Frederic Padilla

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.

In vitro measurement of the frequency-dependent attenuation in cancellous bone between 0.2 and 2 MHz

Our goal was to evaluate the frequency dependence of the ultrasonic attenuation coefficient in cancellous bone. Estimates were obtained in immersion, using a substitution method in the through-transmit mode, by scanning 14 human bone specimens (calcaneus). Measurements were performed with three pairs of focused transducers with a center frequency of 0.5, 1.0, and 2.25 MHz, respectively in order to cover an extended frequency bandwidth (0.2-1.7 MHz). When the experimental attenuation coefficient values were modeled with a nonlinear power fit alpha(f)=alpha0 +alpha(I)f(n), the attenuation coefficient was found to increase as f(1.09+/-0.3) over the measurement bandwidth. However, a substantial variation of the exponent n (0.4-2.2) within specimens and also between specimens was observed. The acoustical parameters were compared to bone mineral density. A highly significant relationship was noted between alpha1 and BMD (r2= 0.75, p< 10(-4)). No correlation was found between n and BMD. Several attenuation mechanisms are discussed as well as the potential impact these results may have in in vivo quantitative measurements.

Acoustic Droplet Vaporization for Enhancement of Thermal Ablation by High Intensity Focused Ultrasound

RATIONALE AND OBJECTIVES Acoustic droplet vaporization (ADV) shows promise for spatial control and acceleration of thermal lesion production. The investigators hypothesized that microbubbles generated by ADV could enhance high-intensity focused ultrasound (HIFU) thermal ablation by controlling and increasing local energy absorption. MATERIALS AND METHODS Thermal lesions were produced in tissue-mimicking phantoms using focused ultrasound (1.44 MHz) with a focal intensity of 4000 W · cm(-2) in degassed water at 37°C. The average lesion volume was measured by visible change in optical opacity and by T2-weighted magnetic resonance imaging. In addition, in vivo HIFU lesions were generated in a canine liver before and after an intravenous injection of droplets with a similar acoustic setup. RESULTS Thermal lesions were sevenfold larger in phantoms containing droplets (3 × 10(5) droplets/mL) compared to phantoms without droplets. The mean lesion volume with a 2-second HIFU exposure in droplet-containing phantoms was comparable to that made by a 5-second exposure in phantoms without droplets. In the in vivo study, the average lesion volumes without and with droplets were 0.017 ± 0.006 cm(3) (n = 4; 5-second exposure) and 0.265 ± 0.005 cm(3) (n = 3; 5-second exposure), respectively, a factor of 15 difference. The shape of ADV bubbles imaged with B-mode ultrasound was very similar to the actual lesion shape as measured optically and by magnetic resonance imaging. CONCLUSION ADV bubbles may facilitate clinical HIFU ablation by reducing treatment time or requisite in situ total acoustic power and provide ultrasonic imaging feedback of the thermal therapy.

Propagation of two longitudinal waves in human cancellous bone: An in vitro study

The ultrasonic wave propagation of fast and slow waves was investigated in vitro in 35 cubic cancellous bone specimens extracted from human femoral heads. Measurements were performed in three orthogonal directions using home-made PVDF transducers excited by a single sinusoidal wave at 1 MHz. The apparent density of the specimens was measured. Two separated fast and slow waves were clearly observed in 16 specimens, mainly in the main load direction. The waveforms and the sound speeds of fast and slow waves were similar to the reported data in bovine bone. The group of specimens in which the two waves were observed did not exhibit statistically higher apparent density than the rest of the specimens, but did exhibit statistically higher acoustic anisotropy ratio. The speeds in the main load direction were higher than those in the other direction. The fast and slow wave speeds were in good agreement with Biots model, showing an increase with bone volume fraction (BV/TV). The ratio of peak amplitudes of the fast and slow waves nonlinearly increased as a function of BV/TV. These results open interesting perspective for acoustic assessment of cancellous bone micro-architecture and especially anisotropy that might lead to an improved assessment of bone strength.

Effects of frequency-dependent attenuation and velocity dispersion on in vitro ultrasound velocity measurements in intact human femur specimens

Numerous studies have shown that ultrasonic velocity measured in bone provides a good assessment of osteoporotic fracture risk. However, a lack of standardization of signal processing techniques used to compute the speed of sound (SOS) complicates the comparison between data obtained with different commercial devices. In this study, 38 intact femurs were tested using a through-transmission technique and SOS determined using different techniques. The resulting difference in measured SOS was determined as functions of the attenuation and the velocity dispersion. A numerical simulation was used to explain how attenuation and dispersion impact two different SOS measurements (group velocity, velocity based on the first zero crossing of the signal). A new method aimed at compensating for attenuation was devised and led to a significant reduction in the difference between SOS obtained with both signal processing techniques. A comparison between SOS and X-ray density measurements indicated that the best correlation was reached for SOS based on the first zero crossing apparently because it used a marker located in the early part of the signal and was less sensitive to multipath interference. The conclusion is that first zero crossing velocity may be preferred to group velocity for ultrasonic assessment at this potential fracture site.

Prediction of backscatter coefficient in trabecular bones using a numerical model of three-dimensional microstructure

A model of ultrasonic backscattering for cancellous bone saturated by water is proposed. This model assumes that scattering is caused by the solid trabeculae and describes the cancellous bone as a weak scattering medium. The backscatter coefficient is related to the spatial Fourier transform of bone microarchitecture and to the density and compressibility fluctuations between the solid trabeculae and the saturating fluid. The computations of the model make use of three-dimensional numerical images of bone microarchitecture, obtained by tomographic reconstructions with a 10 microm spatial resolution. With this model, the predictions of the frequency dependence and of the magnitude of the backscatter coefficient are reasonably accurate. The theoretical predictions are compared to experimental data obtained on 19 specimens. An accuracy error of approximately 1 dB was found (difference between the averaged experimental values and theoretical predictions). One limit of the model may come from inaccurate values of trabecular bone characteristics needed for the computations (density and longitudinal velocity), which are yet to be precisely determined for human trabecular bone. However, the model is only slightly sensitive to variations of bone material properties. It was found that an accuracy error of 2.2 dB at maximum resulted from inaccurate a priori values of bone material properties. A computation of the elastic mean free path in the medium suggests that multiple scattering plays a minor role in the working frequency bandwidth (0.4-1.2 MHz). It follows from these results that a weak scattering medium model may be appropriate to describe scattering from trabecular bone.

Phase and group velocities of fast and slow compressional waves in trabecular bone

This Letter is an extension to a multilayer model of porous bone first proposed by Hughes et al. [Ultrasound Med. Biol. 25, 811-821 (1999)]. Both slow and fast compressional waves propagate when the acoustic wave propagation is parallel to the trabecular alignment. However, a slow wave disappears at high refraction angles. To explain this phenomenon, the multilayer model is extended to compute group velocity surface and arrival times with an angle. Two major effects are highlighted as the refraction angle increases. First, the energy of the slow wave is refracted from the phase propagation direction. Second, the signals of fast and slow waves overlap. As a consequence, the slow wave may not be observed for a refraction angle greater than 40 degrees, which is in agreement with previous experimental data published by Hughes et al. and others.

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.

Theoretical and experimental studies of surface waves on solid–fluid interfaces when the value of the fluid sound velocity is located between the shear and the longitudinal ones in the solid

The existence of two surface waves propagating on a plane solid–fluid interface is demonstrated when the value of the fluid sound velocity is located between the shear and the longitudinal ones in the solid. First, the Scholte–Stoneley dispersion equation is studied analytically and numerically to find the roots corresponding to the Stoneley and the Rayleigh waves. The anatomy of each one is then described with the formalism of the evanescent plane waves: both waves are unleaky. Finally, the results are confirmed experimentally by measuring the times of flight on a Plexiglas–water interface and on a PVC–water interface.

A device for in vivo measurements of quantitative ultrasound variables at the human proximal femur

Quantitative ultrasound (QUS) at the calcaneus has similar power as a bone mineral density (BMD)- measurement using DXA for the prediction of osteoporotic fracture risk. Ultrasound equipment is less expensive than DXA and free of ionizing radiation. As a mechanical wave, QUS has the potential of measuring different bone properties than dual X-ray absorptiometry (DXA,) which depends on X-ray attenuation and might be developed into a tool of comprehensive assessment of bone strength. However, site- specific DXA at the proximal femur shows best performance in the prediction of hip fractures. To combine the potential of QUS with measurements directly at the femur, we developed a device for in vivo QUS measurements at this site. Methods comprise ultrasound transmission through the bone, reflection from the bone surface, and backscat- ter from the inner trabecular structure. The complete area of the proximal femur can be scanned except at the femoral head, which interferes with the ilium. To avoid edge artifacts, a subregion of the proximal femur in the trochanteric region was selected as measurement region. First, in vivo measurements demonstrate a good signal to noise ratio and proper depiction of the proximal femur on an attenuation image. Our results demonstrate the feasibility of in vivo measurements. Further improvements can be expected by refinement of the scanning technique and data evaluation method to enhance the potential of the new method for the estimation of bone strength.