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.

In this systematic review, we foresee what could be the approved scenario in the next few years for CAR-T cell therapies directed against hematological and solid tumor malignancies. China and the USA are the leading regions in numbers of clinical studies involving CAR-T. Hematological antigens CD19 and BCMA are the most targeted, followed by mesothelin, GPC3, CEA, MUC1, HER2, and EGFR for solid tumors. Most CAR constructs are second-generation, although third and fourth generations are being largely explored. Moreover, the benefit of combining CAR-T treatment with immune checkpoint inhibitors and other drugs is also being assessed. Data regarding product formulation and administration, such as cell phenotype, transfection technique, and cell dosage, are scarce and could not be retrieved. Better tracking of trials’ status and results on the ClinicalTrials.gov database should aid in a more concise and general view of the ongoing clinical trials involving CAR-T cell therapy.

The present study evaluated the seasonal variation of a population of Hypena sp. in the Gruta Taboa (Sete Lagoas, Minas Gerais, Brazil), in relation to changes in temperature and humidity during the dry (July 1999 and July 2000) and rainy (January 2000 and January 2001) seasons. The Hypena sp. population responded to external seasonality, being distributed closer to the cave entrance during the rainy season, in which temperature and humidity fluctuated around 21 °C and 85%, respectively. During the dry season abundance was higher in sections farther from the entrance (deeper sections) (19.2 °C temperature and 80% humidity). The results showed that this species is influenced by external environmental factors, even in a tropical region where the external climate fluctuations are lower compared to temperate regions.

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.

Mathematical and computational modeling have been increasingly applied in many areas of cancer research, aiming to improve the understanding of tumorigenic mechanisms and to suggest more effective therapy protocols. The mathematical description of the tumor growth dynamics is often made using the exponential, logistic, and Gompertz models. However, recent literature has suggested that the Allee effect may play an important role in the early stages of tumor dynamics, including cancer relapse and metastasis. For a model to provide reliable predictions, it is necessary to have a rigorous evaluation of the uncertainty inherent in the modeling process. In this work, our main objective is to show how a model framework that integrates sensitivity analysis, model calibration, and model selection techniques can improve and systematically characterize model and data uncertainties. We investigate five distinct models with different complexities, which encompass the exponential, logistic, Gompertz, and weak and strong Allee effects dynamics. Using tumor growth data published in the literature, we perform a global sensitivity analysis, apply a Bayesian framework for parameter inference, evaluate the associated sensitivity matrices, and use different information criteria for model selection (First- and Second-Order Akaike Information Criteria and Bayesian Information Criterion). We show that such a wider methodology allows having a more detailed picture of each model assumption and uncertainty, calibration reliability, ultimately improving tumor mathematical description. The used in vivo data suggested the existence of both a competitive effect among tumor cells and a weak Allee effect in the growth dynamics. The proposed model framework highlights the need for more detailed experimental studies on the influence of the Allee effect on the analyzed cancer scenario.

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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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 presents a 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 on patient-specific characteristics. We present a mathematical model which 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 dynamic 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 as potential markers 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.