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

The first extension of the virtual fieldsmethod to the reconstruction of heterogeneous stiffnessproperties from 3D bulk full-field displacementdata is presented in this paper. Data are provided byMagnetic Resonance Imaging (MRI). Two main issuesare addressed: 1. the identification of the stiffness ratiobetween two different media in a heterogeneoussolid; 2. the reconstruction of stiffness heterogeneitiesburied in a heterogeneous solid. The approach is basedon a finite element discretization of the equilibriumequations. It is tested on experimental full-field dataobtained on a phantom with the stimulated echo MRItechnique. The phantom is made of a stiff sphericalinclusion buried within a lower modulus material. Preliminaryindependent tests showed that the material ofthe inclusion was four times stiffer than the surroundingmaterial. This ratio value is correctly identified byour approach directly on the phantom with the MRIdata. Moreover, the modulus distribution is promisinglyreconstructed across the whole investigated volume.However, the resulting modulus distribution ishighly variable. This is explained by the fact that the approach relies on a second order differentiation of thedata, which tends to amplify noise. Noise is significantlyreduced by using appropriate filtering algorithms

Rigid fixation for facial osteotomies in fibrous dysplasia: a histological study

Palpation is routinely used for the evaluation of mechanical properties of tissue in regions that are accessible to touch. This means of detecting pathology using the “stiffness” of the tissue is more that 2000 years old. Even today it is common for surgeons to find lesions during surgery that have been missed by advanced imaging methods. Palpation is subjective and limited to individual experience and to the accessibility of the tissue region to touch. It appears that a means of noninvasively imaging elastic modulus (the ratio of applied stress to strain) may be useful to distinguish tissues and pathologic processes based on mechanical properties such as elastic modulus [1]. To this end many approaches have been developed over the years [2–9]. The approaches have been to use conventional imaging methods to measure the mechanical response of tissue to mechanical stress. Static, quasi-static or cyclic stresses have been applied. The resulting strains have been measured using ultrasound [1–9] or MRI [10–15] and the related elastic modulus has been computed from visco-elastic models of tissue mechanics. Recently a new MRI phase contrast technique has been reported in which transverse strain waves propagating in tissue are imaged [13, 14, 16]. Because the wavelengths of propagating waves are related to density and the shear modulus and because the wavelengths of transverse waves for low frequency is on the order of millimeters this method promises to have good resolution and to be sensitive to the shear modulus. This paper reviews the theory of the method, presents some applications and discusses the implications of the method