Mechanical Stimuli in Prediction of Trabecular Bone Adaptation: Numerical Comparison

Adaptation is the process, with which bone responds to changes in loading environment and modifies its properties and organisation to meet the mechanical demands. Trabecular bone undergoes significant adaptation when subjected to external forces, accomplished through resorption of old and fractured bone and formation of a new bone material. These processes are assumed to be driven by mechanical stimuli of bone-matrix deformation sensed by bone mechanosensory cells. Although numerous in vivo and in vitro experimental evidence of trabecular bone morphology adaptation was obtained, the exact nature of mechanical stimuli triggering biological responses (i.e., osteoclastic resorption and osteoblastic formation) is still debated. This study aims to compare different mechanical stimuli with regard to their ability to initiate the load-induced adaptation in trabecular bone. For this purpose, a 2D model of two trabeculae, connected at their basement, with bone marrow in the intertrabecular space was developed. The finite-element method was implemented for the model loaded in compression to calculate magnitudes of several candidates of the bone-adaptation stimuli. A user material subroutine was developed to relate a magnitude of each candidate to changes in the shape of trabeculae

Trabecula-level mechanoadaptation: numerical analysis of morphological changes

Background: Bone is a living material that, unlike man-made ones, demonstrates continuous adaptation of its structure and mechanical properties to resist the imposed mechanical loading. Adaptation in trabecular bone is characterised by improvement of its stiffness in the loading direction and respective realignment of trabecular load-bearing architecture. Considerable experimental and simulation evidence of trabecular bone adaptation to its mechanical environment at the tissue- and organ-levels was obtained, while little attention was given to the trabecula-level of this process. This study aims to describe and classify load-driven morphological changes at the level of individual trabeculae and to propose their drivers. Method: For this purpose, a well-established mechanoregulation-based numerical model of bone adaptation was implemented in a user-defined subroutine that changed the structural and mechanical properties of trabeculae based on the magnitude of a mechanical stimulus. This subroutine was used in conjunction with finite-element models of variously shaped structures representing trabeculae loaded in compression or shear. Results: In all analysed cases, trabeculae underwent morphological evolution under applied compressive or shear loading. Among twelve cases analysed, six main mechanisms of morphological evolution were established: reorientation, splitting, merging, full resorption, thinning, and thickening. Moreover, all simulated cases presented the ability to reduce the mean value of von Mises stress while increasing their ability to resist compressive/shear loading during adaptation. Conclusion: This study evaluated morphological and mechanical changes in trabeculae of different shapes in response to compressive or shear loadings and compared them based on the analysis of von Mises stress distribution as well as profiles of normal and shear stresses in the trabeculae at different stages of their adaptation.</p

Mechanoregulated trabecular bone adaptation: progress report on in silico approaches

Adaptation is the process by which bone responds to changes in loading environment and modulates its properties and spatial organization to meet the mechanical demands. Adaptation in trabecular bone is achieved through increase in bone mass and alignment of trabecular-bone morphology along the loading direction. This transformation of internal microstructure is governed by mechanical stimuli sensed by mechanosensory cells in the bone matrix. Realisation of adaptation in the form of local bone-resorption and -formation activities as a function of mechanical stimuli is still debated. In silico modelling is a useful tool for simulation of various scenarios that cannot be investigated in vivo and particularly well suited for prediction of trabecular bone adaptation. This progress report presents the recent advances in in silico modelling of mechanoregulated adaptation at the scale of trabecular bone tissue. Four well-established bone-adaptation models are reviewed in terms of their recent improvements and validation. They consider various mechanical factors: (i) strain energy density, (ii) strain and damage, (iii) stress nonuniformity and (iv) daily stress. Contradictions of these models are discussed and their ability to describe adequately a real-life mechanoregulation process in bone is compared. </p

Mechanical stimuli in prediction of trabecular bone adaptation: numerical comparison

Adaptation is the process, with which bone responds to changes in loading environment and modifies its properties and organisation to meet the mechanical demands. Trabecular bone undergoes significant adaptation when subjected to external forces, accomplished through resorption of old and fractured bone and formation of a new bone material. These processes are assumed to be driven by mechanical stimuli of bone-matrix deformation sensed by bone mechanosensory cells. Although numerous in vivo and in vitro experimental evidence of trabecular bone morphology adaptation was obtained, the exact nature of mechanical stimuli triggering biological responses (i.e., osteoclastic resorption and osteoblastic formation) is still debated. This study aims to compare different mechanical stimuli with regard to their ability to initiate the load-induced adaptation in trabecular bone. For this purpose, a 2D model of two trabeculae, connected at their basement, with bone marrow in the intertrabecular space was developed. The finite-element method was implemented for the model loaded in compression to calculate magnitudes of several candidates of the bone-adaptation stimuli. A user material subroutine was developed to relate a magnitude of each candidate to changes in the shape of trabeculae.</p

Effect of microstructure on trabecular-bone fracture: numerical analysis

Trabecular bone tissue with its complicated microstructural morphology can exhibit complex and random fracture patterns. This paper focuses on the effect of morphology of bone tissue on processes of its deformation and fracture. For this purpose, three-dimensional unit cells of trabecular bone tissue were generated based on the scans of human distal tibial bone obtained with high-resolution peripheral quantitative computed tomography (HR-pQCT). Mechanical behavior of porous structure of trabecular bone was investigated under conditions of applied tensile and compressive loads employing a model of degradation of elastic properties, numerically implemented with finite-element analysis. The calculations were performed in Simulia Abaqus using the UMAT custom subroutine

Failure behaviour of human trabecular bone

A trabecular bone tissue with its complex microstructural morphology can demonstrate a complex and random pattern of fracture. This paper analyses the effect of material’s mechanical behaviour on failure modelling of human trabecular bone. For this purpose, a 3D unit cell of trabecular tissue was obtained from scans of human distal tibia performed with high-resolution peripheral quantitative computed tomography (HR-pQCT). In simulations, two types of fracture of trabeculae were considered - brittle and ductile, with respective elastic and elastoplastic formulations. Two types of loading – tension and compression – were applied to the unit cell in order to assess its stress state and locations of the failure onset. Positions of damaged areas in case of brittle-fracture approach differed for tension and compression, while the same damage regions were observed for the ductile criterion in both loading conditions. It was found that the first modelling approach resulted in about two times higher effective strength of trabecular bone as compared to that for the second approach: 11.49 MPa and 4.94 MPa, respectively. The calculated values of effective strength for brittle and ductile material models are in good agreement with the magnitudes of tensile and compressive strength of trabecular bone reported in the literature. Effective parameters of the trabecular bone tissue – ultimate compressive and tensile strength as well as yield stress – are considerably lower than those of individual trabeculae: some 8% of the respective magnitudes for trabeculae