This first measurement of ultrasound absorption in bone can be used to estimate the amount of heat deposition based on knowledge of the acoustic field.

† These authors contributed equally to this work Optical wavefront-shaping has emerged as a powerful tool to manipulate light in strongly scattering media 1, 2 . It enables diffraction-limited focusing 3 and imaging 4, 5 at depths where conventional microscopy techniques fail 6 . However, while most wavefront-shaping works to-date exploited direct access to the target 2-5, 7-11 or implanted probes 12, 13 , the challenge is to apply it non-invasively inside complex samples. Ultrasonic-tagging techniques have been recently demonstrated 14-18 but these require a sequential point-bypoint acquisition, a major drawback for imaging applications. Here, we introduce a novel approach to non-invasively measure the optical transmission-matrix 5 inside a scattering medium, exploiting the photo-acoustic effect 19-23 . Our approach allows for the first time to simultaneously discriminate, localize, and selectively focus light on multiple targets inside a scattering sample, as well as to recover and exploit the scattering medium properties. Combining the powerful approach of the transmission-matrix with the advantages of photoacoustic imaging 19-21 opens the path towards deep-tissue imaging and light-delivery utilizing endogenous optical contrast.

The ultrasonic axial transmission technique, used to assess cortical shells of long bones, is investigated using numerical simulations based on a three-dimensional (3D) finite difference code. We focus our interest on the effects of 3D cortical bone geometry (curvature, cortical thickness), anisotropy, and microporosity on speed of sound (SOS) measurements for different frequencies in the MHz range. We first show that SOS values measured on tubular cortical shells are identical to those measured on cortical plates of equal thickness. Anisotropy of cortical bone is then shown to have a major impact on SOS measurement as a function of cortical thickness. The range of SOS values measured on anisotropic bone is half the range found when bone is considered isotropic. Dependence of thickness occurs for cortical shell thinner than 0.5 x lambda(bone) in anisotropic bone (lambda(bone): wavelength in bone), whereas it occurs for cortical shell thinner than lambda(bone) when anisotropy is neglected. Sensitivity of SOS along the bone axis to intracortical microporosity is shown to be approximately -20 m s(-1) per percent of porosity. Using homogenized porous bone, we finally show that the cortical depth that contributes to lateral wave SOS measurement is approximately 1-1.5 mm for frequencies ranging from 500 kHz to 2 MHz under classical in vivo measurement conditions.

We investigate theoretically the photoacoustic generation by a gold nanosphere in water in the thermoelastic regime. Specifically, we consider the long-pulse illumination regime, in which the time for electron-phonon thermalisation can be neglected and photoacoustic wave generation arises solely from the thermo-elastic stress caused by the temperature increase of the nanosphere or its liquid environment. Photoacoustic signals are predicted based on the successive resolution of a thermal diffusion problem and a thermoelastic problem, taking into account the finite size of the gold nanosphere, thermoelastic and elastic properties of both water and gold, and the temperaturedependence of the thermal expansion coefficient of water. For sufficiently high illumination fluences, this temperature dependence yields a nonlinear relationship between the photoacoustic amplitude and the fluence. For nanosecond pulses in the linear regime, we show that more than 90 % of the emitted photoacoustic energy is generated in water, and the thickness of the generating layer around the particle scales close to the square root of the pulse duration. The amplitude of the photoacoustic wave in the linear regime are accurately predicted by the point-absorber model introduced by Calasso et al. [], but our results demonstrate that this model significantly overestimates the amplitude of photoacoustic waves in the nonlinear regime. We therefore provide quantitative estimates of a critical energy, defined as the absorbed energy required such that the nonlinear contribution is equal to that of the linear contribution. Our results suggest that the critical energy scales as the volume of water over which heat diffuses during the illumination pulse. Moreover, thermal nonlinearity is shown to be expected only for sufficiently high ultrasound frequency. Finally, we show that the relationship between the photoacoustic amplitude and the equilibrium temperature at sufficiently high fluence reflects the thermal diffusion at the nanoscale around the gold nanosphere. CONTENTS

In recent years, quantitative ultrasound (QUS) has played an increasing role in the assessment of bone status. The axial transmission technique allows to investigate skeletal sites such as the cortical layer of long bones (radius, tibia), inadequate to through-transmission techniques. Nevertheless, the type of propagation involved along bone specimens has not been clearly elucidated. Axial transmission is investigated here by means of two-dimensional simulations at 1 MHz. We focus our interest on the apparent speed of sound (SOS) of the first arriving signal (FAS). Its dependence on the thickness of the plate is discussed and compared to previous work. Different time criteria are used to derive the apparent SOS of the FAS as a function of source-receiver distance. Frequency-wave number analysis is performed in order to understand the type of propagation involved. For thick plates (thickness>lambdabone, longitudinal wavelength in bone), and for a limited range of source-receiver distances, the FAS corresponds to the lateral wave. Its velocity equals the longitudinal bulk velocity of the bone. For plate thickness less than lambdabone, some plate modes contribute to the FAS, and the apparent SOS decreases with the thickness in a way that depends on both the time criterion and on the source-receiver distance. The FAS corresponds neither to the lateral wave nor to a single plate mode. For very thin plates (thickness< lambdabone/4), the apparent SOS tends towards the velocity of the lowest order symmetrical vibration mode (S0 Lamb mode).

This paper is devoted to mathematical modelling in photo-acoustic imaging of small absorbers. We propose a new method for reconstructing small absorbing regions inside a bounded domain from boundary measurements of the induced acoustic signal. We also show the focusing property of the backpropagated acoustic signal. Indeed, we provide two different methods for locating a targeted optical absorber from boundary measurements of the induced acoustic signal. The first method consists of a MUltiple Signal Classification (MUSIC) type algorithm and the second one uses a multi-frequency approach. We also show results of computational experiments to demonstrate efficiency of the algorithms.

Three-dimensional numerical simulations of ultrasound transmission were performed through 31 trabecular bone samples measured by synchrotron microtomography. The synchrotron microtomography provided high resolution 3D mappings of bone structures, which were used as the input geometry in the simulation software developed in our laboratory. While absorption (i.e. the absorption of ultrasound through dissipative mechanisms) was not taken into account in the algorithm, the simulations reproduced major phenomena observed in real through-transmission experiments in trabecular bone. The simulated attenuation (i.e. the decrease of the transmitted ultrasonic energy) varies linearly with frequency in the MHz frequency range. Both the speed of sound (SOS) and the slope of the normalized frequency-dependent attenuation (nBUA) increase with the bone volume fraction. Twenty-five out of the thirty-one samples exhibited negative velocity dispersion. One sample was rotated to align the main orientation of the trabecular structure with the direction of ultrasonic propagation, leading to the observation of a fast and a slow wave. Coupling numerical simulation with real bone architecture therefore provides a powerful tool to investigate the physics of ultrasound propagation in trabecular structures. As an illustration, comparison between results obtained on bone modelled either as a fluid or a solid structure suggested the major role of mode conversion of the incident acoustic wave to shear waves in bone to explain the large contribution of scattering to the overall attenuation.

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