Quantification of spatial and phenotypic heterogeneity in an agent-based model of tumour-macrophage interactions

Abstract

We introduce a new spatial statistic, the weighted pair correlation function (wPCF). The wPCF extends the existing pair correlation function (PCF) and cross-PCF to describe spatial relationships between points marked with combinations of discrete and continuous labels. We validate its use through application to a new agent-based model (ABM) which simulates interactions between macrophages and tumour cells. These interactions are influenced by the spatial positions of the cells and by macrophage phenotype, a continuous variable that ranges from anti-tumour to pro-tumour. By varying model parameters that regulate macrophage phenotype, we show that the ABM exhibits behaviours which resemble the ‘three Es of cancer immunoediting’: Equilibrium, Escape, and Elimination. We use the wPCF to analyse synthetic images generated by the ABM. We show that the wPCF generates a ‘human readable’ statistical summary of where macrophages with different phenotypes are located relative to both blood vessels and tumour cells. We also define a distinct ‘PCF signature’ that characterises each of the three Es of immunoediting, by combining wPCF measurements with the cross-PCF describing interactions between vessels and tumour cells. By applying dimension reduction techniques to this signature, we identify its key features and train a support vector machine classifier to distinguish between simulation outputs based on their PCF signature. This proof-of-concept study shows how multiple spatial statistics can be combined to analyse the complex spatial features that the ABM generates, and to partition them into interpretable groups. The intricate spatial features produced by the ABM are similar to those generated by state-of-the-art multiplex imaging techniques which distinguish the spatial distribution and intensity of multiple biomarkers in biological tissue regions. Applying methods such as the wPCF to multiplex imaging data would exploit the continuous variation in biomarker intensities and generate more detailed characterisation of the spatial and phenotypic heterogeneity in tissue samples.

A seven‐step guide to spatial, agent‐based modelling of tumour evolution

“…(2022) used an SABM to investigate the evolutionary rescue of drug‐resistant tumour subclones; Saha et al. (2023) used an SABM to investigate adaptive cancer therapy; and Bull and Byrne (2023) used an SABM to simulate interactions between macrophages and tumour cells.…”

“…Typical applications include understanding tumour development, inferring the effects of driver mutations, and predicting treatment outcomes. For example in recent studies, Aif et al (2022) used an SABM to investigate the evolutionary rescue of drug-resistant tumour subclones; Saha et al (2023) used an SABM to investigate adaptive cancer therapy; and Bull and Byrne (2023) used an SABM to simulate interactions between macrophages and tumour cells.…”

A new paradigm considering multicellular adhesion, repulsion and attraction represents diverse cellular tile patterns

“…Here, we emphasize that finding alternative indices for angle statistics to improve the data analysis of hexagonal versus tetragonal tile patterns is a timely research topic. Similar strategies for fitting parameters using summary statistics, pattern simplicity scores or persistent-homology approaches have been used to characterize pattern formation in several mathematical biology models, see [30, 31, 4, 3, 2, 26] for instance. Our study provides a mathematical basis for studying a wide range of tile patterns found in biological and non-biological systems.…”

“…We analyze this behavior using angle summary statistics to discern among hexagonal and tetragonal like patterns. Similar strategies based on summary statistics have been used in pattern classification for different purposes in mathematical biology [30, 31, 3, 2].…”

New Strategies for Macrophage Re-Education in Cancer: An Update

“…The spatial distribution of macrophages within the tumor conditions their polarization in relation to signals from the TME and interaction with other tumor and non-tumor cells. A new statistical function applied to an agent-based model (ABM), which takes into account the spatial distribution of macrophages within the tumor and the interaction with tumor cells, gives an idea of which macrophages should be targeted for re-education [ 127 ].…”