Simulations of ultrasound propagation in random arrangements of elliptic scatterers: occurrence of two longitudinal waves

What kind of waves are measured in trabecular bone?

The paper discusses the fundamental mechanisms underlying the interaction between ultrasound and trabecular bone, which is considered a two-phase material. When fluid-saturated cancellous bone is interrogated by ultrasound, in some cases, one or two wave modes are observed. Many authors claim that these waves correspond to the fast and slow waves predicted by Biot's theory of elastic wave propagation in fluid-saturated porous media. Within our analysis of the physical conditions, predictions of the existing two-phase models of the propagation of ultrasonic waves in the material as well as numerical simulations for fluid-saturated trabecular bone were performed. On the basis of the theoretical results (from numerical studies) and arguments presented in this paper, we aimed to answer the question of whether two waves observed in ultrasonic wave transmission studies can be interpreted as the fast and slow waves predicted by Biot's theory.

Lesion Imaging and Target Detection in Multiple Scattering (LITMUS) Media

We present an ultrasound algorithm [lesion imaging and target detection in multiple scattering (LITMUS)] suited to image lesions (hypoechoic) or targets (hyperechoic) in highly complex structures. In such media, standard ultrasound imaging techniques fail to detect lesions or targets due to aberrations and the loss of linearity between propagation distance and propagation time, caused by multiple scattering of ultrasound waves. The present algorithm (LITMUS) has the capability to predict the location as well as the size of such lesions/targets by using the multiple scattered ultrasound signals to its advantage. In this experimental and computational study, we use an ultrasound linear array. Lesions/targets are embedded at varying depths inside multiple scattering media with varying density of scatterers. In the simulations, plastic scatterers are used as the source of multiple scattering in a propagation medium (water). In the experiments, melamine sponges are used, with air alveoli as the scattering source. For multiple locations along the transducer, the incoherent backscattered intensity of the backscattered signals is extracted and the linear growth of the diffusive halo over time is tracked. Sudden changes in this growth indicate the presence of a region with reduced heterogeneity, indicative of the presence of a lesion/target. This methodology is combined with a depression detection algorithm to predict the size and location of the lesion/targets with high fidelity, despite the presence of strong heterogeneity and multiple scattering.

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

Finite difference time domain model of ultrasound propagation in agarose scaffold containing collagen or chondrocytes

Measurement of ultrasound backscattering is a promising diagnostic technique for arthroscopic evaluation of articular cartilage. However, contribution of collagen and chondrocytes on ultrasound backscattering and speed of sound in cartilage is not fully understood and is experimentally difficult to study. Agarose hydrogels have been used in tissue engineering applications of cartilage. Therefore, the aim of this study was to simulate the propagation of high frequency ultrasound (40 MHz) in agarose scaffolds with varying concentrations of chondrocytes (1 to 32 × 10(6) cells/ml) and collagen (1.56-200 mg/ml) using transversely isotropic two-dimensional finite difference time domain method (FDTD). Backscatter and speed of sound were evaluated from the simulated pulse-echo and through transmission measurements, respectively. Ultrasound backscatter increased with increasing collagen and chondrocyte concentrations. Furthermore, speed of sound increased with increasing collagen concentration. However, this was not observed with increasing chondrocyte concentrations. The present study suggests that the FDTD method may have some applicability in simulations of ultrasound scattering and propagation in constructs containing collagen and chondrocytes. Findings of this study indicate the significant role of collagen and chondrocytes as ultrasound scatterers and can aid in development of modeling approaches for understanding how cartilage architecture affects to the propagation of high frequency ultrasound.

Experimental observation of ultrasound fast and slow waves through three-dimensional printed trabecular bone phantoms

In this paper, ultrasound measurements of 1:1 scale three-dimensional (3D) printed trabecular bone phantoms are reported. The micro-structure of a trabecular horse bone sample was obtained via synchrotron x-ray microtomography, converted to a 3D binary data set, and successfully 3D-printed at scale 1:1. Ultrasound through-transmission experiments were also performed through a highly anisotropic version of this structure, obtained by elongating the digitized structure prior to 3D printing. As in real anisotropic trabecular bone, both the fast and slow waves were observed. This illustrates the potential of stereolithography and the relevance of such bone phantoms for the study of ultrasound propagation in bone.

New perspectives in echographic diagnosis of osteoporosis on hip and spine

Currently, the accepted "gold standard" method for bone mineral density (BMD) measurement and osteoporosis diagnosis is dual-energy X-ray absorptiometry (DXA). However, actual DXA effectiveness is limited by several factors, including intrinsic accuracy uncertainties and possible errors in patient positioning and/or post-acquisition data analysis. DXA employment is also restricted by the typical issues related to ionizing radiation employment (high costs, need of dedicated structures and certified operators, unsuitability for population screenings). The only commercially-available alternative to DXA is represented by "quantitative ultrasound" (QUS) approaches, which are radiation-free, cheaper and portable, but they cannot be applied on the reference anatomical sites (lumbar spine and proximal femur). Therefore, their documented clinical usefulness is restricted to calcaneal applications on elderly patients (aged over 65 y), in combination with clinical risk factors and only for the identification of healthy subjects at low fracture risk. Literature-reported studies performed some QUS measurements on proximal femur, but their clinical translation is mostly hindered by intrinsic factors (e.g., device bulkiness). An innovative ultrasound methodology has been recently introduced, which performs a combined analysis of B-mode images and corresponding "raw" radiofrequency signals acquired during an echographic scan of the target reference anatomical site, providing two novel parameters: Osteoporosis Score and Fragility Score, indicative of BMD level and bone strength, respectively. This article will provide a brief review of the available systems for osteoporosis diagnosis in clinical routine contexts, followed by a synthesis of the most promising research results on the latest ultrasound developments for early osteoporosis diagnosis and fracture prevention.

Mechanical assessment of cervical remodelling in pregnancy: insight from a synthetic model

During the gestation and the cervical remodelling, several changes occur progressively in the structure of the tissue. An increase in the hydration, disorganisation of collagen network and decrease in elasticity can be observed. The collagen structure disorganisation is particularly complex: collagen fibres turn thicker and more wavy as the gestation progresses in a transition from relatively straight fibres to wavy fibres, while pores between collagen fibres become larger and separated. Shear wave elastography is a promising but not yet fully understood tool to assess these structural changes and the cervix׳s ability to dilate. To this end, a numerical histo-mechanical model is proposed in the present study, which aims at linking variations in the microscopic histo-biomechanical processes with shear wave propagation characteristics. Parametric simulations are carried out for a broad range of mechanical and geometrical parameters. Results show a direct relationship between the histological and morphological changes during pregnancy and the viscoelastic behaviour of the tissue.

Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot's and multiple scattering models

This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finite-difference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensemble-averaged transmitted wave (also known as the coherent wave) are measured in various configurations. As in real cancellous bone, one or two longitudinal modes emerge, depending on the micro-structure. The results are confronted with two standard theoretical approaches: Biot's theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical first-order approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot's theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study two-wave propagation, unlike Biot's model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot's theory. Finally we investigate the phase-shift between waves in the fluid and the solid structure, and compare them to Biot's predictions of in-phase and out-of-phase motions.

Ultrasound to assess bone quality

Bone quality is determined by a variety of compositional, micro- and ultrastructural properties of the mineralized tissue matrix. In contrast to X-ray-based methods, the interaction of acoustic waves with bone tissue carries information about elastic and structural properties of the tissue. Quantitative ultrasound (QUS) methods represent powerful alternatives to ionizing x-ray based assessment of fracture risk. New in vivo applicable methods permit measurements of fracture-relevant properties, [eg, cortical thickness and stiffness at fragile anatomic regions (eg, the distal radius and the proximal femur)]. Experimentally, resonance ultrasound spectroscopy and acoustic microscopy can be used to assess the mesoscale stiffness tensor and elastic maps of the tissue matrix at microscale resolution, respectively. QUS methods, thus, currently represent the most promising approach for noninvasive assessment of components of fragility beyond bone mass and bone microstructure providing prospects for improved assessment of fracture risk.

Numerical investigation of ultrasonic attenuation through 2D trabecular bone structures reconstructed from CT scans and random realizations

In this paper, we compare ultrasound interrogations of actual CT-scanned images of trabecular bone with artificial randomly constructed bone. Even though it is known that actual bone does not have randomly distributed trabeculae, we find that the ultrasound attenuations are close enough to cast doubt on any microstructural information, such as trabeculae width and distance between trabeculae, being gleaned from such experiments. More precisely, we perform numerical simulations of ultrasound interrogation on cancellous bone to investigate the phenomenon of ultrasound attenuation as a function of excitation frequency and bone porosity. The theoretical model is based on acoustic propagation equations for a composite fluid-solid material and is solved by a staggered-grid finite-difference scheme in the time domain. Numerical experiments are performed on two-dimensional bone samples reconstructed from CT-scanned images of real human calcaneus and from random distributions of fluid-solid particles generated via the turning bands method. A detailed comparison is performed on various parameters such as the attenuation rate and speed of sound through the bone samples as well as the normalized broadband ultrasound attenuation coefficient. Comparing results from these two types of bone samples allows us to assess the role of bone microstructure in ultrasound attenuation. It is found that the random model provides suitable bone samples for ultrasound interrogation in the transverse direction of the trabecular network.