Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems.

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Two-phase model of compressive stress induced on a surrounding hyperelastic medium by an expanding tumour.

In vitro experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an externally-supplied, diffusible nutrient (e.g., oxygen), affect the tumour's growth dynamics. In this article, we present a mathematical model that describes these in vitro experiments. We use the model to understand how tumour growth generates mechanical deformations in the hydrogel and how these deformations in turn influence the tumour's growth. The hydrogel is viewed as a nonlinear hyperelastic material and the tumour is modelled as a two-phase mixture, comprising a viscous tumour cell phase and an isotropic, inviscid interstitial fluid phase. Using a combination of numerical and analytical techniques, we show how the tumour's growth dynamics change as the mechanical properties of the hydrogel vary. When the hydrogel is soft, nutrient availability dominates the dynamics: the tumour evolves to a large equilibrium configuration where the proliferation rate of nutrient-rich cells on the tumour boundary balances the death rate of nutrient-starved cells in the central, necrotic core. As the hydrogel stiffness increases, mechanical resistance to growth increases and the tumour's equilibrium size decreases. Indeed, for small tumours embedded in stiff hydrogels, the inhibitory force experienced by the tumour cells may be so large that the tumour is eliminated. Analysis of the model identifies parameter regimes in which the presence of the hydrogel drives tumour elimination.

Spatiotemporal spread of Plasmodium falciparum mutations for resistance to sulfadoxine-pyrimethamine across Africa, 1990-2020.

BACKGROUND: Sulfadoxine-pyrimethamine (SP) is recommended in Africa in several antimalarial preventive regimens including Intermittent Preventive Treatment in pregnant women (IPTp), Intermittent Preventive Treatment in infants (IPTi) and Seasonal Malaria Chemoprevention (SMC). The effectiveness of SP-based preventive treatments are threatened in areas where Plasmodium falciparum resistance to SP is high. The prevalence of mutations in the dihydropteroate synthase gene (pfdhps) can be used to monitor SP effectiveness. IPTi-SP is recommended only in areas where the prevalence of the pfdhps540E mutation is below 50%. It has also been suggested that IPTp-SP does not have a protective effect in areas where the pfdhps581G mutation, exceeds 10%. However, pfdhps mutation prevalence data in Africa are extremely heterogenous and scattered, with data completely missing from many areas. METHODS AND FINDINGS: The WWARN SP Molecular Surveyor database was designed to summarize dihydrofolate reductase (pfdhfr) and pfdhps gene mutation prevalence data. In this paper, pfdhps mutation prevalence data was used to generate continuous spatiotemporal surface maps of the estimated prevalence of the SP resistance markers pfdhps437G, pfdhps540E, and pfdhps581G in Africa from 1990 to 2020 using a geostatistical model, with a Bayesian inference framework to estimate uncertainty. The maps of estimated prevalence show an expansion of the pfdhps437G mutations across the entire continent over the last three decades. The pfdhps540E mutation emerged from limited foci in East Africa to currently exceeding 50% estimated prevalence in most of East and South East Africa. pfdhps540E distribution is expanding at low or moderate prevalence in central Africa and a predicted focus in West Africa. Although the pfdhps581G mutation spread from one focus in East Africa in 2000, to exceeding 10% estimated prevalence in several foci in 2010, the predicted distribution of the marker did not expand in 2020, however our analysis indicated high uncertainty in areas where pfdhps581G is present. Uncertainty was higher in spatial regions where the prevalence of a marker is intermediate or where prevalence is changing over time. CONCLUSIONS: The WWARN SP Molecular Surveyor database and a set of continuous spatiotemporal surface maps were built to provide users with standardized, current information on resistance marker distribution and prevalence estimates. According to the maps, the high prevalence of pfdhps540E mutation was to date restricted to East and South East Africa, which is reassuring for continued use of IPTi and SMC in West Africa, but continuous monitoring is needed as the pfdhps540E distribution is expanding. Several foci where pfdhps581G prevalence exceeded 10% were identified. More data on the pfdhps581G distribution in these areas needs to be collected to guide IPTp-SP recommendations. Prevalence and uncertainty maps can be utilized together to strategically identify sites where increased surveillance can be most informative. This study combines a molecular marker database and predictive modelling to highlight areas of concern, which can be used to support decisions in public health, highlight knowledge gaps in certain regions, and guide future research.

A Current Perspective on Wound Healing and Tumour-Induced Angiogenesis.

Angiogenesis, or capillary growth from pre-existing vasculature, is an essential component of several physiological processes, both vital and pathological. These include dermal wound healing and tumour growth that together pose some of the most significant challenges to healthcare systems worldwide. Over the last few decades, mathematical modelling has proven to be a valuable tool for unravelling the complex network of interactions that underlie such processes. Moreover, theoretical frameworks that describe some of the mechanical and chemical aspects of angiogenesis inherent in wound healing and tumour growth have revealed intriguing similarities between the two processes. In this review, we highlight some of the significant contributions made by mathematical models of tumour-induced and wound healing angiogenesis and illustrate how advances in each field have been made using insights from the other. We also detail some open problems that could be addressed through a combination of theoretical and experimental approaches.

A mathematical model of the use of supplemental oxygen to combat surgical site infection.

Infections are a common complication of any surgery, often requiring a recovery period in hospital. Supplemental oxygen therapy administered during and immediately after surgery is thought to enhance the immune response to bacterial contamination. However, aerobic bacteria thrive in oxygen-rich environments, and so it is unclear whether oxygen has a net positive effect on recovery. Here, we develop a mathematical model of post-surgery infection to investigate the efficacy of supplemental oxygen therapy on surgical-site infections. A 4-species, coupled, set of non-linear partial differential equations that describes the space-time dependence of neutrophils, bacteria, chemoattractant and oxygen is developed and analysed to determine its underlying properties. Through numerical solutions, we quantify the efficacy of different supplemental oxygen regimes on the treatment of surgical site infections in wounds of different initial bacterial load. A sensitivity analysis is performed to investigate the robustness of the predictions to changes in the model parameters. The numerical results are in good agreement with analyses of the associated well-mixed model. Our model findings provide insight into how the nature of the contaminant and its initial density influence bacterial infection dynamics in the surgical wound.