Quantifying uniaxial prestress and waveguide effects on dynamic elastography estimates for a cylindrical rod

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of materials by noninvasively measuring mechanical wave motion in them. The target motion is typically transversely-polarized relative to the wave propagation direction, such as bulk shear wave motion. In addition to neglecting waveguide effects caused by small lengths in one dimension or more, many reconstruction strategies also ignore nonzero, non-isotropic static preloads. Significant anisotropic prestress is inherent to the functional role of some biological materials of interest, which also are small in size relative to shear wavelengths in one or more dimensions. A cylindrically shaped polymer structure with isotropic material properties is statically elongated along its axis while its response to circumferentially-, axially-, and radially-polarized vibratory excitation is measured using optical or magnetic resonance elastography. Computational finite element simulations augment and aid in the interpretation of experimental measurements. We examine the interplay between uniaxial prestress and waveguide effects. A coordinate transformation approach previously used to simplify the reconstruction of un-prestressed transversely isotropic material properties based on elastography measurements is adapted with partial success to estimate material viscoelastic properties and prestress conditions without requiring advanced knowledge of either.

Decoupling Uniaxial Tensile Prestress and Waveguide Effects From Estimates of the Complex Shear Modulus in a Cylindrical Structure Using Transverse-Polarized Dynamic Elastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a configuration, inspired by muscle elastography but generalizable to other applications, is analytically and experimentally studied. A hyperelastic polymer phantom cylinder is statically elongated in the axial direction while its response to transverse-polarized vibratory excitation is measured. We examine the interplay between uniaxial prestress and waveguide effects in this muscle-like tissue phantom using computational finite element simulations and magnetic resonance elastography measurements. Finite deformations caused by prestress coupled with waveguide effects lead to results that are predicted by a coordinate transformation approach that has been previously used to simplify reconstruction of anisotropic properties using elastography. Here, the approach estimates material viscoelastic properties that are independent of the nonhomogeneous prestress conditions without requiring advanced knowledge of those stress conditions.

Biaxial Tensile Prestress and Waveguide Effects on Estimates of the Complex Shear Modulus Using Optical-Based Dynamic Elastography in Plate-Like Soft Tissue Phantoms

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a novel configuration, inspired by corneal elastography but generalizable to other applications, is studied. A polymer phantom layer is statically elongated via an in-plane biaxial normal stress while the phantom's response to transverse vibratory excitation is measured. We examine the interplay between biaxial prestress and waveguide effects in this plate-like tissue phantom. Finite static deformations caused by prestressing coupled with waveguide effects lead to results that are predicted by a novel coordinate transformation approach previously used to simplify reconstruction of anisotropic properties. Here, the approach estimates material viscoelastic properties independent of the nonzero prestress conditions without requiring advanced knowledge of those stress conditions.

Tabletop MR elastography for investigating effects of the freeze-thaw cycle on the mechanical properties of biological tissues

PURPOSE

We aimed at characterizing the effects of the freeze-thaw cycle (FTC) on ex vivo specimens of porcine muscle, liver, kidney, and brain using tabletop magnetic resonance elastography (MRE) combined with rheological modeling. While frozen tissue banks potentially facilitate access to large amounts of well-preserved biospecimens, the impact of the FTC on their viscoelastic properties remains elusive.

METHODS

In this proof-of-concept study, fresh specimens from porcine lumbar muscle (n = 6), liver (n = 6), kidney (n = 6), and brain (n = 6) were examined before and after the FTC using 0.5T tabletop MRE at 500 Hz, 1000 Hz, 1500 Hz, and 2000 Hz. Seven standard rheological models (Maxwell, Springpot, Voigt, Zener, Jeffrey, fractional Voigt, fractional Zener) were employed to calculate frequency independent viscoelastic parameters.

RESULTS

The Zener rheological model showed the best fit quality for tissues before and after FTC in the investigated frequency range. Global rheological behavior after the FTC was softer for all tissues. Differences in mechanical parameters between tissues were preserved after the FTC and showed similar trends as before the FTC. Moreover, rheological fit quality improved after the FTC - a result that will be beneficial in investigating frozen tissue bank samples.

CONCLUSION

Multifrequency tabletop MRE allows rheological characterization of tissue samples before and after the FTC. Our results encourage further biomechanical characterization of frozen tissue bank samples, which may provide valuable information on the diagnostic potential of elastographic methods.

The combined importance of finite dimensions, anisotropy, and pre-stress in acoustoelastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties that are altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasistatic tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article, we review how prestress alters both bulk mechanical wave motion and wave motion in one- and two-dimensional waveguides. Key findings are linked to studies on skeletal muscle and the human cornea, as one- and two-dimensional waveguide examples. This study highlights the underappreciated combined acoustoelastic and waveguide challenge to elastography. Can elastography truly determine viscoelastic properties of a material when what it is measuring is affected by both these material properties and unknown prestress and other boundary conditions?

Investigating the heterogeneity of viscoelastic properties in prostate cancer using MR elastography at 9.4T in fresh prostatectomy specimens

PURPOSE

To quantify the heterogeneity of viscoelastic tissue properties in prostatectomy specimens from men with prostate cancer (PC) using MR elastography (MRE) with histopathology as reference.

METHODS

Twelve fresh prostatectomy specimens were examined in a preclinical 9.4T MRI scanner. Maps of the complex shear modulus (|G*| in kPa) with its real and imaginary part (G' and G" in kPa) were calculated at 500 Hz. Prostates were divided into 12 segments for segment-wise measurement of viscoelastic properties and histopathology. Coefficients of variation (CVs in %) were calculated for quantification of heterogeneity.

RESULTS

Group-averaged values of cancerous vs. benign segments were significantly increased: |G*| of 12.13 kPa vs. 6.14 kPa, G' of 10.84 kPa vs. 5.44 kPa and G" of 5.45 kPa vs. 2.92 kPa, all p < 0.001. In contrast, CVs were significantly increased for benign segments: 23.59% vs. 26.32% (p = 0.014) for |G*|, 27.05% vs. 37.84% (p < 0.003) for G', and 36.51% vs. 50.37% (p = 0.008) for G".

DISCUSSION

PC is characterized by a stiff yet homogeneous biomechanical signature, which may be due to the unique nondestructive growth pattern of PC with intervening stroma, providing a rigid scaffold in the affected area. In turn, increased heterogeneity in benign prostate segments may be attributable to the presence of different prostate zones with involvement by specific nonmalignant pathology.

Optical coherence elastography for assessing the influence of intraocular pressure on elastic wave dispersion in the cornea

The cornea is a highly specialized organ that relies on its mechanical stiffness to maintain its aspheric geometry and refractive power, and corneal diseases such as keratoconus have been linked to abnormal tissue stiffness and biomechanics. Dynamic optical coherence elastography (OCE) is a clinically promising non-contact and non-destructive imaging technique that can provide measurements of corneal tissue stiffness directly in vivo. The method relies on the concepts of elastography where shear waves are generated and imaged within a tissue to obtain mechanical properties such as tissue stiffness. The accuracy of OCE-based measurements is ultimately dependent on the mathematical theories used to model wave behavior in the tissue of interest. In the cornea, elastic waves propagate as guided wave modes which are highly dispersive and can be mathematically complex to model. While recent groups have developed detailed theories for estimating corneal tissue properties from guided wave behavior, the effects of intraocular pressure (IOP)-induced prestress have not yet been considered. It is known that prestress alone can strongly influence wave behavior, in addition to the associated non-linear changes in tissue properties. This present study shows that failure to account for the effects of prestress may result in overestimations of the corneal shear moduli, particularly at high IOPs. We first examined the potential effects of IOP and IOP-induced prestress using a combination of approximate mathematical theories describing wave behavior in thin plates with observations made from data published in the OCE literature. Through wave dispersion analysis, we deduce that IOP introduces a tensile hoop stress and may also influence an elastic foundational effect that were observable in the low-frequency components of the dispersion curves. These effects were incorporated into recently developed models of wave behavior in nearly incompressible, transversely isotropic (NITI) materials. Fitting of the modified NITI model with ex vivo porcine corneal data demonstrated that incorporation of the effects of IOP resulted in reduced estimates of corneal shear moduli. We believe this demonstrates that overestimation of corneal stiffness occurs if IOP is not taken into consideration. Our work may be helpful in separating inherent corneal stiffness properties that are independent of IOP; changes in these properties and in IOP are distinct, clinically relevant issues that affect the cornea health.

Axially- and torsionally-polarized radially converging shear wave MRE in an anisotropic phantom made via Embedded Direct Ink Writing

Magnetic Resonance Elastography (MRE) is a non-invasive imaging method to quantitatively map the shear viscoelastic properties of soft tissues. In this study, Embedded Direct Ink Writing is used to fabricate a muscle mimicking anisotropic phantom that may serve as a standard for imaging studies of anisotropic materials. The technique allowed us to obtain a long shelf life silicone-based phantom expressing transverse isotropic mechanical properties. Another goal of the present investigation is to introduce a torsionally-polarized, radially-converging shear wave actuation method for MRE. The implemented design for this novel setup was first validated via its application to isotropic and homogeneous gelatin phantoms. Then, a comparison of the resulting complex wave images from axially- and torsionally-polarized MRE on the developed anisotropic phantom and on a skeletal muscle murine sample is presented, highlighting the value of using multiple actuation and motion encoding polarization directions when studying anisotropic materials.

Measuring viscoelastic parameters in Magnetic Resonance Elastography: a comparison at high and low magnetic field intensity

Magnetic Resonance Elastography (MRE) is a non-invasive imaging technique which involves motion-encoding MRI for the estimation of the shear viscoelastic properties of soft tissues through the study of shear wave propagation. The technique has been found informative for disease diagnosis, as well as for monitoring of the effects of therapies. The development of MRE and its validation have been supported by the use of tissue-mimicking phantoms. In this paper we present our new MRE protocol using a low magnetic field tabletop MRI device at 0.5 T and sinusoidal uniaxial excitation in a geometrical focusing condition. Results obtained for gelatin are compared to those previously obtained using high magnetic field MRE at 11.7 T. A multi-frequency investigation is also provided via a comparison of commonly used rheological models: Maxwell, Springpot, Voigt, Zener, Jeffrey, fractional Voigt and fractional Zener. Complex shear modulus values were comparable when processed from images acquired with the tabletop low field scanner and the high field scanner. This study serves as a validation of the presented tabletop MRE protocol and paves the way for MRE experiments on ex-vivo tissue samples in both normal and pathological conditions.

Analytical solution based on spatial distortion for a time-harmonic Green's function in a transverse isotropic viscoelastic solid

A strategy of spatial distortion to make an anisotropic problem become isotropic has been previously validated in two-dimensional transverse isotropic (TI) viscoelastic cases. Here, the approach is extended to the three-dimensional problem by considering the time-harmonic point force response (Green's function) in a TI viscoelastic material. The resulting wave field, exactly solvable using a Radon transform with numerical integration, is approximated via spatial distortion of the closed form analytical solution to the isotropic case. Different distortions are used, depending on whether the polarization of the wave motion is orthogonal to the axis of isotropy, with the approximation yielding differing levels of accuracy.

MR elastography: Principles, guidelines, and terminology

Magnetic resonance elastography (MRE) is a phase contrast-based MRI technique that can measure displacement due to propagating mechanical waves, from which material properties such as shear modulus can be calculated. Magnetic resonance elastography can be thought of as quantitative, noninvasive palpation. It is increasing in clinical importance, has become widespread in the diagnosis and staging of liver fibrosis, and additional clinical applications are being explored. However, publications have reported MRE results using many different parameters, acquisition techniques, processing methods, and varied nomenclature. The diversity of terminology can lead to confusion (particularly among clinicians) about the meaning of and interpretation of MRE results. This paper was written by the MRE Guidelines Committee, a group formalized at the first meeting of the ISMRM MRE Study Group, to clarify and move toward standardization of MRE nomenclature. The purpose of this paper is to (1) explain MRE terminology and concepts to those not familiar with them, (2) define "good practices" for practitioners of MRE, and (3) identify opportunities to standardize terminology, to avoid confusion.

Early Detection of Acute Chest Syndrome Through Electronic Recording and Analysis of Auscultatory Percussion

Acute chest syndrome (ACS) is the leading cause of death among people with sickle cell disease. ACS is clinically defined and diagnosed by the presence of a new pulmonary infiltrate on chest imaging with accompanying fever and respiratory symptoms like hypoxia, tachypnea, and shortness of breath. However, the characteristic chest x-ray (CXR) findings necessary for a clinical diagnosis of ACS can be difficult to detect, as is determining which patient needs a CXR. This makes early detection difficult; but it is critical in order to limit ACS severity and subsequent fatalities. This research project looks to apply percussion and auscultation techniques that can provide an immediate diagnosis of acute pulmonary conditions by using an automated standard percussive input and electronic auscultation for computational analysis of the measured signal. Measurements on sickle cell patients having ACS, vaso-occlusive crisis (VOC), and regular clinic visits (healthy) were recorded and analyzed. Average intensity of sound transmission through the chest and lungs was determined in the ACS and healthy subject groups, revealing an average of 10–14 dB decrease in sound intensity in the ACS group compared to the healthy group. A random under-sampling boosted tree classification model identified with 94% accuracy the positive ACS and healthy observations. The analysis also revealed unique measurable changes in a small number of cases clinically classified as complicated VOC, which later developed into ACS. This suggests the developed approach may also have early predictive capability, identifying patients at risk for developing ACS prior to current clinical practice.

Sound transmission in human thorax through airway insonification: an experimental and computational study with diagnostic applications

Pulmonary diseases and injury lead to structural and functional changes in the lung parenchyma and airways, often resulting in measurable sound transmission changes on the chest wall surface. Additionally, noninvasive imaging of externally driven mechanical wave motion in the chest (e.g., using magnetic resonance elastography) can provide information about lung stiffness and other structural property changes which may be of diagnostic value. In the present study, a comprehensive computational simulation (in silico) model was developed to simulate sound wave propagation in the airways, parenchyma, and chest wall under normal and pathological conditions that create distributed structural (e.g., pneumothoraces) and diffuse material (e.g., fibrosis) changes, as well as a localized structural and material changes as may be seen with a neoplasm. Experiments were carried out in normal subjects to validate the baseline model. Sound waves with frequency content from 50 to 600 Hz were introduced into the airways of three healthy human subjects through the mouth, and transthoracic transmitted waves were measured by scanning laser Doppler vibrometry at the chest wall surface. The computational model predictions of a frequency-dependent decreased sound transmission due to pneumothorax were consistent with experimental measurements reported in previous work. Predictions for the case of fibrosis show that while shear wave motion is altered, changes to compression wave propagation are negligible, and thus, insonification, which primarily drives compression waves, is not ideal to detect the presence of fibrosis. Results from the numerical simulation of a tumor show an increase in the wavelength of propagating waves in the immediate vicinity of the tumor region. Graphical abstract.

Simulation of bronchial airway acoustics in healthy and asthmatic subjects

The onset and development of many airway pathologies affect sound propagation throughout the respiratory system; changes in respiratory sounds are detected primarily by auscultation, which is highly skill dependent. The aim of the present study was to compare healthy and asthmatic pulmonary acoustics by applying a 1D model of wave propagation on CT-based patient-specific geometries. High-resolution CT lung images were acquired in five healthy volunteers and five asthmatic patients at total lung capacity (TLC) and functional residual capacity (FRC). Tracheobronchial trees were reconstructed from CT images. Acoustic pressure, impedance and wall radial velocity were measured by simulating acoustic wave propagation of two external, acoustic pressure waves (1 Pa, 200 and 600 Hz) from the trachea level to the 4th generation. In asthmatic patients, acoustic pressure averaged across the last three generations showed a reduction equal to 29.7% (p<0.01) at FRC, at 200 Hz; input and terminal impedance were 34.5% (p<0.05) higher both at FRC and TLC; wall radial velocity was more than 80% (p<0.05) lower in higher generations both at FRC and TLC. Airway differences in asthma alter acoustic parameters at FRC and TLC, with the greatest difference at FRC and 200 Hz. Acoustic wave propagation analysis represents a quantitative approach that has potential to objectively characterize airway differences in individuals with diseases such as asthma.

Converging super-elliptic torsional shear waves in a bounded transverse isotropic viscoelastic material with nonhomogeneous outer boundary

A theoretical approach was recently introduced [Guidetti and Royston, J. Acoust. Soc. Am. 144, 2312-2323 (2018)] for the radially converging slow shear wave pattern in transverse isotropic materials subjected to axisymmetric excitation normal to the axis of isotropy at the outer boundary of the material. This approach is enabled via transformation to an elliptic coordinate system with isotropic properties. The approach is extended to converging fast shear waves driven by axisymmetric torsional motion polarized in a plane containing the axis of isotropy. The approach involves transformation to a super-elliptic shape with isotropic properties and use of a numerically efficient boundary value approximation.

Converging super-elliptic torsional shear waves in a bounded transverse isotropic viscoelastic material with nonhomogeneous outer boundary

A theoretical approach was recently introduced [Guidetti and Royston, J. Acoust. Soc. Am. 144, 2312-2323 (2018)] for the radially converging slow shear wave pattern in transverse isotropic materials subjected to axisymmetric excitation normal to the axis of isotropy at the outer boundary of the material. This approach is enabled via transformation to an elliptic coordinate system with isotropic properties. The approach is extended to converging fast shear waves driven by axisymmetric torsional motion polarized in a plane containing the axis of isotropy. The approach involves transformation to a super-elliptic shape with isotropic properties and use of a numerically efficient boundary value approximation.

Changes in shear wave propagation within skeletal muscle during active and passive force generation

Muscle force can be generated actively through changes in neural excitation, and passively through externally imposed changes in muscle length. Disease and injury can disrupt force generation, but it can be challenging to separate passive from active contributions to these changes. Ultrasound elastography is a promising tool for characterizing the mechanical properties of muscles and the forces that they generate. Most prior work using ultrasound elastography in muscle has focused on the group velocity of shear waves, which increases with increasing muscle force. Few studies have quantified the phase velocity, which depends on the viscoelastic properties of muscle. Since passive and active forces within muscle involve different structures for force transmission, we hypothesized that measures of phase velocity could detect changes in shear wave propagation during active and passive conditions that cannot be detected when considering only group velocity. We measured phase and group velocity in the human biceps brachii during active and passive force generation and quantified the differences in estimates of shear elasticity obtained from each of these measurements. We found that measures of group velocity consistently overestimate the shear elasticity of muscle. We used a Voigt model to characterize the phase velocity and found that the estimated time constant for the Voigt model provided a way to distinguish between passive and active force generation. Our results demonstrate that shear wave elastography can be used to distinguish between passive and active force generation when it is used to characterize the phase velocity of shear waves propagating in muscle.

An investigation into the relationship between inhomogeneity and wave shapes in phantoms and ex vivo skeletal muscle using Magnetic Resonance Elastography and finite element analysis

Soft biological tissues such as skeletal muscle and brain white matter can be inhomogeneous and anisotropic due to the presence of fibers. Unlike biological tissue, phantoms with known microstructure and defined mechanical properties enable a quantitative assessment and systematic investigation of the influence of inhomogeneities on the nature of shear wave propagation. This study introduces a mathematical measure for the wave shape, which the authors call as the 1-Norm, to determine the conditions under which homogenization may be a valid approach. This is achieved through experimentation using the Magnetic Resonance Elastography technique on 3D printed inhomogeneous fiber phantoms as well as on ex-vivo porcine lumbus muscle. In addition, Finite Element Analysis is used as a tool to decouple the effects of directional anisotropy from those of inhomogeneity. A correlation is then established between the values of 1-Norm derived from the wave front geometry, and the spacing (d) between neighboring inhomogeneities (spherical inclusions or fibers and fiber intersections in phantoms and muscle). Smaller values of 1-Norm indicate less wave scattering at the locations of fiber intersections, which implies that the wave propagation may be approximated to that of a homogeneous medium; homogenization may not be a valid approximation when significant scattering occurs at the locations of inhomogeneities. In conclusion, the current study proposes 1-Norm as a quantitative measure of the magnitude of wave scattering in a medium, which can potentially be used as a homogeneity index of a biological tissue.

Analytical solution for diverging elliptic shear wave in bounded and unbounded transverse isotropic viscoelastic material with nonhomogeneous inner boundary

A theoretical approach was recently introduced by Guidetti and Royston [J. Acoust. Soc. Am. 144, 2312-2323 (2018)] for the radially converging elliptic shear wave pattern in transverse isotropic materials subjected to axisymmetric excitation normal to the fiber axis at the outer boundary of the material. This approach is enabled via a transformation to an elliptic coordinate system with isotropic properties. The approach is extended to the case of diverging shear waves radiating from a cylindrical rod that is axially oscillating perpendicular to the axis of isotropy and parallel to the plane of isotropy.

Acoustic Methods for Pulmonary Diagnosis

Recent developments in sensor technology and computational analysis methods enable new strategies to measure and interpret lung acoustic signals that originate internally, such as breathing or vocal sounds, or are externally introduced, such as in chest percussion or airway insonification. A better understanding of these sounds has resulted in a new instrumentation that allows for highly accurate as well as portable options for measurement in the hospital, in the clinic, and even at home. This review outlines the instrumentation for acoustic stimulation and measurement of the lungs. We first review the fundamentals of acoustic lung signals and the pathophysiology of the diseases that these signals are used to detect. Then, we focus on different methods of measuring and creating signals that have been used in recent research for pulmonary disease diagnosis. These new methods, combined with signal processing and modeling techniques, lead to a reduction in noise and allow improved feature extraction and signal classification. We conclude by presenting the results of human subject studies taking advantage of both the instrumentation and signal processing tools to accurately diagnose common lung diseases. This paper emphasizes the active areas of research within modern lung acoustics and encourages the standardization of future work in this field.

Analytical solution for converging elliptic shear wave in a bounded transverse isotropic viscoelastic material with nonhomogeneous outer boundary

Dynamic elastography methods-based on optical, ultrasonic, or magnetic resonance imaging-are being developed for quantitatively mapping the shear viscoelastic properties of biological tissues, which are often altered by disease and injury. These diagnostic imaging methods involve analysis of shear wave motion in order to estimate or reconstruct the tissue's shear viscoelastic properties. Most reconstruction methods to date have assumed isotropic tissue properties. However, application to tissues like skeletal muscle and brain white matter with aligned fibrous structure resulting in local transverse isotropic mechanical properties would benefit from analysis that takes into consideration anisotropy. A theoretical approach is developed for the elliptic shear wave pattern observed in transverse isotropic materials subjected to axisymmetric excitation creating radially converging shear waves normal to the fiber axis. This approach, utilizing Mathieu functions, is enabled via a transformation to an elliptic coordinate system with isotropic properties and a ratio of minor and major axes matching the ratio of shear wavelengths perpendicular and parallel to the plane of isotropy in the transverse isotropic material. The approach is validated via numerical finite element analysis case studies. This strategy of coordinate transformation to equivalent isotropic systems could aid in analysis of other anisotropic tissue structures.

Anisotropic composite material phantom to improve skeletal muscle characterization using magnetic resonance elastography

The presence and progression of neuromuscular pathology, including spasticity, Duchenne's muscular dystrophy and hyperthyroidism, has been correlated with changes in the intrinsic mechanical properties of skeletal muscle tissue. Tools for noninvasively measuring and monitoring these properties, such as Magnetic Resonance Elastography (MRE), could benefit basic research into understanding neuromuscular pathologies, as well as translational research to develop therapies, by providing a means of assessing and tracking their efficacy. Dynamic elastography methods for noninvasive measurement of tissue mechanical properties have been under development for nearly three decades. Much of the technological development to date, for both Ultrasound (US)-based and Magnetic Resonance Imaging (MRI)-based strategies, has been grounded in assumptions of local homogeneity and isotropy. Striated skeletal and cardiac muscle, as well as brain white matter and soft tissue in some other organ regions, exhibit a fibrous microstructure which entails heterogeneity and anisotropic response; as one seeks to improve the accuracy and resolution in mechanical property assessment, heterogeneity and anisotropy need to be accounted for in order to optimize both the dynamic elastography experimental protocol and the interpretation of the measurements. Advances in elastography methodology at every step have been aided by the use of tissue-mimicking phantoms. The aim of the present study was to develop and characterize a heterogeneous composite phantom design with uniform controllable anisotropic properties meant to be comparable to the frequency-dependent anisotropic properties of skeletal muscle. MRE experiments and computational finite element (FE) studies were conducted on a novel 3D-printed composite phantom design. The displacement maps obtained from simulation and experiment show the same elliptical shaped wavefronts elongated in the plane where the structure presents higher shear modulus. The model exhibits a degree of anisotropy in line with literature data from skeletal muscle tissue MRE experiments. FE simulations of the MRE experiments provide insight into proper interpretation of experimental measurements, and help to quantify the importance of heterogeneity in the anisotropic material at different scales.

Finite Element Based Optimization of Human Fingertip Optical Elastography

Dynamic elastography methods attempt to quantitatively map soft tissue viscoelastic properties. Application to the fingertip, relevant to medical diagnostics and to improving tactile interfaces, is a novel and challenging application, given the small target size. In this feasibility study, an annular actuator placed on the surface of the fingertip and driven harmonically at multiple frequencies sequentially creates geometrically focused surface (GFS) waves. These surface wave propagation patterns are measured using scanning laser Doppler vibrometry. Reconstruction (the inverse problem) is performed in order to estimate fingertip soft tissue viscoelastic properties. The study identifies limitations of an analytical approach and introduces an optimization approach that utilizes a finite element (FE) model. Measurement at multiple frequencies reveals limitations of an assumption of homogeneity of material properties. Identified shear viscoelastic properties increase significantly as frequency increases and the depth of penetration of the surface wave is reduced, indicating that the fingertip is significantly stiffer near its surface.

Localization of adventitious respiratory sounds

In a recent publication by Henry and Royston [J. Acoust. Soc. Am. 142, 1774-1783 (2017)], an algorithm was introduced to calculate the acoustic response to externally introduced and endogenous respiratory sounds within a realistic, patient-specific subglottal airway tree. This work is extended using an efficient numerical boundary element (BE) approach to calculate the resulting radiated sound field from the airway tree into the lung parenchyma taking into account the surrounding chest wall. Within the BE model of the left lung parenchyma, comprised of more than 6000 triangular surface elements, more than 30 000 monopoles are used to approximate complex airway-originated acoustic sources. The chest wall is modeled as a boundary condition on the parenchymal surface. Several cases were simulated, including a bronchoconstricted lung that had an internal acoustic source introduced in a bronchiole, approximating a wheeze. An acoustic source localization algorithm coupled to the BE model estimated the wheeze source location to within a few millimeters based solely on the acoustic field at the surface. Improved noninvasive means of locating adventitious respiratory sounds may enhance an understanding of acoustic changes correlated to pathology, and potentially provide improved noninvasive tools for the diagnosis of pulmonary diseases that uniquely alter acoustics.

A multiscale analytical model of bronchial airway acoustics

Sound transmission and resulting airway wall vibration in a complex multiscale viscoelastic model of the subglottal bronchial tree was calculated using a modified one-dimensional (1D) branching acoustic waveguide approach. This is an extension of previous work to enable use of complex airway trees that are partially derived from subject-specific medical images, without the need for self-similarity in the geometric structure. The approach was validated numerically for simplified airway geometries, as well as experimentally by comparison to previous studies. A comprehensive conducting airway tree with about 60 000 branches was then modified to create fibrotic, bronchoconstrictive, and pulmonary infiltrate conditions. The fibrotic case-systemic increase in soft tissue stiffness-increased the Helmholtz resonance frequency due to the increased acoustic impedance. Bronchoconstriction, with geometric changes in small conducting airways, decreased acoustic energy transmission to the peripheral airways due in part to the increased impedance mismatch between airway orders. Pulmonary infiltrate significantly altered the local acoustic field in the affected lobe. Calculation of acoustic differences between healthy versus pathologic cases can be used to enhance the understanding of vibro-acoustic changes correlated to pathology, and potentially provide improved tools for the diagnosis of pulmonary diseases that uniquely alter the acoustics of the airways.

Scattering and Diffraction of Elastodynamic Waves in a Concentric Cylindrical Phantom for MR Elastography

AIM

The focus of this paper is to report on the design and construction of a multiply connected phantom for use in magnetic resonance elastography (MRE)-an imaging technique that allows for the noninvasive visualization of the displacement field throughout an object from externally driven harmonic motion-as well as its inverse modeling with a closed-form analytic solution which is derived herein from first principles.

METHODS

Mathematically, the phantom is described as two infinite concentric circular cylinders with unequal complex shear moduli, harmonically vibrated at the exterior surface in a direction along their common axis. Each concentric cylinder is made of a hydrocolloid with its own specific solute concentration. They are assembled in a multistep process for which custom scaffolding was designed and built. A customized spin-echo-based MR elastography sequence with a sinusoidal motion-sensitizing gradient was used for data acquisition on a 9.4 T Agilent small-animal MR scanner. Complex moduli obtained from the inverse model are used to solve the forward problem with a finite-element method.

RESULTS

Both complex shear moduli show a significant frequency dependence (p 0.001) in keeping with previous work.

CONCLUSION

The novel multiply connected phantom and mathematical model are validated as a viable tool for MRE studies.

SIGNIFICANCE

On a small enough scale much of physiology can be mathematically modeled with basic geometric shapes, e.g., a cylinder representing a blood vessel. This study demonstrates the possibility of elegant mathematical analysis of phantoms specifically designed and carefully constructed for biomedical MRE studies.

Cardiac MR elastography of the mouse: Initial results

PURPOSE

Many cardiovascular diseases are associated with abnormal function of myocardial contractility or dilatability, which is related to elasticity changes of the myocardium over the cardiac cycle. The mouse is a common animal model in studies of the progression of various cardiomyopathies. We introduce a novel noninvasive approach using microscopic scale MR elastography (MRE) to measure the myocardium stiffness change during the cardiac cycle on a mouse model.

METHODS

A harmonic mechanical wave of 400 Hz was introduced into the mouse body. An electrocardiograph-gated and respiratory-gated fractional encoding cine-MRE pulse sequence was applied to encode the resulting oscillatory motion on a short-axis slice of the heart. Five healthy mice (age range, 3-13.5 mo) were examined. The weighted summation effective stiffness of the left ventricle wall during the cardiac cycle was estimated.

RESULTS

The ratio of stiffness at end diastole and end systole was 0.5-0.67. Additionally, variation in shear wave amplitude in the left ventricle wall throughout the cardiac cycle was measured and found to correlate with estimates of stiffness variation.

CONCLUSION

This study demonstrates the feasibility of implementing cardiac MRE on a mouse model. Magn Reson Med 76:1879-1886, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Dynamic viscoelastic models of human skin using optical elastography

A novel technique for measuring in vivo human skin viscoelastic properties using optical elastography has been developed. The technique uses geometrically focused surface (GFS) waves that allow for wide bandwidth measurements of the wave field. An analytical solution for the case of a radiating annular disk surface source was fit to experimentally measured GFS waves, enabling an estimate of the frequency-dependent surface wavenumber, which can then be related to the dynamic shear modulus. Several viscoelastic models were then fit to the dynamic shear modulus dispersion curve. Viscoelastic models were evaluated based on their overall quality of fit and variability amongst healthy volunteers. An Ecoflex phantom was used to validate the procedure and results by comparison to similar studies using the same type of phantom. For skin results, it was found that the 'α' parameters from the fractional models had the least variability, with coefficients of variability of 0.15, and 0.16. The best fitting models were the standard linear solid, and the fractional Voigt, with a mean fit correlation coefficient, R(2), of 0.93, 0.89, respectively. This study has demonstrated the efficacy of this new method, and with larger studies the viscoelastic skin models could be used to identify various skin diseases and their response to treatment.

Sound transmission in porcine thorax through airway insonification

Many pulmonary injuries and pathologies may lead to structural and functional changes in the lungs resulting in measurable sound transmission changes on the chest surface. Additionally, noninvasive imaging of externally driven mechanical wave motion in the chest (e.g., using magnetic resonance elastography) can provide information about lung structural property changes and, hence, may be of diagnostic value. In the present study, a comprehensive computational simulation (in silico) model was developed to simulate sound wave propagation in the airways, lung, and chest wall under normal and pneumothorax conditions. Experiments were carried out to validate the model. Here, sound waves with frequency content from 50 to 700 Hz were introduced into airways of five porcine subjects via an endotracheal tube, and transmitted waves were measured by scanning laser Doppler vibrometry at the chest wall surface. The computational model predictions of decreased sound transmission with pneumothorax were consistent with experimental measurements. The in silico model can also be used to visualize wave propagation inside and on the chest wall surface for other pulmonary pathologies, which may help in developing and interpreting diagnostic procedures that utilize sound and vibration.

A model of lung parenchyma stress relaxation using fractional viscoelasticity

Some pulmonary diseases and injuries are believed to correlate with lung viscoelasticity changes. Hence, a better understanding of lung viscoelastic models could provide new perspectives on the progression of lung pathology and trauma. In the presented study, stress relaxation measurements were performed to quantify relaxation behavior of pig lungs. Results have uncovered certain trends, including an initial steep decay followed by a slow asymptotic relaxation, which would be better described by a power law than exponential decay. The fractional standard linear solid (FSLS) and two integer order viscoelastic models - standard linear solid (SLS) and generalized Maxwell (GM) - were used to fit the stress relaxation curves; the FSLS was found to be a better fit. It is suggested that fractional order viscoelastic models, which have nonlocal, multi-scale attributes and exhibit power law behavior, better capture the lung parenchyma viscoelastic behavior.

Pneumothorax effects on pulmonary acoustic transmission

Pneumothorax (PTX) is an abnormal accumulation of air between the lung and the chest wall. It is a relatively common and potentially life-threatening condition encountered in patients who are critically ill or have experienced trauma. Auscultatory signs of PTX include decreased breath sounds during the physical examination. The objective of this exploratory study was to investigate the changes in sound transmission in the thorax due to PTX in humans. Nineteen human subjects who underwent video-assisted thoracic surgery, during which lung collapse is a normal part of the surgery, participated in the study. After subjects were intubated and mechanically ventilated, sounds were introduced into their airways via an endotracheal tube. Sounds were then measured over the chest surface before and after lung collapse. PTX caused small changes in acoustic transmission for frequencies below 400 Hz. A larger decrease in sound transmission was observed from 400 to 600 Hz, possibly due to the stronger acoustic transmission blocking of the pleural air. At frequencies above 1 kHz, the sound waves became weaker and so did their changes with PTX. The study elucidated some of the possible mechanisms of sound propagation changes with PTX. Sound transmission measurement was able to distinguish between baseline and PTX states in this small patient group. Future studies are needed to evaluate this technique in a wider population.

Experimental and Computational Studies of Sound Transmission in a Branching Airway Network Embedded in a Compliant Viscoelastic Medium

Breath sounds are often used to aid in the diagnosis of pulmonary disease. Mechanical and numerical models could be used to enhance our understanding of relevant sound transmission phenomena. Sound transmission in an airway mimicking phantom was investigated using a mechanical model with a branching airway network embedded in a compliant viscoelastic medium. The Horsfield self-consistent model for the bronchial tree was adopted to topologically couple the individual airway segments into the branching airway network. The acoustics of the bifurcating airway segments were measured by microphones and calculated analytically. Airway phantom surface motion was measured using scanning laser Doppler vibrometry. Finite element simulations of sound transmission in the airway phantom were performed. Good agreement was achieved between experiments and simulations. The validated computational approach can provide insight into sound transmission simulations in real lungs.

Ultra wideband (0.5-16 kHz) MR elastography for robust shear viscoelasticity model identification

Changes in the viscoelastic parameters of soft biological tissues often correlate with progression of disease, trauma or injury, and response to treatment. Identifying the most appropriate viscoelastic model, then estimating and monitoring the corresponding parameters of that model can improve insight into the underlying tissue structural changes. MR Elastography (MRE) provides a quantitative method of measuring tissue viscoelasticity. In a previous study by the authors (Yasar et al 2013 Magn. Reson. Med. 70 479-89), a silicone-based phantom material was examined over the frequency range of 200 Hz-7.75 kHz using MRE, an unprecedented bandwidth at that time. Six viscoelastic models including four integer order models and two fractional order models, were fit to the wideband viscoelastic data (measured storage and loss moduli as a function of frequency). The 'fractional Voigt' model (spring and springpot in parallel) exhibited the best fit and was even able to fit the entire frequency band well when it was identified based only on a small portion of the band. This paper is an extension of that study with a wider frequency range from 500 Hz to 16 kHz. Furthermore, more fractional order viscoelastic models are added to the comparison pool. It is found that added complexity of the viscoelastic model provides only marginal improvement over the 'fractional Voigt' model. And, again, the fractional order models show significant improvement over integer order viscoelastic models that have as many or more fitting parameters.

Comparison of Poroviscoelastic Models for Sound and Vibration in the Lungs

Noninvasive measurement of mechanical wave motion (sound and vibration) in the lungs may be of diagnostic value, as it can provide information about the mechanical properties of the lungs, which in turn are affected by disease and injury. In this study, two previously derived theoretical models of the vibroacoustic behavior of the lung parenchyma are compared: (1) a Biot theory of poroviscoelasticity and (2) an effective medium theory for compression wave behavior (also known as a "bubble swarm" model). A fractional derivative formulation of shear viscoelasticity is integrated into both models. A measurable "fast" compression wave speed predicted by the Biot theory formulation has a significant frequency dependence that is not predicted by the effective medium theory. Biot theory also predicts a slow compression wave. The experimentally measured fast compression wave speed and attenuation in a pig lung ex vivo model agreed well with the Biot theory. To obtain the parameters for the Biot theory prediction, the following experiments were undertaken: quasistatic mechanical indentation measurements were performed to estimate the lung static shear modulus; surface wave measurements were performed to estimate lung tissue shear viscoelasticity; and flow permeability was measured on dried lung specimens. This study suggests that the Biot theory may provide a more robust and accurate model than the effective medium theory for wave propagation in the lungs over a wider frequency range.

A comprehensive computational model of sound transmission through the porcine lung

A comprehensive computational simulation model of sound transmission through the porcine lung is introduced and experimentally evaluated. This "subject-specific" model utilizes parenchymal and major airway geometry derived from x-ray CT images. The lung parenchyma is modeled as a poroviscoelastic material using Biot theory. A finite element (FE) mesh of the lung that includes airway detail is created and used in comsol FE software to simulate the vibroacoustic response of the lung to sound input at the trachea. The FE simulation model is validated by comparing simulation results to experimental measurements using scanning laser Doppler vibrometry on the surface of an excised, preserved lung. The FE model can also be used to calculate and visualize vibroacoustic pressure and motion inside the lung and its airways caused by the acoustic input. The effect of diffuse lung fibrosis and of a local tumor on the lung acoustic response is simulated and visualized using the FE model. In the future, this type of visualization can be compared and matched with experimentally obtained elastographic images to better quantify regional lung material properties to noninvasively diagnose and stage disease and response to treatment.

Sound transmission in the chest under surface excitation: an experimental and computational study with diagnostic applications

Chest physical examination often includes performing chest percussion, which involves introducing sound stimulus to the chest wall and detecting an audible change. This approach relies on observations that underlying acoustic transmission, coupling, and resonance patterns can be altered by chest structure changes due to pathologies. More accurate detection and quantification of these acoustic alterations may provide further useful diagnostic information. To elucidate the physical processes involved, a realistic computer model of sound transmission in the chest is helpful. In the present study, a computational model was developed and validated by comparing its predictions with results from animal and human experiments which involved applying acoustic excitation to the anterior chest, while detecting skin vibrations at the posterior chest. To investigate the effect of pathology on sound transmission, the computational model was used to simulate the effects of pneumothorax on sounds introduced at the anterior chest and detected at the posterior. Model predictions and experimental results showed similar trends. The model also predicted wave patterns inside the chest, which may be used to assess results of elastography measurements. Future animal and human tests may expand the predictive power of the model to include acoustic behavior for a wider range of pulmonary conditions.

Mechanical characterization of tissue-engineered cartilage using microscopic magnetic resonance elastography

Knowledge of mechanical properties of tissue-engineered cartilage is essential for the optimization of cartilage tissue engineering strategies. Microscopic magnetic resonance elastography (μMRE) is a recently developed MR-based technique that can nondestructively visualize shear wave motion. From the observed wave pattern in MR phase images the tissue mechanical properties (e.g., shear modulus or stiffness) can be extracted. For quantification of the dynamic shear properties of small and stiff tissue-engineered cartilage, μMRE needs to be performed at frequencies in the kilohertz range. However, at frequencies greater than 1 kHz shear waves are rapidly attenuated in soft tissues. In this study μMRE, with geometric focusing, was used to overcome the rapid wave attenuation at high frequencies, enabling the measurement of the shear modulus of tissue-engineered cartilage. This methodology was first tested at a frequency of 5 kHz using a model system composed of alginate beads embedded in agarose, and then applied to evaluate extracellular matrix development in a chondrocyte pellet over a 3-week culture period. The shear stiffness in the pellet was found to increase over time (from 6.4 to 16.4 kPa), and the increase was correlated with both the proteoglycan content and the collagen content of the chondrocyte pellets (R(2)=0.776 and 0.724, respectively). Our study demonstrates that μMRE when performed with geometric focusing can be used to calculate and map the shear properties within tissue-engineered cartilage during its development.

Sample interval modulation for the simultaneous acquisition of displacement vector data in magnetic resonance elastography: theory and application

SampLe Interval Modulation-magnetic resonance elastography (SLIM-MRE) is introduced for simultaneously encoding all three displacement projections of a monofrequency vibration into the MR signal phase. In SLIM-MRE, the individual displacement components are observed using different sample intervals. In doing so, the components are modulated with different apparent frequencies in the MR signal phase expressed as a harmonic function of the start time of the motion encoding gradients and can thus be decomposed by applying a Fourier transform to the sampled multidirectional MR phases. In this work, the theoretical foundations of SLIM-MRE are presented and the new idea is implemented using a high field (11.7 T) vertical bore magnetic resonance imaging system on an inhomogeneous agarose gel phantom sample. The local frequency estimation-derived stiffness values were the same within the error margins for both the new SLIM-MRE method and for conventional MRE, while the number of temporally-resolved MRE experiments needed for each study was reduced from three to one. In this work, we present for the first time, monofrequency displacement data along three sensitization directions that were acquired simultaneously and stored in the same k-space.

Selective spectral displacement projection for multifrequency MRE

We introduce a new motion encoding concept for the displacement vector in multifrequency magnetic resonance elastography (MRE). Selective spectral displacement projection (SDP)-MRE can be applied to a vibration spectrum composed of three frequencies and exploits the filter condition of MRE for selecting one frequency each per spatial motion encoding direction. The selected components are simultaneously encoded in the phase of the MR signal. Therefore, the total MR phase is represented by a sum of phase portions, each corresponding to a distinct spatial projection and vibration frequency. The individual components can be obtained by applying a Fourier-transform to the temporally resolved phase images. SDP-MRE reduces the number of temporally resolved MRE experiments for data acquisition by a factor of 3, while providing similar wave images as found using conventional monofrequency MRE.

Wideband MR elastography for viscoelasticity model identification

The growing clinical use of MR elastography requires the development of new quantitative standards for measuring tissue stiffness. Here, we examine a soft tissue mimicking phantom material (Ecoflex) over a wide frequency range (200 Hz to 7.75 kHz). The recorded data are fit to a cohort of viscoelastic models of varying complexity (integer and fractional order). This was accomplished using multiple sample sizes by employing geometric focusing of the shear wave front to compensate for the changes in wavelength and attenuation over this broad range of frequencies. The simple axisymmetric geometry and shear wave front of this experiment allows us to calculate the frequency-dependent complex-valued shear modulus of the material. The data were fit to several common models of linear viscoelasticity, including those with fractional derivative operators, and we identified the best possible matches over both a limited frequency band (often used in clinical studies) and over the entire frequency span considered. In addition to demonstrating the superior capability of the fractional order viscoelastic models, this study highlights the advantages of measuring the complex-valued shear modulus over as wide a range of frequencies as possible.

Estimating material viscoelastic properties based on surface wave measurements: a comparison of techniques and modeling assumptions

Previous studies of the first author and others have focused on low audible frequency (<1 kHz) shear and surface wave motion in and on a viscoelastic material comprised of or representative of soft biological tissue. A specific case considered has been surface (Rayleigh) wave motion caused by a circular disk located on the surface and oscillating normal to it. Different approaches to identifying the type and coefficients of a viscoelastic model of the material based on these measurements have been proposed. One approach has been to optimize coefficients in an assumed viscoelastic model type to match measurements of the frequency-dependent Rayleigh wave speed. Another approach has been to optimize coefficients in an assumed viscoelastic model type to match the complex-valued frequency response function (FRF) between the excitation location and points at known radial distances from it. In the present article, the relative merits of these approaches are explored theoretically, computationally, and experimentally. It is concluded that matching the complex-valued FRF may provide a better estimate of the viscoelastic model type and parameter values; though, as the studies herein show, there are inherent limitations to identifying viscoelastic properties based on surface wave measurements.

Investigating a compact phantom and setup for testing body sound transducers

Contact transducers are a key element in experiments involving body sounds. The characteristics of these devices are often not known with accuracy. There are no standardized calibration setups or procedures for testing these sensors. This study investigated the characteristics of a new computer-controlled sound source phantom for testing sensors. Results suggested that sensors with different sizes require special phantom requirements. The effectiveness of certain approaches on increasing the spatial and spectral uniformity of the phantom surface signal was studied. Non-uniformities > 20 dB were removable, which can be particularly helpful in comparing the characteristics of different size sensors more accurately.

Spinal subarachnoid space pressure measurements in an in vitro spinal stenosis model: implications on syringomyelia theories

Full explanation for the pathogenesis of syringomyelia (SM), a neuropathology characterized by the formation of a cystic cavity (syrinx) in the spinal cord (SC), has not yet been provided. It has been hypothesized that abnormal cerebrospinal fluid (CSF) pressure, caused by subarachnoid space (SAS) flow blockage (stenosis), is an underlying cause of syrinx formation and subsequent pain in the patient. However, paucity in detailed in vivo pressure data has made theoretical explanations for the syrinx difficult to reconcile. In order to understand the complex pressure environment, four simplified in vitro models were constructed to have anatomical similarities with post-traumatic SM and Chiari malformation related SM. Experimental geometry and properties were based on in vivo data and incorporated pertinent elements such as a realistic CSF flow waveform, spinal stenosis, syrinx, flexible SC, and flexible spinal column. The presence of a spinal stenosis in the SAS caused peak-to-peak cerebrospinal fluid CSF pressure fluctuations to increase rostral to the stenosis. Pressure with both stenosis and syrinx present was complex. Overall, the interaction of the syrinx and stenosis resulted in a diastolic valve mechanism and rostral tensioning of the SC. In all experiments, the blockage was shown to increase and dissociate SAS pressure, while the axial pressure distribution in the syrinx remained uniform. These results highlight the importance of the properties of the SC and spinal SAS, such as compliance and permeability, and provide data for comparison with computational models. Further research examining the influence of stenosis size and location, and the importance of tissue properties, is warranted.

Rayleigh-Lamb wave propagation on a fractional order viscoelastic plate

A previous study of the authors published in this journal focused on mechanical wave motion in a viscoelastic material representative of biological tissue [Meral et al., J. Acoust. Soc. Am. 126, 3278-3285 (2009)]. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and sub-surface sources were considered. It was shown that a fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time, resulted in closer agreement with experiment as compared with conventional (integer order) models, such as those of Voigt and Zener. In the present study, this analysis is extended to another configuration and wave type: out-of-plane response of a viscoelastic plate to harmonic anti-symmetric Lamb wave excitation. Theoretical solutions are compared with experimental measurements for a polymeric tissue mimicking phantom material. As in the previous configurations the fractional order modeling assumption improves the match between theory and experiment over a wider frequency range. Experimental complexities in the present study and the reliability of the different approaches for quantifying the shear viscoelastic properties of the material are discussed.

Surface response of a fractional order viscoelastic halfspace to surface and subsurface sources

Previous studies by the second author published in this journal focused on low audible frequency (40-400 Hz) shear and surface wave motion in and on a viscoelastic material representative of biological tissue. Specific cases considered were that of surface wave motion on a halfspace caused by a finite rigid circular disk located on the surface and oscillating normal to it [Royston et al., J. Acoust. Soc. Am. 106, 3678-3686 (1999)] and compression, shear, and surface wave motion in a halfspace generated by a subsurface finite dipole [Royston et al., J. Acoust. Soc. Am. 113, 1109-1121 (2003)]. In both studies, a Voigt model of viscoelasticity was assumed in the theoretical treatment, which resulted in agreement between theoretical predictions and experimental measurements over a limited frequency range. In the present article, the linear viscoelastic assumption in these two prior works is revisited to consider a (still linear) fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time. It is shown that in both excitation source configurations, the fractional order Voigt model assumption improves the match of theory to experiment over a wider frequency range (in some cases up to the measured range of 700 Hz).

Experimental and Computational Models for Simulating Sound Propagation Within the Lungs

An acoustic boundary element model is used to simulate sound propagation in the lung parenchyma and surrounding chest wall. It is validated theoretically and numerically and then compared with experimental studies on lung-chest phantom models that simulate the lung pathology of pneumothorax. Studies quantify the effect of the simulated lung pathology on the resulting acoustic field measured at the phantom chest surface. This work is relevant to the development of advanced auscultatory techniques for lung, vascular, and cardiac sounds within the torso that utilize multiple noninvasive sensors to create acoustic images of the sound generation and transmission to identify certain pathologies.