Finite element models have been used for the last 50 years to investigate relationships between bone geometry, material properties, mechanical loading, and bone mechanoadaptation. FE models provide complementary information to experimental studies and clinical observations and can be used to explain experiments or design new experiments. FE models are also a critical part of the prosthetic design process to understand bone remodeling around the prosthesis. This historical perspective will cover the highlights of what we have learned from 50 years of bone modeling.

Bone is a complex hierarchically arranged structure which is constantly adapting to mechanical demands. To understand and model this so-called remodelling process, mainly three scales must be considered: the macroscopic (organ) scale, the mesoscopic (tissue) scale as well as the cellular scale. In trabecular bone, active osteoclasts and active osteoblasts remodel individual trabeculae at the cellular scale. On the so-called mesoscopic (tissue) scale, the size and shape of individual trabeculae changes, which on the macroscopic (organ) scale can be observed as a change in bone density. Macroscopic mechanical loading affects the stress/strain state in the mesostructure and thus influences the bone cell activities and the remodelling process.

To capture these multiscale interactions, the aim of this work is to develop a three-scale approach to bone remodelling including mechanical feedback that combines the advantages of already established models to describe remodelling at the macroscopic, the mesoscopic and the cellular scale. Therefore, a continuum approach based on the theory of open system thermodynamics is used to represent the remodelling process on the macroscale. Approaches on the macroscopic scale are usually based on average material properties and locally adjust bone density to mechanical use following Wolff's law. Our macroscopic approach can also account for non-linearity, is efficient and numerically stable. Moreover, it is easily extendable to other aspects such as anisotropy, age dependence and biological availability of nutrients and hormones. However, it does not explicitly consider the very irregular trabecular structure of cancellous bone. On the mesoscale of our approach, the trabecular structure is modelled in a simplified way as an ideal truss network, where each trabecular is represented by a truss element. This approach requires much less computational effort than pixel- or voxel-based models, which are able to represent real geometries but are considered inefficient in a multi-scale context. On the microscale, a bone cell population model is used to capture the coupled activities of bone cells in the remodelling process. The main focus is first on the development and verification of a remodelling algorithm that captures all three scales. The remodelling algorithm is tested on benchmark problems of mechanical overload and disuse and applied to more complex geometries.

Mechanical loading is essential for maintaining homeostasis and driving adaptation of the skeleton. Disruption of this mechanically-driven bone remodeling process has been linked to bone loss and increased fracture risk. The etiology of bone pathology is complex, particularly in cases involving metabolic bone diseases, and no current serological biomarkers directly reflect bone mechanical quality. Rather, indirect measures like bone mineral density, clinical risk prediction tools, or visual interpretation of imaging are used to drive treatment decisions. As a result, the prognostic limitations of most clinical assessments reinforce patterns of care that tend to be conservative and reactive waiting for clinical pathology to present unambiguously – rather than proactive and preventive. Despite these challenges, innovation in medical imaging and increasingly accessible computational power have made it possible to computationally measure the mechanical properties of bone via image-based finite element analysis. Moreover, longitudinal clinical studies have also shown that the combined use of high-resolution peripheral quantitative computed tomography (HR-pQCT) and micro-finite element analysis can be used to measure load-driven bone remodelling in vivo. This powerful combination enables the assessment of bone formation and resorption (i.e., remodeling) and quantification of the relationship between this remodeling and mechanical loading (i.e., mechanoregulation) at the microstructural level over time.

Despite the promise of such advanced imaging and computational methods in clinical studies, there remain technological challenges to widespread implementation. These challenges include variations in image quality due to image noise and patient motion, which confound the precision and reproducibility of bone density, geometry, mechanical, cortical, and trabecular structure measurements. Additionally, segmentation protocols and image processing pipelines often require manual input or augmentation, prohibiting the high-throughput analysis that would be required for clinical implementation. Finally, to push such imaging and computational methods for mechanobiological bone remodeling studies from bench (supercomputer) to bedside (clinical computing) in the hospital environment these methods need to be repeatable and validated.

With this in mind, this talk will (1) explore the challenges associated with the assessment of dynamic bone morphometry in vivo; (2) link bone microarchitecture and functional outcomes using the finite-element method in patient populations with metabolic bone disease such as osteoporosis and diabetes mellitus; and (3) evaluate the potential for such in silico modelling to serve as a clinical tool for monitoring changes in bone health over time. With continued evolution of technology and best practices, the utility of bone mechanical biomarkers using image-based finite element analysis will undoubtedly increase, revolutionizing standard of care in bone health.

Understanding how the loss in the mechanical environment is associated with bone loss is challenging. Endocortical bone loss due to the disuse of muscles has been recently reported in the literature[1], which shows that bone loss was focused on the posterior surface at the distal section; however, it shifted to the anterior lateral surface at the proximal end. Interestingly, it conveys that bone loss is site specific along the bone length. However, the cause of bone loss in disuse conditions is unknown. In this work, we aim to decipher such an underlying mechanism.

Recently load-induced fluid flow inside the lacune canaliculi network (LCN) has caught the attention of researchers as a primary stimulus. In loaded bone, fluid flow will be higher at the endocortical surface and negligible at the periosteal surface due to its permeable and impermeable nature, respectively. It seems reasonable to assume that in the case of a disuse condition, the maximum loss of fluid flow will occur at the endocortical surface.

Hence, the present work explores the loss of fluid flow related to disuse and aims to develop a mathematical model that can correctly predict the site of bone loss. We use the loss of dissipation energy density due to disuse as a stimulus as it follows the trend of loss of fluid velocity. Accordingly, we hypothesized that the site of maximum loss of dissipation energy density due to fluid flow corresponds to the site of maximum loss of bone tissue. To test our hypothesis, a poroelasticity-based finite element model of a simplified geometry was subjected to the physiological loading condition. The fluid velocity computed from the above analysis is used to calculate the dissipation energy density (φ_phys). Simultaneously, we assume that the disuse of bone causes no fluid flow, and the corresponding dissipation energy density is denoted as (φ_disuse). Therefore, the dissipation loss can be written as φ_phys- φ_disuse: this dissipation loss and experimental bone loss data reported by Ausk et al.[1] are coupled to develop a novel mathematical model that predicts the site of cortical bone loss with spatial accuracy.

The developed mathematical model first predicts bone loss given in the literature at distal (p value= 0.89, Watson U² test) and midshaft (p value= 0.78, Watson U² test). However, it overestimates bone loss at the proximal section. Based on the availability of experimental data, the developed model can be extended to predict other disuse conditions such as spaceflight, prolonged bed rest, etc.

[1] B. J. Ausk, P. Huber, S. L. Poliachik, S. D. Bain, S. Srinivasan, and T. S. Gross, “Cortical bone resorption following muscle paralysis is spatially heterogeneous,” Bone, vol. 50, no. 1, pp. 14–22, Jan. 2012, doi: 10.1016/j.bone.2011.08.028.