Establishing the relationship between loading parameters and bone adaptation

Predicting trabecular arrangement in the proximal femur: An artificial neural network approach for varied geometries and load cases

Machine learning (ML) and deep learning (DL) approaches can solve the same problems as the finite element method (FEM) with a high degree of accuracy in a fraction of the required time, by learning from previously presented data. In this work, the bone remodelling phenomenon was modelled using feed-forward neural networks (NN), by gathering a dataset of density distribution comprising several geometries and load cases. The model should output for some point in the domain the its apparent density, taking into consideration the geometric and loading parameters of the model . After training. the trabecular distribution obtained with the NN was similar to the FEM while the analysis was performed in a fraction of the time, having shown a reduction from 1020 s to 0.064 s. It is expected that the results can be extended to different structures if a different dataset is acquired. In summary, the ML approach allows for significant savings in computational time while presenting accurate results.

Prediction of cortical bone mineral apposition rate in response to loading using an adaptive neuro-fuzzy inference system

Daily activities such as aerobic movements and athletic events found effective in mitigating bone loss as it promotes osteogenesis. Computational model considered normal strain, or strain energy density as a stimulus to predict site specific osteogenesis. This model, however, fails to predict site specific osteogenesis as cortical bone surfaces exhibit different remodelling rate to mechanical loading. Remodelling rate or mineral apposition rate depends upon the loading parameters such as loading cycle, frequency, and magnitude of strain. Therefore, the present study aims to develop an adaptive neuro-fuzzy inference system (ANFIS) model for finding a robust relationship between loading parameters like strain magnitude, frequency, and cycle, and a bone remodelling parameter i.e. mineral apposition rate (MAR). The model is trained, tested, and checked with the experimental data. The results indicate that ANFIS model outperformed state of the art Artificial Neural Network (ANN) models during the prediction of MAR at periosteal and endosteal surface. A strong corelation R² = 0.92 and R² = 0.97 was observed at 70% of the input data at periosteal and endosteal surface respectively. Result concludes that endosteal surface was more promisable as compared to periosteal surface in predicting accurate MAR. The outcomes of present study may be used to precisely predict site-specific osteogenesis in cortical bone as function of loading parameters.

How Artificial Intelligence and Machine Learning Is Assisting Us to Extract Meaning from Data on Bone Mechanics?

Dramatic advancements in interdisciplinary research with the fourth paradigm of science, especially the implementation of computer science, nourish the potential for artificial intelligence (AI), machine learning (ML), and artificial neural network (ANN) algorithms to be applied to studies concerning mechanics of bones. Despite recent enormous advancement in techniques, gaining deep knowledge to find correlations between bone shape, material, mechanical, and physical responses as well as properties is a daunting task. This is due to both complexity of the material itself and the convoluted shapes that this complex material forms. Moreover, many uncertainties and ambiguities exist concerning the use of traditional computational techniques that hinders gaining a full comprehension of this advanced biological material. This book chapter offers a review of literature on the use of AI, ML, and ANN in the study of bone mechanics research. A main question as to why to implement AI and ML in the mechanics of bones is fully addressed and explained. This chapter also introduces AI and ML and elaborates on the main features of ML algorithms such as learning paradigms, subtypes, main ideas with examples, performance metrics, training algorithms, and training datasets. As a frequently employed ML algorithm in bone mechanics, feedforward ANNs are discussed to make their taxonomy and working principles more readily comprehensible to researchers. A summary as well as detailed review of papers that employed ANNs to learn from collected data on bone mechanics are presented. Reviewing literature on the use of these data-driven tools is essential since their wider application has the potential to: improve clinical assessments enabling real-time simulations; avoid and/or minimize injuries; and, encourage early detection of such injuries in the first place.

Effect of ageing on microstructure and fracture behavior of cortical bone as determined by experiment and Extended Finite Element Method (XFEM)

Bone fracture is a severe health concern; therefore, understanding the causes of bone fracture are crucial. This paper investigates the microstructure and fracture behaviour of cadaveric cortical bone of two different groups (Young, n= 6; Aged, n=7). The microstructure is obtained from µ-CT images, and the material parameters are measured with nanoindentation. Fracture behaviour in transverse and longitudinal orientations is investigated experimentally and numerically. The results show that the Haversian canal (HC) size increases and the osteon wall thickness (OWT) decreases significantly in the aged group, whereas a nonsignificant difference is found in tissue properties. The crack initiation (J_ic) and crack growth (J_grow) toughness of the aged group are found to be significantly lower (p<0.01) than the young group in the transverse orientation; however, for the longitudinal orientation, only the value of J_ic in the aged group is found significantly lower. Further, a 4-phase XFEM (based on micro-CT image) model is developed to investigate the crack propagation behaviour in both orientations. For the transverse orientation, results show that in the aged group, the crack initially follows the cementline and then penetrates the osteon, whereas, in the young group, it propagates along the cementline. These results are in agreement with experimental results where the decrease in J_grow is more significant than the J_ic in the aged group. This study suggests that ageing leads to a larger HC and reduced OWT, which weakens the crack deflection ability and causes fragility fracture. Further, the XFEM results indicate that the presence of a small microcrack in the vicinity of a major crack tip causes an increase in the critical stress intensity factor.

Prediction of mechanical properties of trabecular bone in patients with type 2 diabetes using damage based finite element method

Type-2 diabetic (T2D) and osteoporosis (OP) suffered patients are more prone to fragile fracture though the nature of alteration in areal bone mineral density (aBMD) in these two cases are completely different. Therefore, it becomes crucial to compare the effect of T2D and OP on alteration in mechanical and structural properties of femoral trabecular bone. This study investigated the effect of T2D, OP, and osteopenia on bone structural and mechanical properties using micro-CT, nanoindentation and compression test. Further, a nanoscale finite element model (FEM) was developed to predict the cause of alteration in mechanical properties. Finally, a damage-based FEM was proposed to predict the pathological related alteration of bone's mechanical response. The obtained results demonstrated that the T2D group had lower volume fraction (-18.25%, p = 0.023), young's modulus (-23.47%, p = 0.124), apparent modulus (-37.15%, p = 0.02), and toughness (-40%, p = 0.001) than the osteoporosis group. The damage-based FE results were found in good agreement with the compression experiment results for all three pathological conditions. Also, nanoscale FEM results demonstrated that the elastic and failure properties of mineralised collagen fibril decreases with increase in crystal size. This study reveals that T2D patients are more prone to fragile fracture in comparison to OP and osteopenia patients. Also, the proposed damage-based FEM can help to predict the risk of fragility fracture for different pathological conditions.

Modeling cortical bone adaptation using strain gradients

Cyclic and low-magnitude loading promotes osteogenesis (i.e. new bone formation). Normal strain, strain energy density and fatigue damage accumulation are typically considered as osteogenic stimuli in computer models to predict site-specific new bone formation. These models however had limited success in explaining osteogenesis near the sites of minimal normal strain, for example, neutral axis of bending. Other stimuli such as fluid motion or strain gradient also stimulate bone formation. In silico studies modeled the new bone formation as a function of fluid motion, however, computation of fluid motion involves complex mathematical calculations. Strain gradients drive fluid flow and thus can also be established as the stimulus. Osteogenic potential of strain gradients is however not well established. The present study establishes strain gradients as osteogenic stimuli. Bending-induced strain gradients are computed at cortical bone cross-sections reported in animal loading in vivo studies. Correlation analysis between strain gradients and site of osteogenesis is analyzed. In silico model is also developed to test the osteogenic potential of strain gradients. The model closely predicts in vivo new bone distribution as a function of strain gradients. The outcome establishes strain gradient as computationally easy and robust stimuli to predict site-specific osteogenesis. The present study may be useful in the development of biomechanical approaches to mitigate bone loss.

Mechano-Regulation of Trabecular Bone Adaptation Is Controlled by the Local in vivo Environment and Logarithmically Dependent on Loading Frequency

It is well-established that cyclic, but not static, mechanical loading has anabolic effects on bone. However, the function describing the relationship between the loading frequency and the amount of bone adaptation remains unclear. Using a combined experimental and computational approach, this study aimed to investigate whether trabecular bone mechano-regulation is controlled by mechanical signals in the local in vivo environment and dependent on loading frequency. Specifically, by combining in vivo micro-computed tomography (micro-CT) imaging with micro-finite element (micro-FE) analysis, we monitored the changes in microstructural as well as the mechanical in vivo environment [strain energy density (SED) and SED gradient] of mouse caudal vertebrae over 4 weeks of either cyclic loading at varying frequencies of 2, 5, or 10 Hz, respectively, or static loading. Higher values of SED and SED gradient on the local tissue level led to an increased probability of trabecular bone formation and a decreased probability of trabecular bone resorption. In all loading groups, the SED gradient was superior in the determination of local bone formation and resorption events as compared to SED. Cyclic loading induced positive net (re)modeling rates when compared to sham and static loading, mainly due to an increase in mineralizing surface and a decrease in eroded surface. Consequently, bone volume fraction increased over time in 2, 5, and 10 Hz (+15%, +21% and +24%, p ≤ 0.0001), while static loading led to a decrease in bone volume fraction (-9%, p ≤ 0.001). Furthermore, regression analysis revealed a logarithmic relationship between loading frequency and the net change in bone volume fraction over the 4 week observation period (R 2 = 0.74). In conclusion, these results suggest that trabecular bone adaptation is regulated by mechanical signals in the local in vivo environment and furthermore, that mechano-regulation is logarithmically dependent on loading frequency with frequencies below a certain threshold having catabolic effects, and those above anabolic effects. This study thereby provides valuable insights toward a better understanding of the mechanical signals influencing trabecular bone formation and resorption in the local in vivo environment.

Study on the biomechanical responses of the loaded bone in macroscale and mesoscale by multiscale poroelastic FE analysis

BACKGROUND

Bone is a hierarchically structured composite material, and different hierarchical levels exhibit diverse material properties and functions. The stress and strain distribution and fluid flow in bone play an important role in the realization of mechanotransduction and bone remodeling.

METHODS

To investigate the mechanotransduction and fluid behaviors in loaded bone, a multiscale method was developed. Based on poroelastic theory, we established the theoretical and FE model of a segment bone to provide basis for researching more complex bone model. The COMSOL Multiphysics software was used to establish different scales of bone models, and the properties of mechanical and fluid behaviors in each scale were investigated.

RESULTS

FE results correlated very well with analytical in macroscopic scale, and the results for the mesoscopic models were about less than 2% different compared to that in the macro-mesoscale models, verifying the correctness of the modeling. In macro-mesoscale, results demonstrated that variations in fluid pressure (FP), fluid velocity (FV), von Mises stress (VMS), and maximum principal strain (MPS) in the position of endosteum, periosteum, osteon, and interstitial bone and these variations can be considerable (up to 10, 8, 4 and 3.5 times difference in maximum FP, FV, VMS, and MPS between the highest and the lowest regions, respectively). With the changing of Young's modulus (E) in each osteon lamella, the strain and stress concentration occurred in different positions and given rise to microscale spatial variations in the fluid pressure field. The heterogeneous distribution of lacunar-canalicular permeability (klcp) in each osteon lamella had various influence on the FP and FV, but had little effect on VMS and MPS.

CONCLUSION

Based on the idealized model presented in this article, the presence of endosteum and periosteum has an important influence on the fluid flow in bone. With the hypothetical parameter values in osteon lamellae, the bone material parameters have effect on the propagation of stress and fluid flow in bone. The model can also incorporate alternative material parameters obtained from different individuals. The suggested method is expected to provide dependable biological information for better understanding the bone mechanotransduction and signal transduction.