CAR T cell therapy in B-cell acute lymphoblastic leukaemia: Insights from mathematical models

Abstract

Immunotherapies use components of the patient immune system to selectively target cancer cells. The use of CAR T cells to treat B-cell malignanciesleukaemias and lymphomas-is one of the most successful examples, with many patients experiencing long-lasting complete responses to this therapy. This treatment works by extracting the patient's T cells and adding them the CAR group, which enables them to recognize and target cells carrying the antigen CD19 + , that is expressed in these haematological tumors.Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T-cells. The model accounts for mature and progenitor B-cells, tumor cells, CAR T cells and side effects by incorporating the main biological processes involved. The model explains the early post-injection dynamics of the different compartments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that provides the maximum CAR T cell 1 These two authors contributed equally to this work.

Dual-Target Car-Ts With on- and off-Tumour Activity May Override Immune Suppression in Solid Cancers: A Mathematical Proof of Concept

“…The maximum mitotic rate ρ C and ρC, related to the stimulation effect of the T cells by the interaction with the targets (CD 19 + or tumour antigen), will depend on the properties of the CAR-T product. These parameters will be taken in the range 0.2-0.9 day −1 according to the values reported in other models [26,37] and in agreement with the fact that stimulated CAR-T cells can perform a few mitotic divisions per day. For current CAR-T products the mean lifetime τ C of activated CAR T cells is in the range of 1-4 weeks [38].…”

“…Eqs. (2a-2b) describe the off-tumour interaction between CAR-T and B cells as in previous works [26] term represents natural cell death, where τ C is the activated CAR-T lifespan. Finally, the term −kC represents the traffic of CAR-T cells to brain areas having active GBM cells, where 0 < k < 1 is the average fraction of CAR-T cells crossing the blood-brain barrier (BBB) and infiltrating the tumour site.…”

“…We will assume that in dual therapy, CAR-T cells are injected after lymphoid depletion treatment to promote expansion of CAR-T by stimulation with B cells as usual. We set the initial number of B lymphocytes to be 2.5 ×10 10 to account for the effect of this treatment [26].…”

“…To do so, we neglected the immune suppression term, that is not present in leukaemias and the parameters related to the type of cancer were chosen as in Ref. [26]. We obtained values of g T and g B around 1-2 ×10 10 cell.…”

“…Mathematical modelling has the potential to help in finding optimal administration protocols, provide a deeper understanding of the dynamics, help in the design of clinical trials and more [19,20]. Some recent mathematical modelling studies have been performed studying different aspects of CAR-T cell therapies [21][22][23][24][25][26][27][28]. In this paper we study in-silico, using a mathematical model, the response of a solid tumour to a dual CAR-T product targeting both CD19 and a tumour-associated antigen.…”