Use of a Rayleigh damping model in elastography

Abstract

A Rayleigh damping model applied to magnetic resonance elastography incorporates attenuation behavior proportionally related to both elastic and inertial forces, and allows two damping parameters to be extracted from an MRI motion dataset. Under time-harmonic conditions, the model can be implemented by the use of complex shear modulus and density, whereas viscoelastic damping models commonly used in elastography consist of only a complex shear modulus, and model only a single damping effect. Simulation studies reveal that the differences between damped elastic behavior resulting from a purely complex shear modulus (CSM damping) and from a purely complex density (CD damping) become larger as the overall level of damping present (indicated by the damping ratio) increases. A plot of results generated from the finite element (FE) model indicate the relative motion differences estimated for a range of damping ratios and CSM/CD damping combinations increase with damping ratio, and can be up to 15% at a damping ratio of 50% and therefore using the correct model for a Rayleigh damped material becomes increasingly important as damping levels increase. Resonance-related effects cause values from this plot to vary by as much as 3% as parameters such as wave speed, frequency, and problem size are altered. These motion differences can be compared to expected noise levels to estimate the parameter resolution achievable by a reconstruction algorithm. An optimization-based global property reconstruction algorithm was developed, and used for testing Rayleigh damping parameter reconstructions with gaussian noise added to the simulated motion input data. The coherent motion errors resulting from altering the combination of the two damping parameters are large enough to allow accurate determination of both of the Rayleigh damping parameters with incoherent noise levels comparable to MR measurements. The accuracy achieved by the global reconstructions was significantly better than would be predicted by examining the motion differences for differing CSM/CD damping combinations, which is likely to be due to the low ratio between number of reconstructed parameters and number of noisy measurements.