A semi-stochastic cell-based model for in vitro infected 'wound' healing through motility reduction: a simulation study.

We consider the migration and viability of individual cells in bacterial-infected cell colonies. Cell movement is assumed to take place as a result of sensing the strain energy density as a mechanical stimulus. The model is based on tracking the motion and viability of each individual cell in a cell colony, and the formalism was published in an earlier paper. The present innovations are an application to a simulation of a 'wound healing assay' in which bacteria infect the wound through impairing the motility of cells and an extension with effects from inertia. Though based on simple principles, the model is based on experiments on living fibroblasts on a flat substrate.

[1]  S. Jonathan Chapman,et al.  Modeling Growth in Biological Materials , 2012, SIAM Rev..

[2]  F J Vermolen,et al.  A finite-element model for healing of cutaneous wounds combining contraction, angiogenesis and closure , 2012, Journal of mathematical biology.

[3]  Roeland M. H. Merks,et al.  Modeling Morphogenesis in silico and in vitro: Towards Quantitative, Predictive, Cell-based Modeling , 2009 .

[4]  Sophia Maggelakis,et al.  Modeling the role of angiogenesis in epidermal wound healing , 2003 .

[5]  Avner Friedman,et al.  Wound angiogenesis as a function of tissue oxygen tension: A mathematical model , 2008, Proceedings of the National Academy of Sciences.

[6]  J A Sherratt,et al.  A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile. , 1995, Journal of theoretical biology.

[7]  F J Vermolen,et al.  A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies , 2012, Biomechanics and modeling in mechanobiology.

[8]  Micah Dembo,et al.  Cell-cell mechanical communication through compliant substrates. , 2008, Biophysical journal.

[9]  Philip K. Maini,et al.  A mechanochemical model for adult dermal wound contraction , 1995 .

[10]  Amit Gefen,et al.  A standardized objective method for continuously measuring the kinematics of cultures covering a mechanically damaged site. , 2012, Medical engineering & physics.

[11]  F. Vermolen,et al.  A mathematical analysis of physiological and morphological aspects of wound closure , 2009, Journal of mathematical biology.

[12]  A. Gefen,et al.  The Influence of Ischemic Factors on the Migration Rates of Cell Types Involved in Cutaneous and Subcutaneous Pressure Ulcers , 2012, Annals of Biomedical Engineering.

[13]  F. Vermolen Simplified Finite-Element Model for Tissue Regeneration with Angiogenesis , 2009 .

[14]  F J Vermolen,et al.  Computer simulations from a finite-element model for wound contraction and closure. , 2010, Journal of tissue viability.

[15]  J D Murray,et al.  Mathematical analysis of a basic model for epidermal wound healing , 1991, Journal of mathematical biology.

[16]  John A. Adam,et al.  A simplified model of wound healing (with particular reference to the critical size defect) , 1999 .

[17]  S. Landis Chronic wound infection and antimicrobial use. , 2008, Advances in skin & wound care.

[18]  A. Gefen Effects of virus size and cell stiffness on forces, work, and pressures driving membrane invagination in a receptor-mediated endocytosis. , 2010, Journal of biomechanical engineering.

[19]  Glazier,et al.  Simulation of biological cell sorting using a two-dimensional extended Potts model. , 1992, Physical review letters.

[20]  M. Plank,et al.  Lattice and non-lattice models of tumour angiogenesis , 2004, Bulletin of mathematical biology.

[21]  S. Luding Introduction to discrete element methods , 2008 .

[22]  Ulrich S Schwarz,et al.  Physical determinants of cell organization in soft media. , 2005, Medical engineering & physics.

[23]  J. Steele Stochastic Calculus and Financial Applications , 2000 .

[24]  H M Byrne,et al.  A model of wound-healing angiogenesis in soft tissue. , 1996, Mathematical biosciences.

[25]  John C. Dallon,et al.  Multiscale modeling of cellular systems in biology , 2010 .

[26]  E. A. Gaffney,et al.  Investigating a simple model of cutaneous wound healing angiogenesis , 2002, Journal of mathematical biology.

[27]  J. Dallon,et al.  A review of fibroblast‐populated collagen lattices , 2008, Wound repair and regeneration : official publication of the Wound Healing Society [and] the European Tissue Repair Society.

[28]  Avner Friedman,et al.  A mathematical model of ischemic cutaneous wounds , 2009, Proceedings of the National Academy of Sciences.

[29]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[30]  Fred J. Vermolen,et al.  On the construction of analytic solutions for a diffusion-reaction equation with a discontinuous switch mechanism , 2008, J. Comput. Appl. Math..

[31]  F. J. Vermolen,et al.  A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts , 2013, Biomechanics and modeling in mechanobiology.