A Systems Approach to Understanding Bone Cell Interactions in Health and Disease

Bone is an important organ performing three essential physiological functions: mechanical support, mineral homeostasis (such as calcium and phosphate) and support of haematopoiesis. In fact, bone diseases in the elderly are associated with high morbidity and increased mortality. Osteoporosis and related skeletal complications are amongst the most important diseases impacting both the quality of life of our aging population and contributing costs to our health care system

Theoretical analysis of the spatio-temporal structure of bone multicellular units

Bone multicellular units (BMUs) maintain the viability of the skeletal tissue by coordinating locally the sequence of bone resorption and bone formation performed by cells of the osteoclastic and osteoblastic lineage. Understanding the emergence and the net bone balance of such structured microsystems out of the complex network of biochemical interactions between bone cells is fundamental for many bone-related diseases and the evaluation of fracture risk. Based on current experimental knowledge, we propose a spatio-temporal continuum model describing the interactions of osteoblastic and osteoclastic cells. We show that this model admits travelling-wave-like solutions with well-confined cell profiles upon specifying external conditions mimicking the environment encountered in cortical bone remodelling. The shapes of the various cell concentration profiles within this travelling structure are intrinsically linked to the parameters of the model such as differentiation, proliferation, and apoptosis rates of bone cells. The internal structure of BMUs is reproduced, allowing for experimental calibration. The spatial distribution of the key regulatory factors can also be exhibited, which in diseased states could give hints as to the biochemical agent most accountable for the disorder

Spatio-temporal structure of cell distribution in cortical Bone Multicellular Units: a mathematical model

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.Comment: 14 pages, 5 figures; v2: Completed model description after Eq. (16), clarified discussion/description after Eq. (23), between Eqs. (29)-(31), and in 2nd bullet point in conclusion

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov's fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current correlation function is found to be integrable in space, in both classical and quantum regimes.Comment: 19 pages, 1 figur

Modelling the anabolic response of bone using a cell population model

To maintain bone mass during bone remodelling, coupling is required between bone resorption and bone formation. This coordination is achieved by a network of autocrine and paracrine signalling molecules between cells of the osteoclastic lineage and cells of the osteoblastic lineage. Mathematical modelling of signalling between cells of both lineages can assist in the interpretation of experimental data, clarify signalling interactions and help develop a deeper understanding of complex bone diseases. Several mathematical models of bone cell interactions have been developed, some including rank–rankl–opg signalling between cells and systemic parathyroid hormone pth. However, to our knowledge these models do not currently include key aspects of some more recent biological evidence for anabolic responses. In this paper, we further develop a mathematical model of bone cell interactions by Pivonka et al. (2008) to include the proliferation of precursor osteoblasts into the model. This inclusion is important to be able to account for wnt signalling, believed to play an important role in the anabolic responses of bone. We show that an increased rate of differentiation to precursor cells or an increased rate of proliferation of precursor osteoblasts themselves both result in increased bone mass. However, modelling these different processes separately enables the new model to represent recent experimental discoveries such as the role of wnt signalling in bone biology and the recruitment of osteoblast progenitor cells by transforming growth factor ββ. Finally, we illustrate the power of the new model's capabilities by applying the model to prostate cancer metastasis to bone. In the bone microenvironment, prostate cancer cells are believed to release some of the same signalling molecules used to coordinate bone remodelling (i.e., wnt and pthrp), enabling the cancer cells to disrupt normal signalling and coordination between bone cells. This disruption can lead to either bone gain or bone loss. We demonstrate that the new computational model developed here is capable of capturing some key observations made on the evolution of the bone mass due to metastasis of prostate cancer to the bone microenvironment

The relationship between porosity and specific surface in human cortical bone is subject specific

A characteristic relationship for bone between bone volume fraction (BV/TV) and specific surface (BS/TV) has previously been proposed based on 2D histological measurements. This relationship has been suggested to be bone intrinsic, i.e., to not depend on bone type, bone site and health state. In these studies, only limited data comes from cortical bone. The aim of this paper was to investigate the relationship between BV/TV and BS/TV in human cortical bone using high-resolution micro-CT imaging and the correlations with subject-specific biometric data such as height, weight, age and sex. Images from femoral cortical bone samples of the Melbourne Femur Collection were obtained using synchrotron radiation micro-CT (SPring8, Japan). Sixteen bone samples from thirteen individuals were analysed in order to find bone volume fraction values ranging from 0.20 to 1. Finally, morphological models of the tissue microstructure were developed to help explain the relationship between BV/TV and BS/TV.\ud \ud Our experimental findings indicate that the BV/TV vs BS/TV relationship is subject specific rather than intrinsic. Sex and pore density were statistically correlated with the individual curves. However no correlation was found with body height, weight or age. Experimental cortical data points deviate from interpolating curves previously proposed in the literature. However, these curves are largely based on data points from trabecular bone samples. This finding challenges the universality of the curve: highly porous cortical bone is significantly different to trabecular bone of the same porosity. Finally, our morphological models suggest that changes in BV/TV within the same sample can be explained by an increase in pore area rather than in pore density. This is consistent with the proposed mechanisms of age-related endocortical bone loss. In addition, these morphological models highlight that the relationship between BV/TV and BS/TV is not linear at high wiry as suggested in the literature but is closer to a square root function