Cristina Blázquez Goñi, Cristina Ferreras, Álvaro Martínez-Rubio, Salvador Chulián, Manuel Ramírez Orellana, Alfonso Navarro-Zapata, María Rosa, Víctor M. Pérez-García, Antonio Pérez Martínez, Matemáticas, [Martínez-Rubio,Á, Chulián,S, Rosa,M] Department of Mathematics, Universidad de Cádiz, Puerto Real, Cádiz, Spain. [Martínez-Rubio,Á, Blázquez Goñi,C, Rosa,M] Biomedical Research and Innovation Institute of Cádiz (INiBICA), Hospital Universitario Puerta del Mar, Cádiz, Spain. [Blázquez Goñi,C] Department of Pediatric Hematology and Oncology, Hospital de Jerez, Cádiz, Spain. [Ramírez Orellana,M] Department of Paediatric Haematology and Oncology, Instituto Investigación Sanitaria La Princesa, Hospital Infantil Universitario Niño Jesús, Madrid, Spain. [Pérez Martínez,A, Navarro-Zapata,A, Ferreras,C] Translational Research in Pediatric Oncology, Hematopoietic Transplantation and Cell Therapy, IdiPAZ, Hospital Universitario La Paz, Madrid, Spain. [Pérez Martínez,A] Pediatric Hemato-Oncology Department, Hospital Universitario La Paz, Madrid, Spain. [Pérez-García,VM] Mathematical Oncology Laboratory (MOLAB), Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, Ciudad Real, Spain. [Pérez-García,VM] Departamento de Matemáticas, Escuela Técnica Superior de Ingenieros Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain., and This work was partially supported by the Fundación Española para la Ciencia y la Tecnología (UCA PR214), the Asociación Pablo Ugarte (APU, Spain), Junta de Comunidades de Castilla-La Mancha (SBPLY/17/180501/000154), Ministry of Science and Technology, Spain (PID2019-110895RB-I00), and Inversión Territorial Integrada de la Provincia de Cádiz (ITI-0038-2019).
Chimeric Antigen Receptor (CAR) T-cell therapy has demonstrated high rates of response in recurrent B-cell Acute Lymphoblastic Leukemia in children and young adults. Despite this success, a fraction of patients' experience relapse after treatment. Relapse is often preceded by recovery of healthy B cells, which suggests loss or dysfunction of CAR T-cells in bone marrow. This site is harder to access, and thus is not monitored as frequently as peripheral blood. Understanding the interplay between B cells, leukemic cells, and CAR T-cells in bone marrow is paramount in ascertaining the causes of lack of response. In this paper, we put forward a mathematical model representing the interaction between constantly renewing B cells, CAR T-cells, and leukemic cells in the bone marrow. Our model accounts for the maturation dynamics of B cells and incorporates effector and memory CAR T-cells. The model provides a plausible description of the dynamics of the various cellular compartments in bone marrow after CAR T infusion. After exploration of the parameter space, we found that the dynamics of CAR T product and disease were independent of the dose injected, initial B-cell load, and leukemia burden. We also show theoretically the importance of CAR T product attributes in determining therapy outcome, and have studied a variety of possible response scenarios, including second dosage schemes. We conclude by setting out ideas for the refinement of the model., This work was partially supported by the Fundacion Espanola para la Ciencia y la Tecnologia (UCA PR214), the Asociacion Pablo Ugarte (APU, Spain), Junta de Comunidades de Castilla-La Mancha (SBPLY/17/180501/000154), Ministry of Science and Technology, Spain (PID2019110895RB-I00), and Inversion Territorial Integrada de la Provincia de Cadiz (ITI-0038-2019).