An ordinary differential equation model for full thickness wounds and the effects of diabetes

Understanding the ideal wound healing mechanistic behavior using in silico modelling perspectives: A review

Complexity of the entire body precludes an accurate assessment of the specific contributions of tissues or cells during the healing process, which might be expensive and time consuming. Because of this, controlling the wound's size, depth, and dimensions may be challenging, and there is not yet an efficient and reliable chronic wound model representation. Furthermore, given the inherent challenges associated with conducting non-invasive in vivo investigations, it becomes peremptory to explore alternative methodologies for studying wound healing. In this context, biologically-realistic mathematical and computational models emerge as a valuable framework that can effectively address this need. Therefore, it might improve our approach to understanding the process at its core. This article will examines all facets of wound healing, including the kinds, pathways, and most current developments in wound treatment worldwide, particularly in silico modelling utilizing both mathematical and structure-based modelling techniques. It may be helpful to identify the crucial traits through the feedback loop of computer models and experimental investigations in order to build innovative therapies to cure wounds. Hence the effectiveness of personalised medicine and more targeted therapy in the healing of wounds may be enhanced by this interdisciplinary expertise.

Chronic wounds: Treatment consensus

The Wound Healing Foundation (WHF) recognised a need for an unbiased consensus on the best treatment of chronic wounds. A panel of 13 experts were invited to a virtual meeting which took place on 27 March 2021. The proceedings were organised in the sub-sections diagnosis, debridement, infection control, dressings, grafting, pain management, oxygen treatment, outcomes and future needs. Eighty percent or better concurrence among the panellists was considered a consensus. A large number of critical questions were discussed and agreed upon. Important takeaways included that wound care needs to be simplified to a point that it can be delivered by the patient or the patient's family. Another one was that telemonitoring, which has proved very useful during the COVID-19 pandemic, can help reduce the frequency of interventions by a visiting nurse or a wound care center. Defining patient expectations is critical to designing a successful treatment. Patient outcomes might include wound specific outcomes such as time to heal, wound size reduction, as well as improvement in quality of life. For those patients with expectations of healing, an aggressive approach to achieve that goal is recommended. When healing is not an expectation, such as in patients receiving palliative wound care, outcomes might include pain reduction, exudate management, odour management and/or other quality of life benefits to wound care.

Mathematical Model Predicts that Acceleration of Diabetic Wound Healing is Dependent on Spatial Distribution of VEGF-A mRNA (AZD8601)

Introduction

Pharmacologic approaches for promoting angiogenesis have been utilized to accelerate healing of chronic wounds in diabetic patients with varying degrees of success. We hypothesize that the distribution of proangiogenic drugs in the wound area critically impacts the rate of closure of diabetic wounds. To evaluate this hypothesis, we developed a mathematical model that predicts how spatial distribution of VEGF-A produced by delivery of a modified mRNA (AZD8601) accelerates diabetic wound healing.

Methods

We modified a previously published model of cutaneous wound healing based on coupled partial differential equations that describe the density of sprouting capillary tips, chemoattractant concentration, and density of blood vessels in a circular wound. Key model parameters identified by a sensitivity analysis were fit to data obtained from an in vivo wound healing study performed in the dorsum of diabetic mice, and a pharmacokinetic model was used to simulate mRNA and VEGF-A distribution following injections with AZD8601. Due to the limited availability of data regarding the spatial distribution of AZD8601 in the wound bed, we performed simulations with perturbations to the location of injections and diffusion coefficient of mRNA to understand the impact of these spatial parameters on wound healing.

Results

When simulating injections delivered at the wound border, the model predicted that injections delivered on day 0 were more effective in accelerating wound healing than injections delivered at later time points. When the location of the injection was varied throughout the wound space, the model predicted that healing could be accelerated by delivering injections a distance of 1–2 mm inside the wound bed when compared to injections delivered on the same day at the wound border. Perturbations to the diffusivity of mRNA predicted that restricting diffusion of mRNA delayed wound healing by creating an accumulation of VEGF-A at the wound border. Alternatively, a high mRNA diffusivity had no effect on wound healing compared to a simulation with vehicle injection due to the rapid loss of mRNA at the wound border to surrounding tissue.

Conclusions

These findings highlight the critical need to consider the location of drug delivery and diffusivity of the drug, parameters not typically explored in pre-clinical experiments, when designing and testing drugs for treating diabetic wounds.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-021-00678-9.

Magnetic fields as a potential therapy for diabetic wounds based on animal experiments and clinical trials

Diabetes mellitus (DM) is a chronic metabolic disorder with various complications that poses a huge worldwide healthcare burden. Wounds in diabetes, especially diabetic foot ulcers (DFUs), are difficult to manage, often leading to prolonged wound repair and even amputation. Wound management in people with diabetes is an extremely clinical and social concern. Nowadays, physical interventions gain much attention and have been widely developed in the fields of tissue regeneration and wound healing. Magnetic fields (MFs)-based devices are translated into clinical practice for the treatment of bone diseases and neurodegenerative disorder. This review attempts to give insight into the mechanisms and applications of MFs in wound care, especially in improving the healing outcomes of diabetic wounds. First, we discuss the pathological conditions associated with chronic diabetic wounds. Next, the mechanisms involved in MFs' effects on wounds are explored. At last, studies and reports regarding the effects of MFs on diabetic wounds from both animal experiments and clinical trials are reviewed. MFs exhibit great potential in promoting wound healing and have been practised in the management of diabetic wounds. Further studies on the exact mechanism of MFs on diabetic wounds and the development of suitable MF-based devices could lead to their increased applications into clinical practice.

Model-Based Analysis Reveals a Sustained and Dose-Dependent Acceleration of Wound Healing by VEGF-A mRNA (AZD8601)

Intradermal delivery of AZD8601, an mRNA designed to produce vascular endothelial growth factor A (VEGF‐A), has previously been shown to accelerate cutaneous wound healing in a murine diabetic model. Here, we develop population pharmacokinetic and pharmacodynamic models aiming to quantify the effect of AZD8601 injections on the dynamics of wound healing. A dataset of 584 open wound area measurements from 131 mice was integrated from 3 independent studies encompassing different doses, dosing timepoints, and number of doses. Evaluation of several candidate models showed that wound healing acceleration is not likely driven directly by time‐dependent VEGF‐A concentration. Instead, we found that administration of AZD8601 induced a sustained acceleration of wound healing depending on the accumulated dose, with a dose producing 50% of the maximal effect of 92 µg. Simulations with this model showed that a single dose of 200 µg AZD8601 can reduce the time to reach 50% wound healing by up to 5 days.

A Bayesian Sequential Learning Framework to Parameterise Continuum Models of Melanoma Invasion into Human Skin

We present a novel framework to parameterise a mathematical model of cell invasion that describes how a population of melanoma cells invades into human skin tissue. Using simple experimental data extracted from complex experimental images, we estimate three model parameters: (i) the melanoma cell proliferation rate, [Formula: see text]; (ii) the melanoma cell diffusivity, D; and (iii) [Formula: see text], a constant that determines the rate that melanoma cells degrade the skin tissue. The Bayesian sequential learning framework involves a sequence of increasingly sophisticated experimental data from: (i) a spatially uniform cell proliferation assay; (ii) a two-dimensional circular barrier assay; and (iii) a three-dimensional invasion assay. The Bayesian sequential learning approach leads to well-defined parameter estimates. In contrast, taking a naive approach that attempts to estimate all parameters from a single set of images from the same experiment fails to produce meaningful results. Overall, our approach to inference is simple-to-implement, computationally efficient, and well suited for many cell biology phenomena that can be described by low-dimensional continuum models using ordinary differential equations and partial differential equations. We anticipate that this Bayesian sequential learning framework will be relevant in other biological contexts where it is challenging to extract detailed, quantitative biological measurements from experimental images and so we must rely on using relatively simple measurements from complex images.

A two-phase model of early fibrous cap formation in atherosclerosis

Atherosclerotic plaque growth is characterised by chronic, non-resolving inflammation that promotes the accumulation of cellular debris and extracellular fat in the inner artery wall. This material is highly thrombogenic, and plaque rupture can lead to the formation of blood clots that occlude major arteries and cause myocardial infarction or stroke. In advanced plaques, vascular smooth muscle cells (SMCs) are recruited from deeper in the artery wall to synthesise a cap of fibrous tissue that stabilises the plaque and sequesters the thrombogenic plaque content from the bloodstream. The fibrous cap provides crucial protection against the clinical consequences of atherosclerosis, but the mechanisms of cap formation are poorly understood. In particular, it is unclear why certain plaques become stable and robust while others become fragile and dangerously vulnerable to rupture. We develop a multiphase model with non-standard boundary conditions to investigate early fibrous cap formation in the atherosclerotic plaque. The model is parameterised using data from a range of in vitro and in vivo studies, and includes highly nonlinear mechanisms of SMC proliferation and migration in response to an endothelium-derived chemical signal. We demonstrate that the model SMC population naturally evolves towards a steady-state, and predict a rate of cap formation and a final plaque SMC content consistent with experimental observations in mice. Parameter sensitivity simulations show that SMC proliferation makes a limited contribution to cap formation, and demonstrate that stable cap formation relies primarily on a critical balance between the rates of SMC recruitment to the plaque, chemotactic SMC migration within the plaque and SMC loss by apoptosis or phenotype change. This model represents the first detailed in silico study of fibrous cap formation in atherosclerosis, and establishes a multiphase modelling framework that can be readily extended to investigate many other aspects of plaque development.

Applicability of Isolates and Fractions of Plant Extracts in Murine Models in Type II Diabetes: A Systematic Review

Type II diabetes mellitus is one of the most common public health problems worldwide. Its increasing prevalence in several countries and the difficult metabolic control of individuals with the disease justify studying strategies for primary prevention. The population has sought alternative and cheaper ways to treat the disease, including the use of plants considered medicinal by the population. In this study, we carried out a systematic review on the applicability of isolates and fractions of plant extracts in animal models in type II diabetes. A literature search was performed in MEDLINE/PubMed and Scopus databases. Studies using other experimental animals (horses, rabbits, and monkeys) and humans as well as articles in Chinese, German, and Russian were excluded. We assessed the quality of the studies included by using the criteria described in the ARRIVE guidelines. In general, the animals that received fractions or isolates presented reduced blood glucose levels, normalization of body weight and plasma insulin levels, and reduced total triglycerides and cholesterol. In addition, we observed wide variation among the analyzed parameters, which hindered comparison between the studies found. In further studies, standardized reports and experimental design would help to establish comparable study groups and advance the overall knowledge, thus facilitating translatability from animal data to human clinical conditions.

Effect of Topical Administration of Fractions and Isolated Molecules from Plant Extracts on Skin Wound Healing: A Systematic Review of Murine Experimental Models

Background and Purpose. Skin wound healing is a dynamic process driven by molecular events responsible for the morphofunctional repair of the injured tissue. In a systematic review, we analyzed the relevance of plant fractions and isolates on skin wound healing. By revising preclinical investigations with murine models, we investigated if the current evidence could support clinical trials. Methods. Studies were selected in the MEDLINE/PubMed and Scopus databases according to the PRISMA statement. All 32 identified studies were submitted to data extraction and the methodological bias was investigated according to ARRIVE strategy. Results. The studies demonstrated that plant fractions and isolates are able to modulate the inflammatory process during skin wound healing, being also effective in attenuating the oxidative tissue damage in the scar tissue and stimulating cell proliferation, neoangiogenesis, collagen synthesis, granulation tissue expansion, reepithelialization, and the wound closure rate. However, we identified serious methodological flaws in all studies, such as the high level of reporting bias and absence of standardized experimental designs, analytical methods, and outcome measures. Conclusion. Considering these limitations, the current evidence generated from flawed methodological animal studies makes it difficult to determine the relevance of herbal medicines to treat skin wounds and derails conducting clinical studies.

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.