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?

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.

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.

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.

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.

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.

Prostate cancer assessment using MR elastography of fresh prostatectomy specimens at 9.4 T.

PURPOSE: Despite its success in the assessment of prostate cancer (PCa), in vivo multiparametric MRI has limitations such as interobserver variability and low specificity. Several MRI methods, among them MR elastography, are currently being discussed as candidates for supplementing conventional multiparametric MRI. This study aims to investigate the detection of PCa in fresh ex vivo human prostatectomy specimens using MR elastography. METHODS: Fourteen fresh prostate specimens from men with clinically significant PCa without formalin fixation or prior radiation therapy were examined by MR elastography at 500 Hz immediately after radical prostatectomy in a 9.4T preclinical scanner. Specimens were divided into 12 segments for both calculation of storage modulus (G' in kilopascals) and pathology (Gleason score) as reference standard. Sensitivity, specificity, and area under the receiver operating characteristic curve were calculated to assess PCa detection. RESULTS: The mean G' and SD were as follows: all segments, 8.74 ± 5.26 kPa; healthy segments, 5.44 ± 4.40 kPa; and cancerous segments, 10.84 ± 4.65 kPa. The difference between healthy and cancerous segments was significant with P ≤ .001. Diagnostic performance assessed with the Youden index was as follows: sensitivity, 69%; specificity, 79%; area under the curve, 0.81; and cutoff, 10.67 kPa. CONCLUSION: Our results suggest that prostate MR elastography has the potential to improve diagnostic performance of multiparametric MRI, especially regarding its 2 major limitations: interobserver variability and low specificity. Particularly the high value for specificity in PCa detection is a stimulating result and encourages further investigation of this method.

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.

Dilatational and shear waves in poro-vioscoelastic media.

Dynamic elastography methods are being developed for quantitatively and noninvasively mapping the viscoelastic properties of biological tissue that are often altered by disease and injury, as well as response to treatment. This involves inducing mechanical wave motion that also can be affected by the multiphase porous nature of the tissue, whether it be consideration of blood perfusion in the vascular network found in many regions of interest, or consideration of air movement in the complex bronchial tree within the lungs. Elastographic mapping requires reconstructing material properties based on interpretation of the measured wave motion. Reconstruction methods that explicitly incorporate poroelastic behavior are an active area of development. In the present article the equivalence of two theoretical approaches to modeling poroelastic behavior is demonstrated specifically in the frequency domain using parameter values that span the range expected in vivo for analysis of blood and air-infused regions. The two methods are known as (1) the mixture or biphasic formulation and (2) the poroelastic approach. The case of acoustic wave propagation in the lungs is specifically addressed by comparison of analytical predictions to recently reported experimental measurements. Establishing and validating this equivalence of theoretical approaches not only strengthens our fundamental understanding of the relevant physics, but also may lead to improved numerical methods for simulation and elastography reconstruction.

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.