Pattern formation and spatiotemporal irregularity in a model for macrophage-tumour interactions

Area of Science:

• Oncology
• Mathematical Biology
• Immunology

Background:

• Solid tumors are heterogeneous, comprising mutant cells alongside normal tissue and recruited cell types like macrophages.
• Tumor-associated macrophages (TAMs) play a complex role, influencing tumor growth through a balance of pro- and anti-tumor effects.

Purpose of the Study:

• To develop and analyze a mathematical model of spatial interactions between macrophages, tumor cells, and normal tissue cells.
• To investigate the role of macrophages in tumor heterogeneity and spatial dynamics.

Main Methods:

• Mathematical modeling of cell-cell interactions and spatial dynamics.
• Analysis of homogeneous steady states and travelling wave solutions.
• Numerical simulations in one and two dimensions.
• Estimation of macrophage motility parameters from experimental data.
• Inclusion of macrophage chemotaxis in the model.

Main Results:

• Normal tissue is unstable to mutant cell introduction, even with immune response, but tumor composition can be altered.
• Travelling wave solutions demonstrate tumor growth and spatial instability behind the wave front.
• Macrophage chemotaxis can lead to spatiotemporal irregularities and permanently transient solutions within growing tumors.
• Model results suggest macrophage infiltration contributes to tumor heterogeneity.

Conclusions:

• Macrophage infiltration and their complex interactions are significant drivers of tumor heterogeneity.
• Mathematical modeling provides insights into the spatial dynamics and instability of solid tumors.
• Further research is warranted to explore the role of macrophages in spatiotemporal variations within human tumors.