A mathematical model for the simulation of the formation and the subsequent regression of hypertrophic scar tissue after dermal wounding

Post-angioplasty remodeling of coronary arteries investigated via a chemo-mechano-biological in silico model

This work presents the application of a chemo-mechano-biological constitutive model of soft tissues for describing tissue inflammatory response to damage in collagen constituents. The material model is implemented into a nonlinear finite element formulation to follow up a coronary standard balloon angioplasty for one year. Numerical results, compared with available in vivo clinical data, show that the model reproduces the temporal dynamics of vessel remodeling associated with subintimal damage. Such dynamics are bimodular, being characterized by an early tissue resorption and lumen enlargement, followed by late tissue growth and vessel constriction. Applicability of the modeling framework in retrospective studies is demonstrated, and future extension towards prospective applications is discussed.

Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

Computational mechanobiology model evaluating healing of postoperative cavities following breast-conserving surgery

Breast cancer is the most commonly diagnosed cancer type worldwide. Given high survivorship, increased focus has been placed on long-term treatment outcomes and patient quality of life. While breast-conserving surgery (BCS) is the preferred treatment strategy for early-stage breast cancer, anticipated healing and breast deformation (cosmetic) outcomes weigh heavily on surgeon and patient selection between BCS and more aggressive mastectomy procedures. Unfortunately, surgical outcomes following BCS are difficult to predict, owing to the complexity of the tissue repair process and significant patient-to-patient variability. To overcome this challenge, we developed a predictive computational mechanobiological model that simulates breast healing and deformation following BCS. The coupled biochemical-biomechanical model incorporates multi-scale cell and tissue mechanics, including collagen deposition and remodeling, collagen-dependent cell migration and contractility, and tissue plastic deformation. Available human clinical data evaluating cavity contraction and histopathological data from an experimental porcine lumpectomy study were used for model calibration. The computational model was successfully fit to data by optimizing biochemical and mechanobiological parameters through Gaussian process surrogates. The calibrated model was then applied to define key mechanobiological parameters and relationships influencing healing and breast deformation outcomes. Variability in patient characteristics including cavity-to-breast volume percentage and breast composition were further evaluated to determine effects on cavity contraction and breast cosmetic outcomes, with simulation outcomes aligning well with previously reported human studies. The proposed model has the potential to assist surgeons and their patients in developing and discussing individualized treatment plans that lead to more satisfying post-surgical outcomes and improved quality of life.

Arterial tissues and their inflammatory response to collagen damage: A continuum in silico model coupling nonlinear mechanics, molecular pathways, and cell behavior

Damage in soft biological tissues causes an inflammatory reaction that initiates a chain of events to repair the tissue. This work presents a continuum model and its in silico implementation that describe the cascade of mechanisms leading to tissue healing, coupling mechanical as well as chemo-biological processes. The mechanics is described by means of a Lagrangian nonlinear continuum mechanics framework and follows the homogenized constrained mixtures theory. Plastic-like damage, growth and remodeling as well as homeostasis are taken into account. The chemo-biological pathways account for two molecular and four cellular species, and are activated by damage of collagen molecules in fibers. To consider proliferation, differentiation, diffusion and chemotaxis of species, diffusion-advection-reaction equations are employed. To the best of authors' knowledge, the proposed model combines for the first time such high number of chemo-mechano-biological mechanisms in a consistent continuum biomechanical framework. The resulting set of coupled differential equations describe balance of linear momentum, evolution of kinematic variables as well as mass balance equations. They are discretized in time according to a backward Euler finite difference scheme, and in space through a finite element Galerkin discretization. The features of the model are firstly demonstrated presenting the species dynamics and highlighting the influence of damage intensities on the growth outcome. In terms of a biaxial test, the chemo-mechano-biological coupling and the model's applicability to reproduce normal as well as pathological healing are shown. A last numerical example underlines the model's applicability to complex loading scenarios and inhomogeneous damage distributions. Concluding, the present work contributes towards comprehensive in silico models in biomechanics and mechanobiology.

Computational Mechanobiology Model Evaluating Healing of Postoperative Cavities Following Breast-Conserving Surgery

Breast cancer is the most commonly diagnosed cancer type worldwide. Given high survivorship, increased focus has been placed on long-term treatment outcomes and patient quality of life. While breast-conserving surgery (BCS) is the preferred treatment strategy for early-stage breast cancer, anticipated healing and breast deformation (cosmetic) outcomes weigh heavily on surgeon and patient selection between BCS and more aggressive mastectomy procedures. Unfortunately, surgical outcomes following BCS are difficult to predict, owing to the complexity of the tissue repair process and significant patient-to-patient variability. To overcome this challenge, we developed a predictive computational mechanobiological model that simulates breast healing and deformation following BCS. The coupled biochemical-biomechanical model incorporates multi-scale cell and tissue mechanics, including collagen deposition and remodeling, collagen-dependent cell migration and contractility, and tissue plastic deformation. Available human clinical data evaluating cavity contraction and histopathological data from an experimental porcine lumpectomy study were used for model calibration. The computational model was successfully fit to data by optimizing biochemical and mechanobiological parameters through the Gaussian Process. The calibrated model was then applied to define key mechanobiological parameters and relationships influencing healing and breast deformation outcomes. Variability in patient characteristics including cavity-to-breast volume percentage and breast composition were further evaluated to determine effects on cavity contraction and breast cosmetic outcomes, with simulation outcomes aligning well with previously reported human studies. The proposed model has the potential to assist surgeons and their patients in developing and discussing individualized treatment plans that lead to more satisfying post-surgical outcomes and improved quality of life.

Stability of a two-dimensional biomorphoelastic model for post-burn contraction

We consider the stability analysis of a two-dimensional model for post-burn contraction. The model is based on morphoelasticity for permanent deformations and combined with a chemical-biological model that incorporates cellular densities, collagen density, and the concentration of chemoattractants. We formulate stability conditions depending on the decay rate of signaling molecules for both the continuous partial differential equations-based problem and the (semi-)discrete representation. We analyze the difference and convergence between the resulting spatial eigenvalues from the continuous and semi-discrete problems.

Sensitivity of a two-dimensional biomorphoelastic model for post-burn contraction

We consider a two-dimensional biomorphoelastic model describing post-burn scar contraction. This model describes skin displacement and the development of the effective Eulerian strain in the tissue. Besides these mechanical components, signaling molecules, fibroblasts, myofibroblasts, and collagen also play a significant role in the model. We perform a sensitivity analysis for the independent parameters of the model and focus on the effects on features of the relative surface area and the total strain energy density. We conclude that the most sensitive parameters are the Poisson's ratio, the equilibrium collagen concentration, the contraction inhibitor constant, and the myofibroblast apoptosis rate. Next to these insights, we perform a sensitivity analysis where the proliferation rates of fibroblasts and myofibroblasts are not the same. The impact of this model adaptation is significant.

In Vivo Models for Hypertrophic Scars—A Systematic Review

Backgroundand Objectives: Hypertrophic scars following surgeries or burns present a serious concern for many patients because these scars not only lead to an aesthetical but also to a functional and psychological burden. Treatment of hypertrophic scars is challenging because despite various treatment options, a low level of evidence hinders preference of any specific treatment plan. To properly identify new therapeutic approaches, the use of in vivo models remains indispensable. A gold standard for hypertrophic scars has not been established to date. This review aims at giving a comprehensive overview of the available in vivo models. Materials and Methods: PubMed and CINAHL were queried for currently existing models. Results: Models with mice, rats, rabbits, pigs, guinea pigs and dogs are used in hypertrophic scar research. Rodent models provide the advantage of ready availability and low costs, but the number of scars per animal is limited due to their relatively small body surface, leading to a high number of test animals which should be avoided according to the 3Rs. Multiple scars per animal can be created in the guinea pig and rabbit ear model; but like other rodent models, these models exhibit low transferability to human conditions. Pig models show a good transferability, but are cost-intensive and require adequate housing facilities. Further, it is not clear if a currently available pig model can deliver clinical and histological features of human hypertrophic scars concurrently. Conclusions: None of the analyzed animal models can be clearly recommended as a standard model in hypertrophic scar research because the particular research question must be considered to elect a suitable model.

The future of burn care from a complexity science perspective

Healthcare is undergoing a profound technological and digital transformation and has become increasingly complex. It is important for burns professionals and researchers to adapt to these developments which may require new ways of thinking and subsequent new strategies. As Einstein has put it: 'We must learn to see the world anew'. The relatively new scientific discipline "Complexity science" can give more direction to this and is the metaphorical open door that should not go unnoticed in view of the burn care of the future. Complexity sciences studies 'why the whole is more than the sum of the parts'. It studies how multiple separate components interact with each other and their environment and how these interactions lead to 'behavior of the system'. Biological systems are always part of smaller and larger systems and exhibit the behavior of adaptivity, hence the name complex adaptive systems. From the perspective of complexity science, a severe burn injury is an extreme disruption of the 'human body system'. But this disruption also applies to the systems at the organ and cellular level. All these systems follow principles of complex systems. Awareness of the scaling process at multilevel helps to understand and manage the complex situation when dealing with severe burn cases. The aim of this paper is to create awareness of the concept of complexity and to demonstrate the value and possibilities of complexity science methods and tools for the future of burn care through examples from preclinical, clinical, and organizational perspective in burn care.

Scar formation from the perspective of complexity science: a new look at the biological system as a whole

A burn wound is a complex systemic disease at multiple levels. Current knowledge of scar formation after burn injury has come from traditional biological and clinical studies. These are normally focused on just a small part of the entire process, which has limited our ability to sufficiently understand the underlying mechanisms and to predict systems behaviour. Scar formation after burn injury is a result of a complex biological system-wound healing. It is a part of a larger whole. In this self-organising system, many components form networks of interactions with each other. These networks of interactions are typically non-linear and change their states dynamically, responding to the environment and showing emergent long-term behaviour. How molecular and cellular data relate to clinical phenomena, especially regarding effective therapies of burn wounds to achieve minimal scarring, is difficult to unravel and comprehend. Complexity science can help bridge this gap by integrating small parts into a larger whole, such that relevant biological mechanisms and data are combined in a computational model to better understand the complexity of the entire biological system. A better understanding of the complex biological system of post-burn scar formation could bring research and treatment regimens to the next level. The aim of this review/position paper is to create more awareness of complexity in scar formation after burn injury by describing the basic principles of complexity science and its potential for burn care professionals.

Research progress of scar repair and its influence on physical and mental health

A scar is a normal and an inevitable physiological response to the natural healing process of wounds or trauma in the human body. The essence of scar is a kind of abnormal and unsound tissue that does not possess the structure, physiological function and vitality of normal skin tissue. Scars not only affect the beauty of the body surface, but also impede the physiological function of the related tissues and organs, and even lead to deformities. Therefore, scar repair is of great significance to patients' appearance, physiological function as well as physical and mental health. Currently, the main approaches for scar repair in clinic are photorejuvenation or fruit acids. The purpose of this study is to investigate the current research progress of scar repair and the impact of scar repair on the physical and mental health of patients.

Mechanobiological wound model for improved design and evaluation of collagen dermal replacement scaffolds

Skin wounds are among the most common and costly medical problems experienced. Despite the myriad of treatment options, such wounds continue to lead to displeasing cosmetic outcomes and also carry a high burden of loss-of-function, scarring, contraction, or nonhealing. As a result, the need exists for new therapeutic options that rapidly and reliably restore skin cosmesis and function. Here we present a new mechanobiological computational model to further the design and evaluation of next-generation regenerative dermal scaffolds fabricated from polymerizable collagen. A Bayesian framework, along with microstructure and mechanical property data from engineered dermal scaffolds and autograft skin, were used to calibrate constitutive models for collagen density, fiber alignment and dispersion, and stiffness. A chemo-bio-mechanical finite element model including collagen, cells, and representative cytokine signaling was adapted to simulate no-fill, dermal scaffold, and autograft skin outcomes observed in a preclinical animal model of full-thickness skin wounds, with a focus on permanent contraction, collagen realignment, and cellularization. Finite element model simulations demonstrated wound cellularization and contraction behavior that was similar to that observed experimentally. A sensitivity analysis suggested collagen fiber stiffness and density are important scaffold design features for predictably controlling wound contraction. Finally, prospective simulations indicated that scaffolds with increased fiber dispersion (isotropy) exhibited reduced and more uniform wound contraction while supporting cell infiltration. By capturing the link between multi-scale scaffold biomechanics and cell-scaffold mechanochemical interactions, simulated healing outcomes aligned well with preclinical animal model data. STATEMENT OF SIGNIFICANCE: Skin wounds continue to be a significant burden to patients, physicians, and the healthcare system. Advancing the mechanistic understanding of the wound healing process, including multi-scale mechanobiological interactions amongst cells, the collagen scaffolding, and signaling molecules, will aide in the design of new skin restoration therapies. This work represents the first step towards integrating mechanobiology-based computational tools with in vitro and in vivo preclinical testing data for improving the design and evaluation of custom-fabricated collagen scaffolds for dermal replacement. Such an approach has potential to expedite development of new and more effective skin restoration therapies as well as improve patient-centered wound treatment.

Immunological mechanisms of scarring and their psychological impact on patients

A scar is a local symptom, which results from severe physical, biological and chemical damage to human skin and soft tissue. Scars can affect both skin appearance and function. The affected skin or soft tissue cannot be completely repaired normally by itself and is replaced by formed fibrous tissue. Patients with scars can develop physical pain and mental conditions, especially those with scars left after burns, scalds and severe traumas. The scar proliferation phase can be up to several years which could be almost unbearable for patients. Also, the atrophic period afterwards makes the patient's face unrecognizable and dysfunctional, causing great physical and mental impairment. Therefore, scar repair is of great clinical importance for patients, and understanding the immunological mechanisms of scar repair is an important prerequisite for the effective treatment of scars. This study is a systematic review of current research advances about the immunological mechanisms of scar repair, so as to provide a reference for the selection of regimens in clinical treatment.

Stability of a one-dimensional morphoelastic model for post-burn contraction

To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {O}}}(h^2)$$\end{document}O(h2). Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

Sensitivity and feasibility of a one-dimensional morphoelastic model for post-burn contraction

We consider a one-dimensional morphoelastic model describing post-burn scar contraction. Contraction can lead to a limited range of motion (contracture). Reported prevalence of burn scar contractures are 58.6% at 3-6 weeks and 20.9% at 12 months post-reconstructive surgery after burns. This model describes the displacement of the dermal layer of the skin and the development of the effective Eulerian strain in the tissue. Besides these components, the model also contains components that play a major role in the skin repair after trauma. These components are signaling molecules, fibroblasts, myofibroblasts, and collagen. We perform a sensitivity analysis for many parameters of the model and use the results for a feasibility study. In this study, we test whether the model is suitable for predicting the extent of contraction in different age groups. To this end, we conduct an extensive literature review to find parameter values. From the sensitivity analysis, we conclude that the most sensitive parameters are the equilibrium collagen concentration in the dermal layer, the apoptosis rate of fibroblasts and myofibroblasts, and the secretion rate of signaling molecules. Further, although we can use the model to simulate significant distinct contraction densities in different age groups, our results differ from what is seen in the clinic. This particularly concerns children and elderly patients. In children we see more intense contractures if the burn injury occurs near a joint, because the growth induces extra forces on the tissue. Elderly patients seem to suffer less from contractures, possibly because of excess skin.

Attenuation corrected-optical coherence tomography for quantitative assessment of skin wound healing and scar morphology

Imaging the structural modifications of underlying tissues is vital to monitor wound healing. Optical coherence tomography (OCT) images high-resolution sub-surface information, but suffers a loss of intensity with depth, limiting quantification. Hence correcting the attenuation loss is important. We performed swept source-OCT of full-thickness excision wounds for 300 days in mice skin. We used single-scatter attenuation models to determine and correct the attenuation loss in the images. The phantom studies established the correspondence of corrected-OCT intensity (reflectivity) with matrix density and hydration. We histologically validated the corrected-OCT and measured the wound healing rate. We noted two distinct phases of healing-rapid and steady-state. We also detected two compartments in normal scars using corrected OCT that otherwise were not visible in the OCT scans. The OCT reflectivity in the scar compartments corresponded to distinct cell populations, mechanical properties and composition. OCT reflectivity has potential applications in evaluating the therapeutic efficacy of healing and characterizing scars.

Can Mathematics and Computational Modeling Help Treat Deep Tissue Injuries?

Objective: Improving the treatment of deep tissue injuries, such as burns, by the use of computational modeling, instead of by animal experiments. Approach: Development of mathematical relations between various parameters and processes. Furthermore, solving the resulting problems through the use of numerical methods, such as finite-element methods. Results: Using our framework, we are able to simulate wound contraction in two dimensions, in which the wound area is followed over time. Our studies indicate that the degree of contraction can be reduced if the appearance of myofibroblasts is inhibited and if their apoptosis is enhanced. Furthermore, after skin grafting, splinting procedures are to be continued as long as TG-beta like growth factor levels are significant. Innovation: A morphoelasticity-based and computational-probabilistic framework for studying the evolution of burn injuries. Conclusion: The current framework is able to reproduce the time evolution of the wound area as observed in clinical results for skin grafts.

Multi-dimensional models for functional testing of keloid scars: In silico, in vitro, organoid, organotypic, ex vivo organ culture, and in vivo models

Keloid scars are described as benign fibro-proliferative dermal outgrowths that commonly occur in pigmented skin post cutaneous injury, and continue to grow beyond the boundary of the original wound margin. There is a lack of thorough understanding of keloid pathogenesis and thus keloid therapeutic options remain ill-defined. In view of the poor response to current therapy and high recurrence rates, there is an unmet need in improving our knowledge and therefore in identifying targeted and effective treatment strategies in management of keloids. Keloid research however, is hampered by a lack of relevant animal models as keloids do not spontaneously occur in animals and are unique to human skin. Therefore, developing novel animal models and nonanimal models for functional evaluation of keloid cells and tissue for better understanding their pathobiology and response to putative candidate therapies are essential. Here, we present the key concepts and relevant emerging research on two-dimensional and three-dimensional cell and tissue models for functional testing of keloid scars. We will describe in detail current models including in vitro mono- and co-cultures, multi-cellular spheroids (organoids) and organotyopic cultures, ex vivo whole skin keloid tissue organ culture models as well as in vivo human patient models. Finally, we discuss the role played by time as the fourth dimension in a novel model that involves sequential temporal biopsies of human patients with keloids (a so called 4D in vivo human model). The use of these unique models will no doubt prove pivotal in identification of new drug targets as well as biomarkers, in functional testing of emerging novel therapeutics, and in enhancing our understanding of keloid disease biology.

A DISCRETE MATHEMATICAL MODEL FOR SINGLE AND COLLECTIVE MOVEMENT IN AMOEBOID CELLS

In this paper, we develop a new discrete mathematical model for individual and collective cell motility. We introduce a mechanical model for the movement of a cell on a two-dimensional rigid surface to describe and investigate the cell–cell and cell–substrate interactions. The cell cytoskeleton is modeled as a series of springs and dashpots connected in parallel. The cell–substrate attachments and the cell protrusions are also included. In particular, this model is used to describe the directed movement of endothelial cells on a Matrigel plate. We compare the results from our model with experimental data. We show that cell density and substrate rigidity play an important role in network formation.

Technologies to monitor the health of loaded skin tissues

There are many situations where the skin and underlying soft tissues are compromised by mechanical loading in the form or pressure, or pressure in combination with shear. If sustained, this can lead to damage in the tissues particularly adjacent to bony prominences, resulting in chronic wounds. An array of bioengineering technologies have been adopted to assess the integrity of loaded soft tissues. This paper aims to review these approaches for the quantification, simulation and early detection of mechanically-induced skin damage. The review considers different measurements at the interface between the skin and support surface/medical device, involving pressure, shear, friction and the local microclimate. The potential of the techniques to monitor the physiological response of the skin to these external stimuli including biophysical measurement devices and sampling of biofluids are critically analysed. In addition, it includes an analysis of medical imaging technologies and computational modelling to provide a means by which tissue deformation can be quantified and thresholds for tissue damage defined. Bioengineering measurement and imaging technologies have provided an insight into the temporal status of loaded skin. Despite the advances in technology, to date, the translation to clinical tools which are robust and cost effective has been limited. There is a need to adapt existing technologies and simulation platforms to enable patients, carers and clinicians to employ appropriate intervention strategies to minimise soft tissue damage.

Prediction of Scar Size in Rats Six Months after Burns Based on Early Post-injury Polarization-Sensitive Optical Frequency Domain Imaging

Hypertrophic scars remain a major clinical problem in the rehabilitation of burn survivors and lead to physical, aesthetic, functional, psychological, and social stresses. Prediction of healing outcome and scar formation is critical for deciding on the best treatment plan. Both subjective and objective scales have been devised to assess scar severity. Whereas scales of the first type preclude cross-comparison between observers, those of the second type are based on imaging modalities that either lack the ability to image individual layers of the scar or only provide very limited fields of view. To overcome these deficiencies, this work aimed at developing a predictive model of scar formation based on polarization sensitive optical frequency domain imaging (PS-OFDI), which offers comprehensive subsurface imaging. We report on a linear regression model that predicts the size of a scar 6 months after third-degree burn injuries in rats based on early post-injury PS-OFDI and measurements of scar area. When predicting the scar area at month 6 based on the homogeneity and the degree of polarization (DOP), which are signatures derived from the PS-OFDI signal, together with the scar area measured at months 2 and 3, we achieved predictions with a Pearson coefficient of 0.57 (p < 10⁻⁴) and a Spearman coefficient of 0.66 (p < 10⁻⁵), which were significant in comparison to prediction models trained on randomly shuffled data. As the model in this study was developed on the rat burn model, the methodology can be used in larger studies that are more relevant to humans; however, the actual model inferred herein is not translatable. Nevertheless, our analysis and modeling methodology can be extended to perform larger wound healing studies in different contexts. This study opens new possibilities for quantitative and objective assessment of scar severity that could help to determine the optimal course of therapy.

A model for one-dimensional morphoelasticity and its application to fibroblast-populated collagen lattices

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the continual remodelling and associated structural changes in biological tissues. Furthermore, models drawn from plasticity theory are difficult to apply and interpret in this context, where there is no equivalent of a yield stress or flow rule. In this work, we describe a novel one-dimensional mathematical model of tissue remodelling based on the multiplicative decomposition of the deformation gradient. We express the mechanical effects of remodelling as an evolution equation for the effective strain, a measure of the difference between the current state and a hypothetical mechanically relaxed state of the tissue. This morphoelastic model combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. A novel feature of our model is that while most models describe growth as a continuous quantity, here we begin with discrete cells and develop a continuum representation of lattice remodelling based on an appropriate limit of the behaviour of discrete cells. To demonstrate the utility of our approach, we use this framework to capture qualitative aspects of the continual remodelling observed in fibroblast-populated collagen lattices, in particular its contraction and its subsequent sudden re-expansion when remodelling is interrupted.

Biomedical implications from a morphoelastic continuum model for the simulation of contracture formation in skin grafts that cover excised burns

A continuum hypothesis-based model is developed for the simulation of the (long term) contraction of skin grafts that cover excised burns in order to obtain suggestions regarding the ideal length of splinting therapy and when to start with this therapy such that the therapy is effective optimally. Tissue is modeled as an isotropic, heterogeneous, morphoelastic solid. With respect to the constituents of the tissue, we selected the following constituents as primary model components: fibroblasts, myofibroblasts, collagen molecules, and a generic signaling molecule. Good agreement is demonstrated with respect to the evolution over time of the surface area of unmeshed skin grafts that cover excised burns between outcomes of computer simulations obtained in this study and scar assessment data gathered previously in a clinical study. Based on the simulation results, we suggest that the optimal point in time to start with splinting therapy is directly after placement of the skin graft on its recipient bed. Furthermore, we suggest that it is desirable to continue with splinting therapy until the concentration of the signaling molecules in the grafted area has become negligible such that the formation of contractures can be prevented. We conclude this study with a presentation of some alternative ideas on how to diminish the degree of contracture formation that are not based on a mechanical intervention, and a discussion about how the presented model can be adjusted.

A mathematical model for the simulation of the contraction of burns

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.

Review on experiment-based two- and three-dimensional models for wound healing

Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers.

Lumican alleviates hypertrophic scarring by suppressing integrin-FAK signaling

Hypertrophic scarring (HS) is an overcompensation of wound healing that increases the risk of cosmetic disfigurement and functional impairment. No gold standard has been established for the treatment or prevention of HS. Our study aims to elucidate the expression and function of lumican in the pathogenesis of HS as well as the underlying mechanism involved in this procedure. An animal model of HS (rabbit ear) was established, and the Ad-lumican vectors were locally injected. Primary fibroblasts isolated from patients with hypertrophic burn scars were used in vitro. Histological and molecular changes in HS pathogenesis were evaluated. The results showed that lumican is significantly reduced in HS tissues and fibroblasts from HS patients as compared to normal skin or cells. Lumican levels were further suppressed in response to TGF-β stimulation. However, lumican upregulation effectively thinned the scar area and inhibited fibroblast proliferation and the cell cycle. Meanwhile, Ad-lumican administration suppressed the deposition of extracellular matrix, such as collagen and CTGF. Ad-lumican injected animals or fibroblasts presented comparable integrin α₂β₁ expression while greatly reduced phosphorylation of FAK compared to the negative control. Moreover, Ad-lumican administration largely enhanced the binding of lumican to integrin α₂β₁ and may thus inhibit the signaling propagation of collagen-integrin α₂β₁. Overall, the restoration of lumican levels contributed to suppressing the HS progression by inhibiting collagen-integrin α₂β₁-FAK signaling.

A biomechanical mathematical model for the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds

A continuum hypothesis-based, biomechanical model is presented for the simulation of the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds that cover a large surface area. Since wound contraction mainly takes place in the dermal layer of the skin, solely a portion of this layer is included explicitly into the model. This portion of dermal layer is modeled as a heterogeneous, orthotropic continuous solid with bulk mechanical properties that are locally dependent on both the local concentration and the local geometrical arrangement of the collagen bundles. With respect to the dynamic regulation of the geometrical arrangement of the collagen bundles, it is assumed that a portion of the collagen molecules are deposited and reoriented in the direction of movement of (myo)fibroblasts. The remainder of the newly secreted collagen molecules are deposited by ratio in the direction of the present collagen bundles. Simulation results show that the distribution of the collagen bundles influences the evolution over time of both the shape of the wounded area and the degree of overall contraction of the wounded area. Interestingly, these effects are solely a consequence of alterations in the initial overall distribution of the collagen bundles, and not a consequence of alterations in the evolution over time of the different cell densities and concentrations of the modeled constituents. In accordance with experimental observations, simulation results show furthermore that ultimately the majority of the collagen molecules ends up permanently oriented toward the center of the wound and in the plane that runs parallel to the surface of the skin.