Emmanuel Bossy

Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models

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.

Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: A 2D simulation study

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).

Three-dimensional simulation of ultrasound propagation through trabecular bone structures measured by synchrotron microtomography

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.

Bidirectional axial transmission can improve accuracy and precision of ultrasonic velocity measurement in cortical bone: a validation on test materials

The axial transmission technique uses a linear arrangement of ultrasonic emitters and receivers placed on a same side of a cortical bone site in contact with the skin, involving ultrasonic propagation along the axis of bone. The velocity of the waves radiated from bone has been shown to reflect bone status. The thickness and composition of soft tissue may vary along the length of the bone, between different skeletal sites, or between subjects. Hence, accurate estimates of velocity require first to eliminate the effect of the overlying soft tissue that is traversed by the ultrasound wave. To correct for such bias without measuring soft tissue properties, we designed new ultrasonic probes in the 1-2 MHz frequency range. It is based on propagation along the bone surface in two opposite directions from two sources placed on both sides of a unique group of receivers. The aim is to obtain an unbiased estimate of the velocity without any intermediate calculation of soft tissue properties, such as thickness variation or velocity. Validation tests were performed on academic material such as Perspex or aluminium. We found that head wave velocity values could be biased by more than 10% for inclination of a few degrees between the test specimen surface and the probe. On test materials, the compensation procedure implemented in our probe led to a relative precision error on velocity measurement lower than 0.2 to 0.3%. These results suggest that the correction procedure allows measuring in vivo velocities independently of soft tissue properties.

An In Vitro Study of the Ultrasonic Axial Transmission Technique at the Radius: 1-MHz Velocity Measurements Are Sensitive to Both Mineralization and Intracortical Porosity

The ultrasonic axial transmission technique allows for investigating skeletal sites such as the cortical layer of long bones (radius, tibia, phalanges). Using synchrotron radiation μCT, we investigated, in vitro, the relationships between 1‐MHz axial transmission SOS measurements at the radius and site‐matched measurements of C.Th, POR, MIN, and vBMD.

Controlling light in scattering media non-invasively using the photoacoustic transmission matrix

An approach is demonstrated that allows the optical transmission matrix to be noninvasively measured over a large volume inside complex samples using a standard photoacoustic imaging set-up. This approach opens the way towards deep-tissue imaging and light delivery utilizing endogenous optical contrast.

Attenuation, scattering, and absorption of ultrasound in the skull bone

PURPOSE Measured values of ultrasound attenuation in bone represent a combination of different loss mechanisms. As a wave is transmitted from a fluid into bone, reflections occur at the interface. In the bone, mode conversion occurs between longitudinal and shear modes and the mechanical wave is scattered by its complex internal microstructure. Finally, part of the wave energy is absorbed by the bone and converted into heat. Due to the complexity of the wave propagation and the difficulty in performing measurements that are capable of separating the various loss mechanisms, there are currently no estimates of the absorption in bone. The aim of this paper is, thus, to quantify the attenuation, scattering, and thermal absorption in bone. METHODS An attenuating model of wave propagation in bone is established and used to develop a three-dimensional finite difference time domain numerical algorithm. Hydrophone and optical heterodyne interferometer measurements of the acoustic field as well as a x-ray microtomography of the bone sample are used to drive the simulations and to measure the attenuation. The acoustic measurements are performed concurrently with an infrared camera that can measure the temperature elevation during insonication. A link between the temperature and the absorption via a three-dimensional thermal simulation is then used to quantify the absorption coefficients for longitudinal and shear waves in cortical bone. RESULTS We demonstrate that only a small part of the attenuation is due to absorption in bone and that the majority of the attenuation is due to reflection, scattering, and mode conversion. In the nine samples of a human used for the study, the absorption time constant for cortical bone was determined to be 1.04 μs ± 28%. This corresponds to a longitudinal absorption of 2.7 dB/cm and a shear absorption of 5.4 dB/cm. The experimentally measured attenuation across the approximately 8 mm thick samples was 13.3 ± 0.97 dB/cm. CONCLUSIONS 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.

Mathematical Modeling in Photoacoustic Imaging of Small Absorbers

This paper is devoted to mathematical modeling in photoacoustic 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 back-propagated 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 multifrequency approach. We also show results of computational experiments to demonstrate efficiency of the algorithms.

Attenuation in trabecular bone: A comparison between numerical simulation and experimental results in human femur

Numerical simulations (finite-difference time domain) are compared to experimental results of ultrasound wave propagation through human trabecular bones. Three-dimensional high-resolution microcomputed tomography reconstructions served as input geometry for the simulation. The numerical simulation took into account scattering, but not absorption. Simulated and experimental values of the attenuation coefficients (alpha, dB/cm) and the normalized broadband ultrasound attenuation (nBUA, dB/cm/MHz) were measured and compared on a set of 28 samples. While experimental and simulated nBUA values were highly correlated (R(2)=0.83), and showed a similar dependence with bone volume fraction, the simulation correctly predicted experimental nBUA values only for low bone volume fraction (BV/TV). Attenuation coefficients were underestimated by the simulation. The absolute difference between experimental and simulated alpha values increased with both BV/TV and frequency. As a function of frequency, the relative difference between experimental and simulated alpha values decreased from 60% around 400 kHz to 30% around 1.2 MHz. Under the assumption that the observed discrepancy expresses the effect of the absorption, our results suggests that nBUA and its dependence on BV/TV can be mostly explained by scattering, and that the relative contribution of scattering to alpha increases with frequency, becoming predominant (>50 %) over absorption for frequencies above 600 kHz.

Improving visibility in photoacoustic imaging using dynamic speckle illumination

In high-frequency photoacoustic imaging with uniform illumination, homogeneous photoabsorbing structures may be invisible because of their large size or limited-view issues. Here we show that, by exploiting dynamic speckle illumination, it is possible to reveal features that are normally invisible with a photoacoustic system comprised of a 20 MHz linear ultrasound array. We demonstrate imaging of a ∅5 mm absorbing cylinder and a 30 μm black thread arranged in a complex shape. The hidden structures are directly retrieved from photoacoustic images recorded for different random speckle illuminations of the phantoms by assessing the variation in the value of each pixel over the illumination patterns.