Challenges in the Modeling of Wound Healing Mechanisms in Soft Biological Tissues

Numerical models have become one of the most powerful tools in biomechanics and mechanobiology allowing highly detailed simulations. One of the fields in which they have broadly evolved during the last years is in soft tissue modeling. Particularly, wound healing in the skin is one of the processes that has been approached by computational models due to the difficulty of performing experimental investigations. During the last decades wound healing simulations have evolved from numerical models which considered only a few number of variables and simple geometries to more complex approximations that take into account a higher number of factors and reproduce more realistic geometries. Moreover, thanks to improved experimental observations, a larger number of processes, such as cellular stress generation or vascular growth, that take place during wound healing have been identified and modeled. This work presents a review of the most relevant wound healing approximations, together with an identification of the most relevant criteria that can be used to classify them. In addition, and looking towards the actual state of the art in the field, some future directions, challenges and improvements are analyzed for future developments.

[1]  J A Sherratt,et al.  A mathematical model for fibro-proliferative wound healing disorders. , 1996, Bulletin of mathematical biology.

[2]  Sophia Maggelakis,et al.  A mathematical model of tissue replacement during epidermal wound healing , 2003 .

[3]  Michel Destrade,et al.  Characterization of the anisotropic mechanical properties of excised human skin. , 2013, Journal of the mechanical behavior of biomedical materials.

[4]  P. Coulombe,et al.  Wound Epithelialization: Accelerationg the Pace of Discovery , 2003 .

[5]  Andrew Taberner,et al.  Modeling the Mechanical Response of In Vivo Human Skin Under a Rich Set of Deformations , 2011, Annals of Biomedical Engineering.

[6]  V. Petrov,et al.  Stimulation of Collagen Production by Transforming Growth Factor-&bgr;1 During Differentiation of Cardiac Fibroblasts to Myofibroblasts , 2002, Hypertension.

[7]  F. Silver,et al.  Viscoelastic properties of human skin and processed dermis , 2001, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[8]  J. Dallon,et al.  A mathematical model of collagen lattice contraction , 2014, Journal of The Royal Society Interface.

[9]  H. Zahouani,et al.  In vivo characterization of viscoelastic properties of human skin using dynamic micro-indentation , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[10]  D. Manoussaki A mechanochemical model of angiogenesis and vasculogenesis , 2003 .

[11]  Giulio Gabbiani,et al.  Mechanisms of force generation and transmission by myofibroblasts. , 2003, Current opinion in biotechnology.

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

[13]  James C Birchall,et al.  An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. , 2013, Journal of the mechanical behavior of biomedical materials.

[14]  J. Lagarde,et al.  In vivo model of the mechanical properties of the human skin under suction , 2000, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[15]  Jan Kottner,et al.  Weight and pressure ulcer occurrence: a secondary data analysis. , 2011, International journal of nursing studies.

[16]  Michael D. Gilchrist,et al.  Automated Estimation of Collagen Fibre Dispersion in the Dermis and its Contribution to the Anisotropic Behaviour of Skin , 2012, Annals of Biomedical Engineering.

[17]  H R Chaudhry,et al.  Optimal patterns for suturing wounds of complex shapes to foster healing. , 2001, Journal of biomechanics.

[18]  J A Sherratt,et al.  Mathematical modeling of corneal epithelial wound healing. , 1994, Mathematical biosciences.

[19]  Ben Fabry,et al.  Single-cell response to stiffness exhibits muscle-like behavior , 2009, Proceedings of the National Academy of Sciences.

[20]  I A Brown,et al.  The biomechanical properties of skin. , 1973, CRC critical reviews in bioengineering.

[21]  Peter L. Williams,et al.  Gray's Anatomy: The Anatomical Basis of Medicine and Surgery , 1996 .

[22]  Bradley C. Wright,et al.  Wound geometry and the kinetics of wound contraction , 1984 .

[23]  W. Risau,et al.  Mechanisms of angiogenesis , 1997, Nature.

[24]  Cwj Cees Oomens,et al.  A numerical‐experimental method to characterize the non‐linear mechanical behaviour of human skin , 2003, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[25]  M J Gómez-Benito,et al.  Nonlinear finite element simulations of injuries with free boundaries: Application to surgical wounds , 2014, International journal for numerical methods in biomedical engineering.

[26]  D. S. Sivia,et al.  Data Analysis , 1996, Encyclopedia of Evolutionary Psychological Science.

[27]  José Manuel García-Aznar,et al.  Numerical modeling of a mechano-chemical theory for wound contraction analysis , 2009 .

[28]  A. Singer,et al.  Cutaneous wound healing. , 1999, The New England journal of medicine.

[29]  James D. Murray Dermal Wound Healing , 1993 .

[30]  E J Hall-Findlay,et al.  A simplified vertical reduction mammaplasty: shortening the learning curve. , 1999, Plastic and reconstructive surgery.

[31]  Richard A.F. Clark,et al.  The Molecular and Cellular Biology of Wound Repair , 2012, Springer US.

[32]  S. Werner,et al.  Wound repair and regeneration , 1994, Nature.

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

[34]  D L Sean McElwain,et al.  A two-compartment mechanochemical model of the roles of transforming growth factor β and tissue tension in dermal wound healing. , 2011, Journal of theoretical biology.

[35]  B. Hinz,et al.  Myofibroblasts and mechano-regulation of connective tissue remodelling , 2002, Nature Reviews Molecular Cell Biology.

[36]  Ming Zhang,et al.  Three-dimensional finite element analysis of the foot during standing--a material sensitivity study. , 2005, Journal of biomechanics.

[37]  G. Wayne Brodland,et al.  Forces driving epithelial wound healing , 2014, Nature Physics.

[38]  D. Foreman,et al.  Control of scarring in adult wounds by neutralising antibody to transforming growth factor β , 1992, The Lancet.

[39]  J. M. García-Aznar,et al.  A phenomenological approach to modelling collective cell movement in 2D , 2013, Biomechanics and modeling in mechanobiology.

[40]  José Manuel García-Aznar,et al.  A Cell-Regulatory Mechanism Involving Feedback between Contraction and Tissue Formation Guides Wound Healing Progression , 2014, PloS one.

[41]  R. Ogden,et al.  Hyperelastic modelling of arterial layers with distributed collagen fibre orientations , 2006, Journal of The Royal Society Interface.

[42]  M. J. Gómez-Benito,et al.  Numerical modelling of the angiogenesis process in wound contraction , 2013, Biomechanics and modeling in mechanobiology.

[43]  J. Weiss,et al.  Finite element implementation of incompressible, transversely isotropic hyperelasticity , 1996 .

[44]  Andrew Taberner,et al.  Measurement of the force-displacement response of in vivo human skin under a rich set of deformations. , 2011, Medical engineering & physics.

[45]  F. Grinnell,et al.  Fibroblast-collagen-matrix contraction: growth-factor signalling and mechanical loading. , 2000, Trends in cell biology.

[46]  Pedro Moreo,et al.  Modeling mechanosensing and its effect on the migration and proliferation of adherent cells. , 2008, Acta biomaterialia.

[47]  E Reina-Romo,et al.  An Interspecies Computational Study on Limb Lengthening , 2010, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[48]  Jeffrey B. Kerr Comprar Functional Histology, 2nd Edition | Jeffrey B. Kerr | 9780729538374 | Mosby , 2010 .

[49]  F J Vermolen,et al.  A semi-stochastic cell-based model for in vitro infected 'wound' healing through motility reduction: a simulation study. , 2013, Journal of theoretical biology.

[50]  Ellen Kuhl,et al.  Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery. , 2014, Computers & structures.

[51]  T. K. Hunt,et al.  Human skin wounds: A major and snowballing threat to public health and the economy , 2009, Wound repair and regeneration : official publication of the Wound Healing Society [and] the European Tissue Repair Society.

[52]  J. Lévêque,et al.  Age-related mechanical properties of human skin: an in vivo study. , 1989, The Journal of investigative dermatology.

[53]  F H Silver,et al.  Viscoelastic behavior of human connective tissues: relative contribution of viscous and elastic components. , 1983, Connective tissue research.

[54]  Philip K Maini,et al.  A Fibrocontractive Mechanochemical Model of Dermal Wound Closure Incorporating Realistic Growth Factor Kinetics , 2012, Bulletin of Mathematical Biology.

[55]  Helen M. Byrne,et al.  Mathematical Model of Hyperbaric Oxygen Therapy Applied to Chronic Diabetic Wounds , 2010, Bulletin of mathematical biology.

[56]  David Ripley Contraction and closure , 2015 .

[57]  Yassine Mofid,et al.  Skin anisotropy in vivo and initial natural stress effect: a quantitative study using high-frequency static elastography. , 2012, Journal of biomechanics.

[58]  J. Folkman,et al.  Role of cell shape in growth control , 1978, Nature.

[59]  R. Clark,et al.  Overview and General Considerations of Wound Repair , 1998 .

[60]  Rudy J. Lapeer,et al.  A Hyperelastic Finite-Element Model of Human Skin for Interactive Real-Time Surgical Simulation , 2011, IEEE Transactions on Biomedical Engineering.

[61]  H Pollock,et al.  Progressive Tension Sutures: A Technique to Reduce Local Complications in Abdominoplasty , 2000, Plastic and reconstructive surgery.

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

[63]  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.

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

[65]  V. Langer,et al.  Zur Anatomie und Physiologie der Haut. I. Über die Spaltbarkeit der Cutis , 1861 .

[66]  P. Coulombe,et al.  Wound epithelialization: accelerating the pace of discovery. , 2003, The Journal of investigative dermatology.

[67]  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.

[68]  Rei Ogawa,et al.  Mechanobiology of scarring , 2011, Wound repair and regeneration : official publication of the Wound Healing Society [and] the European Tissue Repair Society.

[69]  Cornelis Vuik,et al.  Numerical Modelling of Epidermal Wound Healing , 2008 .

[70]  James D. Murray,et al.  Spatial pattern formation in biology: I. Dermal wound healing. II. Bacterial patterns , 1998 .

[71]  Jonathan A. Sherratt,et al.  Models of epidermal wound healing , 1990, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[72]  Savita Khanna,et al.  Characterization of a preclinical model of chronic ischemic wound. , 2009, Physiological genomics.

[73]  B. Hinz,et al.  Mechanical tension controls granulation tissue contractile activity and myofibroblast differentiation. , 2001, The American journal of pathology.

[74]  Claudio Cobelli,et al.  3D finite element model of the diabetic neuropathic foot: a gait analysis driven approach. , 2014, Journal of biomechanics.

[75]  R T Tranquillo,et al.  Continuum model of fibroblast-driven wound contraction: inflammation-mediation. , 1992, Journal of theoretical biology.

[76]  Helen M. Byrne,et al.  A Three Species Model to Simulate Application of Hyperbaric Oxygen Therapy to Chronic Wounds , 2009, PLoS Comput. Biol..

[77]  K Motegi,et al.  Postoperative scars and cleavage lines. , 1975, The Bulletin of Tokyo Medical and Dental University.

[78]  Cameron Luke Hall,et al.  Modelling of some biological materials using continuum mechanics , 2008 .

[79]  E. Howard,et al.  Transforming growth factor-beta1 promotes the morphological and functional differentiation of the myofibroblast. , 2000, Experimental cell research.