Mathematical models for CAR T immunotherapy and CD19 dynamics in leukemia: a comparative analysis
Chimeric Antigen Receptor (CAR) T cell therapy has emerged as a successful treatment for relapsed or refractory hematological malignancies, particularly for B cell Acute Lymphoblastic Leukemia (B ALL), where CD19 targeted therapies have achieved high initial remission rates. However, relapse after treatment remains a major clinical challenge, frequently associated with antigen escape mechanisms and the emergence of CD19$^-$ leukemic cells. Understanding the interaction between CAR T cells and antigen expression dynamics is, therefore, essential for improving therapeutic efficacy and long-term patient outcomes. In this work, we develop and comparatively analyze novel mathematical models describing CAR T immunotherapy and CD19 dynamics in leukemia. Our proposed framework combines compartmental ordinary differential equation (ODE) formulations as well as partial differential equation (PDE) systems. Both methods are able to capture the evolution of leukemic populations under immune pressure and, in particular, the models explicitly distinguish between CD19$^+$ and CD19$^-$ leukemic cells and incorporate bidirectional phenotypic transitions regulated by CAR T activity. The developed models provide biologically interpretable and computationally efficient tools for studying treatment response, resistance, and relapse mechanisms in CAR T cell therapy. We compare the ability of the different modeling approaches to reproduce CD19 antigen modulation and CAR T efficacy dynamics. We also propose sensitivity analyses to study the parameters' influence on the models' dynamics. Our work contributes to the mathematical understanding of antigen-driven resistance and offers a basis for future optimization and personalization of CAR T therapeutic strategies in leukemia.