Rocío Picón-González

arXiv2026

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.

math.DS↗

arXiv2026

A Systematic Framework for Evaluating Topological Representations in Single-Cell Classification

Recent advances in biomedicine generate high-dimensional single-cell data that describe cellular heterogeneity with unprecedented detail, but their geometric complexity and non-linear structure often limit the effectiveness of conventional statistical tools. Topological Data Analysis (TDA) provides a mathematical framework for characterizing the shape of data through persistent homology, which extracts structural features such as connected components and cycles across multiple scales. In this work, we propose a systematic two-level framework for evaluating topological representations in high-dimensional single-cell classification. The first level ($R_1$) performs statistical screening of topological descriptors based on separability between clinical groups, whereas the second level ($R_2$) evaluates their predictive utility in supervised classification models. This design makes it possible to compare representations not only in terms of discriminative performance, but also in terms of robustness to analytical choices. We illustrate the framework using bone marrow flow cytometry data from pediatric acute lymphoblastic leukemia, with a particular focus on relapse stratification. The results show that different topological representations vary substantially in both statistical separability and predictive stability, with Betti Curves and Persistence Silhouettes showing more robust behavior than Persistence Images in this cohort. Overall, the study provides a reproducible methodological framework for the systematic comparison of topological descriptors in complex biomedical point clouds.

math.GN↗