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 τ rank coefficient τ = 0.51, p < 0.001). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to a time variant stimulus. Such models could be used in the design of more efficient loading protocols and drug therapies that target the relevant physiological mechanisms.

A novel algorithm to predict bone changes in the mouse tibia properties under physiological conditions

“…Currently, the development of new treatments for diseases relies on preclinical interventions on cell cultures and animal models. A computational model of bone remodelling can be used to test novel interventions in silico and speed up the discovery-to-market time and reduce the cost of novel interventions (Pereira et al 2015;Schulte et al 2013b).…”

“…However, many studies on mouse models have demonstrated that the mechanical environment is a key determinant of bone remodelling in long bones and vertebrae (Birkhold et al 2017;Pereira et al 2015;Webster et al 2012). The form-function relationship where bone adapts its shape and material properties is referred to as Wolff's law (Wolff 1892), and many bone mechanistic mechanoregulation models in finite element analysis (FEA) have been developed to relate the mechanical stimuli to the bone adaptation (Cheong et al 2018a;Pereira et al 2015;Villette and Phillips 2017). Most of these algorithms are based on Frost's Mechanostat Theory, where bone apposition occurs above a higher, apposition limit and resorption occurs below a lower, resorption limit (Frost 2001).…”

“…Most of these algorithms are based on Frost's Mechanostat Theory, where bone apposition occurs above a higher, apposition limit and resorption occurs below a lower, resorption limit (Frost 2001). These algorithms have been applied in continuum FEA to predict the internal architecture of bone (Huiskes et al 1987), extracortical bone formation (Cheong et al 2018a), ingrowth in tissue engineered implants (Byrne et al 2007), and response to external mechanical loading (Pereira et al 2015) with realistic results.…”

“…Micro-FEA in the mouse tibia has mainly been limited to predicting the strain and stiffness of the mouse tibia, and correlating the results with time-lapsed testing and digital volume correlation (Birkhold et al 2017;Giorgi and Dall'Ara 2018;Oliviero et al 2018;Patel et al 2014). Bone remodelling in whole murine tibia has only been modelled using tetrahedral elements with an inhomogeneous mesh size, and by comparing the predicted shape and density of the loaded leg to the non-loaded contralateral leg (Carriero et al 2018;Pereira et al 2015), under the strong assumption that the control leg did not undergo adaptive changes since the start of the experiment. The spatial match of remodelled regions in the caudal vertebra and tibia found by previous studies was accurate in approximately 50% of the surface (Pereira et al 2015;Schulte et al 2013b), but the remodelling parameters were determined for a loaded model, which may be different under physiological loading.…”

The interplay between bone healing and remodeling around dental implants

“…In the present study internal changes in bone material properties in response to the mechanical environment is investigated. Although it has been shown that bone remodeling depends on the fluid velocity as well as the mechanical signals in the solid phase47 , only the latter one was used in this work and bone and other tissue types were modeled as isotropic elastic materials. The effect of using a poroelastic model during bone remodeling should be considered in the future.In nature and in this work, the end state of the healing phase serves as the initial condition of the remodeling phase.…”