A Finite Element Analysis on the Viscoelasticity of Postmenopausal Compact Bone Utilizing a Complex Collagen D-spacing Model

• Main Author: Cummings, Austin C
• Format: Others
• Published: DigitalCommons@CalPoly 2015
• Subjects: D-spacing; Menopause; Bone; Viscoelasticity; Biomechanics; FEA; Biomechanics and Biotransport
• Online Access: https://digitalcommons.calpoly.edu/theses/1454; https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=2537&context=theses

The nanoscale dimension known as D-spacing describes the staggering of collagen molecules, which are fundamental to the biphasic makeup of bone tissue. This dimension was long assumed to be constant, but recent studies have shown that the periodicity of collagen is variable. Given that the arrangement of collagen molecules is closely related to the degree of bone mineralization, recent studies have begun to look at D-spacing as a potential factor in the ongoing effort to battle postmenopausal osteoporosis. The theoretical models presented by previous studies have only opted to model a single collagen-hydroxyapatite period, so the creation of an intricate computational approach that more exhaustively models a network of collagen and mineral is well-warranted. Sheep present an excellent opportunity to examine metabolic disorders, as their bone structure similar to that of the human skeleton. Six Rambouillet-cross ewes were used for the purpose of gathering experimental data. Three ewes underwent a sham surgery (controls), while an ovariectomy (OVX) was performed on the remaining three sheep. Each sheep was sacrificed after 12 months and their radius and ulna were harvested for atomic force microscopy and mechanical testing. Each sheep bone produced up to 25 beam samples that were available for analysis, and two were randomly selected from each test sheep. The cranial anatomical sector was selected for testing as it replicates the tensile loading condition characteristically experienced by collagen molecules and its exclusive examination removes any unintended variation due to bone section. Experimental D-spacing measurements were used in a finite element software, Abaqus, to create the ``Complex Model'': a large-scale, 2-D staggered array representation of collagen and hydroxyapatite periodicity. D-spacings intrinsic variability was mimicked through a Gaussian distribution that randomly determined periodic lengths based on provided experimental data. The model was generated with these random conditions for 2 x 100 units. Safeguards were implemented to ensure appropriate ratios of collagen to hydroxyapatite throughout the randomization. Collagen was assigned viscoelastic material properties originally developed by Dr. Frank Richter and modified by Miguel Mendoza. Hydroxyapatite was modeled as an elastic isotropic material. Four models were created using randomized D-spacings from control sheep and four separate models were created based on OVX sheep. Tangent delta--a damping characteristic--was recorded to evaluate bone viscoelasticity across four test frequencies: 1, 3, 9, and 15 Hz. Results strongly suggest that the Complex Model matches experimental findings more accurately than previous computational approaches. These results indicate the complicated network of many collagen units is an essential parameter of adequate modeling. A repeated measures analysis of variance was performed to examine the differences between control and OVX sheep. After adjusting for all other predictors, at the 1% significance level, after adjusting for all other variables, there is not enough evidence to convince this study that the Surgical Treatment alone has a significant impact on output tangent delta. This finding leads this study to conclude that OVX is fully accounted for within the Complex Model through the inclusion of its D-spacing, and the answers to bone's complicated mechanical properties during estrogen loss may lie in how OVX changes collagen viscoelasticity. Significant interactions were found between the Model Type and the Test Frequency. A Tukey-Kramer pairwise comparison was performed between Complex and Experimental data, which determined the Complex Model did not behave statistically differently from experimental findings at 15 Hz. This result suggests the Complex Model may begin to be validated to experimental results in a statistically meaningfully way that is a first for this style of FEA approach. The flexibility implemented in the randomization of the Complex Model welcomes refinement primarily in modeling viscoelasticity and fine-tuning the representation of mineralization. Through adjusting these material characteristics, the Complex Model may become an even more powerful tool in examining bone viscoelasticity and metabolic disorders.