Modeling Viscoelastic Behavior in Compact Bone through a Distribution of Collagen D-Spacing: A Finite Element Analysis
Available at: https://digitalcommons.calpoly.edu/theses/1512
Date of Award
MS in Biomedical Engineering
Biomedical and General Engineering
Osteoporosis affects nearly 54 million people in the United States. The cost associated with treatment is estimated to be $19 billion per year and is expected to grow yearly. D-spacing is the staggering of collagen molecules found at the nanoscopic level. Previously thought to have a constant value, recent studies have found that D-spacing has a distribution of values throughout the tissue. As part of an ongoing effort in understanding the mechanisms that are affected by osteoporosis, a finite element model was developed to explore the effects of D-spacing distribution on the viscoelastic material properties of bone tissue. The goal of this computational model was to mimic the viscoelastic properties of different sectors of bone tissue that have been treated under different loading conditions (tension and compression).
An appropriate animal model was required to allow for the development of an accurate computational model. Although they don't exhibit similar hormonal cycles as humans, sheep are an excellent animal model for bone research as they experience Haversian bone remodeling, are docile, relatively inexpensive, and have skeletons similar in size and mechanical properties to humans. For this study, six Rambouillet-cross ewes were either ovariectomized (OVX) or underwent a sham surgery (control). After twelve months post-surgery, the ewes were euthanized and rectangular beam bone samples were collected from different sectors of the ulna/radius bones. Dynamic mechanical analysis was performed on these samples and the viscoelastic property, tangent delta, was measured from each analysis at varying frequencies.
Using experimental measurements, the Composite Model was developed on finite element analysis software, Abaqus. The model was generated through a Python script that uses experimental D-spacing mean and standard deviation data to create a large two-dimensional model composed of two hundred collagen and hydroxyapatite complexes with varying D-spacing lengths. Multiple security measurements were implemented to ensure biological relevance. Collagen was assigned viscoelastic material properties through a user subroutine material property. Four models for each sector of interest (caudal and cranial) were generated. Each model was loaded under appropriate loading conditions and tangent delta was recorded for each test frequency.
Results from the Composite Model matched the experimental data more accurately than previous computational models, suggesting a superior model. The results implied that a large network of collagen and hydroxyapatite complexes in series and parallel are effective at modeling bone under different loading conditions. This computational model shows promise in the bone research field. A lot of flexibility was implemented in the model development process, making refinements easy to be performed. This study provides a stepping-stone in computational tooling on examining the effects of metabolic bone diseases on viscoelasticity.