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Register a new userOn Stress Driven Diffusion in Bone -- An Experimental Study
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Abstract The transport of nutrients or signal constituents that stimulate growth of bone tissue is supposed to be affected by a static mechanical load. It follows from basic thermodynamical principles that constituents causing volumetric change are dragged along the gradients of hydrostatic stress. The present preliminary study examines the behaviour of iodine present in the medullary cavity of a bovine long bone exposed to mechanical load. A section of the bone is x-ray scanned with the static load present, with and without the iodine. The resulting distribution in a selected 2D plane is numerically evaluated using a discrete Radons inverse transform. The result suggests that iodine is a useful constituent with a good attenuation effect on the x-ray beam and clearly reveals the temporal distribution of its transport through the bone. It further result shows some indication that stress does affect the iodine distribution.
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Age-related bone loss and postmenopausal osteoporosis are disorders of bone remodelling, in which less bone is reformed than resorbed. Yet, this dysregulation of bone remodelling does not occur equally in all bone regions. Loss of bone is more pronounced near and at the endocortex, leading to cortical wall thinning and medullary cavity expansion, a process sometimes referred to as trabecularisation or cancellisation. Cortical wall thinning is of primary concern in osteoporosis due to the strong deterioration of bone mechanical properties that it is associated with. In this paper, we examine the possibility that the non-uniformity of microscopic bone surface availability could explain the non-uniformity of bone loss in osteoporosis. We use a computational model of bone remodelling in which microscopic bone surface availability influences bone turnover rate and simulate the evolution of the bone volume fraction profile across the midshaft of a long bone. We find that bone loss is accelerated near the endocortical wall where the specific surface is highest. Over time, this leads to a substantial reduction of cortical wall thickness from the endosteum. The associated expansion of the medullary cavity can be made to match experimentally observed cross-sectional data from the Melbourne Femur Collection. Finally, we calculate the redistribution of the mechanical stresses in this evolving bone structure and show that mechanical load becomes critically transferred to the periosteal cortical bone.
Bone is a biomaterial undergoing continuous renewal. The renewal process is known as bone remodelling and is operated by bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts). Both biochemical and biomechanical regulatory mechanisms have been identified in the interaction between osteoclasts and osteoblasts. Here we focus on an additional and poorly understood potential regulatory mechanism of bone cells, that involves the morphology of the microstructure of bone. Bone cells can only remove and replace bone at a bone surface. However, the microscopic availability of bone surface depends in turn on the ever-changing bone microstructure. The importance of this geometrical dependence is unknown and difficult to quantify experimentally. Therefore, we develop a sophisticated mathematical model of bone cell interactions that takes into account biochemical, biomechanical and geometrical regulations. We then investigate numerically the influence of bone surface availability in bone remodelling within a representative bone tissue sample. The interdependence between the bone cells activity, which modifies the bone microstructure, and changes in the microscopic bone surface availability, which in turn influences bone cell development and activity, is implemented using a remarkable experimental relationship between bone specific surface and bone porosity. Our model suggests that geometrical regulation of the activation of new remodelling events could have a significant effect on bone porosity and bone stiffness. On the other hand, geometrical regulation of late stages of osteoblast and osteoclast differentiation seems less significant. We conclude that the development of osteoporosis is probably accelerated by this geometrical regulation in cortical bone, but probably slowed down in trabecular bone.
Continuum bone remodelling is an important tool for predicting the effects of mechanical stimuli on bone density evolution. While the modelling of only cancellous bone is considered in many studies based on continuum bone remodelling, this work presents an approach of modelling also cortical bone and the interaction of both bone types. The distinction between bone types is made by introducing an initial volume fraction. A simple point-wise example is used to study the behaviour of novel model options, as well as a proximal femur example, where the interaction of both bone types is demonstrated using initial density distributions. The results of the proposed model options indicate that the consideration of cortical bone remarkably changes the density evolution of cancellous bone, and should therefore not be neglected.
Bone remodelling is carried out by `bone multicellular units (BMUs) in which active osteoclasts and active osteoblasts are spatially and temporally coupled. The refilling of new bone by osteoblasts towards the back of the BMU occurs at a rate that depends both on the number of osteoblasts and on their secretory activity. In cortical bone, a linear phenomenological relationship between matrix apposition rate (MAR) and BMU cavity radius is found experimentally. How this relationship emerges from the combination of complex, nonlinear regulations of osteoblast number and secretory activity is unknown. Here, we extend our previous mathematical model of cell development within a single BMU to investigate how osteoblast number and osteoblast secretory activity vary along the BMUs closing cone. MARs predicted by the model are compared with data from tetracycline double labelling experiments. We find that the linear phenomenological relationship observed in these experiments between MAR and BMU cavity radius holds for most of the refilling phase simulated by our model, but not near the start and end of refilling. This suggests that at a particular bone site undergoing remodelling, bone formation starts and ends rapidly. Our model also suggests that part of the observed cross-sectional variability in tetracycline data may be due to different bone sites being refilled by BMUs at different stages of their lifetime. The different stages of a BMUs lifetime depend on whether the cell populations within the BMU are still developing or have reached a quasi-steady state while travelling through bone. We find that due to their longer lifespan, active osteoblasts reach a quasi-steady distribution more slowly than active osteoclasts. We suggest that this fact may locally enlarge the Haversian canal diameter (due to a local lack of osteoblasts compared to osteoclasts) near the BMUs point of origin.
During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to analyze the mechanisms controlling tissue morphogenesis. Recently, a mechanical measurement method based on force inference from cell shapes and connectivity has been developed. It is non-invasive, and can provide space-time maps of force and stress within an epithelial tissue, up to prefactors. We previously performed a comparative study of three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces. In the present study, to further validate and compare the three force inference methods, we tested their robustness by measuring temporal fluctuation of estimated forces. Quantitative data of cell-level dynamics in a developing tissue suggests that variation of forces and stress will remain small within a short period of time ($sim$minutes). Here, we showed that cell-junction tensions and global stress inferred by the Bayesian force inference method varied less with time than those inferred by the method that estimates only tension. In contrast, the amplitude of temporal fluctuations of estimated cell pressures differs less between different methods. Altogether, the present study strengthens the validity and robustness of the Bayesian force-inference method.
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