Canards in advection-reaction-diffusion systems in one spatial dimension

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions. The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

An analysis of exosomes from keratinocytes and fibroblasts

In recent years, many studies have provided evidence that exosomes secreted by cells contain various components, including microRNAs [1]. It is thought that exosomes have important roles in many biological processes. However, the role of exosomes and their components, especially miRNAs, in wound healing is poorly understood. In order to understand whether or not primary human epidermal keratinocytes and dermal fibroblasts, two important cell types contributing to wound healing process, release exosomes and what species of wound healing-associated miRNAs accumulate in these vesicles, this project will use a combination of methods to isolate and characterize exosomes, to profile exosomal cargo’s, especially miRNAs in exosomes. The results showed that keratinocytes and fibroblasts released exosomes into conditioned media and these exosomes contain some target miRNAs.

An Australian native plant: A novel antimicrobial for the treatment of MRSA

Chronic wounds, often associated with venous and arterial ulcers, diabetes and pressure sores, is an area of great concern. In Australia, the cost of treating chronic wounds is conservatively estimated at $285 million/annum for the treatment of pressure ulcers and $654 million annually for the treatment and management of leg ulcers. Current figures indicate that more than seven million people suffer from chronic wounds worldwide with Australians accounting for approximately 600,000 of this number. Bacterial infection of the wound site is a major issue as contamination of a chronic wound with methicillin-resistant Staphylococcus aureus (MRSA) significantly delays wound healing. Further, once systemic, current antibiotic therapies capable of treating the infection are limited. Aboriginal bush medicine has been used for thousands of years for the treatment of wounds and sores. Hence, we selected a native Australian plant to evaluate its bactericidal activity against MRSA.

The role of inflammation in cutaneous repair

Inflammation is a fundamental component of the normal adult wound healing response occurring even in the absence of infection. It performs many beneficial roles such as the clearing of damaged cells and extracellular matrix (ECM), the removal of pathogens that might other wise multiply and spread, and the secretion of mediators that regulate other aspects of wound healing such as proliferation, re-epithelialisation and wound remodelling. Yet, excess and/or prolonged inflammation is detrimental to wound healing and leads to increased fibrosis and scarring, which can be disfiguring and, in cases such as contractures, can lead to disability. Furthermore, excessive inflammation is a major contributing factor to the persistence of chronic non-healing wounds, which are “stuck” in the inflammatory phase of healing and fail to reepithelialise. Current research suggest that the type of immune cells, their timing and the level of inflammation in a wound could have dramatic effect on whether a wound heals in a timely fashion and the final quality of the repaired tissue. Studies suggest that altering the level of inflammation might be beneficial in terms of reducing scarring and improving the rate of healing in chronic wounds. This review looks at the role of the major immune cells in normal and impaired wound healing and strategies that might be used to reduce inflammation in wounds.

Identifying relationships between symptom clusters and quality of life in adults with chronic mixed venous and arterial leg ulcers

The objective of this study was to identify symptom clusters and their effect on quality of life (QOL) of adults with chronic leg ulcers of mixed venous and arterial aetiology. A secondary analysis of data from four existing prospective longitudinal studies conducted by a wound healing research group in Australia was undertaken. A total of 110 patients who met the inclusion criteria were selected for this study. Exploratory factor analysis (EFA) was used to identify symptom clusters and correlational analyses to examine relationships between the identified symptom clusters and QOL. The EFA identified two distinct symptom clusters: a 'systemic symptom cluster' consisting of pain, fatigue and depressive symptoms; and a 'localised-leg symptom cluster' including pain, fatigue, oedema, lower limb inflammation and exudate. Physical QOL correlated significantly with the systemic symptom cluster (r = -0·055, P < 0·0001) and the localised-leg symptom cluster (r = -0·054, P < 0·0001), whereas mental QOL was associated only with the systemic symptom cluster (r = -0·038, P = 0·01). The results suggest that appropriate intervention strategies targeting specific symptom clusters should be developed. Targeting patients with symptom clusters is particularly important because they are at high risk and the most vulnerable for reduced QOL.

Mathematical models for collective cell spreading

Collective cell spreading is frequently observed in development, tissue repair and disease progression. Mathematical modelling used in conjunction with experimental investigation can provide key insights into the mechanisms driving the spread of cell populations. In this study, we investigated how experimental and modelling frameworks can be used to identify several key features underlying collective cell spreading. In particular, we were able to independently quantify the roles of cell motility and cell proliferation in a spreading cell population, and investigate how these roles are influenced by factors such as the initial cell density, type of cell population and the assay geometry.

Targeting EMT in cancer: opportunities for pharmacological intervention

•EMT is important for embryonic development, wound healing, and placentation. •Some cancers appear to exploit this process for increased metastatic potential. •Therefore, this pathway is of great therapeutic interest in the treatment of cancer. The spread of cancer cells to distant organs represents a major clinical challenge in the treatment of cancer. Epithelial–mesenchymal transition (EMT) has emerged as a key regulator of metastasis in some cancers by conferring an invasive phenotype. As well as facilitating metastasis, EMT is thought to generate cancer stem cells and contribute to therapy resistance. Therefore, the EMT pathway is of great therapeutic interest in the treatment of cancer and could be targeted either to prevent tumor dissemination in patients at high risk of developing metastatic lesions or to eradicate existing metastatic cancer cells in patients with more advanced disease. In this review, we discuss approaches for the design of EMT-based therapies in cancer, summarize evidence for some of the proposed EMT targets, and review the potential advantages and pitfalls of each approach

Multiphasic scaffolds for periodontal tissue engineering

For a successful clinical outcome, periodontal regeneration requires the coordinated response of multiple soft and hard tissues (periodontal ligament, gingiva, cementum, and bone) during the wound-healing process. Tissue-engineered constructs for regeneration of the periodontium must be of a complex 3-dimensional shape and adequate size and demonstrate biomechanical stability over time. A critical requirement is the ability to promote the formation of functional periodontal attachment between regenerated alveolar bone, and newly formed cementum on the root surface. This review outlines the current advances in multiphasic scaffold fabrication and how these scaffolds can be combined with cell- and growth factor-based approaches to form tissue-engineered constructs capable of recapitulating the complex temporal and spatial wound-healing events that will lead to predictable periodontal regeneration. This can be achieved through a variety of approaches, with promising strategies characterized by the use of scaffolds that can deliver and stabilize cells capable of cementogenesis onto the root surface, provide biomechanical cues that encourage perpendicular alignment of periodontal fibers to the root surface, and provide osteogenic cues and appropriate space to facilitate bone regeneration. Progress on the development of multiphasic constructs for periodontal tissue engineering is in the early stages of development, and these constructs need to be tested in large animal models and, ultimately, human clinical trials.

Characteristics of microbial drug resistance and its correlates in chronic diabetic foot ulcer infections

While virulence factors and the biofilm-forming capabilities of microbes are the key regulators of the wound healing process, the host immune response may also contribute in the events following wound closure or exacerbation of non-closure. We examined samples from diabetic and non-diabetic foot ulcers/wounds for microbial association and tested the microbes for their antibiotic susceptibility and ability to produce biofilms. A total of 1074 bacterial strains were obtained with staphylococci, Pseudomonas, Citrobacter and enterococci as major colonizers in diabetic samples. Though non-diabetic samples had a similar assemblage, the frequency of occurrence of different groups of bacteria was different. Gram-negative bacteria were found to be more prevalent in the diabetic wound environment while Gram-positive bacteria were predominant in non-diabetic ulcers. A higher frequency of monomicrobial infection was observed in samples from non-diabetic individuals when compared to samples from diabetic patients. The prevalence of different groups of bacteria varied when the samples were stratified according to age and sex of the individuals. Several multidrug-resistant strains were observed among the samples tested and most of these strains produced moderate to high levels of biofilms. The weakened immune response in diabetic individuals and synergism among pathogenic micro-organisms may be the critical factors that determine the delicate balance of the wound healing process.

Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Background: Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model. Results: The Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF. Conclusions: Our approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.

Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

The 2015 IWGDF guidance documents on prevention and management of foot problems in diabetes: Development of an evidence-based global consensus

Foot problems complicating diabetes are a source of major patient suffering and societal costs. Investing in evidence-based, internationally appropriate diabetic foot care guidance is likely among the most cost-effective forms of healthcare expenditure, provided it is goal-focused and properly implemented. The International Working Group on the Diabetic Foot (IWGDF) has been publishing and updating international Practical Guidelines since 1999. The 2015 updates are based on systematic reviews of the literature, and recommendations are formulated using the Grading of Recommendations Assessment Development and Evaluation system. As such, we changed the name from 'Practical Guidelines' to 'Guidance'. In this article we describe the development of the 2015 IWGDF Guidance documents on prevention and management of foot problems in diabetes. This Guidance consists of five documents, prepared by five working groups of international experts. These documents provide guidance related to foot complications in persons with diabetes on: prevention; footwear and offloading; peripheral artery disease; infections; and, wound healing interventions. Based on these five documents, the IWGDF Editorial Board produced a summary guidance for daily practice. The resultant of this process, after reviewed by the Editorial Board and by international IWGDF members of all documents, is an evidence-based global consensus on prevention and management of foot problems in diabetes. Plans are already under way to implement this Guidance. We believe that following the recommendations of the 2015 IWGDF Guidance will almost certainly result in improved management of foot problems in persons with diabetes and a subsequent worldwide reduction in the tragedies caused by these foot problems.

The Use of Mesenchymal Stromal Cells in the Treatment of Diseases of the Cornea

As a key component of the ocular surface required for vision, the cornea has been extensively studied as a site for cell and tissue-based therapies. Historically, these treatments have consisted of donor corneal tissue transplants, but cultivated epithelial autografts have become established over the last 15 years as a routine treatment for ocular surface disease. Ultimately, these treatments are performed with the intention of restoring corneal transparency and a smooth ocular surface. The degree of success, however, is often dependent upon the inherent level of corneal inflammation at time of treatment. In this regard, the anti-inflammatory and immuno-modulatory properties of mesenchymal stromal cells (MSC) have drawn attention to these cells as potential therapeutic agents for corneal repair. The origins for MSC-based therapies are founded in part on observations of the recruitment of endogenous bone marrow-derived cells to injured corneas, however, an increasing quantity of data is emerging for MSC administered following their isolation and ex vivo expansion from a variety of tissues including bone marrow, adipose tissue, umbilical cord and dental pulp. In brief, evidence has emerged of cultured MSC, or their secreted products, having a positive impact on corneal wound healing and retention of corneal allografts in animal models. Optimal dosage, route of administration and timing of treatment, however, all remain active areas of investigation. Intriguingly, amidst these studies, have emerged reports of MSC transdifferentiation into corneal cells. Clearest evidence has been obtained with respect to expression of markers associated with the phenotype of corneal stromal cells. In contrast, the evidence for MSC conversion to corneal epithelial cell types remains inconclusive. In any case, the conversion of MSC into corneal cells seems unlikely to be an essential requirement for their clinical use. This field of research has recently become more complicated by reports of MSC-like properties for cultures established from the peripheral corneal stroma (limbal stroma). The relationship and relative value of corneal-MSC compared to traditional sources of MSC such as bone marrow are at present unclear. This chapter is divided into four main parts. After providing a concise overview of corneal structure and function, we will highlight the types of corneal diseases that are likely to benefit from the anti-inflammatory and immuno-modulatory properties of MSC. We will subsequently summarize the evidence supporting the case for MSC-based therapies in the treatment of corneal diseases. In the third section we will review the literature concerning the keratogenic potential of MSC. Finally, we will review the more recent literature indicating the presence of MSC-like cells derived from corneal tissue.

Evaluation of the AlgerBrush II rotating burr as a tool for inducing ocular surface failure in the New Zealand White rabbit

The New Zealand White rabbit has been widely used as a model of limbal stem cell deficiency (LSCD). Current techniques for experimental induction of LSCD utilize caustic chemicals, or organic solvents applied in conjunction with a surgical limbectomy. While generally successful in depleting epithelial progenitors, the depth and severity of injury is difficult to control using chemical-based methods. Moreover, the anterior chamber can be easily perforated while surgically excising the corneal limbus. In the interest of creating a safer and more defined LSCD model, we have therefore evaluated a mechanical debridement technique based upon use of the AlgerBrush II rotating burr. An initial comparison of debridement techniques was conducted in situ using 24 eyes in freshly acquired New Zealand White rabbit cadavers. Techniques for comparison (4 eyes each) included: (1) non-wounded control, (2) surgical limbectomy followed by treatment with 100% (v/v) n-heptanol to remove the corneal epithelium (1-2 minutes), (3) treatment of both limbus and cornea with n-heptanol alone, (4) treatment of both limbus and cornea with 20% (v/v) ethanol (2-3 minutes), (5) a 2.5-mm rounded burr applied to both the limbus and cornea, and (6) a 1-mm pointed burr applied to the limbus, followed by the 2.5-mm rounded burr applied to the cornea. All corneas were excised and processed for histology immediately following debridement. A panel of four assessors subsequently scored the degree of epithelial debridement within the cornea and limbus using masked slides. The 2.5-mm burr most consistently removed the corneal and limbal epithelia. Islands of limbal epithelial cells were occasionally retained following surgical limbectomy/heptanol treatment, or use of the 1-mm burr. Limbal epithelial cells were consistently retained following treatment with either ethanol or n-heptanol alone, with ethanol being the least effective treatment overall. The 2.5-mm burr method was subsequently evaluated in the right eye of 3 live rabbits by weekly clinical assessments (photography and slit lamp examination) for up to 5 weeks, followed by histological analyses (hematoxylin & eosin stain, periodic acid-Schiff stain and immunohistochemistry for keratin 3 and 13). All 3 eyes that had been completely debrided using the 2.5-mm burr displayed symptoms of ocular surface failure as defined by retention of a prominent epithelial defect (~40% of corneal surface at 5 weeks), corneal neovascularization (2 to 3 quadrants), reduced corneal transparency and conjunctivalization of the corneal surface (demonstrated by the presence of goblet cells and/or staining for keratin 13). In conclusion, our findings indicate that the AlgerBrush II rotating burr is an effective method for the establishment of ocular surface failure in New Zealand White rabbits. In particular, we recommend use of the 2.5-mm rotating burr for improved efficiency of epithelial debridement and safety compared to surgical limbectomy.