Lev Podshivalov, Ph.D Thesis

On the Road to Personalized Medicine: 3D Hierarchical Geometric Modeling and Multiscale Finite Element Analysis as a Base for Individualized Medical Diagnosis of Bone Structure

Supervisors: Prof. Anath Fischer, Prof. Zvi Pinhas Bar-Yoseph

Bones are composed of hierarchical bio-composite materials characterized by complex multi-scale structural geometry and behavior. Thus, a multi-scale approach for mechanical analysis of bone is imperative.

In this work, a new alternative method for individualized mechanical analysis of bone trabecular structure has been developed. This new method closes the gap between the classic homogenization approach for macro-scale models and the more recent micro finite elements method that is applied directly to micro-scale high-resolution models. The method is based on multiresolution geometrical modeling that in effect generates intermediate structural levels. A new method for estimating multiscale material properties has also been developed to facilitate reliable and efficient mechanical analysis. The computational model is validated by comparing the strain energy at all levels, which must remain constant. In essence, the proposed method efficiently integrates geometric multiresolution modeling and multiscale finite element analysis into a single computational system. Solution of high resolution micro-scale models is impractical on a single processor. Therefore, a non-overlapping domain-based method was also utilized throughout the entire workflow, starting with reconstructing the geometric model from micro-CT images and continuing with multi-scale finite element analysis and finally visualization.

The developed method can be utilized in two modes: (a) it can allow physicians to zoom-in dynamically and focus on the Volume of Interest (VOI), thus paving the way for a large class of investigations into the mechanical behavior of bone structure; and (b) the entire multi-domain model can be solved for different levels of resolution, allowing rapid solution of the entire model at an intermediate structural level that provides a sufficient level of details. The feasibility of this multi-scale FE method is demonstrated on a vertebra model reconstructed from ?CT images.

The proposed method has the potential to be used in a comprehensive computerized diagnostic expert system for a variety of applications, among them diagnosis and prognosis of bone diseases, scaffold design, response to drug treatment, bone strength prediction and surgery planning.