Immunotherapy has gained great momentum with chimeric antigen receptor T cell (CAR-T) therapy, in which patient’s T lymphocytes are genetically manipulated to recognize tumor-specific antigens, increasing tumor elimination efficiency. In recent years, CAR-T cell immunotherapy for hematological malignancies achieved a great response rate in patients and is a very promising therapy for several other malignancies. Each new CAR design requires a preclinical proof-of-concept experiment using immunodeficient mouse models. The absence of a functional immune system in these mice makes them simple and suitable for use as mathematical models. In this work, we develop a three-population mathematical model to describe tumor response to CAR-T cell immunotherapy in immunodeficient mouse models, encompassing interactions between a non-solid tumor and CAR-T cells (effector and long-term memory). We account for several phenomena, such as tumor-induced immunosuppression, memory pool formation, and conversion of memory into effector CAR-T cells in the presence of new tumor cells. Individual donor and tumor specificities are considered uncertainties in the model parameters. Our model is able to reproduce several CAR-T cell immunotherapy scenarios, with different CAR receptors and tumor targets reported in the literature. We found that therapy effectiveness mostly depends on specific parameters such as the differentiation of effector to memory CAR-T cells, CAR-T cytotoxic capacity, tumor growth rate, and tumor-induced immunosuppression. In summary, our model can contribute to reducing and optimizing the number of in vivo experiments with in silico tests to select specific scenarios that could be tested in experimental research. Such an in silico laboratory is an easy-to-run open-source simulator, built on a Shiny R-based platform called CARTmath. It contains the results of this manuscript as examples and documentation. The developed model together with the CARTmath platform have potential use in assessing different CAR-T cell immunotherapy protocols and its associated efficacy, becoming an accessory for in silico trials.

Continuing tyrosine kinase inhibitor mediated targeting of the BCR-ABL1 oncoprotein is the standard therapy for chronic myeloid leukemia and allows for a sustained disease control in the majority of patients. While therapy cessation for patients appeared as a safe option for about half of the optimally responding patients, a systematic assessment of long-term tyrosine kinase inhibitor dose de-escalation is missing. We use a mathematical model to analyze and consistently describe biphasic treatment responses from tyrosine kinase inhibitor treated patients from two independent clinical phase-3 trials. Scale estimates reveal that drug efficiency determines the initial response while the long-term behavior is limited by the rare activation of leukemic stem cells. We use this mathematical framework to investigate the influence of different dosing regimens on the treatment outcome. We provide strong evidence suggesting that tyrosine kinase inhibitor dose de-escalation (at least 50%) does not lead to a reduction of long-term treatment efficiency for most patients, which have already achieved sustained remission, and maintains the secondary decline of BCR-ABL1 levels. We demonstrate that continuous BCR-ABL1 monitoring provides patient-specific predictions of an optimal reduced dose not decreasing the anti-leukemic effect on residual leukemic stem cells. Our results are consistent with the interim results of the DESTINY trial and provide clinically testable predictions. Our results suggest that dose halving should be considered as a long-term treatment option for well-responding chronic myeloid leukemia patients under continuing maintenance therapy with tyrosine kinase inhibitors. We emphasize the clinical potential of this approach to reduce treatment-related side-effects and therapy costs.

Chimeric Antigen Receptor (CAR)-T cell immunotherapy revolutionized cancer treatment and consists of the genetic modification of T lymphocytes with a CAR gene, aiming to increase their ability to recognize and kill antigen-specific tumor cells. The dynamics of CAR-T cell responses in patients present multiphasic kinetics with distribution, expansion, contraction, and persistence phases. The characteristics and duration of each phase depend on the tumor type, the infused product, and patient-specific characteristics. We present a mathematical model that describes the multiphasic CAR-T cell dynamics resulting from the interplay between CAR-T and tumor cells, considering patient and product heterogeneities. The CAR-T cell population is divided into functional (distributed and effector), memory, and exhausted CAR-T cell phenotypes. The model is able to describe the diversity of CAR-T cell dynamical behaviors in different patients and hematological cancers as well as their therapy outcomes. Our results indicate that the joint assessment of the area under the concentration-time curve in the first 28 days and the corresponding fraction of non-exhausted CAR-T cells may be considered a potential marker to classify therapy responses. Overall, the analysis of different CAR-T cell phenotypes can be a key aspect for a better understanding of the whole CAR-T cell dynamics.

Recent clinical findings in patients with chronic myeloid leukemia (CML) suggest that the risk of molecular recurrence after stopping tyrosine kinase inhibitor (TKI) treatment substantially depends on an individual's leukemia-specific immune response. However, it is still not possible to prospectively identify patients that will remain in treatment-free remission (TFR). Here, we used an ordinary differential equation model for CML, which explicitly includes an antileukemic immunologic effect, and applied it to 21 patients with CML for whom BCR-ABL1/ABL1 time courses had been quantified before and after TKI cessation. Immunologic control was conceptually necessary to explain TFR as observed in about half of the patients. Fitting the model simulations to data, we identified patient-specific parameters and classified patients into three different groups according to their predicted immune system configuration (“immunologic landscapes”). While one class of patients required complete CML eradication to achieve TFR, other patients were able to control residual leukemia levels after treatment cessation. Among them were a third class of patients that maintained TFR only if an optimal balance between leukemia abundance and immunologic activation was achieved before treatment cessation. Model simulations further suggested that changes in the BCR-ABL1 dynamics resulting from TKI dose reduction convey information about the patient-specific immune system and allow prediction of outcome after treatment cessation. This inference of individual immunologic configurations based on treatment alterations can also be applied to other cancer types in which the endogenous immune system supports maintenance therapy, long-term disease control, or even cure. Significance: This mathematical modeling approach provides strong evidence that different immunologic configurations in patients with CML determine their response to therapy cessation and that dose reductions can help to prospectively infer different risk groups. See related commentary by Triche Jr, p. 2083

Four time-dependent dengue transmission models are considered in order to fit the incidence data from the City of Campinas, Brazil, recorded from October 1^st 1995 to September 30^th 2012. The entomological parameters are allowed to depend on temperature and precipitation, while the carrying capacity and the hatching of eggs depend only on precipitation. The whole period of incidence of dengue is split into four periods, due to the fact that the model is formulated considering the circulation of only one serotype. Dengue transmission parameters from human to mosquito and mosquito to human are fitted for each one of the periods. The time varying partial and overall effective reproduction numbers are obtained to explain the incidence of dengue provided by the models.

Chimeric antigen receptor (CAR)-T cell therapy holds significant potential for cancer treatment, although disease relapse and cytokine release syndrome (CRS) remain as frequent clinical challenges. To better understand the mechanisms underlying the temporal dynamics of CAR-T cell therapy response and CRS, we developed a novel multi-layer mathematical model incorporating antigen-mediated CAR-T cell expansion, antigen-negative resistance, and macrophage-associated cytokine release. Three key mechanisms of macrophage activation are considered: release of damage-associated molecular patterns, antigen-binding mediated activation, and CD40-CD40L contact. The model accurately describes 25 patient time courses with different responses and IL-6 cytokine kinetics. We successfully link the dynamic shape of the response to interpretable model parameters and investigate the influence of CAR-T cell dose and initial tumor burden on the occurrence of cytokine release and treatment outcome. By disentangling the timeline of macrophage activation, the model identified distinct contributions of each activation mechanism, suggesting the CD40-CD40L axis as a major driver of cytokine release and a clinically feasible target to control the activation process and modulate cytokine peak height. Our multi-layer model provides a comprehensive framework for understanding the complex interactions between CAR-T cells, tumor cells, and macrophages during therapy.