fusion phage : novel expression vectors that display cloned antigens on the virion surface[END_REF] ; it was later shown that antibody fragments could be successfully displayed on phage [START_REF] Wacker | Structural Features for Functional Selectivity at Serotonin Receptors[END_REF]. The technique is based on the insertion of DNA fragments into bacteriophage genes to create fusion proteins with the foreign sequence in the middle. Viral particles contain the encoding DNA and display the encoded peptide on the surface of their capsides. Combinatorial libraries of peptides can be produced with complexities of 10 9 and screened to isolate peptides that bind to biological samples ranging from purified macromolecules to in vivo pathological tissues.

In vivo screening, with targets on endothelial cells or on tissues where the accessibility is the product of the pathological condition (e.g. tumoral cells), produces large repertoires of peptides for which the use of NGS technologies made possible a global overview. A typical setup for biomarker discovery study is the differential analysis of two repertoires corresponding to two different conditions (say, healthy vs. pathological).

Previous studies for screening of peptide libraries for organ-specific binding [START_REF] Pasqualini | Organ targeting in vivo using phage display peptide libraries[END_REF] studied sequence composition and similarity in this context. Arap et al. has shown that the distribution of the ligand-receptor pairs is nonrandom regarding organ specificity [START_REF] Arap | Steps toward mapping the human vasculature by phage display[END_REF]. However, in order to prevent the problem related to the sparce count of the 20 7 possible 7-mers, they were broken into 3-mers. The work of Kolonin [START_REF] Kolonin | Synchronous selection of homing peptides for multiple tissues by in vivo phage display[END_REF] is based on the presence of those 3-mers inside the candidate peptide-bound receptors, which identifies these targeted receptors and sites of ligands involved in receptor interaction.

In this paper we assume the working hypothesis that certain peptides mimic physiological interactions of proteins that contain a sub-sequence similar to these peptides. However, sequence similarity of peptides with a protein is a weak signal. Fine-tuned and efficient mapping of the complete peptides against the proteome of interest and an appropriate scoring function are thus the central points of our solution. In this manuscript we mainly focus on the mapping step.

The underlying assumption of our work is that small peptides mimic molecular interactions of larger proteins. This assumption is based on a number of observations :

-Proteins containing similar sub-sequences tend to themselves be homologous ; -These sub-sequences align at the same locations where homologous proteins align among themselves ; -These locations are strongly preserved by the evolutionary process (and are mostly located within functional domains) ; Moreover, a recent study [START_REF] London | Can Self-Inhibitory Peptides be Derived from the Interfaces of Globular Protein-Protein Interactions ?[END_REF] shows that most of the energy in proteins' interactions is located in short linear segments, and most of these segments bind independently of their context, which further supports our working hypothesis.

Given a peptide repertoire R = {r} where all peptides r have the same size s ∈ [START_REF] London | Can Self-Inhibitory Peptides be Derived from the Interfaces of Globular Protein-Protein Interactions ?[END_REF][START_REF] Smith | Identification of common molecular subsequences[END_REF] and proteome P = {p}, each peptide r is mapped against P , which produces a set of mapping locations L r . This mapping is restricted to an ungapped alignment up to a certain similarity score threshold t. Once the peptides are mapped on the proteins, each peptide r is scored by integrating its mapping scores for all locations L r combined with the scores of other peptides over the same L r . Intuitively, it singles out those peptides that participate in those locations that are mapped by many other peptides. Consequently, the scoring function is highly sensitive to the detection of the complete set of peptides that map at a certain location L r . This is why it is essential for a given peptide to uncover all the mappings over the given threshold t.

Pipeline

Our solution is implemented as a pipeline with three major steps (see figure Fig. 1 here below). 2. Given this repertoire and a subject database, each peptide is mapped on each protein of the database.

Given the list of mappings, a scoring function sorts the peptides.

In this manuscript we concentrate on the computationally challenging step : mapping of the peptide repertoire against the proteome. We formulate this problem as simultaneous matching of multiple patterns against multiple strings and propose an algorithmically efficient solution.

State of the art

The central computational problem concerns mapping of R over P , which is known as the string matching problem. There exists a number of well-known algorithms for string matching 1 . They can be classified in two categories : exact and fuzzy matching.

1. In this section we only quote seminal works and citations are in no way exhaustive.

Exact matching can itself be subdivided in two major algorithmic classes.

-Matching a simple pattern against a single string. These algorithms are of limited interest for our problem since we need to match multiple patterns against multiple strings. However, they provide a complexity reference point where we would match each peptide one by one against each protein. Classical examples are Boyer-Moore [START_REF] Boyer | A fast string searching algorithm[END_REF] and the text-partitioning matching [START_REF] Kim | A new string-pattern matching algorithm using partitioning and hashing efficiently[END_REF]. -Matching multiple patterns against a single string.

These algorithms make it possible to map R (our multiples patterns) against the proteins of the proteome one by one. A classical example of this class of algorithms is the Aho-Corasick [START_REF] Aho | Efficient string matching : an aid to bibliographic search[END_REF]. Fuzzy matching approaches can also be classified in two major classes, both relying on the notion of metric space.

-Approximate matching These algorithms use the metric space to find the set of similar words. A well-known example of the underlying distance measure is the Damerau-Levenshtein distance [START_REF] Damerau | A technique for computer detection and correction of spelling errors[END_REF] used in many spell-checkers. -Sequence alignment These algorithms are particularly widespread in bioinformatics. Indeed, in this context, character mismatch or insertion/deletion are often seen as mutation points in the evolutionary process. Metric space usually relies on a substitution score matrix rather than on a fixed score in the case of mismatch. Classical examples are Smith-Waterman [START_REF] Smith | Identification of common molecular subsequences[END_REF] and BLAST [START_REF] Altschul | Basic local alignment search tool[END_REF] for local alignment and Needleman-Wunch [START_REF] Needleman | A general method applicable to the search for similarities in the amino acid sequence of two proteins[END_REF] for global alignment. On one hand, our application case requires fuzzy matching, since we are looking for similarity between peptides and protein sequences. Moreover, we rely on a substitution matrix for sequence similarity. On the other hand, this is not a classical fuzzy matching problem since we are interested in the ungapped alignments. It is also important to obtain all the positions where peptides match on the proteins. Consequently, neither probabilistic (e.g, BLAST) nor best-match (e.g, Needleman-Wunsch) approaches can be used.

Mapping

First we preprocess the proteome P = {p}. Since we are interested in the ungapped alignments, this can be seen as fragmenting each p by a sliding window of size s, which gives us F = {f }, where f are proteic sub-sequences, that we call fragments, of size s. The problem can be now seen as matching R against F . However, this would be computationally inefficient.

To overcome this problem, we encode P in a compact way by constructing the keyword tree [START_REF] Gusfield | Algorithms on Strings, Trees and Sequences : Computer Science and Computational Biology[END_REF] S of F . Information on the positions L f of each fragment and the proteins where it belongs is stored in the leaves of the tree. Another keyword tree Q is constructed for the repertoire R. To be efficient, the construction of S involves the intermediate construction of a suffix tree (over a finite alphabet, see [START_REF] Ukkonen | On-line construction of suffix trees[END_REF]) where only the prefixes of size s of each suffix are kept.

Given a keyword tree Q (S, respectively), we denote by Q n (S n , respectively) any node of this tree. Each node contains a letter, node map that represents a tree edge. Given a node Q n and a letter l, Q n [l] denotes following the corresponding edge and reaching the child of Q n ; S n .data denotes the protein, position set map.

The problem can then be formulated as mapping the two keyword trees one against another. The general matching scheme is presented in the algorithm 1 here below. This algorithm can be trivially used to perform exact matching by replacing the scoring function by an equality comparison between l 1 and l 2 . The thresholding function then becomes a placeholder present only to check the validity of the boolean score.

Similarity score

Since our mapping is ungapped, in order to compute the similarity between a peptide r and a fragment f , it is sufficient to compute the letter-wise substitution cost based on a substitution matrix M , namely :

Algorithm 1 Recursive mapping of Q onto S function M A P F U N C T I O N(Q n , S n ,
score r/f = 2 lr∈r,l f ∈f M (l r , l f ) lr∈r M (l r , l r ) l f ∈f M (l f , l f )
.

Using this formula, similarity of two exact same words is 1.0 and the similarity score drops with each substitution involved. Algorithm 1 is recursive, consequently, both similarity score computation and the thresholding have to respect the recursivity.

-For the similarity this implies to maintain through the recursive call both the numerator and the denominator independently. And it is within the thresholding function that the fraction is computed. -For the thresholding this implies that the threshold value has to be defined as function of the number of letters that have been processed, which means that it is different for each tree depth. Were this computation done naively, it would require to check for the threshold only when all of the letters have been processed. Indeed, the first processed letters may drop the score below the threshold even if the similarity score can increase after that. In the recursive solution we can compute at each tree depth, given the word size s and the maximal value in the substitution matrix max(M ), the maximal similarity score with respect to the letters that have already been processed.

Resulting functions can be seen in the algorithm 2.

Figure 1 .

 1 Figure 1. Peptides scoring pipeline

Algorithm 2

 2 Recursive scoring and thresholdingfunction S I M I L A R I T Y F U N C T I O N(l 1 , l 2 , score : (num, den)) n ← 2M (l 1 , l 2 ) d ← M (l 1 , l 1 ) + M (l 2 , l 2 ) return pair (num + n, den + d) end function function T H R E S H O L D I N G(score : (num, den), depth) k ← 2(s -depth -1) max(M ) return (num + k)/(den + k) > t end function

  word, score, depth = 0) W ← empty set of word, data pairs for each letterl 1 ∈ Q n do for each letter l 2 ∈ S n do new score ← S I M I L A R I T Y F U N C T I O N(l 1 , l 2 , score) if T H R E S H O L D I N G(new score, depth) then new word ← C O N C AT(word, l 1 ) if Q n is a leaf node then ⊲ Sn is necessarily a leaf too add (new word, Sn.data) pair to W else W ← W ∪ M A P F U N C T I O N(Q n [l 1 ], S n [l 2 ], new word, new score, depth + 1)

	end if
	end if
	end for
	end for
	return W
	end function


Vladimer Kobayashi

Pierre Maret

Fabrice Muhlenbach
email: fabrice.muhlenbach@univ-st-etienne.fr

Pierre-René Lhérisson

Integration and Evolution of Data Mining Models in Ubiquitous Health Telemonitoring Systems

Keywords: Ubiquitous systems, telemonitoring, eHealth, data mining models

Ubiquitous Health Telemonitoring Systems collect low level data with the aim to ameliorate the health condition of patients. Models from data mining are created to compute indicators regarding their status and activity (habits, abnormalities). Models can also help generate feedbacks and recommendations for patients as well as for remote formal and informal care givers. Essential features are that the models can be easily updated whenever new information is available and that data generated from the models can be readily accessible as well as sensed data. This paper addresses the challenge of conveniently incorporating in a Ubiquitous Health Telemonitoring System the creation, the use, and the updating of data mining models. We conducted first runs and generated results showing the feasibility as well as the effectiveness of the system.

Introduction

Healthcare provides a rich domain for the application of ubiquitous computing [START_REF] Kim | Ubiquitous healthcare: Technology and service[END_REF]. We used the term Ubiquitous Health Telemonitoring System (UHTS) to encapsulate the conglomeration of various technologies and techniques that facilitate human health monitoring at a distance. Technologies and techniques inconspicuously work together to give patients freedom in mobility, thereby maintaining their independent living. A quick survey of literature would reveal that a significant number of UHTSs have already been implemented. At their core, health telemonitoring systems are expected to accomplish two basic tasks, i.e. able to continuously collect data from patients wherever they are, and allow communication between patient and medical staff at a distance.

We can distinguish existing UHTSs as to how they handle and process the data they collect. It is worth noting that many systems only use, if they use at all, low level data processing techniques. Data sensed from patients are transmitted and screened and selected data are stored in static and centralized repositories and sporadically accessed by the concerned individuals. There are efforts to incorporate higher level analytics to the stored data [START_REF] Viswanathan | Data mining in ubiquitous healthcare[END_REF] but there is no straightforward solution as to how the results in the form of knowledge models (obtained from applying higher level analytics such as data mining techniques) are integrated back to the system and how these knowledge models could be evolved in the presence of new data. In retrospect existing systems lack an important layer that is altogether able to develop, incorporate, and evolve models as well as make the results accessible to various stakeholders in a manner that is relevant, timely, and unrestricted by location. Our belief is that any system that collects data must also make use of the data to improve the operations of the system and subsequently would lead to the amelioration of the condition of the main target user. In the case of UHTS the main users are the patients to which we aim to improve or maintain their health condition. The motivation is to create models that can compute indicators regarding the status and activity of patients. Moreover the indicators constitute different levels of information (from detailed to coarse-grained) that will also be used either to generate automatic suited feedbacks (to patients or to care givers). An essential feature is that the models can be conveniently updated whenever new information or new scenarios are available. The challenge is for the entire process of creating, using, and updating models should be efficiently incorporated in the ubiquitous telemonitoring system and, to generate information available to the right stakeholders. In this paper we offered a solution to the challenge through the development of an additional component that permitted the associated tasks.

Features of Ubiquitous Health Telemonitoring System

The primary users of a UHTS are the patient and the medical practitioner, usually a physician. We can include more users as we add tasks and features in the system. The features of UHTS are enumerated next. 5. Integration of models to generate higher level information from data. 6. Storing of the higher level information as health data. 7. Automatic recommendations and feedback to stakeholders (patient, etc.).

Requirements for Knowledge-Enriched Ubiquitous Health Telemonitoring System

Our implementation of UHTS has been reported recently in a paper explaining its different components [START_REF] Luca | The comprehensive health information system: a platform for privacy-aware and social health monitoring[END_REF]. The system is aptly called CHISel'd (Comprehensive Health Information System). We enhanced this system by supplying a component that accommodated models from data mining procedures. Moreover it has the capability to generate and store higher-level information inferred from sensed data. We call it the Knowledge Engine (KE) component. We named the improved system: Knowledge-Enriched Ubiquitous Health Telemonitoring System (KE-UHTS). Figure 1 shows the relationship among the different parts of a KE-UHTS.

Fig. 1: The Knowledge-Enriched UHTS.

We identified four requirements of the Knowledge-Engine component:

1. Models from data mining could be easily added, modified, and deleted.

2. Possibility of patient-model customization within the platform.

3. Model-generated outputs (representing high level medical or activity information) are stored into the database. 4. Automatic recommendations and feedbacks are generated (through longterm use of the system) [START_REF] Xavier Amatriain | Data mining methods for recommender systems[END_REF].

The intended users of the Knowledge-Engine component are the doctor and the researcher. The task of the researcher is to implement data mining algorithms and consequently to create the models. The role of the doctor is two-fold. The first role is to assist the researcher in the model creation process by providing domain expert knowledge and the second role is to validate the models. Also, the doctor is responsible for the assignment of feedbacks associated to the output of the models.

Implementation of the Knowledge Engine Component

Here we explain an implementation of KE Component with respect to CHISel'd. We started by making a choice regarding the tools we used to create the engine.

We selected the R software1 to implement the data mining algorithms and we produced R scripts to store the created models. We picked the Java programming language to create an application that acted as the interface. The whole application is actually a combination of a Java interface (serving as the front-end) and the R software (serving as the back-end and doing all the model building and computational tasks). We call this application the P-JR (Program-Java-R) application (Figure 2). What the doctor sees most of the time is the Java interface where majority of the activities such as model-patient assignment and process initiation/termination are effected. The Java interface also maintains a list of available patients and available models so that the doctor can easily make these associations. In the P-JR application, when model running is activated it connects to the medical database to fetch the relevant raw data, when the data are collected the calculation commences, and finally the output from the model are written back to the database. In the database, we distinguished between raw data: the data collected directly from the patients; and context data: the data generated by the models. As for with raw data, the context data can also be accessed by stakeholders given the appropriate privileges.

We tested the KE component by creating test models and we have successfully completed the entire process. It starts by (a) entering the model (the doctor loads a R file and gives a description), then (b) the doctor assigns the model to a patient and activates the running of the model, next (c) each running of a model for a patient is a thread that can be stopped or killed, (d) the model reads raw data and generates output (context data) which is stored in the database, then (e) the data is made available for visualization on digital assistants, and (f) the raw and context data is used to generate new models or to modify existing ones and the steps are repeated.

Medical raw data as well as context data in the database can be accessed by stakeholders from their digital assistant (android application on a mobile device) and depending on their access rights ( [START_REF] Luca | The comprehensive health information system: a platform for privacy-aware and social health monitoring[END_REF]). Through long-term use of the system we will be able to accumulate historical records regarding patient-model assignments and model-feedback associations. The gathered information will be used to improve the system to enable it to give automatic recommendations and oriented feedbacks.

Conclusion and Future Work

In this paper we have discussed and successfully demonstrated the development of a Knowledge Engine (KE) component that is crucial to any Ubiquitous Health Telemonitoring Systems (UHTS). The KE component is very well adapted for ubiquitous telemonitoring where raw data should be processed in real-time and high level information are computed and accessible on demand. The KE component is useful to implement the whole process, from model design to its integration and use into the system, i.e. the generation of context data. This is intended to help better monitor and support patients. Our approach makes it possible the dynamic inclusion of models created from data mining algorithms. We implemented the engine as a new component in an existing UHTS called CHISel'd which makes it a fully functional KE-UHTS. New data generated from the models is available in real-time and accessible from anywhere for instance on mobile devices. Also, new data is used to develop more models or to improve existing ones. Our next goal is to populate the model repository, conduct experiments to assess the over-all efficiency and reliability of the system, and to improve the operations in the interface.

1 .

 1 Collection, Transmission, and Storing of health data from patient. 2. Communication between patient and physician. 3. Communication with other health stakeholders forming the patient social support groups. 4. Access privileges mechanism to the health data, under the control of the patient and with the advice of the doctor Additionally, we propose to consider these features:

Fig. 2 :

 2 Fig. 2: The Knowledge-Engine showing the front-end and back-end programs.

http://www.r-project.org/