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.

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

Numerical models have become one of the most powerful tools in biomechanics and mechanobiology allowing highly detailed simulations. One of the fields in which they have broadly evolved during the last years is in soft tissue modeling. Particularly, wound healing in the skin is one of the processes that has been approached by computational models due to the difficulty of performing experimental investigations. During the last decades wound healing simulations have evolved from numerical models which considered only a few number of variables and simple geometries to more complex approximations that take into account a higher number of factors and reproduce more realistic geometries. Moreover, thanks to improved experimental observations, a larger number of processes, such as cellular stress generation or vascular growth, that take place during wound healing have been identified and modeled. This work presents a review of the most relevant wound healing approximations, together with an identification of the most relevant criteria that can be used to classify them. In addition, and looking towards the actual state of the art in the field, some future directions, challenges and improvements are analyzed for future developments.

Nonlinear finite element simulations of injuries with free boundaries: application to surgical wounds.

Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds.

Numerical modelling of the angiogenesis process in wound contraction.

Angiogenesis consists of the growth of new blood vessels from the pre-existing vasculature. This phenomenon takes place in several biological processes, including wound healing. In this work, we present a mathematical model of angiogenesis applied to skin wound healing. The developed model includes biological (capillaries and fibroblasts), chemical (oxygen and angiogenic growth factor concentrations) and mechanical factors (cell traction forces and extracellular matrix deformation) that influence the evolution of the healing process. A novelty from previous works, apart from the coupling of angiogenesis and wound contraction, is the more realistic modelling of skin as a hyperelastic material. Large deformations are addressed using an updated Lagrangian approach. The coupled non-linear model is solved with the finite element method, and the process is studied over two wound geometries (circular and elliptical) of the same area. The results indicate that the elliptical wound vascularizes two days earlier than the circular wound but that they experience a similar contraction level, reducing its size by 25 %.

A finite-element model for healing of cutaneous wounds combining contraction, angiogenesis and closure.

A simplified finite-element model for wound healing is proposed. The model takes into account the sequential steps of dermal regeneration, wound contraction, angiogenesis and wound closure. An innovation in the present study is the combination of the aforementioned partially overlapping processes, which can be used to deliver novel insights into the process of wound healing, such as geometry related influences, as well as the influence of coupling between the various existing subprocesses on the actual healing behavior. The model confirms the clinical observation that epidermal closure proceeds by a crawling and climbing mechanism at the early stages, and by a stratification process in layers parallel to the skin surface at the later stages. The local epidermal oxygen content may play an important role here. The model can also be used to investigate the influence of local injection of hormones that stimulate partial processes occurring during wound healing. These insights can be used to improve wound healing treatments.

Computer simulations from a finite-element model for wound contraction and closure.

Some implications from a simplified finite-element model are given in this study. The model takes into account the sequential steps of wound contraction, angiogenesis and wound closure. An innovation in the present study is the combination of these partially overlapping processes, yielding novel insights into the process of wound healing, such as geometry related influences, and could be used to investigate the influence of local injection of hormones that stimulate partial processes occurring during wound healing. These insights can be used to improve wound-healing treatments. The model consists of nonlinearly coupled diffusion-reaction and visco-elastic equations, in which transport, production and decay of oxygen, growth factors and various cell types. The present paper provides results of the healing of deep wounds under several regimes of endothelial and epithelial cell migration, and the results are interpreted in a biological sense.

A mathematical analysis of physiological and morphological aspects of wound closure.

A computational algorithm to study the evolution of complex wound morphologies is developed based on a model of wound closure by cell mitosis and migration due to Adam [Math Comput Model 30(5-6):23-32, 1999]. A detailed analysis of the model provides estimated values for the incubation and healing times. Furthermore, a set of inequalities are defined which demarcate conditions of complete, partial and non-healing. Numerical results show a significant delay in the healing progress whenever diffusion of the epidermic growth factor responsible for cell mitosis is slower than cell migration. Results for general wound morphologies show that healing is always initiated at regions with high curvatures and that the evolution of the wound is very sensitive to physiological parameters.