Structural failure and fracture of immature bone

Radiological features alone do not allow the discrimination between accidental paediatric long bone fractures or those caused by child abuse. Therefore, for those cases where the child is unable to communicate coherently, there is a clinical need to elucidate the mechanisms behind each fracture to provide a forensic biomechanical tool for clinical implementation. 5 months old ovine femurs and tibiae were used as surrogates for paediatric specimens and were subjected to micro-CT scans to obtain their geometrical and material properties. A novel methodology to align long bones so that they would be loaded in a state of pure bending and torsion was developed and compared against the use of a standard anatomical coordinate system. The second moment of area and its coefficient of variation (COV) for each alignment method were calculated to ascertain the reference axes that minimised the effect of eccentric loading. Wilcoxon-signed rank test showed a significant reduction in COV of the second moment of area using this new method, indicating that the bone has a more regular cross-section when this methodology is implemented. The algorithm generated the locations of subject-specific landmarks that can be used as a reference to align the bones in experimental testing. A low-cost platform that synchronized the data acquisition from the tensile testing machine and the strain gauges was built and used with a high speed camera to capture the fracture pattern in four-point bending at three strain rates and in torsion at two different strain rates, following commonly reported case histories. Finite element (FE) models of ovine tibiae in their optimised alignment were generated to replicate the fracture patterns that were obtained. Fracture initiation and propagation was simulated through the use of element deletion with a maximum principal strain criterion. The experiments produced transverse, oblique, and spiral fractures consistently, which were correlated with the finite element analysis, demonstrating the ability of this pipeline to now be adapted for use in forensic analysis.Open Acces

The Role of the Loading Condition in Predictions of Bone Adaptation in a Mouse Tibial Loading Model

The in vivo mouse tibial loading model is used to evaluate the effectiveness of mechanical loading treatment against skeletal diseases. Although studies have correlated bone adaptation with the induced mechanical stimulus, predictions of bone remodeling remained poor, and the interaction between external and physiological loading in engendering bone changes have not been determined. The aim of this study was to determine the effect of passive mechanical loading on the strain distribution in the mouse tibia and its predictions of bone adaptation. Longitudinal micro-computed tomography (micro-CT) imaging was performed over 2 weeks of cyclic loading from weeks 18 to 22 of age, to quantify the shape change, remodeling, and changes in densitometric properties. Micro-CT based finite element analysis coupled with an optimization algorithm for bone remodeling was used to predict bone adaptation under physiological loads, nominal 12N axial load and combined nominal 12N axial load superimposed to the physiological load. The results showed that despite large differences in the strain energy density magnitudes and distributions across the tibial length, the overall accuracy of the model and the spatial match were similar for all evaluated loading conditions. Predictions of densitometric properties were most similar to the experimental data for combined loading, followed closely by physiological loading conditions, despite no significant difference between these two predicted groups. However, all predicted densitometric properties were significantly different for the 12N and the combined loading conditions. The results suggest that computational modeling of bone’s adaptive response to passive mechanical loading should include the contribution of daily physiological load

The effect of strontium and silicon substituted hydroxyapatite electrochemical coatings on bone ingrowth and osseointegration of selective laser sintered porous metal implants

Additive manufactured, porous bone implants have the potential to improve osseointegration and reduce failure rates of orthopaedic devices. Substantially porous implants are increasingly used in a number of orthopaedic applications. HA plasma spraying-a line of sight process-cannot coat the inner surfaces of substantially porous structures, whereas electrochemical deposition of calcium phosphate can fully coat the inner surfaces of porous implants for improved bioactivity, but the osseous response of different types of hydroxyapatite (HA) coatings with ionic substitutions has not been evaluated for implants in the same in vivo model. In this study, laser sintered Ti6Al4V implants with pore sizes of Ø 700 μm and Ø 1500 μm were electrochemically coated with HA, silicon-substituted HA (SiHA), and strontium-substituted HA (SrHA), and implanted in ovine femoral condylar defects. Implants were retrieved after 6 weeks and histological and histomorphometric evaluation were compared to electrochemically coated implants with uncoated and HA plasma sprayed controls. The HA, SiHA and SrHA coatings had Ca:P, Ca:(P+Si) and (Ca+Sr):P ratios of 1.53, 1.14 and 1.32 respectively. Electrochemically coated implants significantly promoted bone attachment to the implant surfaces of the inner pores and displayed improved osseointegration compared to uncoated scaffolds for both pore sizes (p<0.001), whereas bone ingrowth was restricted to the surface for HA plasma coated or uncoated implants. Electrochemically coated HA implants achieved the highest osseointegration, followed by SrHA coated implants, and both coatings exhibited significantly more bone growth than plasma sprayed groups (p≤0.01 for all 4 cases). SiHA had significantly more osseointegration when compared against the uncoated control, but no significant difference compared with other coatings. There was no significant difference in ingrowth or osseointegration between pore sizes, and the bone-implant-contact was significantly higher in the electrochemical HA than in SiHA or SrHA. These results suggest that osseointegration is insensitive to pore size, whereas surface modification through the presence of an osteoconductive coating plays an important role in improving osseointegration, which may be critically important for extensively porous implants

A novel adaptive algorithm for 3D finite element analysis to model extracortical bone growth

Extracortical bone growth with osseointegration of bone onto the shaft of massive bone tumour implants is an important clinical outcome for long-term implant survival. A new computational algorithm combining geometrical shape changes and bone adaptation in 3D Finite Element simulations has been developed, using a soft tissue envelope mesh, a novel concept of osteoconnectivity, and bone remodelling theory. The effects of varying the initial tissue density, spatial influence function and time step were investigated. The methodology demonstrated good correspondence to radiological results for a segmental prosthesis

Novel adaptive finite element algorithms to predict bone ingrowth in additive manufactured porous implants

Bone loss caused by stress shielding of metallic implants is a concern, as it can potentially lead to long-term implant failure. Surface coating and reducing structural stiffness of implants are two ways to improve bone ingrowth and osteointegration. Additive manufacturing, through selective laser sintering (SLS) or electron beam melting (EBM) of metallic alloys, can produce porous implants with bone ingrowth regions that enhance osteointegration and improve clinical outcomes. Histology of porous Ti6Al4V plugs of two pore sizes with and without electrochemically deposited hydroxyapatite coating, implanted in ovine condyles, showed that bone formation did not penetrate deep into the porous structure, whilst significantly increased bone growth along coated pore surfaces (osteointegration) was observed. Finite Element simulations, combining new algorithms to model bone ingrowth and the effect of surface modification on osteoconduction, were verified with the histology results. The results showed stress shielding of porous implants made from conventional titanium alloy due to material stiffness and implant geometry, limiting ingrowth and osteointegration. Simulations for reduced implant material stiffness predicted increased bone ingrowth. For low modulus Titanium-tantalum alloy (Ti-70%Ta), reduced stress shielding and enhanced bone ingrowth into the porous implant was found, leading to improved mechanical interlock. Algorithms predicted osteoconductive coating to promote both osteointegration and bone ingrowth into the inner pores when they were coated. These new Finite Element algorithms show that using implant materials with lower elastic modulus, osteoconductive coatings or improved implant design could lead to increased bone remodelling that optimises tissue regeneration, fulfilling the potential of enhanced porosity and complex implant designs made possible by additive layer manufacturing techniques

Determination of an initial stage of the bone tissue ingrowth into titanium matrix by cell adhesion model

For achieving early intervention treatment to help patients delay or avoid joint replacement surgery, a personalized scaffold should be designed coupling the effects of mechanical, fluid mechanical, chemical, and biological factors on tissue regeneration, which results in time- and cost-consuming trial-and-error analyses to investigate the in vivo test and related experimental tests. To optimize the fluid mechanical and material properties to predict osteogenesis and cartilage regeneration for the in vivo and clinical trial, a simulation approach is developed for scaffold design, which is composed of a volume of a fluid model for simulating the bone marrow filling process of the bone marrow and air, as well as a discrete phase model and a cell impingement model for tracking cell movement during bone marrow fillings. The bone marrow is treated as a non-Newtonian fluid, rather than a Newtonian fluid, because of its viscoelastic property. The simulation results indicated that the biofunctional bionic scaffold with a dense layer to prevent the bone marrow flow to the cartilage layer and synovia to flow into the trabecular bone area guarantee good osteogenesis and cartilage regeneration, which leads to high-accuracy in vivo tests in sheep . This approach not only predicts the final bioperformance of the scaffold but also could optimize the scaffold structure and materials by their biochemical, biological, and biomechanical properties

Assessing Cortical Bone Adaptation using a Multiscale, Mechanobiological Approach based on Beam-theory, and the Limitations of Contralateral Endpoint Imaging

IntroductionMechanical loading is well known to influence bone mass [1]. Experimental studies on mice tibiae have shown the adaptation response occurs quasi-linearly with respect to external load magnitude and varies at different regions throughout a bone [2,3,4]. Long bones are known to act similar to beams [5]; here, we use beam theory as a more rapid alternative to μFE to formulate a multiscale, mechanobiological model of bone adaptation in the mouse tibia. Two major objectives of this work are:1.Determine a numerical link between mechanical loading and localized bone adaptation rates.2.Guide the development of bone adaptation algorithms to predict adaptive responses based on applied loads.MethodsData used here was collected by Sugiyama et al. [2] and Roberts et al. [6]. Both groups investigated mechanical adaptation following induced bone loss (Sugiyama: sciatic neurectomy, multiple peak loads, endpoint contralateral μCT imaging. Roberts: ovariectomy, singular peak load, longitudinal μCT imaging). Data collected by Roberts et al. was used in the development of the algorithm to identify adaptation parameters before applying it to the Sugiyama et al.’s comprehensive loading dataset.Loaded and control tibiae were aligned through volumetric registration before selecting cross-sections for analysis. Cross-sections were then aligned through rotation with respect to Imin, and translation to align the marrow cavity centroid. The mechanical adaptation algorithm follows an iterative four step procedure: 1) extract cortical surface points (η¬i), calculate cross-sectional mechanical properties, 2) convert external loads into adaptive signals through beam theory analysis, 3) compare adaptive signals against a mechanostat model, and 4) apply adaptive changes to η¬i. This process is repeated each day until the end of experiment.ResultsPreliminary results of the simulation for periosteal formation are in good agreement with experimental findings. Considering the Roberts dataset, principal strain signal could predict the adaptive response to within one pixel of error for ~87% of the periosteum, shown in Figure 1. When analysing the Sugiyama dataset, statistical significance could not be found for adaptive changes on a surface-based level. Figure 1: Comparison of Roberts experimental (blue) and simulated (red) cortical adaptive changes in the midshaft of the mouse tibia [6].DiscussionAxial strains calculated through beam theory have been shown as effective drivers of mechanical adaptation on cortical surfaces. However, due to biological variation between loaded and contralateral limbs, local surface changes are difficult to determine from endpoint imaging studies as load induced bone gains are within the same range as geometric variation of limbs. To overcome this, future work will use surface changes to identify adaptation parameters but will be compared on a cortical thickness level which has shown to be statistically significant [3]. Furthermore, we intend to expand this model by including cell dynamics to present a biologically accurate representation of the adaptation response.References1.Wolff J. Das Gesetz der Transformation der Knochen, 18922.Sugiyama et al, J Bone Miner Res., 27:1784-1793, 2012.3.Miller et al, Front. Bioeng. Biotechnol., 9:671606, 2021.4.Galea et al, Bone, 133:115255, 20205.Ashrafi et al, Biomech Model Mechanobiol. 19:2499-523, 20206.Roberts et al, Sci Rep, 10:8889, 202

A Multiscale, Mechanobiological Model of Cortical Bone Adaptation due to PTH and Mechanical Loading

INTRODUCTIONOsteoporosis (OP) is among the most prevalent bone diseases, causing significant health risks to those affected. Both Parathyroid hormone (PTH) and mechanical loading (ML) have shown synergistic benefits when used against OP [1]. Computational models have been created to simulate the adaptive response to these stimuli; however, these models either investigate adaptation at the organ level [1] or don’t explicitly model biological regulation of bone [2].We present a multiscale, mechanobiological model for combined PTH and ML treatments. This model combines beam theory (BT) and bone cell population modeling (BCPM) to biologically describe adaptation in the mouse tibia, with the primary objective to provide a platform to explore treatment dosage combinations and subsequent anabolic benefitsMETHODLongitudinal μCT data from Roberts et al. [3] was used to calibrate/validate the model. Adaptation is investigated at a cross-sectional level, where the periosteum and endosteum are mapped as discrete x/y coordinates. The algorithm follows five steps: 1) cross-sectional mechanical properties are calculated, 2) an adaptive signal (Ψ) is calculated from external ML at all points using BT and region-specific mechanostat models, 3) Ψ and PTH concentrations are used as regulators in the BCPM which calculates osteoblasts (OB) and osteoclasts (OC) populations at all cortical points, 4) formation or resorption events occur at each cortical point, based on differences in OB and OC activity, 5) x/y coordinates of the cortical surfaces are updated. These five steps are run iteratively at a time step of one day and continue as per experimental procedures outlined in [3]. The ML algorithm was first created as a standalone model, with the BCPM and PTH functionality still in development.RESULTSCurrent developments of the simulations have focused on mechanically induced adaptation using four region-based Wolff type adaptation laws (i.e., combinations of periosteum/endosteum and tension/compression). Results from the ML-based model show that longitudinal strain, coupled with region specific mechanostats, can predict the adaptive response to mechanical loading. Preliminary results of a hybrid BT + BCPM model show the adaptive response could be predicted to within one pixel (~10μm) of error for ~76% of the periosteum, shown in Figure 1. However, optimization has not yet been performed.Figure 1: Comparison of experimental (blue) and simulated (red) adaptive changes across the periosteal surface in the midshaft of the mouse tibia using a BT + BCPM model [3].CONCLUSIONSStrains calculated through BT have been shown as effective drivers of mechanical adaptation on the periosteal surface. Continued work will see the implementation of the BT + BCPM on the endosteal surface and an optimization of parameters, followed by the inclusion of PTH treatments. Once completed, the hybrid model will allow for rapid investigation of the adaptive response to combined treatment methods, allowing for exploration into optimizing patient-specific treatments for those suffering from OP.REFERENCES1. Acta Biomat., 136:291-305, 2021.2. Biomech Model Mechanobiol, 19(5):1765-1780, 2020.3. Sci Rep, 10:8889, 2020

Assessing cortical bone adaptation using a multiscale, mechanobiological approach based on beam-theory

IntroductionMechanical loading (i.e., exercise) is well known to influence bone mass. Experimental studies in mice tibia have shown that the adaptation response occurs quasi-linearly with respect to external load magnitude. The response has also been identified to occur at different spatial locations throughout a bone.While μFE modelling is the gold standard to obtain strain distributions in a whole bone, long bones are known to act mechanically like beams; Here, we use beam theory equations as an alternative method to rapidly calculate strain distributions within cortical bone tissue in the mouse tibia.Using the strain distribution across the tibia, we then formulate a multiscale mechanobiology model of bone adaptation. The aim of this work is to rapidly calculate adaptive strain signals and bone’s subsequent adaptation response. Two major objectives are:1. Determine a numerical link between mechanical loading and localized bone adaptation rates.2. Guide the development of bone adaptation algorithms to predict bone anabolic and catabolic responses based on applied loads. Materials and MethodsData used here was collected by our collaborators from the University of Sheffield. In summary, 6 skeletally mature mice were subjected to a 10 N right tibial axial load three times a week on weeks 2 and 4 of a 5-week schedule. Right tibiae were scanned on weeks 1, 3, 5 and 7 using high resolution μCT (isotropic voxel size = 10.4 μm).Mouse tibia μCT images were rigidly registered to a common reference frame and, and the bone geometry is extracted through segmentation. The mechanical adaptation algorithm follows the 4 steps outlined in Figure 1A, applied to four selected cross-sections: 1) cortical surface points (η¬i) are extracted, and cross-sectional properties are calculated, 2) external loads (F) are converted into an adaptive signal (Ψ) through beam theory analysis, 3) the adaptive signal is compared against a mechanostat model, and 4) changes are applied to η¬i as required. This process is repeated each day until the end of experiment.The adaptive response was measured by comparing the position of the surface after the adaptation algorithm to the original state. Changes were calculated as a net distance between the two states. Model parameters were adjusted based on comparison of simulated net distance between experimental and simulated findings. ResultsPreliminary results of the simulation for periosteal formation are in good agreement with experimental findings. Considering a 10 N load case, a gradient-based formation response using a longitudinal strain signal provides qualitatively similar trends to those found experimentally as shown in Figure 1B.Conclusion and Future WorkThe strains calculated through beam theory have been shown as effective drivers of mechanical adaptation on the cortical surface. Parametric studies are being conducted to determine the optimal simulation conditions that best describe the adaptive response. Furthermore, we intend to expand this model through the inclusion of cell dynamics to present a biologically accurate representation of the adaptation response.<br/

A Multiscale, Mechanobiological Model of Cortical Bone Adaptation due to PTH and Mechanical Loading

IntroductionOsteoporosis (OP) is among the most prevalent bone diseases, causing significant health concerns and potential injury to those affected. PTH(1-34) is used to treat severe OP, however exercise is well known to provide anabolic benefits; combining these two treatments has shown to provide synergistic benefits to overall bone health [1]. Significant experimental work has been undertaken to understand how PTH and mechanical loading (ML) therapies influence bone formation. Currently, efforts have been made in creating computational models capable of predicting bone’s adaptive response to these stimuli. However, these models either consider PTH as a simple mechano-regulated system [1] or investigate adaptation at the organ level [2], and thus don’t accurately represent the mechanobiological regulation of bone.Here, we present a multiscale mechanobiological model for combined PTH and ML. This model combines beam theory (BT) with a bone cell population model (BCPM) to biologically describe the adaptive response in the mouse tibia. The objectives of this work are to:1.Numerically determine a mechanistic link between ML, PTH and the adaptive response2.Provide a platform to explore treatment dosage combinations and subsequent adaptive changesMethodsLongitudinal data used in the calibration/validation of this model was collected by Roberts et al. [3]. This data covers three treatment types: ML monotherapy, PTH monotherapy, and a dual PTH + ML therapy. Mouse tibiae were longitudinally scanned using μCT and rigidly registered in AMIRA. Image analysis and modelling being conducted in MATLAB.Cortical bone adaptation is investigated at a cross-sectional level, where the periosteal and endosteal envelopes are mapped as discrete x/y coordinates. The algorithm follows four steps: 1) cross-sectional mechanical properties are calculated using BT, 2) external ML is converted into an adaptive signal (Ψ) at the cortical surface, 3) Ψ and PTH concentration are used as regulatory functions for the BCPM which calculates osteoblasts (OB) and osteoclasts (OC) numbers at cortical surfaces. 4) formation or resorption events occur at a given cortical point based on bone volume fraction, determined as the difference in OB and OC activity. Subsequently, the x/y coordinates of the cortical surface envelopes are updated. These four steps are iteratively run at a time step of one day and terminated at the endpoint of the experiment.ResultsPreliminary results of the simulations have focused on mechanical-based adaptation using a Wolff type adaptation law. Results show that longitudinal strain is a good mechanical signal (Ψ) to drive bone adaptation response. The adaptive response could be predicted to within one pixel (~10μm) of error for ~87% of the periosteum, as shown in Figure 1. Figure 1: Comparison of experimental (blue) and simulated (red) adaptive changes across the periosteal and endosteal surfaces in the midshaft of the mouse tibia [3].DiscussionStrains calculated through BT have been shown as effective drivers of mechanical adaptation on the cortical surface. Work has begun on modifying a previously proposed BCPM [2] into a surface-based representation for use in mouse tibiae studies. Once completed, the BT + BCPM will provide the means for rapid investigation of the adaptive response, allowing for exploration into optimizing patient-specific treatments for those suffering from OP.References1.Cheong et al, Acta Biomat., 136:291-305, 2021.2.Lavaill et al, Biomech Model Mechanobiol, 19(5):1765-1780, 2020.3.Roberts et al., Sci Rep, 10:8889, 2020