Three-dimensional analysis of shear wave propagation observed by in vivo magnetic resonance elastography of the brain

Abstract

Dynamic magnetic resonance elastography (MRE) is a non-invasive method for the quantitative determination of the mechanical properties of soft tissues in vivo. In MRE, shear waves are generated in the tissue and visualized using phase-sensitive MR imaging methods. The resulting two-dimensional (2-D) wave images can reveal in-plane elastic properties when possible geometrical biases of the wave patterns are taken into account. In this study, 3-D MRE experiments of in vivo human brain are analyzed to gain knowledge about the direction of wave propagation and to deduce in-plane elastic properties. The direction of wave propagation was determined using a new algorithm which identifies minimal wave velocities along rays from the surface into the brain. It was possible to quantify biases of the elastic parameters due to projections onto coronal, sagittal and transversal image planes in 2-D MRE. It was found that the in-plane shear modulus is increasingly overestimated when the image slice is displaced from narrow slabs of 2–5 cm through the center of the brain. The mean shear modulus of the brain was deduced from 4-D wave data with about 3.5 kPa. Using the proposed slice positions in 2-D MRE, this shear modulus can be reproduced with an acceptable error within a fraction of the full 3-D examination time.

Introduction

For centuries, palpation has been used as the primary test for pathological tissue change. The sensitivity of the method is based on the mechanical resistance of soft tissue to compression and shear deformations, which varies in orders of magnitude throughout the human body. However, manual palpation is a subjective method limited to soft tissues in the vicinity of the body surface. Therefore, dynamic magnetic resonance elastography (MRE) was developed as a non-invasive method for quantitatively measuring the viscoelastic properties of human soft tissue in vivo [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. In contrast to static MRE, where static or quasi-static tissue deformations are applied, dynamic MRE is based on the application of low-frequency acoustic waves penetrating the tissue of interest. Short dynamic excitation pulses are used in transient dynamic MRE, whereas steady-state dynamic MRE – the subject of this study – uses several motion cycles or continuous excitations. The tissue motion is magnetically encoded in the MR phase signal by synchronously oscillating gradients. The wave images display a phase-difference contrast that is sensitive to deflections smaller than 1 μm. In dynamic MRE, if the direction of wave propagation lies in the image plane and boundary effects and viscosity are negligible, the wavelength of the observed wave patterns is related to the elasticity of the tissue.

Comparisons of dynamic MRE with independent shear modulus-determining methods have shown that MRE provides correct quantities in tissue phantoms [1], [11], [12], [13]. Promising studies have recently shown that MRE is able to quantify elastic parameters in well-shielded organs such as the prostate, kidney and liver, where manual palpation is restricted [14], [15], [16], [17].

Dynamic MRE is especially suited for assessing in vivo brain elasticities. In contrast to manual examination, application of static MRE and ultrasound elastography, this technique is capable of producing results despite the mechanical shielding of the skull. The feasibility of using MRE to acquire wave images of the brain has been demonstrated by several studies [18], [19], [20], [21], [22], [23], [24], [25]. For mechanical excitation of the brain, the entire head is vibrated, causing indirectly induced shear waves. Thus, the full three-dimensional (3-D) wave field has to be acquired to correctly measure the resulting convolute wave vector field in the brain. Despite the ability of MRE to detect all components of the full wave field, most brain MRE studies are, in order to save time, based on the acquisition of the wave field in a single image plane followed by a 2-D shear modulus reconstruction. However, a 2-D projection through a 3-D wave field can yield geometrical biases that can result in misinterpretation of the determined planar shear modulus. It has been shown that even for tissue phantoms with simple geometries the wave-propagation process is truly 3-D and the full 3-D wave field has to be considered for an accurate reconstruction of elasticity images [26]. The full 3-D displacement field is particularly important for the brain – with its complex anatomy, shape and mechanisms of indirect wave excitation – in order to deduce correct elastic coefficients.

Thus, in this study, the wave propagation through the brain of a volunteer was analyzed by measuring all wave field components. Assuming isotropy, the final wave field analysis was restricted to the scalar field of the deflection component that has shown the largest penetration depth of the acoustic waves into the brain. The temporal evolution of this component was acquired and these 4-D data were analyzed using a new algorithm that allows the direction of shear wave propagation to be determined. The algorithm is profile-based and assumes that the minimum wavelength indicates the direction of wave propagation from the origin of the ray [27]. The shear modulus of brain tissue determined via this method is compared with the results of a direct inversion of 2-D data and data given in the literature.

The aim of the present study was, therefore, to characterize the regions with the best correlation between wave propagation and images with a transversal, coronal or sagittal orientation. Within these regions, fast in vivo 2-D MRE can then be applied with a minimized error range in order to quantify the shear modulus of brain tissue. This reduction in scan time is a crucial precondition for forthcoming studies of patients suffering from brain diseases.