(Dr. Robert Guldberg, advisor)

"Digital Imaged-Based Finite Element Modeling: Simulation of Mechanically-Induced Bone Formation"

Abstract

It is widely understood that bone has the remarkable ability to adapt to its mechanical environment.  Consistent adaptational responses suggest that bone’s ordered internal structures can be partly explained by site-specific loading rates and history.  However, local mechanical signals that drive bone adaptation have not been determined.

Finite element modeling is a powerful engineering tool that provides a method to investigate stress/strain fields in response to various loading conditions.  Because bone is a load-bearing structure in the body, finite element modeling has been introduced into the field of bone mechanics.  Digital imaged-based finite element modeling (DIBFEM) has been developed to aid in the modeling of the complex biologic structures common to bone mechanics.  While previously validated for apparent solutions, the DIBFEM local solution behavior has not been investigated.  Using a simple beam model, this study showed local solution convergence utilizing a boundary-specific filter for model resolutions of 20 elements/diameter.

With the ability to analyze the local stress/strain solutions, DIBFEM has been utilized to develop simulations of bone adaptation.  Previous work suggests that high strain energy density (SED) gradients may regulate local bone adaptation.  Based on this assumption, a high-resolution finite element simulation was developed utilizing SED gradient as the objective function.  Both early modeling and remodeling were simulated using initial conditions as found in previous in vivo repair studies.  Two- and three-dimensional comparisons to in vivo results, utilizing standard bone stereology, indicate that this simulation method was able to predict bone microstructures with physiological morphologies.  It was found that SED gradients, opposed to SED alone, produced structures with parameters closer to in vivo results.  Understanding the mechanical parameters driving bone adaptation may help in many orthopaedic applications, such as fracture fixation and surface integration of medical devices.