Spatial quantification and mathematical modelling of tissue development

In this thesis, we study biological tissue development, during which cells organise themselves into structures which perform a specific function. Understanding how particular types of mechanisms lead to the emergence of various cell patterns in tissues is the main motivation of this research. Quantifying the tissue patterns is a first step towards understanding which mechanisms are at work in particular experiments. For this purpose, we develop pair-correlation functions (PCFs) which quantify how a spatial distribution of cells deviates from complete spatial randomness over specified directions. We evaluate the usefulness of PCFs for studying the three-dimensional organisation of cells in tumour spheroids and show that the PCFs robustly reveal information about their spatial structure. In particular, we demonstrate that the boundary that separates the necrotic and viable zones in the tumour spheroids can be detected using the PCF with a high degree of accuracy. We then turn to development of mathematical models to investigate the types of patterns that can arise from simple hypothesised interactions between cells. We begin in Chapter 3 by developing an on-lattice agent-based model (ABM) to investigate tumour spheroid growth using two different culture methods: suspension culture, and culture within a microgel. Our results suggest that stratifying the seeded cells into multiple layers and also reducing cell death are the key effects of the microgel that enable it to produce more uniformly-sized spheroids. In Chapter 4, we extend the ABM to study systems with two interacting species. A huge variety of aggregation patterns can arise in these systems, depending upon the underlying attractive-repulsive mechanisms. More specifically, we show that the run-and chase mechanism can produce a striped pattern, similar to that observed on the skin of zebrafish. Finally, we develop a non-local continuous model, approximating the mean behaviour of the ABM. This provides a connection between the cell-level and population-level models of tissue development. A linear stability analysis of the continuous model allows us to investigate parameter regimes that produce striped patterns. Importantly, we also point out the disparities that may arise between the behaviours of the continuous and discrete models, which highlights the importance of considering the underlying biological constraints in using the continuous approximated models. In particular, we show that the derivation of the approximate continuum model from the ABM introduces terms representing cell-size effects. These terms can lead to the emergence of stripes in cases where they would not be predicted in the similar continuum model of Painter et al. (2015), which does not include these terms. The combination of spatial quantification and mathematical modelling (using both continuous and discrete methods) developed in this work helps us to gain a better understanding of tissue development. Our approach provides a novel means to investigate the underpinning mechanisms of tissue development by combining model simulations with analysis of biological and synthetic data using the pair-correlation functions.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 201

Codes

Every file has an information in itself about what it doe

Global economic costs due to vivax malaria and the potential impact of its radical cure: A modelling study.

BackgroundIn 2017, an estimated 14 million cases of Plasmodium vivax malaria were reported from Asia, Central and South America, and the Horn of Africa. The clinical burden of vivax malaria is largely driven by its ability to form dormant liver stages (hypnozoites) that can reactivate to cause recurrent episodes of malaria. Elimination of both the blood and liver stages of the parasites ("radical cure") is required to achieve a sustained clinical response and prevent ongoing transmission of the parasite. Novel treatment options and point-of-care diagnostics are now available to ensure that radical cure can be administered safely and effectively. We quantified the global economic cost of vivax malaria and estimated the potential cost benefit of a policy of radical cure after testing patients for glucose-6-phosphate dehydrogenase (G6PD) deficiency.Methods and findingsEstimates of the healthcare provider and household costs due to vivax malaria were collated and combined with national case estimates for 44 endemic countries in 2017. These provider and household costs were compared with those that would be incurred under 2 scenarios for radical cure following G6PD screening: (1) complete adherence following daily supervised primaquine therapy and (2) unsupervised treatment with an assumed 40% effectiveness. A probabilistic sensitivity analysis generated credible intervals (CrIs) for the estimates. Globally, the annual cost of vivax malaria was US$359 million (95$222 to 563 million), attributable to 14.2 million cases of vivax malaria in 2017. From a societal perspective, adopting a policy of G6PD deficiency screening and supervision of primaquine to all eligible patients would prevent 6.1 million cases and reduce the global cost of vivax malaria to US$266 million (95$161 to 415 million), although healthcare provider costs would increase by US$39 million. If perfect adherence could be achieved with a single visit, then the global cost would fall further to US$225 million, equivalent to $135 million in cost savings from the baseline global costs. A policy of unsupervised primaquine reduced the cost to US$342 million (95% CrI: US$209 to 532 million) while preventing 2.1 million cases. Limitations of the study include partial availability of country-level cost data and parameter uncertainty for the proportion of patients prescribed primaquine, patient adherence to a full course of primaquine, and effectiveness of primaquine when unsupervised.ConclusionsOur modelling study highlights a substantial global economic burden of vivax malaria that could be reduced through investment in safe and effective radical cure achieved by routine screening for G6PD deficiency and supervision of treatment. Novel, low-cost interventions for improving adherence to primaquine to ensure effective radical cure and widespread access to screening for G6PD deficiency will be critical to achieving the timely global elimination of P. vivax

Quantification of the dynamics of antibody response to malaria to inform sero-surveillance in pregnant women

Background Malaria remains a major public health threat and tools sensitive to detect infections in low malaria transmission areas are needed to progress elimination efforts. Pregnant women are particularly vulnerable to malaria infections. Throughout pregnancy they access routine antenatal care, presenting a unique sentinel population to apply novel sero-surveillance tools to measure malaria transmission. The aim of this study was to quantify the dynamic antibody responses to multiple antigens during pregnancy so as to identify a single or multiple antibody response of exposure to malaria in pregnancy. Methods This study involved a secondary analysis of antibody responses to six parasite antigens [five commonly studied merozoite antigens and the variant surface antigen 2-chondroitin sulphate A (VAR2CSA), a pregnancy-specific erythrocytic antigen] measured by enzyme-linked immunosorbent assay (ELISA) over the gestation period until delivery (median of 7 measurements/woman) in 250 pregnant women who attended antenatal clinics located at the Thai-Myanmar border. A multivariate mixture linear mixed model was used to cluster the pregnant women into groups that have similar longitudinal antibody responses to all six antigens over the gestational period using a Bayesian approach. The variable-specific entropy was calculated to identify the antibody responses that have the highest influence on the classification of the women into clusters, and subsequent agreement with grouping of women based on exposure to malaria during pregnancy. Results Of the 250 pregnant women, 135 had a Plasmodium infection detected by light microscopy during pregnancy (39% Plasmodium falciparum only, 33% Plasmodium vivax only and 28% mixed/other species), defined as cases. The antibody responses to all six antigens accurately identified the women who did not have a malaria infection detected during pregnancy (93%, 107/115 controls). Antibody responses to P. falciparum merozoite surface protein 3 (PfMSP3) and P. vivax apical membrane antigen 1 (PvAMA1) were the least dynamic. Antibody responses to the antigens P. falciparum apical membrane antigen 1 (PfAMA1) and PfVAR2CSA were able to identify the majority of the cases more accurately (63%, 85/135). Conclusion These findings suggest that the combination of antibodies, PfAMA1 and PfVAR2CSA, may be useful for sero-surveillance of malaria infections in pregnant women, particularly in low malaria transmission settings. Further investigation of other antibody markers is warranted considering these antibodies combined only detected 63% of the malaria infections during pregnancy

Quantification of parasite clearance in Plasmodium knowlesi infections.

Funder: University of Melbourne's Research ScholarshipBACKGROUND: The incidence of zoonotic Plasmodium knowlesi infections in humans is rising in Southeast Asia, leading to clinical studies to monitor the efficacy of anti-malarial treatments for knowlesi malaria. One of the key outcomes of anti-malarial drug efficacy is parasite clearance. For Plasmodium falciparum, parasite clearance is typically estimated using a two-stage method, that involves estimating parasite clearance for individual patients followed by pooling of individual estimates to derive population estimates. An alternative approach is Bayesian hierarchical modelling which simultaneously analyses all parasite-time patient profiles to determine parasite clearance. This study compared these methods for estimating parasite clearance in P. knowlesi treatment efficacy studies, with typically fewer parasite measurements per patient due to high susceptibility to anti-malarials. METHODS: Using parasite clearance data from 714 patients with knowlesi malaria and enrolled in three trials, the Worldwide Antimalarial Resistance Network (WWARN) Parasite Clearance Estimator (PCE) standard two-stage approach and Bayesian hierarchical modelling were compared. Both methods estimate the parasite clearance rate from a model that incorporates a lag phase, slope, and tail phase for the parasitaemia profiles. RESULTS: The standard two-stage approach successfully estimated the parasite clearance rate for 678 patients, with 36 (5%) patients excluded due to an insufficient number of available parasitaemia measurements. The Bayesian hierarchical estimation method was applied to the parasitaemia data of all 714 patients. Overall, the Bayesian method estimated a faster population mean parasite clearance (0.36/h, 95% credible interval [0.18, 0.65]) compared to the standard two-stage method (0.26/h, 95% confidence interval [0.11, 0.46]), with better model fits (compared visually). Artemisinin-based combination therapy (ACT) is more effective in treating P. knowlesi than chloroquine, as confirmed by both methods, with a mean estimated parasite clearance half-life of 2.5 and 3.6 h, respectively using the standard two-stage method, and 1.8 and 2.9 h using the Bayesian method. CONCLUSION: For clinical studies of P. knowlesi with frequent parasite measurements, the standard two-stage approach (WWARN's PCE) is recommended as this method is straightforward to implement. For studies with fewer parasite measurements per patient, the Bayesian approach should be considered. Regardless of method used, ACT is more efficacious than chloroquine, confirming the findings of the original trials

Quantification of parasite clearance in Plasmodium knowlesi infections

Background The incidence of zoonotic Plasmodium knowlesi infections in humans is rising in Southeast Asia, leading to clinical studies to monitor the efficacy of anti-malarial treatments for knowlesi malaria. One of the key outcomes of anti-malarial drug efficacy is parasite clearance. For Plasmodium falciparum, parasite clearance is typically estimated using a two-stage method, that involves estimating parasite clearance for individual patients followed by pooling of individual estimates to derive population estimates. An alternative approach is Bayesian hierarchical modelling which simultaneously analyses all parasite-time patient profiles to determine parasite clearance. This study compared these methods for estimating parasite clearance in P. knowlesi treatment efficacy studies, with typically fewer parasite measurements per patient due to high susceptibility to anti-malarials. Methods Using parasite clearance data from 714 patients with knowlesi malaria and enrolled in three trials, the Worldwide Antimalarial Resistance Network (WWARN) Parasite Clearance Estimator (PCE) standard two-stage approach and Bayesian hierarchical modelling were compared. Both methods estimate the parasite clearance rate from a model that incorporates a lag phase, slope, and tail phase for the parasitaemia profiles. Results The standard two-stage approach successfully estimated the parasite clearance rate for 678 patients, with 36 (5%) patients excluded due to an insufficient number of available parasitaemia measurements. The Bayesian hierarchical estimation method was applied to the parasitaemia data of all 714 patients. Overall, the Bayesian method estimated a faster population mean parasite clearance (0.36/h, 95% credible interval [0.18, 0.65]) compared to the standard two-stage method (0.26/h, 95% confidence interval [0.11, 0.46]), with better model fits (compared visually). Artemisinin-based combination therapy (ACT) is more effective in treating P. knowlesi than chloroquine, as confirmed by both methods, with a mean estimated parasite clearance half-life of 2.5 and 3.6 h, respectively using the standard two-stage method, and 1.8 and 2.9 h using the Bayesian method. Conclusion For clinical studies of P. knowlesi with frequent parasite measurements, the standard two-stage approach (WWARN’s PCE) is recommended as this method is straightforward to implement. For studies with fewer parasite measurements per patient, the Bayesian approach should be considered. Regardless of method used, ACT is more efficacious than chloroquine, confirming the findings of the original trials.</p

Developing a multivariate prediction model of antibody features associated with protection of malaria-infected pregnant women from placental malaria

Background: Plasmodium falciparum causes placental malaria, which results in adverse outcomes for mother and child. P. falciparum-infected erythrocytes that express the parasite protein VAR2CSA on their surface can bind to placental chondroitin sulfate A. It has been hypothesized that naturally acquired antibodies towards VAR2CSA protect against placental infection, but it has proven difficult to identify robust antibody correlates of protection from disease. The objective of this study was to develop a prediction model using antibody features that could identify women protected from placental malaria. Methods: We used a systems serology approach with elastic net-regularized logistic regression, partial least squares discriminant analysis, and a case-control study design to identify naturally acquired antibody features mid-pregnancy that were associated with protection from placental malaria at delivery in a cohort of 77 pregnant women from Madang, Papua New Guinea. Results: The machine learning techniques selected 6 out of 169 measured antibody features towards VAR2CSA that could predict (with 86% accuracy) whether a woman would subsequently have active placental malaria infection at delivery. Selected features included previously described associations with inhibition of placental binding and/or opsonic phagocytosis of infected erythrocytes, and network analysis indicated that there are not one but multiple pathways to protection from placental malaria. Conclusions: We have identified candidate antibody features that could accurately identify malaria-infected women as protected from placental infection. It is likely that there are multiple pathways to protection against placental malaria. Funding: This study was supported by the National Health and Medical Research Council (Nos. APP1143946, GNT1145303, APP1092789, APP1140509, and APP1104975)