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.

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?

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

1-Norm waveform analysis for MR elastography-based quantification of inhomogeneity: Effects of the freeze-thaw cycle and Alzheimer's disease.

BACKGROUND: Despite its success in the mechanical characterization of biological tissues, magnetic resonance elastography (MRE) uses ill-posed wave inversions to estimate tissue stiffness. 1-Norm has been recently introduced as a mathematical measure for the scattering of mechanical waves due to inhomogeneities based on an analysis of the delineated contours of wave displacement. PURPOSE: To investigate 1-Norm as an MRE-based quantitative biomarker of mechanical inhomogeneities arising from microscopic structural tissue alterations caused by the freeze-thaw cycle (FTC) or Alzheimer's disease (AD). METHODS: In this proof-of-concept study, we prospectively investigated excised porcine kidney (n = 6), liver (n = 6), and muscle (n = 6) before vs. after the FTC at 500-2000 Hz and excised murine brain of healthy controls (n = 3) vs. 5xFAD species with AD (n = 3) at 1200-1800 Hz using 0.5 T tabletop MRE. 1-Norm analysis was compared with conventional wave inversion. RESULTS: While the FTC reduced both stiffness and inhomogeneity in kidney, liver, and muscle tissue, AD led to lower brain stiffness but more pronounced mechanical inhomogeneity. CONCLUSION: Our preliminary results show that 1-Norm is sensitive to tissue mechanical inhomogeneity due to FTC and AD without relying on ill-posed wave inversion techniques. 1-Norm has the potential to be used as an MRE-based diagnostic biomarker independent of stiffness to characterize abnormal conditions that involve changes in tissue mechanical inhomogeneity.

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.

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.

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.