Murad Hossain

Estimation of degree of anisotropy in transversely isotropic (TI) elastic materials from Acoustic Radiation Force (ARF)-induced peak displacements

In this work, we evaluate if directional differences in the mechanical properties of transversely anisotropic (TI) materials may be interrogated using Acoustic Radiation Force Impulse (ARFI) imaging. We hypothesize that ARFI-induced peak displacements (PDs) will vary depending on the orientation of the ARFI excitation to the TI materials axis of symmetry (AoS) when an asymmetrical ARFI excitation is employed, but not when a symmetrical ARFI excitation is used. We further hypothesize that the ratio of the PDs induced with the long axis of an asymmetrical ARFI excitation oriented along versus across the material AoS will be related to the degree of anisotropy of the material. These hypothesizes were tested in silico using finite element method (FEM) models and Field II. ARFI excitations had F/1.5, 3, 4, or 5 focal configurations, with the F/1.5 case having the most asymmetrical and the F/5 case having the most symmetrical point spread function (2D PSF) at the focal depth. These excitations were implemented for ARFI imaging in 18 different TI materials with varying degrees of anisotropy. The ratio of PDs at the focal depth when the AoS was oriented along versus across the long axis of the ARFI-2D PSF was calculated. The degree of anisotropy in the materials was represented by the ratio of the longitudinal and transverse shear modulus and by the ratio of the longitudinal and transverse Youngs modulus. To describe the relationship between the ratio of PDs and material anisotropy, piecewise linear regression of the ratio of PDs versus the ratio of shear moduli and of the ratio of PDs versus the ratio of Youngs moduli were calculated. The slopes were highest for the F/1.5 ARFI excitation, indicating that the ratio of PDs was most strongly impacted by the material orientation when the ARFI impulse was most asymmetrical. On the contrary, the slope was roughly zero for the F/5 ARFI excitation, which indicates that PD did not depend on the orientation of the material when the ARFI excitation was symmetrical. These results suggest that symmetrical ARFI focal configurations are desirable when the orientation of the ARFI excitation to the AoS is not specifically known and standardization of measurement is important, such as for longitudinal or cross-sectional studies of anisotropic organs. However, asymmetrical focal configurations are useful for exploiting anisotropy. Finally, the ratio of PDs reflects degree of anisotropy in TI materials.

On the quantitative potential of Viscoelastic Response (VisR) ultrasound using matrix array transducers: In silico demonstration

VisR ultrasound is an acoustic radiation force (ARF)-based imaging method that fits induced displacements to a 1D mass-spring-damper (MSD) model to estimate the ratio of viscous to elastic moduli, τ, in viscoelastic materials. A source of error in VisR τ estimation is complex and interrelated 3D system inertia. We hypothesize that error due to system inertia may be reduced by minimizing the volumetric extent of the employed ARF excitations, i.e. by reducing elevational and lateral F/#s using a matrix array transducer. This hypothesis was tested in silico using finite element method (FEM) models and Field II simulating homogeneous viscoelastic materials and viscoelastic materials with inclusions. In homogeneous viscoelastic materials, decreasing the elevational F/# from 5.0 to 0.75 yielded 62.5%, 96.7%, and 223.69% decreases in the median percent error in VisR τ estimates in materials with Youngs modulus of 10, 50, and 100 kPa, respectively. In viscoelastic materials with inclusions, the elevational F/0.75 focal configuration better delineated inclusion borders in comparison to F/5.0, and measured contrast was closer to the true contrast. The CNRs achieved using elevational F/0.75 was 1.25 - 5.0 times higher than those from F/5.0. These results show that as the volumetric extent of ARF excitations decreases by reducing the elevational F/#, VisR τ estimates more closely approximate the true material τ. These results suggest that error in quantitative VisR τ estimates would be reduced by using a transducer capable of elevational focusing.

Evaluation of renal transplant status using viscoelastic response (VisR) ultrasound: A pilot clinical study

The current gold standard for monitoring renal transplant status is invasive biopsy, which is controversial due to its associated risk for morbidity and costs. A relevant biopsy alternative could be an imaging technique that exploits the viscoelastic properties of tissue given that renal disease may result in altered viscoelastic relationships between pelvis and parenchyma. Tissue viscoelasticity is delineated by VisR ultrasound, an acoustic radiation force (ARF)-based imaging method, by fitting displacements induced by two ARF impulses to the Mass Spring Damper (MSD) model. We hypothesize that VisR measures are relevant for noninvasively distinguishing biopsied and non-biopsied allografts by assessing viscoelastic similarity between pelvis and parenchyma in renal transplant patients. VisR derived metrics: τ, relative elasticity (RE), and relative viscosity (RV) were calculated in the regions of interest (ROI): outer, center, and inner parenchyma and outer and inner pelvis. The ratios of a given VisR measure for all possible ROI combinations were compared (Wilcoxon rank sum) between biopsied and non-biopsied patients. VisR τ, RE, and RV distinguished chronic allograft nephropathy, glomerulonephritis, vascular disease, and tubular and/or interstitial scarring in biopsied versus non-biopsied allografts (p <; 0.05). These results suggest that VisR measures may be relevant metrics for noninvasively monitoring renal transplant health.

Acoustic Radiation Force Impulse-Induced Peak Displacements Reflect Degree of Anisotropy in Transversely Isotropic Elastic Materials

In transversely isotropic (TI) materials, mechanical properties (Young’s modulus, shear modulus, and Poisson’s ratio) are different along versus across the axis of symmetry (AoS). In this paper, the feasibility of interrogating such directional mechanical property differences using acoustic radiation force impulse (ARFI) imaging is investigated. We herein test the hypotheses that: 1) ARFI-induced peak displacements (PDs) vary with TI material orientations when an asymmetrical ARFI excitation point spread function (PSF) is used, but not when a symmetrical ARFI PSF is employed and 2) the ratio of PDs induced with the long axis of an asymmetrical ARFI PSF oriented along versus across the material’s AoS is related to the degree of anisotropy of the material. These hypotheses were tested in silico using finite-element method (FEM) models and Field II. ARFI excitations had F/1.5, 3, 4, or 5 focal configurations, with the F/1.5 and F/5 cases having the most asymmetrical and symmetrical PSFs at the focal depth, respectively. These excitations were implemented for ARFI imaging in 52 different simulated TI materials with varying degrees of anisotropy, and the ratio of ARFI-induced PDs was calculated. The change in the ratio of PDs with respect to the anisotropy of the materials was highest for the F/1.5, indicating that PD was most strongly impacted by the material orientation when the ARFI excitation was the most asymmetrical. On the contrary, the ratio of PDs did not depend on the anisotropy of the material for the F/5 ARFI excitation, suggesting that PD did not depend on material orientation when the ARFI excitation was symmetrical. Finally, the ratio of PDs achieved using asymmetrical ARFI PSF reflected the degree of anisotropy in TI materials. These results support that symmetrical ARFI focal configurations are desirable when the orientation of the ARFI excitation to the AoS is not specifically known and measurement standardization is important, such as for longitudinal or cross-sectional studies of anisotropic organs. However, asymmetrical focal configurations are useful for exploiting anisotropy, which may be diagnostically relevant. Feasibility for future experimental implementation is demonstrated by simulating ultrasonic displacement tracking and by varying the ARF duration.

Evaluating Renal Transplant Status Using Viscoelastic Response (VisR) Ultrasound

Chronic kidney disease is most desirably and cost-effectively treated by renal transplantation, but graft survival is a major challenge. Although irreversible graft damage can be averted by timely treatment, intervention is delayed when early graft dysfunction goes undetected by standard clinical metrics. A more sensitive and specific parameter for delineating graft health could be the viscoelastic properties of the renal parenchyma, which are interrogated non-invasively by Viscoelastic Response (VisR) ultrasound, a new acoustic radiation force (ARF)-based imaging method. Assessing the performance of VisR imaging in delineating histologically confirmed renal transplant pathologies in vivo is the purpose of the study described here. VisR imaging was performed in patients with (n = 19) and without (n = 25) clinical indication for renal allograft biopsy. The median values of VisR outcome metrics (τ, relative elasticity [RE] and relative viscosity [RV]) were calculated in five regions of interest that were manually delineated in the parenchyma (outer, center and inner) and in the pelvis (outer and inner). The ratios of a given VisR metric for all possible region-of-interest combinations were calculated, and the corresponding ratios were statistically compared between biopsied patients subdivided by diagnostic categories versus non-biopsied, control allografts using the two-sample Wilcoxon test (p <0.05). Although τ ratios non-specifically differentiated allografts with vascular disease, tubular/interstitial scarring, chronic allograft nephropathy and glomerulonephritis from non-biopsied control allografts, RE distinguished only allografts with vascular disease and tubular/interstitial scarring, and RV distinguished only vascular disease. These results suggest that allografts with scarring and vascular disease can be identified using non-invasive VisR RE and RV metrics.

Viscoelastic response (VisR)-derived relative elasticity and relative viscosity reflect tissue elasticity and viscosity: In silico and experimental demonstration in liver

VisR ultrasound characterizes the viscoelastic properties of tissue by fitting acoustic radiation force (ARF)-induced displacements in the region of ARF excitation to a 1D mass-spring-damper (MSD) model. Viscosity and elasticity are found separately from each other but relative to the applied ARF amplitude. We refer to these parameters as ‘relative elasticity (RE)’ and ‘relative viscosity (RV)’. We hypothesize that RE and RV linearly correlate to true elasticity and viscosity in tissue.

Viscoelastic response (VisR)-derived relative elasticity and relative viscosity reflect true elasticity and viscosity, in silico

VisR ultrasound characterizes the viscoelastic properties of tissue by fitting acoustic radiation force (ARF)-induced displacements in the region of ARF excitation to a 1D mass-spring-damper (MSD) model. By so doing, viscosity and elasticity are found separately from each other but relative to the applied ARF amplitude. We refer to these parameters as ‘relative elasticity (RE)’ and ‘relative viscosity (RV)’. We herein test the hypothesis that RE and RV linearly correlate to true elasticity and viscosity, in silico. VisR imaging was simulated in 144 homogeneous, isotropic, viscoelastic materials with varying elasticity and viscosity using finite element model (FEM) and Field II simulation. RE linearly correlated with shear elasticity of the modeled materials, with R2 = 1.0. For a given elasticity, RE values varied by 2.5% on average when the shear viscosity was changed from 0.1 to 1.3 Pa.s. Similarly, RV linearly correlated with shear viscosity (R2 ≥ 0.99); however, for a given viscosity, RV values varied by 112.7% on average when shear elasticity changed from 3.33 to 20 kPa. This high degree of variation in RV was due to complex 3D system inertia, with greater inertial effects in stiffer materials. This confounding impact of elasticity on RV was compensated by using the natural frequency parameter, ω. After so compensating, corrected RV varied by < 1.0% on average for a given viscosity when the shear elasticity changed from 3.3 to 20 kPa. These results suggest the potential of VisR ultrasound for independently evaluating elastic and viscous properties in tissue.

2D ARFI and Viscoelastic Response (VisR) anisotropy imaging in skeletal muscle

Tissue mechanical anisotropy has been shown to be diagnostically relevant in numerous clinical applications. Anisotropy can be assessed using acoustic radiation force-based techniques, including Acoustic Radiation Force Impulse (ARFI) and Viscoelastic Response (VisR) ultrasound. In this work, ARFI peak displacement (PD), as well as VisR relative elasticity (RE) and relative viscosity (RV), were implemented to image mechanical anisotropy in ex vivo porcine posas major muscle. Two psoas major samples were imaged in this work. The first sample was imaged whole. The second sample was sectioned into a 1 cm-diameter cylinder (with cylinder height oriented along the muscle fibers) and embedded into an isotropic gelatin phantom for imaging. ARFI and VisR were performed on both muscle samples using a linear array transducer mounted to a translation and rotation stage. By rotating the transducer 90o as it stepped across a 2D imaging field of view, PD, RE, and RV were measured along and across muscle fibers. Then, the ratios of PD, RE, and RV measurements made along versus across the muscle fibers were calculated, and these ratios were parametrically rendered in to 2D images representing degree of anisotropy. In the whole psoas major, PD anisotropy ratio was 1.08 +− 0.11, the RE anisotropy ratio was 0.94 +− 0.09 and the RV ratio was 0.94 +− 0.08. These PD and RE anisotropy ratios suggest that the longitudinal shear elastic modulus was greater than the transverse shear elastic modulus, which agrees with previous studies on muscle anisotropy. The RV results suggest that the longitudinal viscous modulus was greater than the transverse viscous modulus. Similar PD, RE, and RV anisotropy ratios were measured in the embedded psoas major section, and contrast ratios were 0.21, 0.14, and 0.30 for PD, RE and RV 2D anisotropy images, respectively. CNR for PD, RE, and RV anisotropy images were 3.26, 2.09 and 2.41, respectively. These results demonstrate that ARFI and VisR anisotropy imaging are relevant for delineating the spatial distribution of anisotropic features in tissue.

In vivo mechanical anisotropy assessment in renal cortex using ARFI peak displacement

The kidney is an anisotropic organ, with higher elasticity along versus across nephrons. The degree of elastic anisotropy in kidney may be diagnostically relevant if properly exploited; however, if improperly controlled, anisotropy may confound stiffness measurements. The purpose of this study is to demonstrate a novel method for selectively exploiting or obviating elastic anisotropy in kidney using Acoustic Radiation Force Impulse (ARFI)-induced peak displacement (PD). The kidneys of three pigs were imaged in vivo at baseline, with venous ligation, and with arterial ligation, and then kidneys were extracted and imaged ex vivo. Imaging was performed with ARF excitation impulses having F/1.5 or F/5.0 focal configurations, and data were acquired with the transducer oriented along and across nephrons alignment in the renal cortex. In addition to ARFI PD, shear wave velocity was measured along and across nephrons to estimate longitudinal and transverse shear elastic moduli. Elastic anisotropy was then assessed as the ratio of PD across versus along nephrons, and as the ratio of shear moduli along versus across nephrons. PD ratio using the F/1.5 ARF linearly correlated with shear moduli ratio (R2 = 0.95). However, PD ratio using the F/5.0 ARF was approximately 1.0 and had weak correlation to shear moduli ratio (R2= 0.56). Further, the average difference in PD measured along versus across nephrons was 2.91 μm for the F/1.5 ARF but was 0.2 μm for the F/5.0 ARF. These results suggest that the F/1.5 ARF excitation exploited elastic anisotropy in the renal cortex, while the F/5.0 ARF excitation obviated it.

In vivo mechanical anisotropy assessment in renal parenchyma using ARFI peak displacement

Renal parenchyma is strongly anisotropic; mechanical properties differ along versus across nephron alignment. In this work, the feasibility of interrogating such directional differences in mechanical property using ARFI is investigated. We hypothesize that: 1) the ratio of ARFI peak displacements (PDs) achieved with the long axis of an asymmetrical ARF PSF oriented along versus across nephron alignment reflects the mechanical degree of anisotropy (DoA); and 2) directional differences in parenchymal mechanical property are detected when using an asymmetrical ARF PSF but obviated when using a symmetrical ARF PSF.