Numerical simulation of the dependence of quantitative ultrasonic parameters on trabecular bone microarchitecture and elastic constants

Clinical Intervention Using Focused Ultrasound (FUS) Stimulation of the Brain in Diverse Neurological Disorders

Various surgical techniques and pharmaceutical treatments have been developed to improve the current technologies of treating brain diseases. Focused ultrasound (FUS) is a new brain stimulation modality that can exert a therapeutic effect on diseased brain cells, with this effect ranging from permanent ablation of the pathological neural circuit to transient excitatory/inhibitory modulation of the neural activity depending on the acoustic energy of choice. With the development of intraoperative imaging technology, FUS has become a clinically available noninvasive neurosurgical option with visual feedback. Over the past 10 years, FUS has shown enormous potential. It can deliver acoustic energy through the physical barrier of the brain and eliminate abnormal brain cells to treat patients with Parkinson's disease and essential tremor. In addition, FUS can help introduce potentially beneficial therapeutics at the exact brain region where they need to be, bypassing the brain's function barrier, which can be applied for a wide range of central nervous system disorders. In this review, we introduce the current FDA-approved clinical applications of FUS, ranging from thermal ablation to blood barrier opening, as well as the emerging applications of FUS in the context of pain control, epilepsy, and neuromodulation. We also discuss the expansion of future applications and challenges. Broadening FUS technologies requires a deep understanding of the effect of ultrasound when targeting various brain structures in diverse disease conditions in the context of skull interface, anatomical structure inside the brain, and pathology.

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.

Numerical Analysis of Ultrasound Backscattered Waves in Cancellous Bone Using a Finite-Difference Time-Domain Method: Isolation of the Backscattered Waves From Various Ranges of Bone Depths

Using a finite-difference time-domain method, ultrasound backscattered waves inside cancellous bone were numerically analyzed to investigate the backscatter mechanism. Two bone models with different thicknesses were modeled with artificial absorbing layers positioned at the back surfaces of the model, and an ultrasound pulse wave was transmitted toward the front surface. By calculating the difference between the simulated waveforms obtained using the two bone models, the backscattered waves from a limited range of depths in cancellous bone could be isolated. The results showed that the fast and slow longitudinal waves, which have previously been observed only in the ultrasound waveform transmitted through the bone, could be distinguished in the backscattered waveform from a deeper bone depth when transmitting the ultrasound wave parallel to the main orientation of the trabecular network. The amplitudes of the fast and slow backscattered waves were more closely correlated with the bone porosity [R2 = 0.84 and 0.66 (p < 0.001), respectively] than the amplitude of the whole (nonisolated) backscattered waves [R2 = 0.48 (p < 0.001)]. In conclusion, the nonisolated backscattered waves could be regarded as the superposition of the fast and slow waves reflected from various bone depths, returning at different times.

The effect of physical loading on calcaneus quantitative ultrasound measurement: a cross-section study

Background

Physical loading leads to a deformation of bone microstructure and may influence quantitative ultrasound (QUS) parameters. This study aims at evaluating the effect of physical loading on bone QUS measurement, and further, on the potential of diagnosing osteoporosis using QUS method under physical loading condition.

Methods

16 healthy young females (control group) and 45 postmenopausal women (divided into 3 groups according to the years since menopause (YSM)) were studied. QUS parameters were measured at calcaneus under self-weight loading (standing) and no loading (sitting) conditions. Weight-normalized QUS parameter (QUS parameter measured under loading condition divided by the weight of the subject) was proposed to evaluate the influence of loading. T-test, One-Way analysis of variance (one way ANOVA) and receiver operating characteristic (ROC) analysis were applied for analysis.

Results

In QUS parameters, mainly normalized broadband ultrasound attenuation (nBUA), measured with loading significantly differed from those measured without loading (p < 0.05). The relative changes of weight-normalized QUS parameters on postmenopausal women with respect to premenopausal women under loading condition were larger than those on traditional QUS parameters measured without loading. In ROC analysis, weight-normalized QUS parameters showed their stronger discriminatory ability for menopause.

Conclusions

Physical loading substantially influenced bone QUS measurement (mainly nBUA). Weight-normalized QUS parameters can discriminate menopause more effectively. By considering the high relationship between menopause and osteoporosis, an inference was drawn that adding physical loading during measurement may be a probable way to improve the QUS based osteoporosis diagnosis.

Relationship between ultrasonic parameters and apparent trabecular bone elastic modulus: a numerical approach

The physical principles underlying quantitative ultrasound (QUS) measurements in trabecular bone are not fully understood. The translation of QUS results into bone strength remains elusive. However, ultrasound being mechanical waves, it is likely to assess apparent bone elasticity. The aim of this study is to derive the sensitivity of QUS parameters to variations of apparent bone elasticity, a surrogate for strength. The geometry of 34 human trabecular bone samples cut in the great trochanter was reconstructed using 3-D synchrotron micro-computed tomography. Finite-difference time-domain simulations coupled to 3-D micro-structural models were performed in the three perpendicular directions for each sample and each direction. A voxel-based micro-finite element linear analysis was employed to compute the apparent Young's modulus (E) of each sample for each direction. For the antero-posterior direction, the predictive power of speed of sound and normalized broadband ultrasonic attenuation to assess E was equal to 0.9 and 0.87, respectively, which is better than what is obtained using bone density alone or coupled with micro-architectural parameters and of the same order of what can be achieved with the fabric tensor approach. When the direction of testing is parallel to the main trabecular orientation, the predictive power of QUS parameters decreases and the fabric tensor approach always gives the best results. This decrease can be explained by the presence of two longitudinal wave modes. Our results, which were obtained using two distinct simulation tools applied on the same set of samples, highlight the potential of QUS techniques to assess bone strength.

Mechanisms for attenuation in cancellous-bone-mimicking phantoms

Broadband ultrasound attenuation (BUA) in cancellous bone is useful for prediction of osteoporotic fracture risk, but its causes are not well understood. To investigate attenuation mechanisms, 9 cancellous-bone-mimicking phantoms containing nylon filaments (simulating bone trabeculae) embedded within soft-tissue-mimicking fluid (simulating marrow) were interrogated. The measurements of frequency-dependent attenuation coefficient had 3 separable components: 1) a linear (with frequency) component attributable to absorption in the soft-tissue-mimicking fluid, 2) a quasilinear (with frequency) component, which may include absorption in and longitudinal-shear mode conversion by the nylon filaments, and 3) a nonlinear (with frequency) component, which may be attributable to longitudinal-longitudinal scattering by the nylon filaments. The slope of total linear (with frequency) attenuation coefficient (sum of components #1 and #2) versus frequency was found to increase linearly with volume fraction, consistent with reported measurements on cancellous bone. Backscatter coefficient measurements in the 9 phantoms supported the claim that the nonlinear (with frequency) component of attenuation coefficient (component #3) was closely associated with longitudinal-longitudinal scattering. This work represents the first experimental separation of these 3 components of attenuation in cancellous bone-mimicking phantoms.

Ultrasonic scattering from cancellous bone: a review

This paper reviews theory, measurements, and computer simulations of scattering from cancellous bone reported by many laboratories. Three theoretical models (binary mixture, Faran cylinder, and weak scattering) for scattering from cancellous bone have demonstrated some consistency with measurements of backscatter. Backscatter is moderately correlated with bone mineral density in human calcaneus in vitro (r(2) = 0.66 - 0.68). Backscatter varies approximately as frequency cubed and trabecular thickness cubed in human calcaneus and femur in vitro. Backscatter from human calcaneus and bovine tibia exhibits substantial anisotropy. So far, backscatter has demonstrated only modest clinical utility. Computer simulation models have helped to elucidate mechanisms underlying scattering from cancellous bones.

Sensitivity of qus parameters to controlled variations of bone strength assessed with a cellular model

The physical principles underlying quantitative ultrasound (QUS) measurements are not fully understood yet. Therefore, the translation of QUS results into bone strength remains elusive. In the present study, we derive the sensitivity of broadband ultrasonic attenuation (BUA) and speed of sound (SOS) to variations of bone strength. For this purpose, a mechanical cellular model is combined to a multiple regression resulting from the analysis of finite-difference time domain (FDTD) simulations. Specifically, we investigate how QUS variables respond to a variation in strength of 10%, realized either by a change in material properties or a change in bone volume fraction (BV/TV). The results show that except when BV/TV is high, the variations of BUA in response to a variation in strength realized by a pure change of BV/TV exceeds the technique imprecision and thus can be detected. When the variation of strength is realized by changes of compressive or shear stiffness, the response in QUS properties is dominated by the variation in C(11), whereas changes in C(44), remaining below the precision error, cannot be detected. The interpretation of these data, however, is not straightforward due to sparse description of elastic properties at the tissue level. To overcome the limitation of the cellular model, more realistic computational models such as micro- finite element analysis have to be considered.

Fast wave ultrasonic propagation in trabecular bone: numerical study of the influence of porosity and structural anisotropy

Our goal is to assess the potential of computational methods as an alternative to analytical models to predict the two longitudinal wave modes observed in cancellous bone and predicted by the Biot theory. A three-dimensional (3D) finite-difference time-domain method is coupled with 34 human femoral trabecular microstructures measured using microcomputed tomography. The main trabecular alignment (MTA) and the degree of anisotropy (DA) were assessed for all samples. DA values were comprised between 1.02 and 1.9. The influence of bone volume fraction (BV/TV) between 5% and 25% on the properties of the fast and slow waves was studied using a dedicated image processing algorithm to modify the initial 3D microstructures. A heuristic method was devised to determine when both wave modes are time separated. The simulations (performed in three perpendicular directions) predicted that both waves generally overlap in time for a direction of propagation perpendicular to the MTA. When these directions are parallel, both waves are separated in time for samples with high DA and BV/TV values. A relationship was found between the least bone volume fraction required for the observation of nonoverlapping waves and the degree of anisotropy: The higher the DA, the lower the least BV/TV.

Dependence of ultrasonic attenuation on bone mass and microstructure in bovine cortical bone

The development of the axial transmission technique now enables in vivo evaluation of cortical bone quality, which plays an important role in bone fragility. Cortical bone is a complex multiscale material, which may be made of different types of microstructure. The interaction between ultrasound and cortical bone remains unclear and most studies have been confined to wave speed analysis. The first aim of this study is to investigate the dependence of the frequency-dependent attenuation on the type of bone microstructure. The second goal is to determine whether broadband ultrasonic attenuation (BUA) is related to volumetric bone mineral density (vBMD) and mass density. Parallelepipedic samples of bovine cortical bone were cut from three specimens and tested in the axial, radial and tangential directions using an ultrasonic transmission device. BUA was evaluated over a 1-MHz wide bandwidth around 4MHz. In addition, the microstructure of each sample was determined using an optical microscope. BUA values measured in porotic microstructure are significantly higher than in Haversian microstructure. The lowest BUA values are obtained for plexiform microstructure. For all structures, BUA in the axial direction is significantly smaller than in the radial and tangential directions. Moreover, BUA is correlated with both vBMD and density (determination coefficient (R2) equal to 0.44 and 0.65, respectively, in the axial direction). BUA variations can be explained by scattering and viscoelastic mechanisms. This study suggests that BUA measurements have the potential to discriminate among different cortical bone microstructures in addition to providing material properties.