Mathematical Oncology

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Lance L. Munn October 28, 2025

Mathematical Models of the Tumor Microenvironment: From Blood Flow to Immunotherapy

Abstract

Understanding the tumor microenvironment and its interactions with the host requires approaches that bridge scales and disciplines. Experimental methods reveal key mechanisms, but mathematical and computational models allow us to integrate them, dissect their contributions, and generate testable predictions. I will present a spectrum of such models spanning biophysical, physiological, and immunological domains. At the biophysical scale, we use lattice Boltzmann and agent-based models to simulate blood and lymphatic cell transport, valve mechanics, and vessel remodeling—capturing emergent processes such as mechanobiological control loops and systemic immune cell activation. At the tissue and tumor scales, poroelastic and multiscale agent-based frameworks elucidate how solid stress, angiogenesis, and plasma leakage alter the tumor environment and affect responses to therapy. Extending these approaches, physiologically based pharmacokinetic and systems biology models integrate vascular normalization, immune activation, and metabolic conditions to predict outcomes of chemotherapy, immunotherapy, CAR T cell delivery, and cancer vaccines.