Determination and analysis of guided wave propagation using magnetic resonance elastography

Abstract

We present a novel extension of standard magnetic resonance elastography (MRE) measurement and analysis methods, which is applicable in cases where the medium is characterized by waveguides or fiber bundles (i.e., muscle) leading to constrained propagation of elastic waves. As a demonstration of this new method, MRI is utilized to identify the pathways of the individual fibers of a stalk of celery, and 3D MRE is then performed throughout the volume containing the celery fibers for a measurement of the displacements. A Helmholtz decomposition is performed permitting a separation of the displacements into longitudinal and transverse components, and an application of a hybrid Radon transform permits a spectral decomposition of wave propagation along the fibers. Dot product projections between these elastic displacements measured in the global coordinate system and three Frenet vectors representing the tangent and two corresponding orthogonal vectors along any particular fiber orientation yield the displacement contributions to wave propagation along the fiber as if it were a waveguide. A sliding window spatial Fourier transform is then performed along the length of each fiber to obtain dispersion images that portray space-wavenumber profiles.

Measurement of the Dynamic Shear Modulus of Mouse Brain Tissue In Vivo by Magnetic Resonance Elastography

“…Following Romano et al [16], a Helmholtz decomposition of the displacement data was used to isolate the transverse component. The Helmholtz-Hodge decomposition was performed in the frequency domain [16]. Frequency domain decomposition introduces some artifacts due to truncation [21].…”

“…, where , , and [16,17]. The transverse, or shear, displacement component describes volume-conserving deformation.…”

“…Shear modulus estimates of a human brain using MRE have been reported by McCracken and colleagues [15]. Romano and co-workers [16] proposed a method to use MRE to study anisotropic materials, particularly transversely isotropic, leading to constrained propagation of elastic waves along the fiber directions in celery. Sinkus et al [17] measured anisotropic and viscoelastic material properties in breast tissue and tumors by fitting MRE data to a corresponding model.…”

Vascular wall elasticity measurement by magnetic resonance imaging

“…Furthermore, in this study we did not compare normal and diseased porcine or human arteries, which would provide more clinically relevant data. Further research would also involve applying wave-guide constrained MRE to analyze more complex modal structures arising within the arteries, as well as to accurately track wave propagation along arbitrarily oriented pathways (18). This study presents a potential reliable, noninvasive method for estimating vascular wall stiffness that may provide new opportunities to understand the natural history and pathophysiology of vascular disease.…”

“…To date, this method has been applied to the breast, brain, and kidneys, but not the vasculature (14 -17). The MRE method is able to image cyclic displacements with very small amplitude and to track these waves, especially within naturally occurring wave guides (18). Because the arteries serve as a natural wave guide, the technique is well suited for imaging the arterial system (19).…”