Multiscale mathematical models of drug and immune cell trafficking to support innovative cancer treatments

Recent advances in oncology have introduced increasingly sophisticated therapeutic strategies, including mRNA-encoded therapeutics, engineered immune cells, and advanced experimental platforms such as Organ-on-Chip systems. Although these technologies differ substantially in their biological mechanisms, they share a common challenge: therapeutic efficacy depends not only on the intrinsic activity of the therapeutic agent, but also on its ability to traffic across multiple biological scales, from systemic circulation to local interactions within the tumor microenvironment. Mathematical modeling provides a natural framework for integrating these interconnected processes and linking heterogeneous experimental observations to quantitative mechanistic predictions. This thesis develops a collection of multiscale mathematical models to investigate drug and immune-cell trafficking in innovative cancer therapies. The first contribution focuses on mRNA-encoded therapeutics and introduces physiologically based pharmacokinetic (PBPK) models that describe the biodistribution of lipid nanoparticles, intracellular mRNA processing, protein translation, and systemic pharmacokinetics of the encoded therapeutic proteins. These models provide a modular framework for studying different mRNA formulations and therapeutic proteins while supporting future applications in translational pharmacology and personalized medicine. The second contribution addresses immune-cell migration in Cancer-on-Chip experiments through a hybrid mathematical model coupling reaction-diffusion equations for chemotactic signaling with particle-based descriptions of individual immune cells. A comprehensive global sensitivity analysis identifies the biological mechanisms that most strongly influence cell migration and provides guidance for model calibration, simplification, and experimental design. The final contribution develops a multiscale model of CAR T-cell therapy by integrating a whole-body PBPK description of CAR T-cell trafficking with a local model of tumor–immune interactions in B-cell lymphoma. This framework links systemic circulation to local proliferation, cytotoxic activity, and tumor-mediated immunosuppression, enabling investigation of how transport and local dynamics jointly determine therapeutic response. Although developed for different biological systems, the three modeling frameworks are united by a common perspective: therapeutic trafficking represents the fundamental connection between molecular processes, cellular behavior, tissue dynamics, and whole-body physiology. Together, these models illustrate how mechanistic mathematical modeling can integrate experimental data across scales, generate biologically interpretable predictions, and support the future development and optimization of innovative cancer therapies.