School of Mathematics and Statistics - Research Publications
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ItemNo Preview AvailableHow quickly does a wound heal? Bayesian calibration of a mathematical model of venous leg ulcer healing(OXFORD UNIV PRESS, 2022-12)Chronic wounds, such as venous leg ulcers, are difficult to treat and can reduce the quality of life for patients. Clinical trials have been conducted to identify the most effective venous leg ulcer treatments and the clinical factors that may indicate whether a wound will successfully heal. More recently, mathematical modelling has been used to gain insight into biological factors that may affect treatment success but are difficult to measure clinically, such as the rate of oxygen flow into wounded tissue. In this work, we calibrate an existing mathematical model using a Bayesian approach with clinical data for individual patients to explore which clinical factors may impact the rate of wound healing for individuals. Although the model describes group-level behaviour well, it is not able to capture individual-level responses in all cases. From the individual-level analysis, we propose distributions for coefficients of clinical factors in a linear regression model, but ultimately find that it is difficult to draw conclusions about which factors lead to faster wound healing based on the existing model and data. This work highlights the challenges of using Bayesian methods to calibrate partial differential equation models to individual patient clinical data. However, the methods used in this work may be modified and extended to calibrate spatiotemporal mathematical models to multiple data sets, such as clinical trials with several patients, to extract additional information from the model and answer outstanding biological questions.
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ItemMultiscale modelling of desquamation in the interfollicular epidermis(PUBLIC LIBRARY SCIENCE, 2022-08)Maintenance of epidermal thickness is critical to the barrier function of the skin. Decreased tissue thickness, specifically in the stratum corneum (the outermost layer of the tissue), causes discomfort and inflammation, and is related to several severe diseases of the tissue. In order to maintain both stratum corneum thickness and overall tissue thickness it is necessary for the system to balance cell proliferation and cell loss. Cell proliferation in the epidermis occurs in the basal layer and causes constant upwards movement in the tissue. Cell loss occurs when dead cells at the top of the tissue are lost to the environment through a process called desquamation. Desquamation is thought to occur through a gradual reduction in adhesion between cells, due to the cleaving of adhesion proteins by enzymes, in the stratum corneum. In this paper we will investigate combining a (mass action) subcellular model of desquamation with a three dimensional (cell centre based) multicellular model of the interfollicular epidermis to better understand maintenance of epidermal thickness. Specifically, our aim is to determine if a hypothesised biological model for the degradation of cell-cell adhesion, from the literature, is sufficient to maintain a steady state tissue thickness. These investigations show the model is able to provide a consistent rate of cell loss in the multicellular model. This loss balances proliferation, and hence maintains a homeostatic tissue thickness. Moreover, we find that multiple proliferative cell populations in the basal layer can be represented by a single proliferative cell population, simplifying investigations with this model. The model is used to investigate a disorder (Netherton Syndrome) which disrupts desquamation. The model shows how biochemical changes can cause disruptions to the tissue, resulting in a reduced tissue thickness and consequently diminishing the protective role of the tissue. A hypothetical treatment result is also investigated: we compare the cases of a partially effective homogeneous treatment (where all cells partially recover) and a totally effective heterogeneous treatment (in which a proportion of the cells totally recover) with the aim to determine the difference in the response of the tissue to these different scenarios. Results show an increased benefit to corneum thickness from the heterogeneous treatment over the homogeneous treatment.
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ItemModel Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility.(Frontiers Media SA, 2022)During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.
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ItemTraffic Patterns of the Migrating Endothelium: How Force Transmission Regulates Vascular Malformation and Functional Shunting During Angiogenic Remodelling(FRONTIERS MEDIA SA, 2022-05-19)Angiogenesis occurs in distinct phases: initial spouting is followed by remodelling in which endothelial cells (ECs) composing blood vessels rearrange by migrating against the direction of flow. Abnormal remodelling can result in vascular malformation. Such is the case in mutation of the Alk1 receptor within the mouse retina which disrupts flow-migration coupling, creating mixed populations of ECs polarised with/against flow which aggregate into arteriovenous malformations (AVMs). The lack of live imaging options in vivo means that the collective EC dynamics that drive AVM and the consequences of mixed populations of polarity remain a mystery. Therefore, our goal is to present a novel agent-based model to provide theoretical insight into EC force transmission and collective dynamics during angiogenic remodelling. Force transmission between neighbouring agents consists of extrusive forces which maintain spacing and cohesive forces which maintain the collective. We performed migration simulations within uniformly polarised populations (against flow) and mixed polarity (with/against flow). Within uniformly polarised populations, extrusive forces stabilised the plexus by facilitating EC intercalation which ensures that cells remained evenly distributed. Excess cohesion disrupts intercalation, resulting in aggregations of cells and functional shunting. Excess cohesion between ECs prevents them from resolving diameter balances within the plexus, leading to prolonged flow reversals which exert a critical behaviour change within the system as they switch the direction of cell migration and traffic patterns at bifurcations. Introducing mixtures of cell polarity dramatically changed the role of extrusive forces within the system. At low extrusion, opposing ECs were able to move past each other; however, at high extrusion the pushing between cells resulted in migration speeds close to zero, forming traffic jams and disrupting migration. In our study, we produced vascular malformations and functional shunting with either excess cohesion between ECs or mixtures of cell polarity. At the centre of both these mechanisms are cell-cell adherens junctions, which are involved in flow sensing/polarity and must remodelling dynamically to allow rearrangements of cells during vascular patterning. Thus, our findings implicate junctional dysfunction as a new target in the treatment and prevention of vascular disease and AVMs.
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ItemPush or Pull? Cell Proliferation and Migration During Wound Healing(Frontiers Media SA, 2022-04-29)Wound healing of the skin is a complex process that is still not well-understood. Wound management is expensive for both individuals and the health system overall, and can reduce quality of life for patients. Given these significant socio-economic impacts, wound healing has long been a focus of scientific research. Recentin vivomouse studies have identified two key regions in wounded skin tissue: A non-proliferative leading edge that actively migrates into wounded space, and a proliferative hub in which cells have enhanced mitotic properties. This work uses mathematical and computational modelling to investigate the effect of changing the mechanical characteristics of cells in these two key regions. In this paper we explore what characteristics are sufficient for wound healing, particularly focusing on cell proliferation, since wounds are not able to repair successfully without sufficient levels of cell division. By considering contact inhibited proliferation, where small cells are unable to divide, we find that a quiescent region develops if the proliferative hub is able to grow over time, essentially limiting the number of cells that are able to divide. In contrast, if the size of the proliferative hub is kept below some threshold, then contact inhibition has a less significant role in wound repair. This work builds upon existing cell-based computational studies of wound healing and could be modified to investigate different stages of wound healing, impaired healing and wound treatments.
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ItemSeven challenges in the multiscale modeling of multicellular tissues(WILEY, 2022-01)The growth and dynamics of multicellular tissues involve tightly regulated and coordinated morphogenetic cell behaviors, such as shape changes, movement, and division, which are governed by subcellular machinery and involve coupling through short- and long-range signals. A key challenge in the fields of developmental biology, tissue engineering and regenerative medicine is to understand how relationships between scales produce emergent tissue-scale behaviors. Recent advances in molecular biology, live-imaging and ex vivo techniques have revolutionized our ability to study these processes experimentally. To fully leverage these techniques and obtain a more comprehensive understanding of the causal relationships underlying tissue dynamics, computational modeling approaches are increasingly spanning multiple spatial and temporal scales, and are coupling cell shape, growth, mechanics, and signaling. Yet such models remain challenging: modeling at each scale requires different areas of technical skills, while integration across scales necessitates the solution to novel mathematical and computational problems. This review aims to summarize recent progress in multiscale modeling of multicellular tissues and to highlight ongoing challenges associated with the construction, implementation, interrogation, and validation of such models. This article is categorized under: Reproductive System Diseases > Computational Models Metabolic Diseases > Computational Models Cancer > Computational Models.