Cortical Bone Adaptation: A Finite-Element Study of the Mouse Tibia

Abstract

Bone is a dynamic tissue that adapts its shape and material properties as a response to changes in mechanical demands. The process by which bone functional adaptation takes places consists of a complex cascade of events, entailing different levels of mechanical and biological regulation, which are still unknown or under debate in the scientific community. Mechanical cues are site-specific factors that play a crucial role in skeletal maintenance and adaptation. The present work is framed within this research area and aims to inspect a hypothetical relationship between organ-level load-induced mechanical cues and the adaptive response of cortical bone. More specifically, this thesis focuses on how loading parameters (such load frequency or the insertion of rest periods between load cycles) alter the mechanical environment in bone tissue (estimated using numerical tools) and, consequently, its adaptive response.

Animal in vivo loading models allow for inducing bone functional adaptation in a controlled environment and are, therefore, a powerful tool in the study of the influence of external loading and loading parameters to bone mechanotransduction. The murine axial tibial loading model was used as platform to trigger cortical bone adaptation in mouse specimens and provide relevant biological and biomechanical information.

The spatial distribution of in vivo functional adaptation in the murine model was assessed via morphological examination of ex vivo μCT scans from loaded and control tibiae of C57BL/6 mice, by contralateral comparison of cross-section geometrical properties and measurements. Calculation of the second moment of area indicated regions of bone formation along the length of the bone. A method for mapping cortical thickness was developed, consisting in the three-dimensional representation of the changes of shell thickness in the diaphysis of a long bone, allowing for explicitly describing how bone adaptation is distributed in space.

The mechanical environment of the cortical shell was estimated using computational models, based on finite-element analysis generated from μCT data, to provide a full field description of mechanical fields. A novel in silico predictive model was coupled to the finite-element models. This mathematical formulation assumed that bone responds instantly to local mechanical cues in an on-off manner and that this response is integrated in time and averaged in space, resulting in a bone formation rate represented by surface displacements. Strain energy density (SED) was initially employed as stimulus to cortical bone formation. The obtained predictions were compared against the 3D cortical adaptation maps from in vivo adaptation, showing that SED is able to reproduce the spatial patterns of changes in bone shape, but has a limited contribution in the study of time-dependent parameters.

Following experimental evidence that suggests that interstitial fluid flow in the lacunar-canalicular system is a stimulus for mechanoadaptation, a simplified 3D poroelastic finite-element model of a beam in bending was developed in order to simulate the behaviour of fluid flow in mouse cortical bone. This model allowed exploration of two important loading parameters that affect mechanoadaptation: load frequency and rest insertion.

A range of intrinsic permeabilities found in literature from 1E-23 to 1E-18 m2 were tested, and fluid velocity was determined. Models with permeabilities down to 1E-21 m2 followed a dose-response relationship between fluid flow and sinusoidal frequency. Smaller orders of magnitude of permeability were relatively insensitive to frequency. It was found that there is a minimum time of rest between loading cycles that is required to maximise fluid motion. These findings suggest that, in addition to biological saturation, fluid flow plays a role in the enhancement of osteogenic response in load regimes that allow recovery periods between consecutive load cycles.

Fluid velocity was then included as a mechanical stimulus in the developed cortical bone adaptation algorithm, in order to determine if, in addition to predicting time-dependent factors, fluid flow could reproduce in vivo spatial patterns. Equivalent predictions to the strain-based simulations were obtained. The presented cortical adaptation algorithm simulated spatial distribution of cortical adaptation with a good agreement between the in vivo measurements and our predictions.

The work presented here provides novel methodological and theoretical approaches to understanding the spatial and temporal parameters of cortical bone adaptation. With a better understanding of the factors that promote bone formation, mechanical loading can be optimized to elicit a maximum osteogenic response.