CAR-T cell immunotherapy involves genetically reprogrammed T-lymphocytes that interact with cancer cells and activate an anti-tumor immune response. This therapy has been approved for clinical use for hematological cancers, but new challenges have emerged in the treatment of solid tumors. Some of the challenges include the heterogeneity of antigen expression found in solid tumors, including antigen-positive non-tumoral cells, the immune inhibitory molecule expression, and CAR-T cell trafficking difficulty within the tumor microenvironment. We proposed a mathematical model to describe the “on-target” and “off-tumor” effects of CAR-T cell therapy on gliomas, and we investigated which parameters influenced the final outcome using a global sensitivity analysis. Our model highlights the dynamics of CAR-T cell therapy, tumor, and healthy populations (antigen-positive glia, antigen-negative glia, and neurons), and it provides novel insight into the consequences of “on-target” “off-tumor” effects, particularly in the neuronal loss.

The use of boundary elements in the analysis of exterior acoustic problems poses challenges at specific frequencies, since fictitious eigenfrequencies may arise at the internal resonances of cavities, leading to inaccurate results or even unstable behavior. To filter out these fictitious eigenfrequencies, a scheme based on the combined Helmholtz integral equation formulation (CHIEF) can be used to prevent the so-called non-uniqueness problem, although it requires additional equations and points. The BEM formulation final accuracy will, however, depend on the correct choice of these points. Here, a strategy to help in defining good approximations for the position and number of such points is proposed, based on an optimization process which maximizes the system matrix’s smallest singular value. The accuracy of the method for exterior radiation problems is investigated using different examples. With low computational cost and simple implementation, the two proposed algorithms automatically circumvent the non-uniqueness problem, aiding the implementation of more stable BEM codes.

Chimeric Antigen Receptor (CAR)-T cell therapy long-term follow-up studies revealed non-durable remissions in a significant number of patients. Some of the mechanisms underlying these relapses include poor CAR T cell cytotoxicity or persistence, as well as antigen loss or lineage switching in tumor cells. In order to investigate how antigen-mediated resistance mechanisms affect therapy outcomes, we develop a mathematical model based on a set of integral-partial differential equations. Using a continuous variable to describe the level of antigen expression of tumor cells, we recapitulated important cellular mechanisms across patients with different therapeutic responses. Fitted with clinical data, the model successfully captured the dynamics of tumor and CAR-T cells for several hematological cancers. Furthermore, the role played by these mechanisms are explored with regard to different biological scenarios, such as pre-existing or acquired mutations, providing a deeper understanding of key factors underlying resistance to CAR-T cell immunotherapy.

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