Quantifying Hepatic Shear Modulus In Vivo Using Acoustic Radiation Force

Abstract

The speed at which shear waves propagate in tissue can be used to quantify the shear modulus of the tissue. As many groups have shown, shear waves can be generated within tissues using focused, impulsive, acoustic radiation force excitations, and the resulting displacement response can be ultrasonically tracked through time. The goals of the work herein are twofold: (i) to develop and validate an algorithm to quantify shear wave speed from radiation force-induced, ultrasonically-detected displacement data that is robust in the presence of poor displacement signal-to-noise ratio and (ii) to apply this algorithm to in vivo datasets acquired in human volunteers to demonstrate the clinical feasibility of using this method to quantify the shear modulus of liver tissue in longitudinal studies. The ultimate clinical application of this work is noninvasive quantification of liver stiffness in the setting of fibrosis and steatosis. In the proposed algorithm, time-to-peak displacement data in response to impulsive acoustic radiation force outside the region of excitation are used to characterize the shear wave speed of a material, which is used to reconstruct the material’s shear modulus. The algorithm is developed and validated using finite element method simulations. By using this algorithm on simulated displacement fields, reconstructions for materials with shear moduli (μ) ranging from 1.3–5 kPa are accurate to within 0.3 kPa, whereas stiffer shear moduli ranging from 10–16 kPa are accurate to within 1.0 kPa. Ultrasonically tracking the displacement data, which introduces jitter in the displacement estimates, does not impede the use of this algorithm to reconstruct accurate shear moduli. By using in vivo data acquired intercostally in 20 volunteers with body mass indices ranging from normal to obese, liver shear moduli have been reconstructed between 0.9 and 3.0 kPa, with an average precision of ±0.4 kPa. These reconstructed liver moduli are consistent with those reported in the literature (μ = 0.75–2.5 kPa) with a similar precision (±0.3 kPa). Repeated intercostal liver shear modulus reconstructions were performed on nine different days in two volunteers over a 105-day period, yielding an average shear modulus of 1.9 ± 0.50 kPa (1.3–2.5 kPa) in the first volunteer and 1.8 ± 0.4 kPa (1.1–3.0 kPa) in the second volunteer. The simulation and in vivo data to date demonstrate that this method is capable of generating accurate and repeatable liver stiffness measurements and appears promising as a clinical tool for quantifying liver stiffness. (E-mail: [email protected])

Introduction

Impulsive acoustic radiation force excitations can be generated in tissue at remote, focused locations, and the resulting dynamic tissue response can be monitored using ultrasonic displacement tracking methods. The rate at which tissue responds to an impulsive excitation, including the speed at which shear waves propagate away from the region of excitation (ROE), can be measured to quantify the tissue’s shear modulus, as originally proposed by Sarvazyan et al. (1998). In contrast to elastographic strain images (Ophir et al 1991, Hall et al 2003, Greenleaf et al 2003) and acoustic radiation force impulse (ARFI) images (Nightingale et al. 2006) that show relative structural stiffness compared with adjacent tissues, the ability to quantify an absolute tissue modulus will be useful for different clinical applications. This approach will allow disease processes that involve the stiffening or softening of tissue without large scale structural changes, such as liver fibrosis and steatosis, to be monitored longitudinally to determine when to initiate/cease treatment protocols and to stage disease progression and resolution.

One of the fundamental difficulties with reconstructing shear moduli from shear wave speeds is generating shear waves in vivo. Systems that use external mechanical excitation (static or dynamic) are challenged in coupling the excitation into the organ/structure of interest, especially if the tissue is deep within the body (Sandrin et al. 2003). The use of focused acoustic energy circumvents this challenge by providing mechanical excitation directly to the focal region of the acoustic beam and generating shear waves directly into the tissue of interest. Impulsive acoustic radiation force excitations generate shear waves within tissues (Sarvazyan et al. 1998). The speed at which these shear waves propagate away from the ROE is related to the shear modulus and density of the tissue; therefore, measuring this shear wave speed facilitates estimation of the tissue’s shear modulus.

There are several methods available to measure the speed of shear waves using dynamic displacement data. Inversion of the Helmholtz equation to reconstruct shear wave speed from displacement data has been used in ARFI and supersonic imaging (Nightingale et al 2003, Bercoff et al 2004). One drawback to this reconstruction method is having to perform second-order differentiation of displacement data in space and time. Jitter associated with ultrasonically tracking these displacement fields (Walker and Trahey 1995, Pinton and Trahey 2006, Palmeri et al 2006) necessitates that significant filtering operations be performed on the displacement data. These filtering operations are computationally intensive and better suited for offline, rather than real-time, processing. An alternative approach to estimating shear wave speed is to use time-of-flight measurements, where the shear wave position is characterized as a function of time. Shear waves can be tracked using correlation-based algorithms (McLaughlin and Renzi 2006a, McLaughlin and Renzi 2006b), or as described herein, time-to-peak (TTP) displacement outside the ROE can be used to estimate shear wave speed.

This manuscript presents an imaging system capable of generating and monitoring radiation force-induced shear waves in human liver in vivo, along with a robust algorithm for reconstructing shear wave speeds from ultrasonically detected displacements to quantify shear moduli. The Background section presents the work of Sarvazyan et al. (1998) that motivated the development of this algorithm, in addition to discussing the general mechanics surrounding shear wave propagation and the use of Helmholtz and Eikonal methods to reconstruct shear wave speed. The Methods section outlines the implementation of the new algorithm, along with describing the simulation and experimental setups used to quantify the accuracy and precision of the algorithm in the clinical context of quantifying liver stiffness. The Results section shows the algorithm applied to simulation data, experimental phantom data and in vivo human liver data. The human studies were performed in 20 volunteers, with the repeatability of this shear modulus reconstruction approach studied in two volunteers over a 105-day period. Additional approaches to optimize this algorithm, along with this algorithm’s limitations, are explored in the Discussion section.