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Register a new userThe Role of Osteocytes in Targeted Bone Remodeling: A Mathematical Model
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Until recently many studies of bone remodeling at the cellular level have focused on the behavior of mature osteoblasts and osteoclasts, and their respective precursor cells, with the role of osteocytes and bone lining cells left largely unexplored. This is particularly true with respect to the mathematical modeling of bone remodeling. However, there is increasing evidence that osteocytes play important roles in the cycle of targeted bone remodeling, in serving as a significant source of RANKL to support osteoclastogenesis, and in secreting the bone formation inhibitor sclerostin. Moreover, there is also increasing interest in sclerostin, an osteocyte-secreted bone formation inhibitor, and its role in regulating local response to changes in the bone microenvironment. Here we develop a cell population model of bone remodeling that includes the role of osteocytes, sclerostin, and allows for the possibility of RANKL expression by osteocyte cell populations. This model extends and complements many of the existing mathematical models for bone remodeling but can be used to explore aspects of the process of bone remodeling that were previously beyond the scope of prior modeling work. Through numerical simulations we demonstrate that our model can be used to theoretically explore many of the most recent experimental results for bone remodeling, and can be utilized to assess the effects of novel bone-targeting agents on the bone remodeling process.
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Bone remodeling involves the coordinated removal of bone by osteoclasts and addition of bone by osteoblasts, a process that is modulated by the prevailing mechanical environment. In this paper a fully coupled model of bone remodeling is developed, based on coupling a bone cell population model with a micromechanical homogenization scheme of bone stiffness. While the former model considers biochemical regulatory mechanisms between bone cells such as the RANK-RANKL-OPG pathway and action of TGF-beta, the latter model allows for accurate upscaling of the mechanical properties of bone. Importantly, we consider bone remodeling as being controlled proportionally to the microscopic strain energy density, on the observation scale where the sensing of the mechanical loading takes place, estimated by means of continuum micromechanics-based strain concentration. This approach allows to address two fundamental questions of bone biology: (i) How do biochemical changes influence bone remodeling and so affect the composition and mechanical properties of bone? and (ii) What mechanisms are responsible for mechanoregulation of bone remodeling? Numerical studies highlight the conceptual advantage of this new approach compared to conventional phenomenological models. It is demonstrated that the proposed model is able to simulate changes of the bone constituent volume fractions that are in qualitative agreement with experimental observations for osteoporotic and disuse syndromes.
The formation of new bone involves both the deposition of bone matrix, and the formation of a network of cells embedded within the bone matrix, called osteocytes. Osteocytes derive from bone-synthesising cells (osteoblasts) that become buried in bone matrix during bone deposition. The generation of osteocytes is a complex process that remains incompletely understood. Whilst osteoblast burial determines the density of osteocytes, the expanding network of osteocytes regulates in turn osteoblast activity and osteoblast burial. In this paper, a spatiotemporal continuous model is proposed to investigate the osteoblast-to-osteocyte transition. The aims of the model are (i) to link dynamic properties of osteocyte generation with properties of the osteocyte network imprinted in bone, and (ii) to investigate Marottis hypothesis that osteocytes prompt the burial of osteoblasts when they become covered with sufficient bone matrix. Osteocyte density is assumed in the model to be generated at the moving bone surface by a combination of osteoblast density, matrix secretory rate, rate of entrapment, and curvature of the bone substrate, but is found to be determined solely by the ratio of the instantaneous burial rate and matrix secretory rate. Osteocyte density does not explicitly depend on osteoblast density nor curvature. Osteocyte apoptosis is also included to distinguish between the density of osteocyte lacuna and the density of live osteocytes. Experimental measurements of osteocyte lacuna densities are used to estimate the rate of burial of osteoblasts in bone matrix. These results suggest that: (i) burial rate decreases during osteonal infilling, and (ii) the control of osteoblast burial by osteocytes is likely to emanate as a collective signal from a large group of osteocytes, rather than from the osteocytes closest to the bone deposition front.
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.
Bone remodelling maintains the functionality of skeletal tissue by locally coordinating bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts) in the form of Bone Multicellular Units (BMUs). Understanding the emergence of such structured units out of the complex network of biochemical interactions between bone cells is essential to extend our fundamental knowledge of normal bone physiology and its disorders. To this end, we propose a spatio-temporal continuum model that integrates some of the most important interaction pathways currently known to exist between cells of the osteoblastic and osteoclastic lineage. This mathematical model allows us to test the significance and completeness of these pathways based on their ability to reproduce the spatio-temporal dynamics of individual BMUs. We show that under suitable conditions, the experimentally-observed structured cell distribution of cortical BMUs is retrieved. The proposed model admits travelling-wave-like solutions for the cell densities with tightly organised profiles, corresponding to the progression of a single remodelling BMU. The shapes of these spatial profiles within the travelling structure can be linked to the intrinsic parameters of the model such as differentiation and apoptosis rates for bone cells. In addition to the cell distribution, the spatial distribution of regulatory factors can also be calculated. This provides new insights on how different regulatory factors exert their action on bone cells leading to cellular spatial and temporal segregation, and functional coordination.
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.
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