Date of Award

Fall 2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)

Department

Mechanical and Industrial Engineering

First Advisor

Kwabena A. Narh

Second Advisor

Rong-Yaw Chen

Third Advisor

Bernard Koplik

Fourth Advisor

Zhiming Ji

Fifth Advisor

Manuel Perez

Abstract

An improved understanding of the mechanical influences that alter the strength of a bone can aid in the refinement of the wide array of currently available techniques to counteract the losses of bone strength that occur due to age or disuse both on Earth and in Space. To address this need, computational modeling methods to quantitatively analyze and compare the effects of mechanical factors on the strength of a targeted bone within a multibone, multimuscle system are developed and implemented in this work. Through a more detailed representation of the system in which the bone acts and the creation of a model that does not require experimentally based parameters, the developed techniques eliminate many of the difficulties that have often hindered these musculoskeletal phenomena from being studied with the tools and methods readily employed in the investigation of their inert mechanical counterparts.

The computational techniques developed couple the determination of the muscle forces acting within the system studied, the stresses they induce within the bones of the system, and the ensuing adaptations of the shape of one of these bones, altering its strength. This is accomplished through the use of gradient based optimization methods, finite element methods, and gradientless optimization methods, respectively. The developed gradientless optimization methods in this work progress the bone shape design toward one with a more uniform state of stress through the relative effects of measures of the local stress state, the global stress state, and the variation of the local stress state over the region being optimized. Quantitative measures of the progression towards a uniformity of the stress state during the optimization process are defined so that relative changes can be directly compared between the various mechanical factors studied. Similarly, methods are developed to independently assess the ability of the conditions studied to induce bone shape alterations that improve the strength of the bone under a standard set of loading conditions.

The implementation of the model in a parametric study of methods to improve the resistance of the tibia bone to stress fractures demonstrates its ability to evaluate the effects of various loading conditions, with forces and stresses studied ranging three orders of magnitude. From this investigation, loading modes are identified that improve the bone's strength in the fracture prone region by up to 20%. The developed computational modeling techniques eliminate the difficulties inherent in the experimental investigation of mechanically based alterations to bone strength and provide a means for the improved understanding and, ultimately, better control of these adaptive phenomena.

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