Attenuation and damping in elastography are naturally of great interest as the presence of these effects in biological tissue goes without question and therefore must be addressed if quantitative assessment of tissue elastic properties is to be achieved. Additionally, given the change in the tissue structure present in the diseases that elastographic imaging seeks to detect and diagnose, there is every reason to expect that the resulting lesions will also exhibit a change in their attenuation behaviour, indicating diagnostic value to any description of the damping property distribution elastographic methods are able to provide.

This thesis will present the unique contribution of the development of several Elastographic models for MR based reconstructions of soft tissue. A method for the reconstruction of both Viscoelastic and Rayleigh damping based damped elastic properties has been developed for use with MR detected time-harmonic motion data and has been shown to lead to reasonable results in both homogeneous and heterogeneous phantoms of varying material types.

A poro-elastic modelling is thought to provide a more accurate description of tissue structure by accounting for, in part, the complex interactions between the solid and fluid phases present in vivo. The foundation for a poro-elastic material behaviour will be explored and presented to support the premise.

A meaningful mapping of the orthotropic shear moduli distributions in three directions has demonstrated enough evidence that the orthotropic MRE can be a feasible technique to determine orthotropic elasticity parameters of a biological tissue, noninvasively. The orthotropic achievements throughout this project can be useful for future clinical cancer diagnostics by augmenting the information obtained from the orthotropic MRE reconstructions between normal tissue and tumours.