Mathematical Analysis of ordinary differential equations (ODE) and fractional order differential equation (FODE) models of CD70 CAR T-cell therapy for gliomas

Abstract

ABSTRACT Chimeric antigen receptor T cells (CAR T-cells) immunotherapy has been successful in the treatment of liquid cancers. Currently, CAR T-cells immunotherapy has been investigated for treatment of solid tumors, including glioblastoma (GBM) (brain cancers). Glioma cells with CD70 expression antigen have been identified as a novel potential CAR T target for glioma. Growing evidence from preclinical studies demonstrated that CD70 CAR T-cells can induce potent antitumor response in xenograft and syngeneic models without adverse effects. However, better understanding of the mechanism of CD70 specific CAR T therapy against GBM in immunosuppressive tumor microenvironment requires improving its efficacy. We propose two types of Mathematical models, one is a system of ordinary differential equations (ODEs) and the other is a system of fractional order ordinary differential equations (FODEs) to explore the kinetics of CAR T-cells killing glioma. Although, the ODE model provides very good results with mouse specific CAR T-cells (mCAR T) and human specific CAR T-cells (hCAR T) immunotherapy against glioma in animal models, the cells memory structure becomes significant which the ODE model does take into consideration. The fractional order differential equations model addresses the cell memory structure. The fractional order differential model shows very encouraging results for CAR T immunotherapy against glioma. Computer simulations based on the models using Python and MATLAB programming languages were used to quantify the anti-tumor efficacy of CD70 specific CAR T-cells against gliomas in xenograft and syngeneic mouse models presented in preclinical studies. The models suggests that the success of CAR T-cells treatment depends on individual tumor, tumor growth rate, CD70 level of expression and dose of the treatment.