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

Impact of oral antithrombotic agents on urinary continence recovery following robot-assisted radical prostatectomy: a retrospective cohort study

BACKGROUND

Robot-assisted radical prostatectomy (RARP) is a preferred minimally invasive surgical treatment for prostate cancer. The number of elderly patients and those with cardiovascular and/or cerebrovascular issues undergoing surgery is increasing, and many of them are taking antithrombotic (AT) agents. However, the effect of AT agents on postoperative urinary recovery has not been adequately studied. In this study, we analyzed the differences in the postoperative recovery of urinary continence and oncological outcomes in patients undergoing RARP for localized prostate cancer between AT agent adherents and non-adherents.

METHODS

A total of 394 patients who underwent conventional anterior RARP between February 2015 and February 2021 were categorized into two groups: those taking oral AT agents (AT group) and the control group. Urinary continence recovery, complications, and oncological outcomes were compared between the groups. A Cox proportional hazards analysis was performed to identify clinical factors that affect urinary continence recovery.

RESULTS

The background data and bleeding complications did not differ significantly between the groups. The recovery of continence was significantly poorer in the AT group in terms of complete pad free (HR: 0.53 [95% CI: 0.39-0.71]) and use of ≤ 1 safety pad (HR: 0.74 [95% CI: 0.59-0.94]). The rate of anastomotic leakage on cystography was significantly higher in the AT group (20.9% vs. 6.7%). A univariate analysis revealed that taking antithrombotic agents, higher prostate-specific antigen levels, and a more advanced clinical stage were associated with a poor urinary continence recovery; a multivariate analysis showed that taking AT agents was an independent factor negatively associated with urinary continence recovery. There was no significant difference between the groups in the positive surgical margin rate (19.0% vs. 23.8%) or the biochemical-recurrence-free rate.

CONCLUSION

Taking oral AT agents may be associated with poor urinary continence recovery after RARP.

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.

Patient-specific computational simulations of wound healing following midline laparotomy closure

In the current study, we developed a new computational methodology to simulate wound healing in soft tissues. We assumed that the injured tissue recovers partially its mechanical strength and stiffness by gradually increasing the volume fraction of collagen fibers. Following the principles of the constrained mixture theory, we assumed that new collagen fibers are deposited at homeostatic tension while the already existing tissue undergoes a permanent deformation due to the effects of remodeling. The model was implemented in the finite-element software Abaqus® through a VUMAT subroutine and applied to a complex and realistic case: simulating wound healing following midline laparotomy closure. The incidence of incisional hernia is still quite significant clinically, and our goal was to investigate different conditions hampering the success of these procedures. We simulated wound healing over periods of 6 months on a patient-specific geometry. One of the outcomes of the finite-element simulations was the width of the wound tissue, which was found to be clinically correlated with the development of incisional hernia after midline laparotomy closure. We studied the impact of different suturing modalities and the effects of situations inducing increased intra-abdominal pressure or its intermittent variations such as coughing. Eventually, the results showed that the main risks of developing an incisional hernia mostly depend on the elastic strains reached in the wound tissue after degradation of the suturing wires. Despite the need for clinical validation, these results are promising for establishing a digital twin of wound healing in midline laparotomy incision.

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.

A novel integrated experimental and computational approach to unravel fibroblast motility in response to chemical gradients in 3D collagen matrices

Fibroblasts play an essential role in tissue repair and regeneration as they migrate to wounded areas to secrete and remodel the extracellular matrix. Fibroblasts recognize chemical substances such as growth factors, which enhance their motility towards the wounded tissues through chemotaxis. Although several studies have characterized single-cell fibroblast motility before, the migration patterns of fibroblasts in response to external factors have not been fully explored in 3D environments. We present a study that combines experimental and computational efforts to characterize the effect of chemical stimuli on the invasion of 3D collagen matrices by fibroblasts. Experimentally, we used microfluidic devices to create chemical gradients using collagen matrices of distinct densities. We evaluated how cell migration patterns were affected by the presence of growth factors and the mechanical properties of the matrix. Based on these results, we present a discrete-based computational model to simulate cell motility, which we calibrated through the quantitative comparison of experimental and computational data via Bayesian optimization. By combining these approaches, we predict that fibroblasts respond to both the presence of chemical factors and their spatial location. Furthermore, our results show that the presence of these chemical gradients could be reproduced by our computational model through increases in the magnitude of cell-generated forces and enhanced cell directionality. Although these model predictions require further experimental validation, we propose that our framework can be applied as a tool that takes advantage of experimental data to guide the calibration of models and predict which mechanisms at the cellular level may justify the experimental findings. Consequently, these new insights may also guide the design of new experiments, tailored to validate the variables of interest identified by the model.

Three-dimensional bioprinting of mucoadhesive scaffolds for the treatment of oral mucosal lesions; an in vitro study

Background

Chronic oral lesions could be a part of some diseases, including mucocutaneous diseases, immunobullous diseases, gastrointestinal diseases, and graft versus host diseases. Systemic steroids are an effective treatment, but they cause unfavorable and even severe systemic side effects. Discontinuation of systemic corticosteroids or other immunosuppressive drugs leads to relapse, confirming the importance of long-term corticosteroid use. The present study aims to fabricate a mucoadhesive scaffold using three-dimensional (3D) bioprinting for sustained drug delivery in oral mucosal lesions to address the clinical need for alternative treatment, especially for those who do not respond to routine therapy.

Methods

3D bioprinting method was used for the fabrication of the scaffolds. Scaffolds were fabricated in three layers; adhesive/drug-containing, backing, and middle layers. For evaluation of the release profile of the drug, artificial saliva was used as the release medium. Mucoadhesive scaffolds were analyzed using a scanning electron microscope (SEM) and SEM surface reconstruction. The pH of mucoadhesive scaffolds and swelling efficacy were measured using a pH meter and Enslin dipositive, respectively. A microprocessor force gauge was used for the measurement of tensile strength. For the evaluation of the cytotoxicity, oral keratinocyte cells' survival rate was evaluated by the MTT method. Folding endurance tests were performed using a stable microsystem texture analyzer and analytic probe mini tensile grips.

Results

All scaffolds had the same drug release trend; An initial rapid explosive release during the first 12 h, followed by a gradual release. The scaffolds showed sustained drug release and continued until the fourth day. The pH of the surface of the scaffolds was 5.3–6.3, and the rate of swelling after 5 h was 28 ± 3.2%. The tensile strength of the scaffolds containing the drug was 7.8 ± 0.12 MPa. The scaffolds were non-irritant to the mucosa, and the folding endurance of the scaffolds was over three hundred times.

Conclusion

The scaffold fabricated using the 3D bioprinting method could be suitable for treating oral mucosal lesions.

Multiscale mechanobiology: Coupling models of adhesion kinetics and nonlinear tissue mechanics

The mechanical behavior of tissues at the macroscale is tightly coupled to cellular activity at the microscale. Dermal wound healing is a prominent example of a complex system in which multiscale mechanics regulate restoration of tissue form and function. In cutaneous wound healing, a fibrin matrix is populated by fibroblasts migrating in from a surrounding tissue made mostly out of collagen. Fibroblasts both respond to mechanical cues, such as fiber alignment and stiffness, as well as exert active stresses needed for wound closure. Here, we develop a multiscale model with a two-way coupling between a microscale cell adhesion model and a macroscale tissue mechanics model. Starting from the well-known model of adhesion kinetics proposed by Bell, we extend the formulation to account for nonlinear mechanics of fibrin and collagen and show how this nonlinear response naturally captures stretch-driven mechanosensing. We then embed the new nonlinear adhesion model into a custom finite element implementation of tissue mechanical equilibrium. Strains and stresses at the tissue level are coupled with the solution of the microscale adhesion model at each integration point of the finite element mesh. In addition, solution of the adhesion model is coupled with the active contractile stress of the cell population. The multiscale model successfully captures the mechanical response of biopolymer fibers and gels, contractile stresses generated by fibroblasts, and stress-strain contours observed during wound healing. We anticipate that this framework will not only increase our understanding of how mechanical cues guide cellular behavior in cutaneous wound healing, but will also be helpful in the study of mechanobiology, growth, and remodeling in other tissues.

Quantitative predictive approaches for Dupuytren disease: a brief review and future perspectives

In this study we review the current state of the art for Dupuytren's disease (DD), while emphasising the need for a better integration of clinical, experimental and quantitative predictive approaches to understand the evolution of the disease and improve current treatments. We start with a brief review of the biology of this disease and current treatment approaches. Then, since certain aspects in the pathogenesis of this disorder have been compared to various biological aspects of wound healing and malignant processes, next we review some in silico (mathematical modelling and simulations) predictive approaches for complex multi-scale biological interactions occurring in wound healing and cancer. We also review the very few in silico approaches for DD, and emphasise the applicability of these approaches to address more biological questions related to this disease. We conclude by proposing new mathematical modelling and computational approaches for DD, which could be used in the absence of animal models to make qualitative and quantitative predictions about the evolution of this disease that could be further tested in vitro.

Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing

During the hemostatic phase of wound healing, vascular injury leads to endothelial cell damage, initiation of a coagulation cascade involving platelets, and formation of a fibrin-rich clot. As this cascade culminates, activation of the protease thrombin occurs and soluble fibrinogen is converted into an insoluble polymerized fibrin network. Fibrin polymerization is critical for bleeding cessation and subsequent stages of wound healing. We develop a cooperative enzyme kinetics model for in vitro fibrin matrix polymerization capturing dynamic interactions among fibrinogen, thrombin, fibrin, and intermediate complexes. A tailored parameter subset selection technique is also developed to evaluate parameter identifiability for a representative data curve for fibrin accumulation in a short-duration in vitro polymerization experiment. Our approach is based on systematic analysis of eigenvalues and eigenvectors of the classical information matrix for simulations of accumulating fibrin matrix via optimization based on a least squares objective function. Results demonstrate robustness of our approach in that a significant reduction in objective function cost is achieved relative to a more ad hoc curve-fitting procedure. Capabilities of this approach to integrate non-overlapping subsets of the data to enhance the evaluation of parameter identifiability are also demonstrated. Unidentifiable reaction rate parameters are screened to determine whether individual reactions can be eliminated from the overall system while preserving the low objective cost. These findings demonstrate the high degree of information within a single fibrin accumulation curve, and a tailored model and parameter subset selection approach for improving optimization and reducing model complexity in the context of polymerization experiments.

Three-dimensional numerical simulation of soft-tissue wound healing using constrained-mixture anisotropic hyperelasticity and gradient-enhanced damage mechanics

Healing of soft biological tissues is the process of self-recovery or self-repair after injury or damage to the extracellular matrix (ECM). In this work, we assume that healing is a stress-driven process, which works at recovering a homeostatic stress metric in the tissue by replacing the damaged ECM with a new undamaged one. For that, a gradient-enhanced continuum healing model is developed for three-dimensional anisotropic tissues using the modified anisotropic Holzapfel-Gasser-Ogden constitutive model. An adaptive stress-driven approach is proposed for the deposition of new collagen fibres during healing with orientations assigned depending on the principal stress direction. The intrinsic length scales of soft tissues are considered through the gradient-enhanced term, and growth and remodelling are simulated by a constrained-mixture model with temporal homogenization. The proposed model is implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three numerical examples have been achieved to illustrate the performance of the proposed model in simulating the healing process with various damage situations, converging towards stress homeostasis. The orientations of newly deposited collagen fibres and the sensitivity to intrinsic length scales are studied through these examples, showing that both have a significant impact on temporal evolutions of the stress distribution and on the size of the damage region. Applications of the approach to carry out in silico experiments of wound healing are promising and show good agreement with existing experiment results.

Computational modelling suggests complex interactions between interstitial flow and tumour angiogenesis

Angiogenesis, the growth of capillaries from pre-existing ones, plays a key role in cancer progression. Tumours release tumour angiogenic factors (TAFs) into the extracellular matrix (ECM) that trigger angiogenesis once they reach the vasculature. The neovasculature provides nutrients and oxygen to the tumour. In the ECM, the interstitial fluid moves driven by pressure differences and may affect the distribution of tumour TAFs, and, in turn, tumour vascularization. In this work, we propose a hybrid mathematical model to investigate the influence of fluid flow in tumour angiogenesis. Our model shows the impact of interstitial flow in a time-evolving capillary network using a continuous approach. The flow model is coupled to a model of angiogenesis that includes tip endothelial cells, filopodia, capillaries and TAFs. The TAF transport equation considers not only diffusive mechanisms but also the convective transport produced by interstitial flow. Our simulations predict a significant alteration of the new vascular networks, which tend to grow more prominently against the flow. The model suggests that interstitial flow may produce increased tumour malignancies and hindered treatments.

A review of accelerated wound healing approaches: biomaterial- assisted tissue remodeling

Nowadays, due to a growing number of tissue injuries, in particular, skin wounds, induction and promotion of tissue healing responses can be considered as a crucial step towards a complete regeneration. Recently, biomaterial design has been oriented towards promoting a powerful, effective, and successful healing. Biomaterials with wound management abilities have been developed for different applications such as providing a native microenvironment and supportive matrices that induce the growth of tissue, creating physical obstacles against microbial contamination, and to be used as delivery systems for therapeutic reagents. Until now, numerous strategies aiming to accelerate the wound healing process have been utilized and studied with their own pros and cons. In this review, tissue remodeling phenomena, wound healing mechanisms, and their related factors will be discussed. In addition, different methods for induction and acceleration of healing via cell therapy, bioactive therapeutic delivery, and/or biomaterial-based approaches will be reviewed.

Mechanism of Oleogel-S10: A triterpene preparation for the treatment of epidermolysis bullosa

Epidermolysis bullosa (EB) is a group of rare heterogeneous, genetic disorders. Currently, there is no effective pharmacological or genetic therapy for all EB subtypes. Dry extract from birch bark and betulin upregulate some pro‐inflammatory mediators and downregulate others. The increase in pro‐inflammatory cytokines is temporary and attenuated over long‐term treatment. This inflammatory stimulus is thought to be prerequisite for a secondary anti‐inflammatory response. Dry extract from birch bark and its active marker substances have also been shown to increase the migration of primary human keratinocytes, accelerate wound closure, and promote differentiation of keratinocytes in vitro and in vivo—processes that are essential for reepithelialization and maintenance of the skin barrier. Comprehensive clinical data are available to support the use of Oleogel‐S10 in the treatment of partial thickness wounds of different etiologies, and a proof‐of‐concept Phase 2 study in patients with dystrophic EB has suggested the potential for faster reepithelialization of wounds treated with Oleogel‐S10.

Gradient-enhanced continuum models of healing in damaged soft tissues

Healing of soft biological tissue is the process of self-recovering or self-repairing the injured or damaged extracellular matrix (ECM). Healing is assumed to be stress-driven, with the objective of returning to a homeostatic stress metrics in the tissue after replacing the damaged ECM with new undamaged one. However, based on the existence of intrinsic length scales in soft tissues, it is thought that computational models of healing should be non-local. In the present study, we introduce for the first time two gradient-enhanced constitutive healing models for soft tissues including non-local variables. The first model combines a continuum damage model with a temporally homogenized growth model, where the growth direction is determined according to local principal stress directions. The second one is based on a gradient-enhanced healing model with continuously recoverable damage variable. Both models are implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three two-dimensional situations simulating the healing process of soft tissues are modeled numerically with both models, and their application for simulation of balloon angioplasty is provided by illustrating the change of damage field and geometry in the media layer throughout the healing process.

Spatial-Temporal Changes of Mechanical Microenvironment in Skin Wounds During Negative Pressure Wound Therapy

Cell migration, proliferation, and differentiation are regulated by mechanical cues during skin wound healing. Negative pressure wound therapy (NPWT) reduces the healing period by optimizing the mechanical microenvironment of the wound bed. Under NPWT, it remains elusive how the mechanical microenvironment (e.g., stiffness, strain gradients) changes both in time and space during wound healing. To illustrate this, the healing time of full-thickness skin wounds under NPWT, with pressure settings ranging from -50 to -150 mm Hg, were evaluated and compared with gauze dressing treatments (control group), and three-dimensional finite element models of full-thickness skin wounds on days 1 and 5 after treatment were developed on the basis of MR 3D imaging data. Shear wave elastography (SWE) was applied to detect the stiffness of wound soft tissue on days 1 and 5, and nonlinear finite element analysis (FEA) was used to represent the spatial-temporal environment of the 3D strain field of the wound under NPWT vs the control group. Compared with the control group, NPWT with -50, -80, and -125 mm Hg promoted wound healing. SWE showed that the elastic modulus of wounded skin increased during healing. Meanwhile, the elastic modulus in wounded skin under NPWT was significantly smaller than in the control group. Strain and its gradient decreased under NPWT during wound healing, while no significant change was observed in the control group. This study, which is based on MR 3D imaging, shear wave elastography, and nonlinear FEA, provides an in-depth understanding of changes of the skin mechanical microenvironment under NPWT in the time-space dimension and the associated wound healing.

Eden Model Simulation of Re-Epithelialization and Angiogenesis of an Epidermal Wound

Among the vital processes of cutaneous wound healing are epithelialization and angiogenesis. The former leads to the successful closure of the wound while the latter ensures that nutrients are delivered to the wound region during and after healing is completed. These processes are regulated by various cytokines and growth factors that subtend their proliferation and migration into the wound region until full healing is attained. Wound epithelialization can be enhanced by the administration of epidermal stem cells (ESC) or impaired by the presence of an infection. This paper uses the Eden model of a growing cluster to independently simulate the processes of epithelialization and angiogenesis in a cutaneous wound for different geometries. Further, simulations illustrating bacterial infection are provided. Our simulation results demonstrate contraction and closure for any wound geometry due to a collective migration of epidermal cells from the wound edge in fractal form and the diffusion of capillary sprouts with the laying down of capillary blocks behind moving tips into the wound area.

Degradation of extracellular matrix regulates osteoblast migration: A microfluidic-based study

Bone regeneration is strongly dependent on the capacity of cells to move in a 3D microenvironment, where a large cascade of signals is activated. To improve the understanding of this complex process and to advance in the knowledge of the role of each specific signal, it is fundamental to analyze the impact of each factor independently. Microfluidic-based cell culture is an appropriate technology to achieve this objective, because it allows recreating realistic 3D local microenvironments by taking into account the extracellular matrix, cells and chemical gradients in an independent or combined scenario. The main aim of this work is to analyze the impact of extracellular matrix properties and growth factor gradients on 3D osteoblast movement, as well as the role of cell matrix degradation. For that, we used collagen-based hydrogels, with and without crosslinkers, under different chemical gradients, and eventually inhibiting metalloproteinases to tweak matrix degradation. We found that osteoblast's 3D migratory patterns were affected by the hydrogel properties and the PDGF-BB gradient, although the strongest regulatory factor was determined by the ability of cells to remodel the matrix.

Improved in vitro models for preclinical drug and formulation screening focusing on 2D and 3D skin and cornea constructs

The present overview deals with current approaches for the improvement of in vitro models for preclinical drug and formulation screening which were elaborated in a joint project at the Center of Pharmaceutical Engineering of the TU Braunschweig. Within this project a special focus was laid on the enhancement of skin and cornea models. For this reason, first, a computation-based approach for in silico modeling of dermal cell proliferation and differentiation was developed. The simulation should for example enhance the understanding of the performed 2D in vitro tests on the antiproliferative effect of hyperforin. A second approach aimed at establishing in vivo-like dynamic conditions in in vitro drug absorption studies in contrast to the commonly used static conditions. The reported Dynamic Micro Tissue Engineering System (DynaMiTES) combines the advantages of in vitro cell culture models and microfluidic systems for the emulation of dynamic drug absorption at different physiological barriers and, later, for the investigation of dynamic culture conditions. Finally, cryopreserved shipping was investigated for a human hemicornea construct. As the implementation of a tissue-engineering laboratory is time-consuming and cost-intensive, commercial availability of advanced 3D human tissue is preferred from a variety of companies. However, for shipping purposes cryopreservation is a challenge to maintain the same quality and performance of the tissue in the laboratory of both, the provider and the customer.

A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues

Remodelling of soft biological tissue is characterized by interacting biochemical and biomechanical events, which change the tissue's microstructure, and, consequently, its macroscopic mechanical properties. Remodelling is a well-defined stage of the healing process, and aims at recovering or repairing the injured extracellular matrix. Like other physiological processes, remodelling is thought to be driven by homeostasis, i.e. it tends to re-establish the properties of the uninjured tissue. However, homeostasis may never be reached, such that remodelling may also appear as a continuous pathological transformation of diseased tissues during aneurysm expansion, for example. A simple constitutive model for soft biological tissues that regards remodelling as homeostatic-driven turnover is developed. Specifically, the recoverable effective tissue damage, whose rate is the sum of a mechanical damage rate and a healing rate, serves as a scalar internal thermodynamic variable. In order to integrate the biochemical and biomechanical aspects of remodelling, the healing rate is, on the one hand, driven by mechanical stimuli, but, on the other hand, subjected to simple metabolic constraints. The proposed model is formulated in accordance with continuum damage mechanics within an open-system thermodynamics framework. The numerical implementation in an in-house finite-element code is described, particularized for Ogden hyperelasticity. Numerical examples illustrate the basic constitutive characteristics of the model and demonstrate its potential in representing aspects of remodelling of soft tissues. Simulation results are verified for their plausibility, but also validated against reported experimental data.

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.

Negative Pressure Wound Therapy in Maxillofacial Applications

Negative pressure wound therapy has greatly advanced the field of wound healing for nearly two decades, by providing a robust surgical adjunct technique for accelerating wound closure in acute and chronic wounds. However, the application of negative pressure wound therapy in maxillofacial applications has been relatively under utilized as a result of the physical articulations and contours of the head and neck that make it challenging to obtain an airtight seal for different negative pressure wound therapy systems. Adapting negative pressure wound therapies for maxillofacial applications could yield significant enhancement of wound closure in maxillofacial applications. The current review summarizes the basic science underlying negative pressure wound therapy, as well as specific maxillofacial procedures that could benefit from negative pressure wound therapy.

Impact of anomalous transport kinetics on the progress of wound healing

This work focuses on the transport kinetics of chemical and cellular species during wound healing. Anomalous transport kinetics, coupling sub- and superdiffusion with chemotaxis, and fractional viscoelasticity of soft tissues are analyzed from a modeling point of view. The paper presents a generalization of well stablished mechano-chemical models of wound contraction (Murphy et al., 2012; Valero et al., 2014) to include the previously mentioned anomalous effects by means of partial differential equations of fractional order. Results show the effect that anomalous dynamics have on the contraction rate and extension and on the distribution of biological species, and indicators of fibroproliferative disorders are identified.

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

A continuum hypothesis-based model is presented for the simulation of the formation and the subsequent regression of hypertrophic scar tissue after dermal wounding. Solely the dermal layer of the skin is modeled explicitly and it is modeled as a heterogeneous, isotropic and compressible neo-Hookean solid. With respect to the constituents of the dermal layer, the following components are selected as primary model components: fibroblasts, myofibroblasts, a generic signaling molecule and collagen molecules. A good match with respect to the evolution of the thickness of the dermal layer of scars between the outcomes of simulations and clinical measurements on hypertrophic scars at different time points after injury in human subjects is demonstrated. Interestingly, the comparison between the outcomes of the simulations and the clinical measurements demonstrates that a relatively high apoptosis rate of myofibroblasts results in scar tissue that behaves more like normal scar tissue with respect to the evolution of the thickness of the tissue over time, while a relatively low apoptosis rate results in scar tissue that behaves like hypertrophic scar tissue with respect to the evolution of the thickness of the tissue over time. Our ultimate goal is to construct models with which the properties of newly generated tissues that form during wound healing can be predicted with a high degree of certainty. The development of the presented model is considered by us as a step toward their construction.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.