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Quantifying the osteocyte network in the human skeleton
No full text<b>Highlights</b>\ud
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- The size of the osteocyte lacunar canalicular network (LCN) is calculated from published data.\ud
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- The average human skeleton has ~ 42 billion osteocytes forming 23 trillion connections.\ud
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- Total surface area of the LCN is 215 m<sup>2</sup>, with 24 mL of fluid around the resident osteocytes.\ud
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- The impact of osteocytic osteolysis and renewal by remodelling are calculated.\ud
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<b>Abstract</b>\ud
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Osteocytes form an extensive cellular network throughout the hard tissue matrix of the skeleton, which is known to regulate skeletal structure. However due to limitations in imaging techniques, the magnitude and complexity of this network remain undefined.\ud
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We have used data from recent papers obtained by new imaging techniques, in order to estimate absolute and relative quantities of the human osteocyte network and form a more complete understanding of the extent and nature of this network.\ud
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We estimate that the total number of osteocytes within the average adult human skeleton is ~ 42 billion and that the total number of osteocyte dendritic projections from these cells is ~ 3.7 trillion. Based on prior measurements of canalicular density and a mathematical model of osteocyte dendritic process branching, we calculate that these cells form a total of 23 trillion connections with each other and with bone surface cells. We estimate the total length of all osteocytic processes connected end-to-end to be 175,000 km. Furthermore, we calculate that the total surface area of the lacuno-canalicular system is 215 m<sup>2</sup>. However, the residing osteocytes leave only enough space for 24 mL of extracellular fluid. Calculations based on measurements in lactation-induced murine osteocytic osteolysis indicate a potential total loss of ~ 16,000 mm<sup>3</sup> (16 mL) of bone by this process in the human skeleton. Finally, based on the average speed of remodelling in the adult, we calculate that 9.1 million osteocytes are replenished throughout the skeleton on a daily basis, indicating the dynamic nature of the osteocyte network.\ud
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We conclude that the osteocyte network is a highly complex communication network, and is much more vast than commonly appreciated. It is at the same order of magnitude as current estimates of the size of the neural network in the brain, even though the formation of the branched network differs between neurons and osteocytes. Furthermore, continual replenishment of large numbers of osteocytes in the process of remodelling allows therapeutic changes to the continually renewed osteoblast population to be rapidly incorporated into the skeleton
Osteocytes as a record of bone formation dynamics: A mathematical model of osteocyte generation in bone matrix
No full textThe 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: \ud
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(i) to link dynamic properties of osteocyte generation with properties of the osteocyte network imprinted in bone, and;\ud
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(ii) to investigate Marotti׳s hypothesis that osteocytes prompt the burial of osteoblasts when they become covered with sufficient bone matrix. \ud
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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: \ud
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(i) burial rate decreases during osteonal infilling, and \ud
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(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
Fluctuation-induced self-force and violation of action-reaction in a nonequilibrium steady state fluid
No full textWe show that the fluctuations of a fluid driven out of equilibrium can induce a net force on a single asymmetric object immersed in it. The force originates in the restriction of the fluid's fluctuations at the object's boundaries, as in the Casimir effect. In contrast to the equilibrium situation, its emergence on a single obstacle is not ruled out by the second law of thermodynamics since the fluid is in a nonequilibrium state. We explicitly calculate this self-force on a deformed circle embedded in a fluid whose density fluctuations obey a stochastic reaction-diffusion equation. When two objects are considered, the presence of self-forces can violate the action-reaction principle. We illustrate this by calculating the internal Casimir-type forces between a circle and a plate. Their sum, instead of vanishing, provides the self-force exerting on the circle-plate assembly
The Casimir effect
No full textThe purpose of these lecture notes is twofold. First we aim at introducing the reader to the basic concepts pertaining to Casimir forces, starting from the seminal work of Casimir. In a broader sense, we also review some aspects of dispersion forces, in particular the status of van der Waals forces in vacuum as well as in a finite density and non zero temperature medium. The Lifshitz theory of forces between dielectric bodies is briefly described. In the second place, the course deals with a more recent analysis of the Casimir force for metals based on an exact microscopic statistical mechanical treatment of matter and field fluctuations. It reveals that charges fluctuations inside the conductors cannot be ignored (as is done in the conventional Casimir calculation). It also helps clarifying present day controversies about the contribution of thermal fluctuations to the force and the proper way to recover the metallic case in the framework of the Lifshitz theory. Finally the occurrence of Casimir forces in critical phenomena is illustrated in the case of the Bose–Einstein condensation in a free Bose gas. The Casimir effect in other contexts (general quantum field theory, particle physics, cosmology, …) is not considered here
A continuous model for the embedment of osteocytes in bone matrix
No full textThe formation of new bone involves both the deposition of bone matrix and the formation of a network of cells embedded within it, called osteocytes. Osteocytes are essential to the detection of micro-damage and to the control of bone renewal. Osteocytes derive from osteoblasts (bone matrix- laying cells) that become trapped in the matrix during the deposition. In turn, osteocytes control osteoblast activity through their interconnected cell processes. In this contribution, a spatiotemporal continuous model is proposed to investigate the osteoblast-to-osteocyte transition. The model elucidates the interplays between speed of new bone formation, rate of entrapment, and curvature of the bone substrate in determining the density of osteocytes in the new bone matrix
Modeling the effect of curvature on the collective behavior of cells growing new tissue
No full textThe growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue’s evolution. Understanding the cellular basis of this control is highly significant for bioscaffold tissue engineering, the evolution of bone microarchitecture, wound healing, and tumor growth. Although previous models have proposed geometrical relationships between tissue growth and curvature, the role of cell density and cell vigor remains poorly understood. We propose a cell-based mathematical model of tissue growth to investigate the systematic influence of curvature on the collective crowding or spreading of tissue-synthesizing cells induced by changes in local tissue surface area during the motion of the interface. Depending on the strength of diffusive damping, the model exhibits complex growth patterns such as undulating motion, efficient smoothing of irregularities, and the generation of cusps. We compare this model with in vitro experiments of tissue deposition in bioscaffolds of different geometries. By including the depletion of active cells, the model is able to capture both smoothing of initial substrate geometry and tissue deposition slowdown as observed experimentally
Towards a cell-based mechanostat theory of bone: The need to account for osteocyte desensitisation and osteocyte replacement
No full textBone׳s mechanostat theory describes the adaptation of bone tissues to their mechanical environment. Many experiments have investigated and observed such structural adaptation. However, there is still much uncertainty about how to define the reference mechanical state at which bone structure is adapted and stable. Clinical and experimental observations show that this reference state varies both in space and in time, over a wide range of timescales. We propose here an osteocyte-based mechanostat theory that encodes the mechanical reference state in osteocyte properties. This theory assumes that osteocytes are initially formed adapted to their current local mechanical environment through modulation of their properties. We distinguish two main types of physiological processes by which osteocytes subsequently modify the reference mechanical state at different timescales. One is cell desensitisation, which occurs rapidly and reversibly during an osteocyte׳s lifetime. The other is the replacement of osteocytes during bone remodelling, which occurs over the long timescales of bone turnover. The novelty of this theory is to propose that long-lasting morphological and genotypic osteocyte properties provide a material basis for a long-term mechanical memory of bone that is gradually reset by bone remodelling. We test this theory by simulating long-term mechanical disuse (modelling spinal cord injury), and short-term mechanical loadings (modelling daily exercises) with a mathematical model. The consideration of osteocyte desensitisation and of osteocyte replacement by remodelling is able to capture a number of phenomena and timescales observed during the mechanical adaptation of bone tissues, lending support to this theory
Violation of the action-reaction principle and self-forces induced by nonequilibrium fluctuations
Get PDFWe show that the extension of Casimir-like forces to fluctuating fluids driven out of equilibrium can exhibit two interrelated phenomena forbidden at equilibrium: self-forces can be induced on single asymmetric objects and the action-reaction principle between two objects can be violated. These effects originate in asymmetric restrictions imposed by the objects' boundaries on the fluid's fluctuations. They are not ruled out by the second law of thermodynamics since the fluid is in a nonequilibrium state. Considering a simple reaction-diffusion model for the fluid, we explicitly calculate the self-force induced on a deformed circle. We also show that the action-reaction principle does not apply for the internal Casimir forces between a circle and a plate. Their sum, instead of vanishing, provides the self-force on the circle-plate assembly.This work is supported by Fondecyt Grants No.
1061112 and No. 3070037, Fondap Grant No. 11980002, and
Snsf Grant No. PBEL2-116909
Equilibrium correlations in charged fluids coupled to the radiation field
No full textWe provide an exact microscopic statistical treatment of particle and field correlations in a system of quantum charges in equilibrium with a classical radiation field. Using the Feynman-Kac-Itô representation of the Gibbs weight, the system of particles is mapped onto a collection of random charged wires. The field degrees of freedom can be integrated out, providing an effective pairwise magnetic potential. We then calculate the contribution of the transverse field coupling to the large-distance particle correlations. The asymptotics of the field correlations in the plasma are also exactly determined
Mathematical modelling of basic multicellular units: The functional units of bone remodeling
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