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

Abstract

Cross-talk between tumour and immune cells, including macrophages, is complex, dynamic and contributes to tumour heterogeneity. In this paper, we introduce a hybrid agent-based model (ABM) to investigate how tumour-macrophage dynamics evolve over time and how they influence spatial patterns of tumour growth. Macrophage phenotype is determined by microenvironmental cues and governs the extent to which macrophages are pro- or anti-tumour, i.e., whether they infiltrate and attack tumour cells, or promote metastasis by guiding tumour cell migration towards blood vessels.We perform extensive ABM simulations to investigate how changes in macrophage sensitivity to microenvironmental cues – specifically, cytokines produced by tumour cells and perivascular fibroblasts – alters their spatial and phenotypic distributions and the tumour’s growth dynamics. We identify outcomes that include: compact tumour growth, tumour elimination, and diffuse patterns of invasion, characterised by clustering of tumour cells and macrophages around blood vessels.We compare the ability of different statistics to characterise the diverse spatial patterns that the ABM generates. These include the weighted pair correlation function (wPCF), a new statistic that quantifies the spatial distributions of cells labelled with a continuous value (e.g., macrophage phenotype). We assess the ability of each statistic to discriminate between the various spatial patterns that the ABM exhibits.By combining statistical analysis with ABM simulations, we show how mechanistic models can be used to generate synthetic data for validation of novel statistics (here, the wPCF) and to assess the extent to which specific statistical descriptions can distinguish different spatial patterns and model behaviours. Such statistics can then be applied to biological imaging data, such as multiplexed medical images, with increased confidence in the interpretation of the results. We show that the wPCF accurately describes differences in macrophage localisation between images, and posit that it would be a valuable tool for analysing multiplexed imaging data.Author summaryMacrophage phenotype is regulated by complex microenvironmental cues. It affects their spatial position and behaviour. In solid tumours, the spatial distribution of macrophages can vary significantly, and correlate with patient prognosis.In this paper, we use an agent-based model (ABM) to investigate how changes in sensitivity to tumour-induced microenvironmental cues affect macrophage phenotype and, in turn, how such phenotypic heterogeneity affects tumour composition and morphology. We illustrate the wide range of tumour outcomes that can arise from changing macrophage sensitivity to microenvironmental cues.We apply a variety of statistics to simulation outputs to characterise the range of observed spatial patterns. Different statistics identify different aspects of these patterns, with the most descriptive characterisations obtained from spatial statistics, such as the weighted pair correlation function (wPCF), that account for both phenotype and cell localisation.More generally, this paper illustrates how ABMs can be used to generate synthetic data which mimics data that can be extracted from different imaging modalities. This synthetic data can be used to test new statistics, like the wPCF, and validate their use for future application to multiplex histological imaging.

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].…”

The role of environmentally mediated drug resistance in facilitating the spatial distribution of residual disease.

“…Individual agent-based models are extensively used to model biological systems on the cellular level, with a variety of approaches and techniques [34,40,41,42,43,44,45].…”