ORCID Profile
0000-0003-3962-5393
Current Organisations
Beaumont Hospital
,
Royal College of Surgeons in Ireland
,
Queensland University of Technology
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Biological Mathematics | Applied Mathematics | Cellular Interactions (incl. Adhesion, Matrix, Cell Wall) | Evolution of Developmental Systems | Dynamical Systems in Applications | Partial Differential Equations | Evolutionary Biology | Biological mathematics | Applied mathematics | Systems Biology
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in the Biological Sciences | Expanding Knowledge in the Mathematical Sciences | Expanding Knowledge in Engineering |
Related Links
Publications
Microscopic theory of the Casimir force at thermal equilibrium: Large-separation asymptotics
Publisher: American Physical Society (APS)
Date: 15-01-2008
Modelling the anabolic response of bone using a cell population model
Publisher: Elsevier BV
Date: 08-2012
DOI: 10.1016/J.JTBI.2012.04.019
Abstract: 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 β. 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.
Quantifying the osteocyte network in the human skeleton
Publisher: Elsevier BV
Date: 06-2015
DOI: 10.1016/J.BONE.2015.02.016
Abstract: 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. 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. 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(2). 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(3) (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. 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.
Cell proliferation and migration explain pore bridging dynamics in 3D printed scaffolds of different pore size
Publisher: Cold Spring Harbor Laboratory
Date: 13-03-2020
DOI: 10.1101/2020.03.12.989053
Abstract: Tissue growth in bioscaffolds is influenced significantly by pore geometry, but how this geometric dependence emerges from dynamic cellular processes such as cell proliferation and cell migration remains poorly understood. Here we investigate the influence of pore size on the time required to bridge pores in thin 3D-printed scaffolds. Experimentally, new tissue infills the pores continually from their perimeter under strong curvature control, which leads the tissue front to round off with time. Despite the varied shapes assumed by the tissue during this evolution, we find that time to bridge a pore simply increases linearly with the overall pore size. To disentangle the biological influence of cell behaviour and the mechanistic influence of geometry in this experimental observation, we propose a simple reaction–diffusion model of tissue growth based on Porous-Fisher invasion of cells into the pores. First, this model provides a good qualitative representation of the evolution of the tissue new tissue in the model grows at an effective rate that depends on the local curvature of the tissue substrate. Second, the model suggests that a linear dependence of bridging time with pore size arises due to geometric reasons alone, not to differences in cell behaviours across pores of different sizes. Our analysis suggests that tissue growth dynamics in these experimental constructs is dominated by mechanistic crowding effects that influence collective cell proliferation and migration processes, and that can be predicted by simple reaction–diffusion models of cells that have robust, consistent behaviours.
A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation
Publisher: The Royal Society
Date: 07-2019
Abstract: Mechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty, we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an in idual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the in idual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. We discuss applications of the model, such as determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.
The relationship between porosity and specific surface in human cortical bone is subject specific
Publisher: Elsevier BV
Date: 03-2015
DOI: 10.1016/J.BONE.2014.11.016
Abstract: 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 s les of the Melbourne Femur Collection were obtained using synchrotron radiation micro-CT (SPring8, Japan). Sixteen bone s les from thirteen in iduals 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. 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 in idual 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 s les. 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 s le 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 BV/TV as suggested in the literature but is closer to a square root function.
Mechanical Cell Competition in Heterogeneous Epithelial Tissues
Publisher: Springer Science and Business Media LLC
Date: 26-09-2020
The role of mechanical interactions in EMT
Publisher: IOP Publishing
Date: 12-05-2021
Abstract: The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial–mesenchymal transition (EMT). Chemical signals, such as TGF- β , produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.
Reconstructed Single-Cell Fate Trajectories Define Lineage Plasticity Windows during Differentiation of Human PSC-Derived Distal Lung Progenitors
Publisher: Elsevier BV
Date: 04-2020
Thermal quantum electrodynamics of nonrelativistic charged fluids
Publisher: American Physical Society (APS)
Date: 30-04-2007
Fluctuation-induced self-force and violation of action-reaction in a nonequilibrium steady state fluid
Publisher: IOP Publishing
Date: 04-2009
Cell proliferation and migration explain pore bridging dynamics in 3D printed scaffolds of different pore size
Publisher: Elsevier BV
Date: 09-2020
The role of mechanical interactions in EMT
Publisher: Cold Spring Harbor Laboratory
Date: 10-12-2020
DOI: 10.1101/2020.12.09.418434
Abstract: The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF- β , produced by surrounding tissue can be up-taken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.
Towards a cell-based mechanostat theory of bone: the need to account for osteocyte desensitisation and osteocyte replacement
Publisher: Elsevier BV
Date: 09-2016
DOI: 10.1016/J.JBIOMECH.2016.05.012
Abstract: Bone׳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.
Mineral density differences between femoral cortical bone and trabecular bone are not explained by turnover rate alone
Publisher: Cold Spring Harbor Laboratory
Date: 09-06-2020
DOI: 10.1101/2020.06.08.141036
Abstract: Bone mineral density distributions (BMDDs) are a measurable property of bone tissues that depends strongly on bone remodelling and mineralisation processes. These processes can vary significantly in health and disease and across skeletal sites, so there is high interest in analysing these processes from experimental BMDDs. Here, we propose a rigorous hypothesis-testing approach based on a mathematical model of mineral heterogeneity in bone due to remodelling and mineralisation, to help explain differences observed between the BMDD of human femoral cortical bone and the BMDD of human trabecular bone. Recent BMDD measurements show that femoral cortical bone possesses a higher bone mineral density, but a similar mineral heterogeneity around the mean compared to trabecular bone. By combining this data with the mathematical model, we are able to test whether this difference in BMDD can be explained by (i) differences in turnover rate (ii) differences in osteoclast resorption behaviour and (iii) differences in mineralisation kinetics between the two bone types. We find that accounting only for differences in turnover rate is inconsistent with the fact that both BMDDs have a similar spread around the mean, and that accounting for differences in osteoclast resorption behaviour leads to biologically inconsistent bone remodelling patterns. We conclude that the kinetics of mineral accumulation in bone matrix must therefore be different in femoral cortical bone and trabecular bone. Although both cortical and trabecular bone are made up of lamellar bone, the different mineralisation kinetics in the two types of bone point towards more profound structural differences than usually assumed.
Mechanical cell competition in heterogeneous epithelial tissues
Publisher: Cold Spring Harbor Laboratory
Date: 09-12-2019
DOI: 10.1101/869495
Abstract: Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are incorporated into the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Using the new discrete model and continuum description, we explore several applications including the evolution of homogeneous tissues experiencing proliferation and death, and competition in a heterogeneous setting with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mechanisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than by having some intrinsic proliferative advantage. We advise when the continuum model is beneficial and demonstrate why naively adding source/sink terms to a continuum model without considering the underlying discrete model may lead to incorrect results.
Model-based data analysis of tissue growth in thin 3D printed scaffolds
Publisher: Cold Spring Harbor Laboratory
Date: 25-03-2021
DOI: 10.1101/2021.03.25.436898
Abstract: Tissue growth in three-dimensional (3D) printed scaffolds enables exploration and control of cell behaviour in biologically realistic geometries. Cell proliferation and migration in these experiments have yet to be explicitly characterised, limiting the ability of experimentalists to determine the effects of various experimental conditions, such as scaffold geometry, on cell behaviour. We consider tissue growth by osteoblastic cells in melt electro-written scaffolds that comprise thin square pores with sizes that we deliberately vary. We collect highly detailed temporal measurements of the average cell density, tissue coverage, and tissue geometry. To quantify tissue growth in terms of the underlying cell proliferation and migration processes, we introduce and calibrate a mechanistic mathematical model based on the Porous-Fisher reaction-diffusion equation. Parameter estimates and uncertainty quantification through profile likelihood analysis reveal consistency in the rate of cell proliferation and steady-state cell density between pore sizes. This analysis also serves as an important model verification tool: while the use of reaction-diffusion models in biology is widespread, the appropriateness of these models to describe tissue growth in 3D scaffolds has yet to be explored. We find that the Porous-Fisher model is able to capture features relating to the cell density and tissue coverage, but is not able to capture geometric features relating to the circularity of the tissue interface. Our analysis identifies two distinct stages of tissue growth, suggests several areas for model refinement, and provides guidance for future experimental work that explores tissue growth in 3D printed scaffolds. Advances in 3D printing technology have led to cell culture experiments that realistically capture natural biological environments. Despite the necessity of quantifying cell behaviour with parameters that can be compared between experiments, many existing mathematical models of tissue growth in these experiments neglect information relating to population size. We consider tissue growth by cells on 3D printed scaffolds that comprise square pores of various sizes in this work. We apply a relatively simple mathematical model based on the Porous-Fisher reaction-diffusion equation to interpret highly detailed measurements relating to both the cell density and the quantity of tissue deposited. We analyse the efficacy of such a model in capturing cell behaviour seen in the experiments and quantify cell behaviour in terms of parameters that carry a biologically meaningful interpretation. Our analysis identifies important areas for model refinement and provides guidance for future data-collection and experimentation that explores tissue growth in 3D printed scaffolds.
How osteons form: A quantitative hypothesis-testing analysis of cortical pore filling and wall asymmetry
Publisher: Cold Spring Harbor Laboratory
Date: 27-10-2023
Modeling the Effect of Curvature on the Collective Behavior of Cells Growing New Tissue
Publisher: Elsevier BV
Date: 2017
Late stages of mineralization and their signature on the bone mineral density distribution
Publisher: Informa UK Limited
Date: 10-05-2018
DOI: 10.1080/03008207.2018.1424149
Abstract: Experimental measurements of bone mineral density distributions (BMDDs) enable a determination of secondary mineralization kinetics in bone, but the maximum degree of mineralization and how this maximum is approached remain uncertain. We thus test computationally different hypotheses on late stages of bone mineralization by simulating BMDDs in low-turnover conditions. An established computational model of the BMDD that accounts for mineralization and remodeling processes was extended to limit mineralization to various maximum calcium capacities of bone. Simulated BMDDs obtained by reducing turnover rate from the reference trabecular BMDD under different assumptions on late stage mineralization kinetics were compared with experimental BMDDs of low-turnover bone. Simulations show that an abrupt stopping of mineralization near a maximum calcium capacity induces a pile-up of minerals in the BMDD statistics that is not observed experimentally. With a smooth decrease of mineralization rate, imposing low maximum calcium capacities helps to match peak location and width of simulated low-turnover BMDDs with peak location and width of experimental BMDDs, but results in a distinctive asymmetric peak shape. No tuning of turnover rate and maximum calcium capacity was able to explain the differences found in experimental BMDDs between trabecular bone (high turnover) and femoral cortical bone (low turnover). Secondary mineralization in human bone does not stop abruptly, but continues slowly up to a calcium content greater than 30 wt% Ca. The similar mineral heterogeneity seen in trabecular and femoral cortical bones at different peak locations was unexplained by the turnover differences tested.
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework
Publisher: The Royal Society
Date: 06-2022
Abstract: Understanding whether a population will survive or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction–diffusion equations, where migration is usually represented as a linear diffusion term, and birth–death is represented with a nonlinear source term. While linear diffusion is most commonly employed to study migration, there are several limitations of this approach, such as the inability of linear diffusion-based models to predict a well-defined population front. One way to overcome this is to generalize the constant diffusivity, D , to a nonlinear diffusivity function D ( C ) , where C 0 is the population density. While the choice of D ( C ) affects long-term survival or extinction of a bistable population, working solely in a continuum framework makes it difficult to understand how the choice of D ( C ) affects survival or extinction. We address this question by working with a discrete simulation model that is easy to interpret. This approach provides clear insight into how the choice of D ( C ) either encourages or suppresses population extinction relative to the classical linear diffusion model.
Investigation of bone resorption within a cortical basic multicellular unit using a lattice-based computational model
Publisher: Elsevier BV
Date: 2012
A free boundary mechanobiological model of epithelial tissues
Publisher: The Royal Society
Date: 11-2020
Abstract: In this study, we couple intracellular signalling and cell-based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in a discrete modelling framework, and new reaction–diffusion equations are derived to describe tissue-level outcomes. The free boundary evolves as a result of the underlying biological mechanisms included in the discrete model. To demonstrate the accuracy of the continuum model, we compare numerical solutions of the discrete and continuum models for two different signalling pathways. First, we study the Rac–Rho pathway where cell- and tissue-level mechanics are directly related to intracellular signalling. Second, we study an activator–inhibitor system which gives rise to spatial and temporal patterning related to Turing patterns. In all cases, the continuum model and free boundary condition accurately reflect the cell-level processes included in the discrete model.
Equilibrium correlations in charged fluids coupled to the radiation field
Publisher: American Physical Society (APS)
Date: 09-03-2006
Travelling waves in a free boundary mechanobiological model of an epithelial tissue
Publisher: Elsevier BV
Date: 2021
Bone refilling in basic multicellular units: Insights into tetracycline double labelling from a computational model
Publisher: Springer Science and Business Media LLC
Date: 30-04-2014
DOI: 10.1007/S10237-013-0495-Y
Abstract: Bone remodelling is carried out by 'bone multicellular units' ([Formula: see text]s) in which active osteoclasts and active osteoblasts are spatially and temporally coupled. The refilling of new bone by osteoblasts towards the back of the [Formula: see text] 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 and [Formula: see text] 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 cortical [Formula: see text] to investigate how osteoblast number and osteoblast secretory activity vary along the [Formula: see text]'s closing cone. The mathematical model is based on biochemical coupling between osteoclasts and osteoblasts of various maturity and includes the differentiation of osteoblasts into osteocytes and bone lining cells, as well as the influence of [Formula: see text] cavity shrinkage on osteoblast development and activity. Matrix apposition rates 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 matrix apposition rate and [Formula: see text] 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, supporting the hypothesis that osteoblasts behave synchronously. 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 [Formula: see text]s at different stages of their lifetime. The different stages of a [Formula: see text]'s lifetime (such as initiation stage, progression stage, and termination stage) depend on whether the cell populations within the [Formula: see text] are still developing or have reached a quasi-steady state whilst 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 [Formula: see text]'s point of origin.
A multiscale mechanobiological model of bone remodelling predicts site-specific bone loss in the femur during osteoporosis and mechanical disuse
Publisher: Springer Science and Business Media LLC
Date: 04-08-2016
DOI: 10.1007/S10237-015-0705-X
Abstract: We propose a multiscale mechanobiological model of bone remodelling to investigate the site-specific evolution of bone volume fraction across the midshaft of a femur. The model includes hormonal regulation and biochemical coupling of bone cell populations, the influence of the microstructure on bone turnover rate, and mechanical adaptation of the tissue. Both microscopic and tissue-scale stress/strain states of the tissue are calculated from macroscopic loads by a combination of beam theory and micromechanical homogenisation. This model is applied to simulate the spatio-temporal evolution of a human midshaft femur scan subjected to two deregulating circumstances: (i) osteoporosis and (ii) mechanical disuse. Both simulated deregulations led to endocortical bone loss, cortical wall thinning and expansion of the medullary cavity, in accordance with experimental findings. Our model suggests that these observations are attributable to a large extent to the influence of the microstructure on bone turnover rate. Mechanical adaptation is found to help preserve intracortical bone matrix near the periosteum. Moreover, it leads to non-uniform cortical wall thickness due to the asymmetry of macroscopic loads introduced by the bending moment. The effect of mechanical adaptation near the endosteum can be greatly affected by whether the mechanical stimulus includes stress concentration effects or not.
Governing Equations of Tissue Modelling and Remodelling: A Unified Generalised Description of Surface and Bulk Balance
Publisher: Public Library of Science (PLoS)
Date: 04-04-2016
Corrigendum to Modelling the anabolic response of bone using a cell population model [J. Theor. Biol. 307 (2012) 42-52]
Publisher: Elsevier BV
Date: 09-2012
Osteocytes as a record of bone formation dynamics: A mathematical model of osteocyte generation in bone matrix
Publisher: Elsevier BV
Date: 2015
DOI: 10.1016/J.JTBI.2014.09.028
Abstract: 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 Marotti׳s 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.
Spatio-temporal structure of cell distribution in cortical bone multicellular units: a mathematical model
Publisher: Elsevier BV
Date: 04-2011
DOI: 10.1016/J.BONE.2010.12.009
Abstract: 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 in idual 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.
The Casimir force at high temperature
Publisher: IOP Publishing
Date: 10-2005
Response to Letter to the Editor: On osteocyte density in the human body
Publisher: Elsevier BV
Date: 07-2016
Corrigendum to “The relationship between porosity and specific surface in human cortical bone is subject specific” [Bone 72 (2015), 109–117]
Publisher: Elsevier BV
Date: 06-2015
A Continuous Model for the Embedment of Osteocytes in Bone Matrix
Publisher: Springer International Publishing
Date: 2014
Theoretical analysis of the spatio-temporal structure of bone multicellular units
Publisher: IOP Publishing
Date: 06-2010
Microscopic Origin of Universality in Casimir Forces
Publisher: Springer Science and Business Media LLC
Date: 04-2005
Curvature dependences of wave propagation in reaction–diffusion models
Publisher: The Royal Society
Date: 12-2022
Abstract: Reaction–diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wavefronts. These waves have important applications in many physical, ecological and biological systems. In this work, we analyse curvature dependences of travelling fronts in a single reaction–diffusion equation with general reaction term. We derive an exact, non-perturbative curvature dependence of the speed of travelling fronts that arises from transverse diffusion occurring parallel to the wavefront. Inward-propagating waves are characterized by three phases: an establishment phase dominated by initial and boundary conditions, a travelling-wave-like phase in which normal velocity matches standard results from singular perturbation theory and a dip-filling phase where the collision and interaction of fronts create additional curvature dependences to their progression rate. We analyse these behaviours and additional curvature dependences using a combination of asymptotic analyses and numerical simulations.
New computational tools and experiments reveal how geometry affects tissue growth in 3D printed scaffolds
Publisher: Elsevier BV
Date: 11-2023
The influence of bone surface availability in bone remodelling-A mathematical model including coupled geometrical and biomechanical regulations of bone cells
Publisher: Elsevier BV
Date: 02-2013
Violation of the action-reaction principle and self-forces induced by nonequilibrium fluctuations
Publisher: American Physical Society (APS)
Date: 25-08-2008
Modelling cell guidance and curvature control in evolving biological tissues
Publisher: Cold Spring Harbor Laboratory
Date: 12-07-2020
DOI: 10.1101/2020.07.10.197020
Abstract: Tissue geometry is an important influence on the evolution of many biological tissues. The local curvature of an evolving tissue induces tissue crowding or spreading, which leads to differential tissue growth rates, and to changes in cellular tension, which can influence cell behaviour. Here, we investigate how directed cell motion interacts with curvature control in evolving biological tissues. Directed cell motion is involved in the generation of angled tissue growth and anisotropic tissue material properties, such as tissue fibre orientation. We develop a new cell-based mathematical model of tissue growth that includes both curvature control and cell guidance mechanisms to investigate their interplay. The model is based on conservation principles applied to the density of tissue synthesising cells at or near the tissue’s moving boundary. The resulting mathematical model is a partial differential equation for cell density on a moving boundary, which is solved numerically using a hybrid front-tracking method called the cell-based particle method. The inclusion of directed cell motion allows us to model new types of biological growth, where tangential cell motion is important for the evolution of the interface, or for the generation of anisotropic tissue properties. We illustrate such situations by applying the model to simulate both the resorption and infilling components of the bone remodelling process, and to simulate root hair growth. We also provide user-friendly MATLAB code to implement the algorithms.
A level-set method for the evolution of cells and tissue during curvature-controlled growth.
Publisher: Wiley
Date: 15-12-2020
DOI: 10.1002/CNM.3279
Abstract: Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic or cell behavioural in nature. The control of geometry on tissue growth has been evidenced in many in vivo and in vitro experiments, including bone remodelling, wound healing, and tissue engineering scaffolds. In this paper, we propose a generalisation of a mathematical model that captures the mechanistic influence of curvature on the joint evolution of cell density and tissue shape during tissue growth. This generalisation allows us to simulate abrupt topological changes such as tissue fragmentation and tissue fusion, as well as three dimensional cases, through a level-set-based method. The level-set method developed introduces another Eulerian field than the level-set function. This additional field represents the surface density of tissue-synthesising cells, anticipated at future locations of the interface. Numerical tests performed with this level-set-based method show that numerical conservation of cells is a good indicator of simulation accuracy, particularly when cusps develop in the tissue's interface. We apply this new model to several situations of curvature-controlled tissue evolutions that include fragmentation and fusion.
Computational modeling of interactions between multiple myeloma and the bone microenvironment
Publisher: Public Library of Science (PLoS)
Date: 08-11-2011
Endocortical bone loss in osteoporosis: the role of bone surface availability
Publisher: Wiley
Date: 07-2013
DOI: 10.1002/CNM.2567
Abstract: Age-related bone loss and postmenopausal osteoporosis are due to a dysregulation of bone remodelling in which less bone is reformed than resorbed. This dysregulation of bone remodelling does not occur with equal strength in all bone regions. Loss of bone is more pronounced near the endocortical surface. This leads to thinning of the cortical wall proceeding from the endosteum, a process sometimes called 'trabecularisation'. In this paper, we investigate the influence of the nonuniform distribution of bone surface within bone tissue for osteoporotic bone losses. We use a spatio-temporal computational model of bone remodelling in which microstructural changes of bone tissue are represented by a phenomenological relationship between bone specific surface and bone porosity. The simulation of an osteoporotic condition by our model shows that the evolution of bone porosity within a bone cross section is significantly influenced by the nonuniform availability of bone surface. Greater bone loss occurs near the endocortical wall, leading to cortical wall thinning and to an expansion of the medullary cavity similar to cross-sectional observations from human femur midshafts. Our model suggests that the rate of cortical wall thinning is fast/slow in the presence/absence of an adjacent trabecular or trabecularised bone compartment.
Related Organisations
EPFL – Swiss Federal Institute Of Technology, Lausanne
Location: Switzerland
ETHZ – Swiss Federal Institute Of Technology, Zürich
Location: Switzerland
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