ABSTRACT of the Doctoral Thesis

Modeling and Validation of Multiscale Lamellar Bone Elasticity

by Andreas G. Reisinger (2011)

The hierarchical structure of bone tissue has been investigated intensively in the last century. Whereas bone composition is described in increasing detail, the microscopic mechanisms leading to the remarkable macroscopic mechanical properties are still barely understood. In this work, the hierarchical organization of lamellar bone, the most abundant bone type in humans and many mammals, is reflected in a multiscale material model that provides anisotropic elastic estimations for the characteristic microscopic bone entities. In that way, a relation between composition and morphology of bone's microstructural motives to its macroscopic elastic behavior is established.

First, the mineralized collagen fibril, the extrafibrillar matrix and the subsequent fibril-array, are modeled using a multiscale mean field method. Fibrils contain collagen type I molecules that are periodically reinforced by mineral platelets. Fibrils are embedded in an extra-fibrillar matrix that consists of a network of non-collagenous proteins and mineral. This uniaxial fibril-array is the basic structure from which all higher hierarchical levels of lamellar bone are built. The influence of mineral and collagen volume fractions, their spatial distribution and elastic properties as well as the effects of porosity on the fibril-array stiffness is investigated. Calculations show that tissue mineralization and collagen stiffness are crucial parameters for describing the lamellar bone's axial and transverse stiffness, whereas mineral distribution and fibril volume fraction are less relevant.

Second, the fibril-array model was tested against nanoindentation measurements in human femoral cortical bone. At the microscopic spots of indentation, the degree of mineralization and fibril orientation was measured and used in the fibril-array model for calculating a corresponding virtual indentation modulus. Averaged model results predicted the measurements well, although the spot-per-spot correlation was surprisingly weak. This shows that the variation of indentation modulus of human lamellar bone cannot be explained by mineralization and orientation only. The result points either towards unevaluated factors like nanoporosity or microdamage that are of possible influence or towards uncertainties within the nanoindentation measurements.

Third, the obtained elastic properties of the fibril array are used as an input for a finite-element unit-cell model of a single bone lamella. The fibril alignment in the lamella rotates according to a fibril orientation pattern. Four known patterns were compared regarding the resulting bone lamella anisotropy and stiffness. It was found that the patterns determine the anisotropy of bone lamellae. The widely known twisted plywood and orthogonal plywood patterns lead to rather isotropic in-plane elastic properties. Unsymmetrical patterns like the 5-sublayer pattern, the x-ray diffraction based pattern lead to a privileged stiffness direction that is inclined to the osteon axis. In the cylindrical setup of an osteon, in which the lamellae are circumferentially disposed, this inclination-angle brings about a helical stiffness winding around the haversian channel.

Fourth, the numerically obtained anisotropic elastic properties of bone lamellae were related to nanoindentation experiments on human osteons. They were performed on three distinct planes on a single osteon to assess the lamella in-plane stiffness in multiple directions. All investigated osteons appeared to be anisotropic with a preferred stiffness alignment along the axial direction with a small average helical winding around the osteon axis. Thus, the experimental results oppose the numerical outcomes of the twisted- and orthogonal plywood pattern, but support the 5-sublayer- and the x-ray diffraction based pattern. No transverse osteons were observed in the mechanical sense.

This work demonstrates that variations in composition and inherent orientation lead to differences in the elastic behavior of lamellar bone on higher length scales. The utilized numerical models allow for a qualitative and quantitative prediction of bone tissue elastic constants. The presented studies are steps toward a deeper understanding of the structure-mechanical function relationship of lamellar bone.

revised 111107 (hjb)