3D heterogeneous stiffness reconstruction using MRI and the Virtual Fields Method

Avril, S., Huntley, J.M., Pierron, F. and Steele, D.D. (2008) 3D heterogeneous stiffness reconstruction using MRI and the Virtual Fields Method. [in special issue: Inverse Problems in Experimental Mechanics] Experimental Mechanics, 48 (4), 479-494. (doi:10.1007/s11340-008-9128-2).

Abstract

The first extension of the virtual fields
method to the reconstruction of heterogeneous stiffness
properties from 3D bulk full-field displacement
data is presented in this paper. Data are provided by
Magnetic Resonance Imaging (MRI). Two main issues
are addressed: 1. the identification of the stiffness ratio
between two different media in a heterogeneous
solid; 2. the reconstruction of stiffness heterogeneities
buried in a heterogeneous solid. The approach is based
on a finite element discretization of the equilibrium
equations. It is tested on experimental full-field data
obtained on a phantom with the stimulated echo MRI
technique. The phantom is made of a stiff spherical
inclusion buried within a lower modulus material. Preliminary
independent tests showed that the material of
the inclusion was four times stiffer than the surrounding
material. This ratio value is correctly identified by
our approach directly on the phantom with the MRI
data. Moreover, the modulus distribution is promisingly
reconstructed across the whole investigated volume.
However, the resulting modulus distribution is
highly variable. This is explained by the fact that the approach relies on a second order differentiation of the
data, which tends to amplify noise. Noise is significantly
reduced by using appropriate filtering algorithms.

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Contributors

Author: F. Pierron

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