Monitoring of in-vitro ultrasonic stimulation of cells by numerical modeling.

Ultrasound stimulation of living tissues is a promising technique that can be safely applied for regenerative treatments. However, the ultrasound-induced mechanotransduction is still not well understood because of the large number of parameters involved at different scales and their difficult experimental accessibility. In this context, in-vitro studies may help to gain insight into the interaction between ultrasound and cells. Nevertheless, to conduct a reliable analysis of ultrasound effects on cell culture, the monitoring of the acoustic intensity delivered to the cells is of prime interest. Thanks to the development of an innovative custom experimental set-up inspired from ultrasound stimulation of bone regeneration conditions, major disturbing phenomena such as multiple reflections and standing wave formation inside the Petri dish are eliminated. Thus, the level of ultrasound stimulation, especially, in terms of spatial average temporal average intensity (ISATA), delivered to the cells can be monitored. Then, to properly estimate the level of ultrasound stimulation, a finite element model representing the experimental in-vitro configuration is developed. The numerical model manages on capturing the characteristics of the experimentally measured acoustic intensity distribution as illustrated by the experimental and numerical ISATA values of 42.3 and 45.8 mW/cm2 respectively, i.e. a relative difference of 8%. The numerical model would therefore allow exploring data inaccessible to experimental measurement and parametric studies to be carried out and facilitates the investigation of different virtual experimental configurations.

Circular antenna for breast ultrasonic diffraction tomography.

Compared to echography, which exploits only the reflected field, ultrasonic diffraction tomography improves image resolution by combining the total diffracted field. For breast cancer imaging, this improvement reinforces contrast between various breast tissues and structures by eliminating some interference phenomena such as speckle and then allowing parameterization of the images. Our work concerns the development of an experimental set-up for fast acquisition of the diffracted field and construction of two-dimensional tomographic images. For this purpose, we developed a multichannel ultrasound circular antenna with eight focused transducers.

Ultrasonic characterization of orthotropic elastic bovine bones.

The aim of the present study was to determine the mechanical properties of bovine bones. An ultrasonic method was used to determine acoustical parameters such as the longitudinal and transverse velocities in the longitudinal and two radial directions of compact bone, i.e., in all directions of the plane. Waves propagating through bovine femoral bones were studied using an ultrasonic scanner for linear and sectorial scanning. The mechanical parameters of compact bone, such the Young's modulus and Poisson's ratio in the orthotropic case, were then determined from the measured velocities. The results are in line with those in the literature.

An alternative ultrasonic method for measuring the elastic properties of cortical bone.

We studied the elastic properties of bone to analyze its mechanical behavior. The basic principles of ultrasonic methods are now well established for varying isotropic media, particularly in the field of biomedical engineering. However, little progress has been made in its application to anisotropic materials. This is largely due to the complex nature of wave propagation in these media. In the present study, the theory of elastic waves is essential because it relates the elastic moduli of a material to the velocity of propagation of these waves along arbitrary directions in a solid. Transducers are generally placed in contact with the samples which are often cubes with parallel faces that are difficult to prepare. The ultrasonic method used here is original, a rough preparation of the bone is sufficient and the sample is rotated. Moreover, to analyze heterogeneity of the structure we measure velocities in different points on the sample. The aim of the present study was to determine in vitro the anisotropic elastic properties of cortical bones. For this purpose, our method allowed measurement of longitudinal and transverse velocities (C(L) and C(T)) in longitudinal (fiber direction) and the radial directions (orthogonal to the fiber direction) of compact bones. Young's modulus E and Poisson's ratio nu, were then deduced from the velocities measured considering the compact bone as transversely isotropic or orthotropic. The results are in line with those of other methods.

Contrast and velocity ultrasonic tomography of long bones.

Our objective is to derive quantitative sound speed images of cortical bone using ultrasonic transmission tomography. Cortical bone is a highly refracting medium, i.e., the sound velocity changes abruptly across the interface between soft tissue and bone. It results in a loss of data compared to classical tomography in soft tissues. In order to correct for degradation by refraction effects, the classical acquisition procedure of projection data is modified: the transducers are oriented according to Snell's law of refraction with the aim of optimizing the sound propagation as parallel longitudinal rays inside the bone. This strategy allows the subsequent application of straight-ray reconstruction by the backprojection technique, which is a classical procedure in x-ray tomography. The method is validated with Plexiglas solid cylinders and tubes immersed in water. Improved sound velocity images are then derived using conventional Radon transform of the experimental time-of-flight data. The method is then extended to in vitro human femur immersed in water. The geometry of the bone cross-section is reconstructed from measurements using ultrasonic reflection tomography. The result is then introduced in the calculation of the position and orientation of the transducers, which are associated with the parallel acoustical paths in bone in the transmission measurements. The procedure leads to significant restoration enhancement over the non corrected image. The mean value of the velocity of 3,200 ms(-1) in the cortical shell is consistent with the values known from literature. These preliminary quantitative images using combined reflected and transmission ultrasound show promise for bone imaging.

Cancellous and cortical bone imaging by reflected tomography.

This paper deals with the inverse scattering problem observed when ultrasonic waves are used to analyze biological media. The objective is to image cancellous and cortical bone by ultrasonic reflected tomography (URT). Because strong contrast and high absorbance bodies such as bones cannot be imaged at usual ultrasonic high frequencies (> 1 MHz), we adapted for low-frequency URT (< 1 MHz) our tomographic set-up and reconstruction and acquisition tools, previously developed for weakly scattered media. Indeed, when the frequency of the transducer decreases, the penetration length of the wave increases, which unfortunately makes resolution poor, inappropriate for bone imagery. To improve resolution, we extend the generalized inversion in the complementary bandwidth of the electro-acoustic set-up (Papoulis deconvolution). This resolution enhancement for human porous vertebrae and human and animal femur showed that high-resolution images can be obtained with low-frequency URT.

Inversion of synthetic and experimental acoustical scattering data for the comparison of two reconstruction methods employing the Born approximation.

This work is concerned with the reconstruction, from measured (synthetic or real) data, of a 2D penetrable fluid-like object of arbitrary cross-section embedded in a fluid of infinite extent and insonified by a plane acoustic wave. Green's theorem is used to provide a domain integral representation of the scattered field. The introduction therein of the Born approximation gives rise to a linearized form of the inverse problem. The actual inversion is carried out by two methods. The first diffraction tomography (DT), exhibits the contrast function very conveniently and explicitly in the form of a wave number/incident angle Fourier transform of the far backscattered field and thus requires measurements of this field for incident waves all around the object and at all frequencies. The second discretized domain integral equation with Born approximation method, is numerically more intensive, but enables a wider choice of configurations and requires less measurements (one or several frequencies, one or several incident waves, choice of measurement points) than the DT method. A comparison of the two methods is carried out by inversion of both simulated and experimental scattered field data.

High resolution low frequency ultrasonic tomography.

Ultrasonic reflection tomography results from a linearization of the inverse acoustic scattering problem, named the inverse Born approximation. The goal of ultrasonic reflection tomography is to obtain reflectivity images from backscattered measurements. This is a Fourier synthesis problem and the first step is to correctly cover the frequency space of the object. For this inverse problem, we use the classical algorithm of tomographic reconstruction by summation of filtered backprojections. In practice, only a limited number of views are available with our mechanical rig, typically 180, and the frequency bandwidth of the pulses is very limited, typically one octave. The resolving power of the system is them limited by the bandwidth of the pulse. Low and high frequencies can be restored by use of a deconvolution algorithm that enhances resolution. We used a deconvolution technique based on the Papoulis method. The advantage of this technique is conservation of the overall frequency information content of the signals. The enhancement procedure was tested by imaging a square aluminium rod with a cross-section less than the wavelength. In this application, the central frequency of the transducer was 250 kHz so that the central wavelength was 6 mm whereas the cross-section of the rod was 4 mm. Although the Born approximation was not theoretically valid in this case (high contrast), a good reconstruction was obtained.