Microscale poroelastic metamodel for efficient mesoscale bone remodelling simulations

Influence of a change in activity regime on femoral bone architecture and failure behaviour

The incidence and morbidity of femoral fractures increases drastically with age. Femoral architecture and associated fracture risk are strongly influenced by loading during physical activities and it has been shown that the rate of loss of bone mineral density is significantly lower for active individuals than inactive. The objective of this work is to evaluate the impact of a cessation of some physical activities on elderly femoral structure and fracture behaviour. The authors previously established a biofidelic finite element model of the femur considered as a structure optimised to loading associated with daily activities. The same structural optimisation algorithm was used here to quantify the changes in bone architecture following cessation of stair climbing and sit-to-stand. Side fall fracture simulations were run on the adapted bone structures using a damage elasticity formulation. Total cortical and trabecular bone volume and failure load reduced in all cases of activity cessation. Bone loss distribution was strongly heterogeneous, with some locations even showing increased bone volume. This work suggests that maintaining the physical activities involved in the daily routine of a young healthy adult would help reduce the risk of femoral fracture in the elderly population by preventing bone loss.

Cortical bone adaptation response is region specific, but not peak load dependent: insights from μ CT image analysis and mechanostat simulations of the mouse tibia loading model

The two major aims of the present study were: (i) quantify localised cortical bone adaptation at the surface level using contralateral endpoint imaging data and image analysis techniques, and (ii) investigate whether cortical bone adaptation responses are universal or region specific and dependent on the respective peak load. For this purpose, we re-analyse previously published μ CT data of the mouse tibia loading model that investigated bone adaptation in response to sciatic neurectomy and various peak load magnitudes (F = 0, 2, 4, 6, 8, 10, 12 N). A beam theory-based approach was developed to simulate cortical bone adaptation in different sections of the tibia, using longitudinal strains as the adaptive stimuli. We developed four mechanostat models: universal, surface-based, strain directional-based, and combined surface and strain direction-based. Rates of bone adaptation in these mechanostat models were computed using an optimisation procedure (131,606 total simulations), performed on a single load case (F = 10 N). Subsequently, the models were validated against the remaining six peak loads. Our findings indicate that local bone adaptation responses are quasi-linear and bone region specific. The mechanostat model which accounted for differences in endosteal and periosteal regions and strain directions (i.e. tensile versus compressive) produced the lowest root mean squared error between simulated and experimental data for all loads, with a combined prediction accuracy of 76.6, 55.0 and 80.7% for periosteal, endosteal, and cortical thickness measurements (in the midshaft of the tibia). The largest root mean squared errors were observed in the transitional loads, i.e. F = 2 to 6 N, where inter-animal variability was highest. Finally, while endpoint imaging studies provide great insights into organ level bone adaptation responses, the between animal and loaded versus control limb variability make simulations of local surface-based adaptation responses challenging.

Optimal placement of fixation system for scaffold-based mandibular reconstruction

A current challenge in bone tissue engineering is to create favourable biomechanical conditions conducive to tissue regeneration for a scaffold implanted in a segmental defect. This is particularly the case immediately following surgical implantation when a firm mechanical union between the scaffold and host bone is yet to be established via osseointegration. For mandibular reconstruction of a large segmental defect, the position of the fixation system is shown here to have a profound effect on the mechanical stimulus (for tissue regeneration within the scaffold), structural strength, and structural stiffness of the tissue scaffold-host bone construct under physiological load. This research combines computer tomography (CT)-based finite element (FE) modelling with multiobjective optimisation to determine the optimal height and angle to place a titanium fixation plate on a reconstructed mandible so as to enhance tissue ingrowth, structural strength and structural stiffness of the scaffold-host bone construct. To this end, the respective design criteria for fixation plate placement are to: (i) maximise the volume of the tissue scaffold experiencing levels of mechanical stimulus sufficient to initiate bone apposition, (ii) minimise peak stress in the scaffold so that it remains intact with a diminished risk of failure and, (iii) minimise scaffold ridge displacement so that the reconstructed jawbone resists deformation under physiological load. First, a CT-based FE model of a reconstructed human mandible implanted with a bioceramic tissue scaffold is developed to visualise and quantify changes in the biomechanical responses as the fixation plate's height and/or angle are varied. The volume of the scaffold experiencing appositional mechanical stimulus is observed to increase with the height of the fixation plate. Also, as the principal load-transfer mechanism to the scaffold is via the fixation system, there is a significant ingress of appositional stimulus from the buccal side towards the centre of the scaffold, notably in the region bounded by the screws. Next, surrogate modelling is implemented to generate bivariate cubic polynomial functions of the three biomechanical responses with respect to the two design variables (height and angle). Finally, as the three design objectives are found to be competing, bi- and tri-objective particle swarm optimisation algorithms are invoked to determine the most optimal Pareto solution, which represents the best possible trade-off between the competing design objectives. It is recommended that consideration be given to placing the fixation system along the upper boundary of the mandible with a small clockwise rotation about its posterior end. The methodology developed here forms a useful decision aid for optimal surgical planning.

Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

Multitechnology Biofabrication: A New Approach for the Manufacturing of Functional Tissue Structures?

Most available 3D biofabrication technologies rely on single-component deposition methods, such as inkjet, extrusion, or light-assisted printing. It is unlikely that any of these technologies used individually would be able to replicate the complexity and functionality of living tissues. Recently, new biofabrication approaches have emerged that integrate multiple manufacturing technologies into a single biofabrication platform. This has led to fabricated structures with improved functionality. In this review, we provide a comprehensive overview of recent advances in the integration of different manufacturing technologies with the aim to fabricate more functional tissue structures. We provide our vision on the future of additive manufacturing (AM) technology, digital design, and the use of artificial intelligence (AI) in the field of biofabrication.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

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

Understanding how bone adapts to mechanical stimuli is fundamental for optimising treatments against musculoskeletal diseases in preclinical studies, but the contribution of physiological loading to bone adaptation in mouse tibia has not been quantified so far. In this study, a novel mechanistic model to predict bone adaptation based on physiological loading was developed and its outputs were compared with longitudinal scans of the mouse tibia. Bone remodelling was driven by the mechanical stimuli estimated from micro-FEA models constructed from micro-CT scans of C57BL/6 female mice (N = 5) from weeks 14 and 20 of age, to predict bone changes in week 16 or 22. Parametric analysis was conducted to evaluate the sensitivity of the models to subject-specific or averaged parameters, parameters from week 14 or week 20, and to strain energy density (SED) or maximum principal strain (ε_maxprinc). The results at week 20 showed no significant difference in bone densitometric properties between experimental and predicted images across the tibia for both stimuli, and 59% and 47% of the predicted voxels matched with the experimental sites in apposition and resorption, respectively. The model was able to reproduce regions of bone apposition in both periosteal and endosteal surfaces (70% and 40% for SED and ε_maxprinc, respectively), but it under-predicted the experimental sites of resorption by over 85%. This study shows for the first time the potential of a subject-specific mechanoregulation algorithm to predict bone changes in a mouse model under physiological loading. Nevertheless, the weak predictions of resorption suggest that a combined stimulus or biological stimuli should be accounted for in the model.

Influence of femoral external shape on internal architecture and fracture risk

The internal architecture of the femur and its fracture behaviour vary greatly between subjects. Femoral architecture and subsequent fracture risk are strongly influenced by load distribution during physical activities of daily living. The objective of this work is to evaluate the impact of outer cortical surface shape as a key affector of load distribution driving femoral structure and fracture behaviour. Different femur cortical shapes are generated using a statistical shape model. Their mesoscale internal architecture is predicted for the same activity regime using a structural optimisation approach previously reported by the authors and fracture under longitudinal compression is simulated. The resulting total volume of bone is similar in all geometries although substantial differences are observed in distribution between trabecular and cortical tissue. Greater neck-shaft and anteversion angles show a protective effect in longitudinal compression while a thinner shaft increases fracture risk.

Rate and age-dependent damage elasticity formulation for efficient hip fracture simulations

Prediction of bone failure is beneficial in a range of clinical situations from screening of osteoporotic patients with high fracture risk to assessment of protective equipment against trauma. Computational efficiency is an important feature to consider when developing failure models for iterative applications, such as patient-specific diagnosis or design of orthopaedic devices. The authors previously developed a methodology to generate efficient mesoscale structural full bone models. The aim of this study was to implement a damage elasticity formulation representative of an elasto-plastic material model with age and strain rate dependencies compatible with these structural models. This material model was assessed in the prediction of femoral fractures in longitudinal compression and side fall scenarios. The simulations predicted failure loads and fracture patterns in good agreement with reported results from experimental studies. The observed influence of strain rate on failure load was consistent with literature. The superiority of a simplified elasto-plastic formulation over an elasto-brittle bone material model was assessed. This computationally efficient damage elasticity formulation was capable of capturing fracture development after onset.