A Fibrocontractive Mechanochemical Model of Dermal Wound Closure Incorporating Realistic Growth Factor Kinetics

Murphy, Kelly E.; Hall, Cameron L.; Maini, Philip K.; McCue, Scott W.; McElwain, D. L. S.

doi:10.1007/s11538-011-9712-y

Cited by 44 publications

(47 citation statements)

References 89 publications

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“…Similar to Olsen et al (1995), we assume that the rate of cell differentiation is dependent on the concentration of the signaling molecule with no cell differentiation taking place in the absence of this signaling molecule. Like others such as Javierre et al (2009), Murphy et al (2012), and Valero et al (2014a; b), we are aware of the fact that this cell differentiation can only take place under conditions of sufficient mechanical stiffness. It seems like a good idea then to incorporate this phenomenon also into the model.…”

Section: Discussionsupporting

confidence: 54%

A mathematical model for the simulation of the contraction of burns

et al. 2016

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A continuum hypothesis-based model is developed for the simulation of the contraction of burns in order to gain new insights into which elements of the healing response might have a substantial influence on this process. Tissue is modeled as a neo-Hookean solid. Furthermore, (myo)fibroblasts, collagen molecules, and a generic signaling molecule are selected as model components. An overview of the custom-made numerical algorithm is presented. Subsequently, good agreement is demonstrated with respect to variability in the evolution of the surface area of burns over time between the outcomes of computer simulations and measurements obtained in an experimental study. In the model this variability is caused by varying the values for some of its parameters simultaneously. A factorial design combined with a regression analysis are used to quantify the individual contributions of these parameter value variations to the dispersion in the surface area of healing burns. The analysis shows that almost all variability in the surface area can be explained by variability in the value for the myofibroblast apoptosis rate and, to a lesser extent, the value for the collagen molecule secretion rate. This suggests that most of the variability in the evolution of the surface area of burns over time in the experimental study might be attributed to variability in these two rates. Finally, a probabilistic analysis is used in order to investigate in more detail the effect of variability in the values for the two rates on the healing process. Results of this analysis are presented and discussed.

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Section: Discussionsupporting

confidence: 54%

A mathematical model for the simulation of the contraction of burns

et al. 2016

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“…As the collagen density increases, the tissue becomes stiffer [29], regulating the volumetric strain of the tissue , which in turn defines the value of and the stresses exerted by the cells on the ECM. We consider also that depends on the concentration of fibroblasts and myofibroblasts, with a term similar to the one proposed by Murphy et al [25]. Contractile forces exerted by fibroblasts can initiate wound closure and myofibroblasts are known to contribute to the transmission of these contraction forces [29], [30].…”

Section: Resultsmentioning

confidence: 99%

“…Adam [18] investigated the occurrence of non-healing wounds and the so-called critical size defect with a simple model that describes the evolution of a generic growth factor activating cell proliferation at the wound edge. Olsen's model [21] has been recently revised by different authors [23]–[25]. These works incorporate the decreased mechanical properties of the granulation tissue and combine for the first time the coupled actions of chemical and mechanical factors on the fibroblast to induce myofibroblast differentiation, although the studies differ in the mechanical stimulus used to drive the differentiation.…”

Section: Introductionmentioning

confidence: 99%

“…Whereas Javierre et al [23] claim that the stress that guides the process is the force exerted by the cells, Murphy et al [24] propose that this stress comes from the elastic component of the ECM. Additionally, Javierre et al [23] investigated the effect of wound shape on the contraction kinetics, whereas Murphy et al [24], [25] focused on a more detailed representation of the biochemical signaling of wound contraction. Furthermore, Javierre et al [23] considered a unique growth factor that regulates differentiation and collagen production, whereas Murphy et al [25] included the chemical kinetics of two different growth factors (PDGF and TGF-) separately.…”

Section: Introductionmentioning

confidence: 99%

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A Cell-Regulatory Mechanism Involving Feedback between Contraction and Tissue Formation Guides Wound Healing Progression

et al. 2014

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Wound healing is a process driven by cells. The ability of cells to sense mechanical stimuli from the extracellular matrix that surrounds them is used to regulate the forces that cells exert on the tissue. Stresses exerted by cells play a central role in wound contraction and have been broadly modelled. Traditionally, these stresses are assumed to be dependent on variables such as the extracellular matrix and cell or collagen densities. However, we postulate that cells are able to regulate the healing process through a mechanosensing mechanism regulated by the contraction that they exert. We propose that cells adjust the contraction level to determine the tissue functions regulating all main activities, such as proliferation, differentiation and matrix production. Hence, a closed-regulatory feedback loop is proposed between contraction and tissue formation. The model consists of a system of partial differential equations that simulates the evolution of fibroblasts, myofibroblasts, collagen and a generic growth factor, as well as the deformation of the extracellular matrix. This model is able to predict the wound healing outcome without requiring the addition of phenomenological laws to describe the time-dependent contraction evolution. We have reproduced two in vivo experiments to evaluate the predictive capacity of the model, and we conclude that there is feedback between the level of cell contraction and the tissue regenerated in the wound.

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“…For this investigation, we assume that this conversion occurs rapidly, and we represent both active and latent forms of TGF-b by a single species, b. Fibroblasts are one of the main sources of TGF-b in wounds [48], and their production of this GF is inhibited if TGF-b is already present [25]. We model this production using a saturation form, in line with the work of Murphy et al [23], with the constant l 21 characterizing the rate of production by fibroblasts and the constant l 23 characterizing the half-maximal rate of production. It has been observed that this production by fibroblasts is downregulated by the presence of keratinocytes [68], and we model this using a downregulatory coefficient l 22 .…”

Section: Mathematical Modelmentioning

confidence: 99%

Modelling the interaction of keratinocytes and fibroblasts during normal and abnormal wound healing processes

et al. 2012

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The crosstalk between fibroblasts and keratinocytes is a vital component of the wound healing process, and involves the activity of a number of growth factors and cytokines. In this work, we develop a mathematical model of this crosstalk in order to elucidate the effects of these interactions on the regeneration of collagen in a wound that heals by second intention. We consider the role of four components that strongly affect this process: transforming growth factor-b, platelet-derived growth factor, interleukin-1 and keratinocyte growth factor. The impact of this network of interactions on the degradation of an initial fibrin clot, as well as its subsequent replacement by a matrix that is mainly composed of collagen, is described through an eight-component system of nonlinear partial differential equations. Numerical results, obtained in a twodimensional domain, highlight key aspects of this multifarious process, such as re-epithelialization. The model is shown to reproduce many of the important features of normal wound healing. In addition, we use the model to simulate the treatment of two pathological cases: chronic hypoxia, which can lead to chronic wounds; and prolonged inflammation, which has been shown to lead to hypertrophic scarring. We find that our model predictions are qualitatively in agreement with previously reported observations and provide an alternative pathway for gaining insight into this complex biological process.

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A Fibrocontractive Mechanochemical Model of Dermal Wound Closure Incorporating Realistic Growth Factor Kinetics

Cited by 44 publications

References 89 publications

A mathematical model for the simulation of the contraction of burns

A mathematical model for the simulation of the contraction of burns

A Cell-Regulatory Mechanism Involving Feedback between Contraction and Tissue Formation Guides Wound Healing Progression

Modelling the interaction of keratinocytes and fibroblasts during normal and abnormal wound healing processes

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