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

A mathematical model for wound healing in the reef-building coral Pocillopora damicornis

Coral reefs, among the most diverse ecosystems on Earth, currently face major threats from pollution, unsustainable fishing practices , and perturbations in environmental parameters brought on by climate change. Corals also sustain regular wounding from other sea life and human activity. Recent reef restoration practices have even involved intentional wounding by systematically breaking coral fragments and relocating them to revitalize damaged reefs, a practice known as microfragmentation. Despite its importance, very little research has explored the inner mechanisms of wound healing in corals. Some reef-building corals have been observed to initiate an immunological response to wounding similar to that observed in mammalian species. Utilizing prior models of wound healing in mammalian species as the mathematical basis, we formulated a mechanistic model of wound healing, including observations of the immune response and tissue repair in scleractinian corals for the species Pocillopora damicornis. The model consists of four differential equations which track changes in remaining wound debris, number of cells involved in inflammation, number of cells involved in proliferation, and amount of wound closure through re-epithelialization. The model is fit to experimental wound size data from linear and circular shaped wounds on a live coral fragment. Mathematical methods, including numerical simulations and local sensitivity analysis, were used to analyze the resulting model. The parameter space was also explored to investigate drivers of other possible wound outcomes. This model serves as a first step in generating mathematical models for wound healing in corals that will not only aid in the understanding of wound healing as a whole, but also help optimize reef restoration practices and predict recovery behavior after major wounding events.

Models for Implant-Induced Capsular Contracture Post Breast Cancer Surgery

Capsular contracture is a painful deformation of scar-tissue that may form around an implant in post-breast cancer reconstruction or cosmetic surgery. Inflammation due to surgical trauma or contamination in the tissue around the implant could account for recruitment of immune cells, and transdifferentiation of resident fibroblasts into cells that deposit abnormally thick collagen. Here we examine this hypothesis using a mathematical model for interacting macrophages, fibroblasts, myofibroblasts, and collagen. Our model demonstrates that cellular response can, together with inflammatory cell recruitment, account for prognoses.

Semi-autonomous wound invasion via matrix-deposited, haptotactic cues

Proper wound healing relies on invasion of fibroblasts via directed migration. While the related experimental and mathematical modeling literature has mainly focused on cell migration directed by soluble cues (chemotaxis), there is ample evidence that fibroblast migration is also directed by insoluble, matrix-bound cues (haptotaxis). Furthermore, numerous studies indicate that fibronectin (FN), a haptotactic ligand for fibroblasts, is present and dynamic in the provisional matrix throughout the proliferative phase of wound healing. In the present work, we show the plausibility of a hypothesis that fibroblasts themselves form and maintain haptotactic gradients in a semi-autonomous fashion. As a precursor to this, we examine the positive control scenario where FN is pre-deposited in the wound matrix, and fibroblasts maintain haptotaxis by removing FN at an appropriate rate. After developing conceptual and quantitative understanding of this scenario, we consider two cases in which fibroblasts activate the latent form of a matrix-loaded cytokine, TGFβ, which upregulates the fibroblasts' own secretion of FN. In the first of these, the latent cytokine is pre-patterned and released by the fibroblasts. In the second, fibroblasts in the wound produce the latent TGFβ, with the presence of the wound providing the only instruction. In all cases, wound invasion is more effective than a negative control model with haptotaxis disabled; however, there is a trade-off between the degree of fibroblast autonomy and the rate of invasion.

Recent advances in decellularized biomaterials for wound healing

The skin is one of the most essential organs in the human body, interacting with the external environment and shielding the body from diseases and excessive water loss. Thus, the loss of the integrity of large portions of the skin due to injury and illness may lead to significant disabilities and even death. Decellularized biomaterials derived from the extracellular matrix of tissues and organs are natural biomaterials with large quantities of bioactive macromolecules and peptides, which possess excellent physical structures and sophisticated biomolecules, and thus, promote wound healing and skin regeneration. Here, we highlighted the applications of decellularized materials in wound repair. First, the wound-healing process was reviewed. Second, we elucidated the mechanisms of several extracellular matrix constitutes in facilitating wound healing. Third, the major categories of decellularized materials in the treatment of cutaneous wounds in numerous preclinical models and over decades of clinical practice were elaborated. Finally, we discussed the current hurdles in the field and anticipated the future challenges and novel avenues for research on decellularized biomaterials-based wound treatment.

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.

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.

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.

Exogenous supply of Hsp47 triggers fibrillar collagen deposition in skin cell cultures in vitro

Background

Collagen is a structural protein that provides mechanical stability and defined architectures to skin. In collagen-based skin disorders this stability is lost, either due to mutations in collagens or in the chaperones involved in collagen assembly. This leads to chronic wounds, skin fragility, and blistering. Existing approaches to treat such conditions rely on administration of small molecules to simulate collagen production, like 4-phenylbutyrate (4-PBA) or growth factors like TGF-β. However, these molecules are not specific for collagen synthesis, and result in unsolicited side effects. Hsp47 is a collagen-specific chaperone with a major role in collagen biosynthesis. Expression levels of Hsp47 correlate with collagen deposition. This article explores the stimulation of collagen deposition by exogenously supplied Hsp47 (collagen specific chaperone) to skin cells, including specific collagen subtypes quantification.

Results

Here we quantify the collagen deposition level and the types of deposited collagens after Hsp47 stimulation in different in vitro cultures of cells from human skin tissue (fibroblasts NHDF, keratinocytes HaCat and endothelial cells HDMEC) and mouse fibroblasts (L929 and MEF). We find upregulated deposition of fibrillar collagen subtypes I, III and V after Hsp47 delivery. Network collagen IV deposition was enhanced in HaCat and HDMECs, while fibril-associated collagen XII was not affected by the increased intracellular Hsp47 levels. The deposition levels of fibrillar collagen were cell-dependent i.e. Hsp47-stimulated fibroblasts deposited significantly higher amount of fibrillar collagen than Hsp47-stimulated HaCat and HDMECs.

Conclusions

A 3-fold enhancement of collagen deposition was observed in fibroblasts upon repeated dosage of Hsp47 within the first 6 days of culture. Our results provide fundamental understanding towards the idea of using Hsp47 as therapeutic protein to treat collagen disorders.

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.

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.