Predicting cortical bone adaptation to axial loading in the mouse tibia

Abstract

The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on-off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's tau rank coefficient \(\tau = 0.51\), \(p<0.001\)). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to time variant stimulus. Such models could be used in the design of more efficient loading protocols and drugs therapies that target the relevant physiological mechanisms.

Mechanical Loading Promotes the Expansion of Primitive Osteoprogenitors and Organizes Matrix and Vascular Morphology in Long Bone Defects

“…But to what forces were the cells responding? Though mechanical stimulation used in this study was compressive in nature with respect to the entire tibia, the tissue-level strain at anterior medial face of the tibia, where the defect is located, has been shown, (12,47) and we have confirmed, to be tensile. Therefore, the vessel and collagen fiber alignment, as well as the cellular responses we observed in this study were presumably in response to this tensile force, though additional data are required for confirmation.…”

Mechano-regulation of bone adaptation is controlled by the localin vivoenvironment and logarithmically dependent on loading frequency

“…An additional limitation of this study was that the micro-FE analysis did not take into account the component of frequency. Although our approach enabled us to link bone remodeling events to mechanical environments in vivo at the local level, the addition of theoretical models that incorporate cellular mechanosensing and intercellular communication [12,[35][36][37] will be highly useful to improve our understanding of the relationship between loading frequency and bone adaptation across multiple scales.…”

Age and Sex Differences in Load‐Induced Tibial Cortical Bone Surface Strain Maps

“…The presented DIC maps can further be used to validate FE models of the tibia loading in C57BL6/J mice, for example, examining the mechanical stimulus for bone adaptation. ( 24,35 ) Using DIC strain maps, we validated a FE model of the bone and correlated the mechanical stimuli to the ensuing spatial changes in osteogenic activity. ( 24 ) We found that fluid velocity predicts bone adaptation in adult bone both periosteally and endosteally, whereas strain energy density fails to predict endosteal bone formation.…”

“…The relationship between the mechanical strains on cortical bone and its adaptation has been explored, particularly using the murine tibial–loading model, by comparing regions of bone formation from in vivo μCT, histology, and recently three‐dimensional fluorochrome mapping coupled with FE models of mechanical stimulus. ( 24,29–35 ) Although comparison of bone adaptation across these studies is challenging because they do not all report changes in the same morphological bone region, they have found that cortical bone in the young murine tibia is very responsive to loading, whereas controversial results have been found in aged bone. Some studies, which have used strain gauges to calibrate the applied load, found that aged bone does not exhibit efficient adaptation at similar strain magnitudes as young bone, interpreting this result as a failure of aged bone to adapt.…”