Effect of Including Periodic Boundary Condition on the Fatigue Behaviour of Cancellous Bone

Trabecular bone consists of complex webbing of plates and struts, in which the properties vary across anatomical sites. The substantial constraint is the reduction on discretization error will reduce time in computation. So it is significant to consider carefully the boundary condition effects when utilizing such a complex multiaxial loading mode. Additionally, multiaxial loading gives distinct effects towards boundary condition compare to uniaxial whereas percentage prediction of fatigue failure is lower and applying of periodic boundary reflect a more precise real loading condition. 3D models of trabecular samples were constructed for FE simulations. The response of the models towards simulated mechanical loading was investigated. Preparation of the models begins with 3D reconstruction of micro-CT stacked images, follows by segmentation, meshing and refurbishing process. The resistance of trabecular bone deformation to loading in both uniaxial and multiaxial modes improved the fatigue life and failure with application of periodic boundary conditions

Computational modelling of trabecular bone using fluid structure interaction approach

While doing daily physiological activities, trabecular bone will experience certain amount of deformation, which causes movement of the bone marrow. The bone marrow movement could affect the bone remodelling process. The properties of the bone will also be affected as the bone marrow acts as a hydraulic stiffening to the trabecular structure. Previous studies on trabecular bone remodelling did not consider the effects of bone marrow movement. Thus, there is a need to perform combined analyses of the bone marrow movement with trabecular structure to assess its effects on the remodelling process under a realistic condition. The aim of this study is to determine the effect of bone marrow movement onto the trabecular bone structure under mechanical loading using fluid-structure interaction (FSI) approach. Two different models of the trabecular bone, namely idealised and actual were constructed. The idealised models were used to correlate the bone marrow behaviour to the trabecular bone morphology. The actual trabecular bone models were constructed to mimic the presence of the bone marrow within the trabecular bone structure during physiological loading. The effects of different orientation of the trabecular structures were also examined. Three numerical approaches which are finite element method, computational fluid dynamics and FSI were employed to evaluate the importance of bone marrow movement effect towards the trabecular bone mechanical properties. The findings show that the bone cells are able to stimulate the bone remodelling process under the normal walking gait loading. The bone marrow behaviour such as shear stress, pressure and permeability, together with bone porosity and surface area, have a significant relationship with a p-value < 0.05. The longitudinal permeability and stiffness were respectively 83% and 56% higher, compared to the transverse orientation. The shear stress during a normal walking phase was in a range of 0.01- 0.27 Pa. These are sufficient to regulate cell response. It was also found that the stiffness of the trabecular bone structure is 22% higher compared to the models without the bone marrow. This finding suggests that the presence of the bone marrow could help to reduce the deformation and stresses on the trabecular bone structure

Computational modelling of trabecular bone structure using fluid-structure interaction approach

While doing daily physiological activities, trabecular bone will experience certain amount of deformation, which causes movement of the bone marrow. The bone marrow movement could affect the bone remodelling process. The properties of the bone will also be affected as the bone marrow acts as a hydraulic stiffening to the trabecular structure. Previous studies on trabecular bone remodelling did not consider the effects of bone marrow movement. Thus, there is a need to perform combined analyses of the bone marrow movement with trabecular structure to assess its effects on the remodelling process under a realistic condition. The aim of this study is to determine the effect of bone marrow movement onto the trabecular bone structure under mechanical loading using fluid-structure interaction (FSI) approach. Two different models of the trabecular bone, namely idealised and actual were constructed. The idealised models were used to correlate the bone marrow behaviour to the trabecular bone morphology. The actual trabecular bone models were constructed to mimic the presence of the bone marrow within the trabecular bone structure during physiological loading. The effects of different orientation of the trabecular structures were also examined. Three numerical approaches which are finite element method, computational fluid dynamics and FSI were employed to evaluate the importance of bone marrow movement effect towards the trabecular bone mechanical properties. The findings show that the bone cells are able to stimulate the bone remodelling process under the normal walking gait loading. The bone marrow behaviour such as shear stress, pressure and permeability, together with bone porosity and surface area, have a significant relationship with a p-value < 0.05. The longitudinal permeability and stiffness were respectively 83% and 56% higher, compared to the transverse orientation. The shear stress during a normal walking phase was in a range of 0.01- 0.27 Pa. These are sufficient to regulate cell response. It was also found that the stiffness of the trabecular bone structure is 22% higher compared to the models without the bone marrow. This finding suggests that the presence of the bone marrow could help to reduce the deformation and stresses on the trabecular bone structure

Observation of impact energy absorption performance on idealised trabecular forms in laser sintered nylon

Purpose - This paper aims to investigate whether the trabecular architecture found in natural bone can be effectively replicated through the selective laser sintering process of Nylon P2200. Design/methodology/approach - Trabecular bone was idealised into a scaled up hexagonal cell proven to replicate the natural structure. The structure was modelled in Solidworks 2013 to form a network of interlinking cells. The specific property analysed was the structure toughness through the measurement of the energy absorbed before sample fracture. Findings - It was found that the impact absorption can be increased with the integration of a greater number of trabecular cells producing a finer resolution and not necessarily by increasing the trabecular size. The information gained from this research may be useful in the design of impact and shock absorbing components, with an emphasis on efficient use of material mass. Research limitations/implications - Designers and engineers may find biomimetic methods of absorbing shock and impact an efficient alternative consideration in design applications. Practical implications - The trabecular architecture should be designed so as to be weaker than the bounding surfaces, ensuring that the individual trabecular experience failure first, maximising their energy absorbing capability through increasing the period of deceleration. The simplest way of doing this is to ensure the rod thickness is less than the bounding material thickness. Originality/value - This work documents original testing of both the RP material and consolidated design of samples of idealised bone structures. It builds on previous work in the area and through the results of empirical testing, derives recommendations for further considerations in this area of design and manufacture of biomimetic structures

A review of trabecular bone functional adaptation: what have we learned from trabecular analyses in extant hominoids and what can we apply to fossils?

Many of the unresolved debates in palaeoanthropology regarding evolution of particular locomotor or manipulative behaviours are founded in differing opinions about the functional significance of the preserved external fossil morphology. However, the plasticity of internal bone morphology, and particularly trabecular bone, allowing it to respond to mechanical loading during life means that it can reveal greater insight into how a bone or joint was used during an individual's lifetime. Analyses of trabecular bone have been commonplace for several decades in a human clinical context. In contrast, the study of trabecular bone as a method for reconstructing joint position, joint loading and ultimately behaviour in extant and fossil non-human primates is comparatively new. Since the initial 2D studies in the late 1970s and 3D analyses in the 1990s, the utility of trabecular bone to reconstruct behaviour in primates has grown to incorporate experimental studies, expanded taxonomic samples and skeletal elements, and improved methodologies. However, this work, in conjunction with research on humans and non-primate mammals, has also revealed the substantial complexity inherent in making functional inferences from variation in trabecular architecture. This review addresses the current understanding of trabecular bone functional adaptation, how it has been applied to hominoids, as well as other primates and, ultimately, how this can be used to better interpret fossil hominoid and hominin morphology. Because the fossil record constrains us to interpreting function largely from bony morphology alone, and typically from isolated bones, analyses of trabecular structure, ideally in conjunction with that of cortical structure and external morphology, can offer the best resource for reconstructing behaviour in the past

Performance of microstructural finite element models in predicting the effective modulus of trabecular bone

Trabecular bone is made up of an irregular, interconnecting framework of rod- and plate-like struts [1], therefore the mechanical properties of the bone may only be determined through experimental testing or detailed Finite Element modelling. Experimental testing requires a sample to be removed from the body, which is not possible in living patients. As such, there is a drive to move away from experimental testing and focus instead on creating accurate patient-specific Finite Element models from CT scans of the bone. The computational “gold-standard” Finite Element model used for trabecular bone, namely the voxel-based method, uses solid tetrahedral elements, which are extremely resource intensive. Vanderoost, et al [2] developed an alternative Finite Element code which discretises the structure into a series of beams and shells. This beam-shell approach vastly reduces the size of the mesh and, consequently, the processing time required for the simulation. In this work, an analysis cycle was developed to determine the apparent modulus of a structure using the beam-shell Finite Element model [2]. The cycle imports micro-CT scans of a structure, discretises the structure into a beam-shell mesh, performs a Finite Element simulation and outputs the apparent modulus of the structure along with a reconstructed image. The analysis cycle was validated by analysing over 3000 artificially generated images, comprising various configurations of cubic lattices, Kelvin cell lattices and octet truss lattices, and comparing the modulus output by the analysis cycle to baseline results obtained through the simulation of known node and element data. The analysis cycle provided predictions within 10% of the baseline value for most lattices, however there were issues associated with the rasterisation of the input images and postprocessing which caused variation in the results. Overall, it was determined that the analysis cycle is capable of capturing the apparent modulus of a variety of different structures. Micro-CT scans of 127 bone specimens were run through the analysis cycle. The results from the beam-shell analysis were compared to results from experimental testing [3] and an equivalent voxel-based analysis. There was a clear trend in both the beam-shell and voxel-based data, however the voxel-based method produced stiffer results than the beam-shell method overall. The beam-shell method showed more scatter than the voxel-based method, but contained less significant outliers. The effective modulus, i.e. the modulus of an inner core region, was determined for 17 of the bone specimens and compared to equivalent experimental results. The beam-shell method captured the increase in stiffness between the apparent modulus and the effective modulus as regularly as the voxel-based method, given appropriate boundary conditions were applied. The results produced by both methods can be improved by the removal of machining artifacts and improved segmentation of the micro-CT scans. This work confirms that the beam-shell method is capable of capturing the apparent modulus of a trabecular bone sample, however the scatter in the data must be reduced for it to be considered a viable alternative to the voxel-based method. It was found that the beamshell method is equally capable of predicting the relationship between apparent modulus and effective modulus as the voxel-based method. In both the beam-shell results and voxel-based results, the accuracy of a particular data point could only be determined by considering the results in reference to additional simulation and experimental data points. In light of these results, researchers should be cautious in reporting simulation results for trabecular bone without additional verification

On incorporating bone microstructure in macro- nite-element models

Bone is porous and has a complex microstructure. This study considers the effect of microstructural morphology on the macrolevel mechanical properties of bone. Improved incorporation of such properties is required to advance current finite element approximations of bone behaviour. A technique to computationally generate realistic trabecular bone microstructures is developed. This provides the possibility of examining the effect of different microstructures on the macrolevel mechanical behaviour of bone. They would also permit direct incorporation of bone microstructure in macroscale finite element analyses without the prohibitive computational and experimental costs of donor-image based mesh generation. Micro- finite-element analyses are used for the first time to evaluate the macrolevel orthotropic elastic constants of cortical bone resulting from variations of microstructural morphology. It is concluded that the ratio of canal volume to tissue volume is the most powerful predictor of cortical bone elastic constants and that considerable periosteal-endosteal variations in these constants can develop with bone loss. The role of microstructure in cortical bone toughness is investigated using nano- finite-element analyses of murine cortical bone samples to simulate the initiation and propagation of microcracks. Results confirm the experimentally observed ability of canal and lacuna pores to act as stress raisers, thereby guiding the growth of microcracks. A novel and numerically efficient strain-based plasticity algorithm is presented which permits easy incorporation of strength anisotropy in finite element analyses of bone. The previously evaluated elastic properties of cortical bone are combined with the developed plasticity algorithm to conduct a detailed macro-finite-element investigation of external fixation of tibial midshaft fractures. Old patients are found to be at considerably higher risk of implant loosening under both unilateral and Ilizarov fixation, compared to younger patients

Verification and Validation of MicroCT-based Finite Element Models of Bone Tissue Biomechanics

Non-destructive 3D micro-computed tomography (microCT) based finite element (microFE) model is popular in estimating bone mechanical properties in recent decades. From a fundamental scientific perspective, as the primary function of the skeleton is mechanical in nature, a lot of related biological and physiological mechanisms are mechano-regulated that becomes evident at the tissue scale. In all these research it is essential to known with the best possible accuracy the displacements, stresses, and strains induced by given loads in the bone tissue. Correspondingly, verification and validation of the microFE model has become crucial in evaluating the quality of its predictions. Because of the complex geometry of cancellous bone tissue, only a few studies have investigated the local convergence behaviour of such models and post-yield behaviour has not been reported. Moreover, the validation of their prediction of local properties remains challenging. Recent technique of digital volume correlation (DVC) combined with microCT images can measure internal displacements and deformation of bone specimen and therefore is able to provide experimental data for validation. However, the strain error of this experimental method tends to be a lot higher (in the order of several thousand microstrains) for spatial resolutions of 10-20 µm, typical element size of microFE models. Strictly speaking no validation of strain is possible. Therefore, the goal of this thesis it to conduct a local convergence study of cancellous bone microFE models generated using three microCT-based tissue modelling methods (homogeneous tetrahedral model, homogeneous hexahedral model and heterogeneous hexahedral model); to validate these models’ prediction in terms of displacement using the novel DVC technique; and finally to compare the strain field predicted by three tissue modelling methods, in order to explore the effect of specific idealisations/simplifications on the prediction of strain