Date of Award

Fall 2013

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Eric A. Nauman

Committee Chair

Eric A. Nauman

Committee Member 1

Corey P. Neu

Committee Member 2

Ganesh Subbarayan- Shastri

Committee Member 3

Thomas M. Talavage


The noninvasive measurement of finite displacements and strains in biomaterials by magnetic resonance imaging (MRI) may be shown to enable mathematical estimates of stress distributions and material properties within structures of the body such as articular cartilage or the intervertebral disc. Such methods will allow for non-contact and patient-specific modeling in a manner not currently possible with traditional mechanical testing or finite element techniques. Therefore, the objective of this thesis was to develop computational methods incorporating imaging-based measures of deformation, composition, and local microstructure to permit nondestructive analysis of a range of complex biomechanical systems.

Finite strain-based models were developed and applied towards the analysis of several biomaterial systems of increasing material complexity. First, a model for the analysis of a homogeneous, single material system was created and applied to juvenile porcine cartilage for both linear and nonlinear material assumptions under plane stress conditions. Through this study, the viability of estimating stresses within a homogeneous material system solely from MRI-based displacement and strain measures could be established. The model was then expanded to encompass single-plane, multi-region structures and applied towards the analysis of regional stresses within a rabbit intervertebral disc degeneration model. This model incorporated imaging-based methods to estimate heterogeneous properties within the disc structure based upon local biochemical composition, and showed that the degeneration state of a tissue system could effectively be visualized through the use of finite strain-based modeling. A multi-constituent mixture-based material model was next implemented in the analysis of agarose gel constructs. Material parameter estimates from this model were found to agree with those determined by an unconfined compression validation model, establishing physical relevance of noninvasive parameter estimates produced by the models. Finally, the mixture-based material model was applied towards an in situ analysis of the human intervertebral disc.