Significance of the Microfluidic Flow Inside the Organ of Corti.

We study the vibration modes of a short section in the middle turn of the gerbil cochlea including both longitudinal and radial interstitial fluid spaces between the pillar cells (PC) and the sensory hair cells to determine the role of the interstitial fluid flow within the organ of corti (OoC). Three detailed finite element (FE) models of the cochlear short section (CSS) are studied. In model 1, the CSS is without fluids; model 2 includes the OoC fluid, but not the exterior scalae fluids; and model 3 is the CSS with both scalae and OoC fluids. We find that: (1) the fundamental mode shape of models 1 or 3 is similar to the classical basilar membrane (BM) bending mode that includes pivoting of the arch of corti, and hence determines the low frequency vibrational mode shape of the cochlea in the presence of the cochlear wave. (2) The fundamental mode shape of model 2 is characterized by a cross-sectional shape change similar to the passive response of the cochlea. This mode shape includes a tilting motion of the inner hair cell (IHC) region, a fluid motion within the tunnel of corti (ToC) in the radial direction and along the OoC, and a bulging motion of the reticular lamina (RL) above the outer hair cell (OHC). Each of these motions provides a plausible mode of excitation of the sensory hair cells. (3) The higher vibrational modes of model 1 are similar to the electrically evoked response within the OoC and suggests that the higher vibrational modes are responsible for the active response of the cochlea. We also observed that the fluid flow through the OoC interstitial space is significant, and the model comparison suggests that the OoC fluid contributes to the biphasic BM motion seen in electrical stimulation experiments. The effect of fluid viscosity on cilium deflection was assessed by performing a transient analysis to calculate the cilium shearing gain. The gain values are found to be within the range of experimentally measured values reported by Dallos et al. (1996, The Cochlea, Springer-Verlag, New York).

Characterization of glioblastoma in an orthotopic mouse model with magnetic resonance elastography.

Glioblastoma (GBM) is the most common primary brain tumor. It is highly malignant and has a correspondingly poor prognosis. Diagnosis and monitoring are mainly accomplished with MRI, but remain challenging in some cases. Therefore, complementary methods for tumor detection and characterization would be beneficial. Using magnetic resonance elastography (MRE), we performed a longitudinal study of the biomechanical properties of intracranially implanted GBM in mice and compared the results to histopathology. The biomechanical parameters of viscoelastic modulus, shear wave speed and phase angle were significantly lower in tumors compared with healthy brain tissue and decreased over time with tumor progression. Moreover, some MRE parameters revealed sub-regions at later tumor stages, which were not easily detectable on anatomical MRI images. Comparison with histopathology showed that softer tumor regions contained necrosis and patches of viable tumor cells. In contrast, areas of densely packed tumor cells and blood vessels identified with histology coincided with higher values of viscoelastic modulus and shear wave speed. Interestingly, the phase angle was independent from these anatomical variations. In summary, MRE depicted longitudinal and morphological changes in GBM and may prove valuable for tumor characterization in patients.

Application of a forward model of axisymmetric shear wave propagation in viscoelastic media to shear wave elastography.

A simple but general solution of Navier's equation for axisymmetric shear wave propagation in a homogeneous isotropic viscoelastic medium is presented. It is well-suited for use as a forward model for some acoustic radiation force impulse based shear wave elastography applications because it does not require precise knowledge of the strength of the source, nor its spatial or temporal distribution. Instead, it depends on two assumptions: (1) the source distribution is axisymmetric and confined to a small region near the axis of symmetry, and (2) the propagation medium is isotropic and homogeneous. The model accounts for the vector polarization of shear waves and exactly represents geometric spreading of the shear wavefield, whether spherical, cylindrical, or neither. It makes no assumption about the frequency dependence of material parameters, i.e., it is material-model independent. Validation using measured shear wavefields excited by acoustic radiation force in a homogeneous gelatin sample show that the model accounts for well over 90% of the measured wavefield "energy." An optimal fit of the model to simulated shear wavefields with noise in a homogeneous viscoelastic medium enables estimation of both the shear storage modulus and shear wave attenuation to within 1%.

Three-dimensional Ultrasound Elasticity Imaging on an Automated Breast Volume Scanning System.

Ultrasound elasticity imaging has demonstrated utility in breast imaging, but it is typically performed with handheld transducers and two-dimensional imaging. Two-dimensional (2D) elastography images tissue stiffness of only a plane and hence suffers from errors due to out-of-plane motion, whereas three-dimensional (3D) data acquisition and motion tracking can be used to track out-of-plane motion that is lost in 2D elastography systems. A commercially available automated breast volume scanning system that acquires 3D ultrasound data with precisely controlled elevational movement of the 1D array ultrasound transducer was employed in this study. A hybrid guided 3D motion-tracking algorithm was developed that first estimated the displacements in one plane using a modified quality-guided search method, and then performed an elevational guided-search for displacement estimation in adjacent planes. To assess the performance of the method, 3D radiofrequency echo data were acquired with this system from a phantom and from an in vivo human breast. For both experiments, the axial displacement fields were smooth and high cross-correlation coefficients were obtained in most of the tracking region. The motion-tracking performance of the new method was compared with a correlation-based exhaustive-search method. For all motion-tracking volume pairs, the average motion-compensated cross-correlation values obtained by the guided-search motion-tracking method were equivalent to those by the exhaustive-search method, and the computation time was about a factor of 10 lesser. Therefore, the proposed 3D ultrasound elasticity imaging method was a more efficient approach to produce a high quality of 3D ultrasound strain image.

Direct Error in Constitutive Equation Formulation for Plane stress Inverse Elasticity Problem.

We present a new computational formulation for inverse problems in elasticity with full field data. The formulation is a variant of an error in the constitutive equation formulation, but allows direct solution for the modulus field and accommodates discontinuous strain fields. The development of the formulation is motivated by the relatively poor performance of current direct formulations, reported so far in literature, in dealing with discontinuities in the strain and material property distribution. The formulation relies on minimizing the error in the constitutive equation, and a momentum equation constraint. Numerical results on model problems show that the formulation is capable handling discontinuous, and noisy strain fields, and also converging with mesh refinement for continuous and discontinuous material property distributions. The application to reconstruct the elastic modulus distribution in solid breast tumors is shown.

A Force-Matched Approach to Large-Strain Nonlinearity in Elasticity Imaging for Breast Lesion Characterization.

OBJECTIVE: Ultrasound elasticity imaging is a class of ultrasound techniques with applications that include the detection of malignancy in breast lesions. Although elasticity imaging traditionally assumes linear elasticity, the large strain elastic response of soft tissue is known to be nonlinear. This study evaluates the nonlinear response of breast lesions for the characterization of malignancy using force measurement and force-controlled compression during ultrasound imaging. METHODS: 54 patients were recruited for this study. A custom force-instrumented compression device was used to apply a controlled force during ultrasound imaging. Motion tracking derived strain was averaged over lesion or background ROIs and matched with compression force. The resulting force-matched strain was used for subsequent analysis and curve fitting. RESULTS: Greater median differences between malignant and benign lesions were observed at higher compressional forces (p-value < 0.05 for compressional forces of 2-6N). Of three candidate functions, a power law function produced the best fit to the force-matched strain. A statistically significant difference in the scaling parameter of the power function between malignant and benign lesions was observed (p-value = 0.025). CONCLUSIONS: We observed a greater separation in average lesion strain between malignant and benign lesions at large compression forces and demonstrated the characterization of this nonlinear effect using a power law model. Using this model, we were able to differentiate between malignant and benign breast lesions. SIGNIFICANCE: With further development, the proposed method to utilize the nonlinear elastic response of breast tissue has the potential for improving non-invasive lesion characterization for potential malignancy.

Multiscale theoretical model shows that aging-related mechanical degradation of cortical bone is driven by microstructural changes in addition to porosity.

This study aims to gain mechanistic understanding of how aging-related changes in the microstructure of cortical bone drive mechanical consequences at the macroscale. To that end, cortical bone was modeled as a bundle of elastic-plastic, parallel fibers, which represented osteons and interstitial tissue, loaded in uniaxial tension. Distinct material properties were assigned to each fiber in either the osteon or interstitial fiber "families." Models representative of mature (20-60 yrs.) bone, and elderly (60+) bone were created by modeling aging via the following changes to the input parameters: (i) increasing porosity from 5% to 15%, (ii) increasing the ratio of the number of osteon fibers relative to interstitial fibers from 40% to 50%, and (iii) changing the fiber material properties from representing mature bone samples to representing elderly bone samples (i.e., increased strength and decreased toughness of interstitial fibers together with decreased toughness of osteon fibers). To understand the respective contributions of these changes, additional models isolating one or two of each of these were also created. From the computed stress-strain curve for the fiber bundle, the yield point (ϵy, σy), ultimate point (ϵu, σu), and toughness (UT) for the bundle as a whole were measured. We found that changes to all three input parameters were required for the model to capture the aging-related decline in cortical bone mechanical properties consistent with those previously reported in the literature. In both mature and elderly bundles, rupture of the interstitial fibers drove the initial loss of strength following the ultimate point. Plasticity and more gradual rupture of the osteons drove the remainder of the response. Both the onset and completion of interstitial fiber rupture occurred at lower strains in the elderly vs. mature case. These findings point to the importance of studying microstructural changes beyond porosity, such as the area fraction of osteons and the material properties of osteon and interstitial tissue, in order to further understanding of aging-related changes in bone.

Discriminating resonant targets from clutter using Lanczos iterated single-channel time reversal.

Power iterated single-channel time-reversal is extended to employ Lanczos iterations. The properties of these algorithms are studied in the presence of varying levels of noise and broadband clutter. It is shown the Lanczos iterated method possesses superior convergence properties in comparison to the standard power iterated technique. Results demonstrate that such algorithms provide an efficient means through which to isolate and extract the properties of resonant scatterers in the presence of noise and coherent interference.

Transversely isotropic elasticity imaging of cancellous bone.

To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ɛ12 is necessary to reconstruct C1212), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of 40 dB is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.

Repeatability of Linear and Nonlinear Elastic Modulus Maps From Repeat Scans in the Breast.

Compression elastography allows the precise measurement of large deformations of soft tissue in vivo. From an image sequence showing tissue undergoing large deformation, an inverse problem for both the linear and nonlinear elastic moduli distributions can be solved. As part of a larger clinical study to evaluate nonlinear elastic modulus maps (NEMs) in breast cancer, we evaluate the repeatability of linear and nonlinear modulus maps from repeat measurements. Within the cohort of subjects scanned to date, 20 had repeat scans. These repeated scans were processed to evaluate NEM repeatability. In vivo data were acquired by a custom-built, digitally controlled, uniaxial compression device with force feedback from the pressure-plate. RF-data were acquired using plane-wave imaging, at a frame-rate of 200 Hz, with a ramp-and-hold compressive force of 8N, applied at 8N/sec. A 2D block-matching algorithm was used to obtain sample-level displacement fields which were then tracked at subsample resolution using 2D cross correlation. Linear and nonlinear elasticity parameters in a modified Veronda-Westmann model of tissue elasticity were estimated using an iterative optimization method. For the repeated scans, B-mode images, strain images, and linear and nonlinear elastic modulus maps are measured and compared. Results indicate that when images are acquired in the same region of tissue and sufficiently high strain is used to recover nonlinearity parameters, then the reconstructed modulus maps are consistent.

Effect of correlation between traction forces on tensional homeostasis in clusters of endothelial cells and fibroblasts.

The ability of cells to maintain a constant level of cytoskeletal tension in response to external and internal disturbances is referred to as tensional homeostasis. It is essential for the normal physiological function of cells and tissues, and for protection against disease progression, including atherosclerosis and cancer. In previous studies, we defined tensional homeostasis as the ability of cells to maintain a consistent level of cytoskeletal tension with low temporal fluctuations. In those studies, we measured temporal fluctuations of cell-substrate traction forces in clusters of endothelial cells and of fibroblasts. We observed those temporal fluctuations to decrease with increasing cluster size in endothelial cells, but not in fibroblasts. We quantified temporal fluctuation, and thus homeostasis, through the coefficient of variation (CV) of the traction field; the lower the value of CV, the closer the cell is to the state of tensional homeostasis. This metric depends on correlation between individual traction forces. In this study, we analyzed the contribution of correlation between traction forces on traction field CV in clusters of endothelial cells and fibroblasts using experimental data that we had obtained previously. Results of our analysis showed that positive correlation between traction forces was detrimental to homeostasis, and that it was cell type-dependent.

Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study.

We present a methodology to image and quantify the shear elastic modulus of three-dimensional (3D) breast tissue volumes held in compression under conditions similar to those of a clinical mammography system. Tissue phantoms are made to mimic the ultrasonic and mechanical properties of breast tissue. Stiff lesions are created in these phantoms with size and modulus contrast values, relative to the background, that are within the range of values of clinical interest. A two-dimensional ultrasound system, scanned elevationally, is used to acquire 3D images of these phantoms as they are held in compression. From two 3D ultrasound images, acquired at different compressed states, a three-dimensional displacement vector field is measured. The measured displacement field is then used to solve an inverse problem, assuming the phantom material to be an incompressible, linear elastic solid, to recover the shear modulus distribution within the imaged volume. The reconstructed values are then compared to values measured independently by direct mechanical testing.

Linear and nonlinear elasticity imaging of soft tissue in vivo: demonstration of feasibility.

We establish the feasibility of imaging the linear and nonlinear elastic properties of soft tissue using ultrasound. We report results for breast tissue where it is conjectured that these properties may be used to discern malignant tumors from benign tumors. We consider and compare three different quantities that describe nonlinear behavior, including the variation of strain distribution with overall strain, the variation of the secant modulus with overall applied strain and finally the distribution of the nonlinear parameter in a fully nonlinear hyperelastic model of the breast tissue.

Lanczos iterated time-reversal.

A new iterative time-reversal algorithm capable of identifying and focusing on multiple scatterers in a relatively small number of iterations is developed. It is recognized that the traditional iterated time-reversal method is based on utilizing power iterations to determine the dominant eigenpairs of the time-reversal operator. The convergence properties of these iterations are known to be suboptimal. Motivated by this, a new method based on Lanczos iterations is developed. In several illustrative examples it is demonstrated that for the same number of transmitted and received signals, the Lanczos iterations based approach is substantially more accurate.

Dispersion in Tissue-Mimicking Gels Measured with Shear Wave Elastography and Torsional Vibration Rheometry.

Dispersion, or the frequency dependence of mechanical parameters, is a primary confounding factor in elastography comparisons. We present a study of dispersion in tissue-mimicking gels over a wide frequency band using a combination of ultrasound shear wave elastography (SWE), and a novel torsional vibration rheometry which allows independent mechanical measurement of SWE samples. Frequency-dependent complex shear modulus was measured in homogeneous gelatin hydrogels of two different bloom strengths while controlling for confounding factors such as temperature, water content and material aging. Furthermore, both techniques measured the same physical samples, thereby eliminating possible variation caused by batch-to-batch gel variation, sample geometry differences and boundary artifacts. The wide-band measurement, from 1 to 1800 Hz, captured a 30%-50% increase in the storage modulus and a nearly linear increase with frequency of the loss modulus. The magnitude of the variation suggests that accounting for dispersion is essential for meaningful comparisons between SWE implementations.

Imaging localized neuronal activity at fast time scales through biomechanics.

Mapping neuronal activity noninvasively is a key requirement for in vivo human neuroscience. Traditional functional magnetic resonance (MR) imaging, with a temporal response of seconds, cannot measure high-level cognitive processes evolving in tens of milliseconds. To advance neuroscience, imaging of fast neuronal processes is required. Here, we show in vivo imaging of fast neuronal processes at 100-ms time scales by quantifying brain biomechanics noninvasively with MR elastography. We show brain stiffness changes of ~10% in response to repetitive electric stimulation of a mouse hind paw over two orders of frequency from 0.1 to 10 Hz. We demonstrate in mice that regional patterns of stiffness modulation are synchronous with stimulus switching and evolve with frequency. For very fast stimuli (100 ms), mechanical changes are mainly located in the thalamus, the relay location for afferent cortical input. Our results demonstrate a new methodology for noninvasively tracking brain functional activity at high speed.

The spatio-temporal strain response of oedematous and nonoedematous tissue to sustained compression in vivo.

Poroelastic theory predicts that compression-induced fluid flow through a medium reveals itself via the spatio-temporal behaviour of the strain field. Such strain behaviour has already been observed in simple poroelastic phantoms using generalised elastographic techniques (Berry et al. 2006a, 2006b). The aim of this current study was to investigate the extent to which these techniques could be applied in vivo to image and interpret the compression-induced time-dependent local strain response in soft tissue. Tissue on both arms of six patients presenting with unilateral lymphoedema was subjected to a sustained compression for up to 500 s, and the induced strain was imaged as a function of time. The strain was found to exhibit time-dependent spatially varying behaviour, which we interpret to be consistent with that of a heterogeneous poroelastic material. This occurred in both arms of all patients, although it was more easily seen in the ipsilateral (affected) arm than in the contralateral (apparently unaffected) arm in five out of the six patients. Further work would appear to be worthwhile to determine if poroelasticity imaging could be used in future both to diagnose lymphoedema and to explore the patho-physiology of the condition.

Customization of the acoustic field produced by a piezoelectric array through interelement delays.

A method for producing a prescribed acoustic pressure field from a piezoelectric array was investigated. The array consisted of 170 elements placed on the inner surface of a 15 cm radius spherical cap. Each element was independently driven by using individual pulsers each capable of generating 1.2 kV. Acoustic field customization was achieved by independently controlling the time when each element was excited. The set of time delays necessary to produce a particular acoustic field was determined by using an optimization scheme. The acoustic field at the focal plane was simulated by using the angular spectrum method, and the optimization searched for the time delays that minimized the least squared difference between the magnitudes of the simulated and desired pressure fields. The acoustic field was shaped in two different ways: the -6 dB focal width was increased to different desired widths and the ring-shaped pressure distributions of various prescribed diameters were produced. For both cases, the set of delays resulting from the respective optimization schemes were confirmed to yield the desired pressure distributions by using simulations and measurements. The simulations, however, predicted peak positive pressures roughly half those obtained from the measurements, which was attributed to the exclusion of nonlinearity in the simulations.

Elastic modulus imaging: some exact solutions of the compressible elastography inverse problem.

We consider several inverse problems motivated by elastography. Given the (possibly transient) displacement field measured everywhere in an isotropic, compressible, linear elastic solid, and given density rho, determine the Lamé parameters lambda and mu. We consider several special cases of this problem: (a) for mu known a priori, lambda is determined by a single deformation field up to a constant. (b) Conversely, for lambda known a priori, mu is determined by a single deformation field up to a constant. This includes as a special case that for which the term [see text]. (c) Finally, if neither lambda nor mu is known a priori, but Poisson's ratio nu is known, then mu and lambda are determined by a single deformation field up to a constant. This includes as a special case plane stress deformations of an incompressible material. Exact analytical solutions valid for 2D, 3D and transient deformations are given for all cases in terms of quadratures. These are used to show that the inverse problem for mu based on the compressible elasticity equations is unstable in the limit lambda --> infinity. Finally, we use the exact solutions as a basis to compute non-trivial modulus distributions in a simulated example.

Reconstructing the adhesion stiffness distribution in a laminated elastic plate: Exact and approximate inverse scattering solutions.

This paper formulates and solves a time harmonic inverse scattering problem to reconstruct the effective stiffness distribution of an adhesive bond in a layered elastic plate. The motivation is based on the assumption that localized adhesion flaws that diminish bond stiffness also tend to diminish bond strength. The formulation is based on the invariant imbedding method, applies to isotropic and anisotropic elastic layers, and is essentially that of identifying embedded acoustic sources in elastic layered structures. This paper presents two solutions for the inverse problem: the Born approximation and the exact solution. The example calculations compare the two solutions and show that when imperfections are too large in either magnitude or extent the accuracy of the Born approximation breaks down. The impact of noise and uncertainties in the background properties in the inversion is also investigated. A regularization strategy is introduced in the exact solution that controls solution sensitivity in regions with low signal to noise ratio.