ABSTRACT
In this paper, we explore the application of Chimeric Antigen Receptor (CAR) T cell therapy for the treatment of Acute Lymphocytic Leukaemia (ALL) by means of in silico experimentation, mathematical modelling through first-order Ordinary Differential Equations and nonlinear systems theory. By combining the latter with systems biology on cancer evolution we were able to establish a sufficient condition on the therapy dose to ensure complete response. The latter is illustrated across multiple numerical simulations when comparing three mathematically formulated administration protocols with one of a phase 1 dose-escalation trial on CAR-T cells for the treatment of ALL on children and young adults. Therefore, both our analytical and in silico results are consistent with real-life scenarios. Finally, our research indicates that tumour cells growth rate and the killing efficacy of the therapy are key factors in the designing of personalised strategies for cancer treatment.