Mathematical modelling of chronic wound healing

Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.

A longitudinal assessment of chronic wound fluid to detect biochemical indicators of healing

Chronic venous leg ulcers are a detrimental health issue plaguing our society, resulting in long term pain, immobility and decreased quality of life for a large proportion of sufferers. The frequency of these chronic wounds has led current research to focus on the wound environment to provide important information regarding the prolonged, fluctuated or static healing patterns of these wounds. Disruption to the normal wound healing process results in release of multiple factors in the wound environment that could correlate to wound chronicity. These biochemical factors can often be detected through non-invasively sampling chronic wound fluid (CWF) from the site of injury. Of note, whilst there are numerous studies comparing acute and chronic wound fluids, there have not been any reports in the literature employing a longitudinal study in order to track biochemical changes in wound fluid as patients transition from a non-healing to healed state. Initially the objective of this study was to identify biochemical changes in CWF associated with wound healing using a proteomic approach. The proteomic approach incorporated a multi-dimensional liquid chromatography fractionation technique coupled with mass spectrometry (MS) to enable identification of proteins present in lower concentrations in CWF. Not surprisingly, many of the proteins identified in wound fluid were acute phase proteins normally expressed during the inflammatory phase of healing. However, the number of proteins positively identified by MS was quite low. This was attributed to the diverse range in concentration of protein species in CWF making it challenging to detect the diagnostically relevant low molecular weight proteins. In view of this, SELDI-TOF MS was also explored as a means to target low molecular weight proteins in sequential patient CWF samples during the course of healing. Unfortunately, the results generated did not yield any peaks of interest that were altered as wounds transitioned to a healed state. During the course of proteomic assessment of CWF, it became evident that a fraction of non-proteinaceous compounds strongly absorbed at 280 nm. Subsequent analyses confirmed that most of these compounds were in fact part of the purine catabolic pathway, possessing distinctive aromatic rings and which results in high absorbance at 254 nm. The accumulation of these purinogenic compounds in CWF suggests that the wound bed is poorly oxygenated resulting in a switch to anaerobic metabolism and consequently ATP breakdown. In addition, the presence of the terminal purine catabolite, uric acid (UA), indicates that the enzyme xanthine oxidoreductase (XOR) catalyses the reaction of hypoxanthine to xanthine and finally to UA. More importantly, the studies provide evidence for the first time of the exogenous presence of XOR in CWF. XOR is the only enzyme in humans capable of catalysing the production of UA in conjunction with a burst of the highly reactive superoxide radical and other oxidants like H2O2. Excessive release of these free radicals in the wound environment can cause cellular damage disrupting the normal wound healing process. In view of this, a sensitive and specific assay was established for monitoring low concentrations of these catabolites in CWF. This procedure involved combining high performance liquid chromatography (HPLC) with tandem mass spectrometry and multiple reaction monitoring (MRM). This application was selective, using specific MRM transitions and HPLC separations for each analyte, making it ideal for the detection and quantitation of purine catabolites in CWF. The results demonstrated that elevated levels of UA were detected in wound fluid obtained from patients with clinically worse ulcers. This suggests that XOR is active in the wound site generating significant amounts of reactive oxygen species (ROS). In addition, analysis of the amount of purine precursors in wound fluid revealed elevated levels of purine precursors in wound fluid from patients with less severe ulcers. Taken together, the results generated in this thesis suggest that monitoring changes of purine catabolites in CWF is likely to provide valuable information regarding the healing patterns of chronic venous leg ulcers. XOR catalysis of purine precursors not only provides a method for monitoring the onset, prognosis and progress of chronic venous leg ulcers, but also provides a potential therapeutic target by inhibiting XOR, thus blocking UA and ROS production. Targeting a combination of these purinogenic compounds and XOR could lead to the development of novel point of care diagnostic tests. Therefore, further investigation of these processes during wound healing will be worthwhile and may assist in elucidating the pathogenesis of this disease state, which in turn may lead to the development of new diagnostics and therapies that target these processes.

Biochemical profiling of proteins and metabolites in wound exudate from chronic wound environments

The lack of fundamental knowledge on the biological processes associated with wound healing represents a significant challenge. Understanding the biochemical changes that occur within a chronic wound could provide insights into the wound environment and enable more effective wound management. We report on the stability of wound fluid samples under various conditions and describe a high-throughput approach to investigate the altered biochemical state within wound samples collected from various types of chronic, ulcerated wounds. Furthermore, we discuss the viability of this approach in the early stages of wound sample protein and metabolite profiling and subsequent biomarker discovery. This approach will facilitate the detection of factors that may correlate with wound severity and/or could be used to monitor the response to a particular treatment.

Proteomics in chronic wound research : potentials in healing and health

Chronic wounds, such as venous and diabetic leg ulcers, represent a significant health and financial burden to individuals and healthcare systems. In worst case scenarios this condition may require the amputation of an affected limb, with significant impact on patient quality of life and health. Presently there are no clinical biochemical analyses used in the diagnosis and management of this condition; moreover few biochemical therapies are accessible to patients. This presents a significant challenge in the efficient and efficacious treatment of chronic wounds by medical practitioners. A number of protein-centric investigations have analysed the wound environment and implicated a suite of molecular species predicted to be involved in the initiation or perpetuation of the condition. However, comprehensive proteomic investigation is yet to be engaged in the analysis of chronic wounds for the identification of molecular diagnostic/prognostic markers of healing or therapeutic targets. This review examines clinical chronic wound research and recommends a path towards proteomic investigation for the discovery of medically significant targets. Additionally, the supplementary documents associated with this review provide the first comprehensive summary of protein-centric, small molecule and elemental analyses in clinical chronic wound research.

Ex vivo investigation of novel wound healing therapies and development of a 3-D human skin equivalent wound model

It has previously been found that complexes comprised of vitronectin and growth factors (VN:GF) enhance keratinocyte protein synthesis and migration. More specifically, these complexes have been shown to significantly enhance the migration of dermal keratinocytes derived from human skin. In view of this, it was thought that these complexes may hold potential as a novel therapy for healing chronic wounds. However, there was no evidence indicating that the VN:GF complexes would retain their effect on keratinocytes in the presence of chronic wound fluid. The studies in this thesis demonstrate for the first time that the VN:GF complexes not only stimulate proliferation and migration of keratinocytes, but also these effects are maintained in the presence of chronic wound fluid in a 2-dimensional (2-D) cell culture model. Whilst the 2-D culture system provided insights into how the cells might respond to the VN:GF complexes, this investigative approach is not ideal as skin is a 3-dimensional (3-D) tissue. In view of this, a 3-D human skin equivalent (HSE) model, which reflects more closely the in vivo environment, was used to test the VN:GF complexes on epidermopoiesis. These studies revealed that the VN:GF complexes enable keratinocytes to migrate, proliferate and differentiate on a de-epidermalised dermis (DED), ultimately forming a fully stratified epidermis. In addition, fibroblasts were seeded on DED and shown to migrate into the DED in the presence of the VN:GF complexes and hyaluronic acid, another important biological factor in the wound healing cascade. This HSE model was then further developed to enable studies examining the potential of the VN:GF complexes in epidermal wound healing. Specifically, a reproducible partial-thickness HSE wound model was created in fully-defined media and monitored as it healed. In this situation, the VN:GF complexes were shown to significantly enhance keratinocyte migration and proliferation, as well as differentiation. This model was also subsequently utilized to assess the wound healing potential of a synthetic fibrin-like gel that had previously been demonstrated to bind growth factors. Of note, keratinocyte re-epitheliasation was shown to be markedly improved in the presence of this 3-D matrix, highlighting its future potential for use as a delivery vehicle for the VN:GF complexes. Furthermore, this synthetic fibrin-like gel was injected into a 4 mm diameter full-thickness wound created in the HSE, both keratinocytes and fibroblasts were shown to migrate into this gel, as revealed by immunofluorescence. Interestingly, keratinocyte migration into this matrix was found to be dependent upon the presence of the fibroblasts. Taken together, these data indicate that reproducible wounds, as created in the HSEs, provide a relevant ex vivo tool to assess potential wound healing therapies. Moreover, the models will decrease our reliance on animals for scientific experimentation. Additionally, it is clear that these models will significantly assist in the development of novel treatments, such as the VN:GF complexes and the synthetic fibrin-like gel described herein, ultimately facilitating their clinical trial in the treatment of chronic wounds.

A three species model to simulate application of hyperbaric oxygen therapy to chronic wounds

Chronic wounds are a significant socioeconomic problem for governments worldwide. Approximately 15% of people who suffer from diabetes will experience a lower-limb ulcer at some stage of their lives, and 24% of these wounds will ultimately result in amputation of the lower limb. Hyperbaric Oxygen Therapy (HBOT) has been shown to aid the healing of chronic wounds; however, the causal reasons for the improved healing remain unclear and hence current HBOT protocols remain empirical. Here we develop a three-species mathematical model of wound healing that is used to simulate the application of hyperbaric oxygen therapy in the treatment of wounds. Based on our modelling, we predict that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds. Furthermore, treatment should continue until healing is complete, and HBOT will not stimulate healing under all circumstances, leading us to conclude that finding the right protocol for an individual patient is crucial if HBOT is to be effective. We provide constraints that depend on the model parameters for the range of HBOT protocols that will stimulate healing. More specifically, we predict that patients with a poor arterial supply of oxygen, high consumption of oxygen by the wound tissue, chronically hypoxic wounds, and/or a dysfunctional endothelial cell response to oxygen are at risk of nonresponsiveness to HBOT. The work of this paper can, in some way, highlight which patients are most likely to respond well to HBOT (for example, those with a good arterial supply), and thus has the potential to assist in improving both the success rate and hence the costeffectiveness of this therapy.

Wound healing angiogenesis : the clinical implications of a simple mathematical model

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.

Sensors and imaging for wound healing : a review

Wound healing involves a complex series of biochemical events and has traditionally been managed with 'low tech' dressings and bandages. The concept that diagnostic and theranostic sensors can complement wound management is rapidly growing in popularity as there is tremendous potential to apply this technology to both acute and chronic wounds. Benefits in sensing the wound environment include reduction of hospitalization time, prevention of amputations and better understanding of the processes which impair healing. This review discusses the state-of-the-art in detection of markers associated with wound healing and infection, utilizing devices imbedded within dressings or as point-of-care techniques to allow for continual or rapid wound assessment and monitoring. Approaches include using biological or chemical sensors of wound exudates and volatiles to directly or indirectly detect bacteria, monitor pH, temperature, oxygen and enzymes. Spectroscopic and imaging techniques are also reviewed as advanced wound monitoring techniques. The review concludes with a discussion of the limitations of and future directions for this field.

The human dimension of nosocomial wound infection : a study in liminality

Nosocomial wound infection is a disease that has to date been primarily understood through the language of science and biomedicine. This paper reports on findings from a sociological, interpretive study that focused on the experiential dimension of this phenomenon. The illness experience of a nosocomial wound infection is examined within a cultural milieu that values the smooth, untroubled body and alternatively ascribes cultural meaning to a body that has a definable illness. Within this context the person with a chronic wound from nosocomial infection defies normative categorisation and is thus situated outside the patterning of society. The human dimension of nosocomial wound infection includes the private, existential and embodied aspects of living with a chronic, infected wound. This report indicates that the experiential dimension is characterised by an embodied state of liminality. People with this illness live an indeterminate existence that is in-between health and illness, cure and disease. As such they have no recognised place in the medical or social world.

Molecular profiling of exudate from chronic ulcerated wounds

Non-healing wounds represent a significant burden to healthcare systems and societies worldwide. Current best practice treatments of chronic wounds can require patients to undergo extensive periods of therapy without any positive outcome. This consumes substantial healthcare resources and severely impacts patient quality of life. At present, there are no measures to predict a patient's response to best practice care. The hypothesis of this thesis was that biochemical markers could be found within the wound fluid of chronic ulcers and these markers could predict the healing outcome of an ulcer undergoing best practice care. Discovery phase proteomic and mass spectrometry techniques were utilised to determine novel proteins that correlated with the healing outcome of ulcers. These candidate biomarkers could be developed into simple dip-stick tools for use in clinical practice. This would aid clinicians in the choice of effective wound management strategies to address hard-to-heal wounds.

Transdisciplinary collaboration in wound care research

The highly complex disorder of chronic wounds is a significant problem. Information is often lacking, dynamically changing, or contradictory and thus acts to impede the progression of research and its translation into clinical care. Transdisciplinary collaboration may play an important role in chronic wound research, permitting key stakeholders with a single, central goal to take a unified approach towards addressing the problem. While transdisciplinary collaboration is not a new concept, its implementation within chronic wound research is relatively new. This is because the research area is still largely dominated by single-discipline researchers or by multiple disciplines working in isolation. Transdisciplinary research is a transcending approach, requiring a greater level of understanding between disciplines and may represent the next leap forward in wound care research. This approach necessitates a deeper understanding by all team members of the co-disciplines involved; where key stakeholders are better equipped to respond to dynamic changes and problems that arise in chronic wound research. In this paper, we illustrate what a transdisciplinary approach in wound care research may entail, with the ultimate goal of such an undertaking to improve understanding of the complexities of wound care, which could lead to potential benefits in wound management.

A hydrogen tethered inhibitor of matrix metalloproteinases

During wound repair, the balance between matrix metalloproteinases (MMPs) and their natural inhibitors (the TIMPs) is crucial for the normal extra cellular matrix turnover. However, the over expression of several MMPs including MMP-1, 2, 3, 8, 9 and MMP-10, combined with abnormally high levels of activation or low expression of TIMPs, may contribute to excessive degradation of connective tissue and formation of chronic ulcers. There are many groups exploring strategies for promoting wound healing involving delivery of growth factors, cells, ECM components and small molecules. Our approach for improving the balance of MMPs is not to add anything more to the wound, but instead to neutralise the over-expressed MMPs using inhibitors tethered to a bandage-like hydrogel. Our in vitro experiments using designed synthetic pseudo peptide inhibitors have been demonstrated to inhibit MMP activity in standard solutions. These inhibitors have also been tethered to polyethylene glycol hydrogels using a facile reaction between the linker unit on the inhibitor and the gel. After tethering the inhibition of MMPs diminishes to some extent and we postulate that this arises due to poor diffusion of the MMPs into the gels. When the tethered inhibitors were tested against chronic wound fluid obtained against patients we observed over 40% inhibition in proteolytic activity suggesting our approach may prove useful in rebalancing MMPs within chronic wounds.