A mathematical model for the simulation of the contraction of burns

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.

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.

The Northwestern Abdominoplasty Scar Model: A Tool for High-Throughput Assessment of Scar Therapeutics

Significance: Scar management is an important concern in plastic surgery. Scar models that best mimic in vivo human scarring are essential for understanding scar development and progression, assessing the efficacy of therapeutics, and providing reliable and valid research outcomes. Recent Advances: In 2016, Lanier et al. proposed a new in vivo patient model, the Northwestern Abdominoplasty Scar Model, that overcomes the prior limitations of both animal and human models, with greater representativeness of the human scarring process, expedited recruitment, smaller sample requirements, and greater flexibility in the types and number of interventions that can be studied simultaneously. Critical Issues: Existing animal models suffer from limitations that impede generalization to human scars. Human scar studies are difficult to conduct and rarely used due to recruitment difficulties, ethical concerns regarding purposeful wounding, and inherent variability based on location, type of scar, and the heterogeneity of the host response between humans. Although overcoming many of these hurdles, the Northwestern Abdominoplasty Scar Model still has a few limitations. In addition, there remains a need for further study of and comparison between the Northwestern Abdominoplasty Scar Model and existing human and animal models, to inspire more widespread acceptance of a standardized human scar model. Future Directions: The Northwestern Abdominoplasty Scar Model is a critical stepping stone toward better human scar models. This model hopefully will inspire other in vivo patient models utilizing elective surgery to overcome recruitment and ethical concerns.

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.