Spatiotemporal Modelling of CAR-T Cell Therapy in Solid Tumours: Mechanisms of Antigen Escape and Immunosuppression

Although chimeric antigen receptor T-cell therapy (CAR-T) has shown substantial efficacy in haematological malignancies, its application to solid tumours remains limited by antigenic heterogeneity, poor effector-cell infiltration, and an immunosuppressive tumour microenvironment. This study aimed to develop a mathematical model of the spatiotemporal dynamics of a solid tumour under CAR-T cell therapy, incorporating the main determinants of therapeutic resistance. We propose a reaction–diffusion model formulated as a system of partial differential equations describing functional and exhausted CAR-T cells, antigen-positive and antigen-negative tumour subpopulations, and chemokine, immunosuppressive, and hypoxic fields. The model was analysed using steady-state analysis and numerical simulations based on a finite-difference scheme. The simulations showed that therapeutic outcome is governed by the combined effects of CAR-T cell infiltration, functional exhaustion, and tumour antigen escape. The model reproduced partial tumour regression followed by persistence of a residual tumour population, the emergence of an antigen-negative component under therapeutic pressure, and reduced treatment efficacy under more strongly immunosuppressive and hypoxic microenvironmental conditions. Repeated simulated CAR-T-cell administration improved tumour control, albeit with diminishing returns. Overall, the proposed model provides a useful framework for analysing resistance mechanisms and optimising CAR-T cell therapy protocols for solid tumours.