  Chimeric antigen receptor (CAR) T-cell based immunotherapy has shown its
potential in treating blood cancers, and its application to solid tumors is
currently being extensively investigated. For glioma brain tumors, various CAR
T-cell targets include IL13Ra2, EGFRvIII, HER2, EphA2, GD2, B7-H3, and
chlorotoxin. In this work, we are interested in developing a mathematical model
of IL13Ra2 targeting CAR T-cells for treating glioma. We focus on extending the
work of Kuznetsov et al. (1994) by considering binding of multiple CAR T-cells
to a single glioma cell, and the dynamics of these multi-cellular conjugates.
Our model more accurately describes experimentally observed CAR T-cell killing
assay data than a model which does not consider cell binding. Moreover, we
derive conditions in the CAR T-cell expansion rate that determines treatment
success or failure. Finally, we show that our model captures distinct CAR
T-cell killing dynamics at low, medium, and high antigen receptor densities in
patient-derived brain tumor cells.
