Less is more: reducing the number of administered chimeric antigen receptor T cells in a mouse model using a mathematically guided approach.

Chimeric antigen receptor T cell (CAR-T) therapy is a novel approved treatment for hematological malignancies, still under development for solid tumors. Here, we use a rate equation-based mathematical model to discover regimens and schedules that maintain efficacy while potentially reducing toxicity by decreasing the amount of CAR-T infused. Tested on an in vivo murine model of spontaneous breast cancer, we show that our mathematical model accurately recapitulates in vivo tumor growth results achieved in the previous experiments. Moreover, we use the mathematical model to predict results of new therapy schedules and successfully prospectively validated these predictions in the in vivo. We conclude that using one tenth and even one percent of a full CAR-T dose used in preclinical trials can achieve efficacious results similar to full dose treatment.

Improving Bacillus Calmette-Guérin (BCG) immunotherapy for bladder cancer by adding interleukin 2 (IL-2): a mathematical model.

One of the treatments offered to non-invasive bladder cancer patients is BCG instillations, using a well-established, time-honoured protocol. Some of the patients, however, do not respond to this protocol. To examine possible changes in the protocol, we provide a platform for in silico testing of alternative protocols for BCG instillations and combinations with IL-2, to be used by urologists in planning new treatment strategies for subpopulations of bladder cancer patients who may benefit from a personalized protocol. We use a systems biology approach to describe the BCG-tumour-immune interplay and translate it into a set of mathematical differential equations. The variables of the equation set are the number of tumour cells, bacteria cells, immune cells, and cytokines participating in the tumour-immune response. Relevant parameters that describe the system's dynamics are taken from a variety of independent literature, unrelated to the clinical trial results assessed by the model predictions. Model simulations use a clinically relevant range of initial tumour sizes (tumour volume) and tumour growth rates (tumour grade), representative of a virtual population of fifty patients. Our model successfully retrieved previous clinical results for BCG induction treatment and BCG maintenance therapy with a complete response (CR) rate of 82%. Furthermore, we designed alternative maintenance protocols, using IL-2 combinations with BCG, which improved success rates up to 86% and 100% of the patients, albeit without considering possible side effects. We have shown our simulation platform to be reliable by demonstrating its ability to retrieve published clinical trial results. We used this platform to predict the outcome of treatment combinations. Our results suggest that the subpopulation of non-responsive patients may benefit from an intensified combined BCG IL-2 maintenance treatment.

Improving T-cell immunotherapy for melanoma through a mathematically motivated strategy: efficacy in numbers?

T-cell mediated immunotherapy for malignant diseases has become an effective treatment option, especially in malignant melanoma. Recent advances have enabled the transfer of high T-cell numbers with high functionality. However, with more T cells becoming technically available for transfer, questions about dose, treatment schedule, and safety become most relevant. Mathematical oncology can simulate tumor characteristics in silico and predict the tumor response to novel therapeutics. Using similar methods to classical pharmacokinetics/pharmacodynamics-type models, mathematical oncology translates the findings into a multiparameter model system and simulates T-cell therapy for malignant diseases. The tumor and immune system dynamics model can provide minimal requirements (in terms of T-cell dose and T-cell functionality) depending on the tumor characteristics (growth rate, residual tumor size) for a clinical study, and help select the best treatment schedule (repetitive doses, minimally required duration, etc.). Here, we present a new mathematical model developed for modeling cellular immunotherapy for melanoma. Computer simulations based on the new model offer an explanation for the observed finding from clinical trials that the patients with the smallest tumor load respond better. We simulate different parameters critical for improvement of cellular therapy for patients with high tumor load of fast-growing tumors. We show that tumor growth rate and tumor load are crucial in predicting the outcome of T-cell therapy. Rather than intuitively extrapolating from experimental data, we demonstrate how mathematical oncology can assist in rational planning of clinical trials.

Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models.

BACKGROUND: Therapeutic vaccination against disseminated prostate cancer (PCa) is partially effective in some PCa patients. We hypothesized that the efficacy of treatment will be enhanced by individualized vaccination regimens tailored by simple mathematical models. METHODOLOGY/PRINCIPAL FINDINGS: We developed a general mathematical model encompassing the basic interactions of a vaccine, immune system and PCa cells, and validated it by the results of a clinical trial testing an allogeneic PCa whole-cell vaccine. For model validation in the absence of any other pertinent marker, we used the clinically measured changes in prostate-specific antigen (PSA) levels as a correlate of tumor burden. Up to 26 PSA levels measured per patient were divided into each patient's training set and his validation set. The training set, used for model personalization, contained the patient's initial sequence of PSA levels; the validation set contained his subsequent PSA data points. Personalized models were simulated to predict changes in tumor burden and PSA levels and predictions were compared to the validation set. The model accurately predicted PSA levels over the entire measured period in 12 of the 15 vaccination-responsive patients (the coefficient of determination between the predicted and observed PSA values was R(2) = 0.972). The model could not account for the inconsistent changes in PSA levels in 3 of the 15 responsive patients at the end of treatment. Each validated personalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccination regimens. Personalized regimens predicted to enhance the effects of therapy differed among the patients. CONCLUSIONS/SIGNIFICANCE: Using a few initial measurements, we constructed robust patient-specific models of PCa immunotherapy, which were retrospectively validated by clinical trial results. Our results emphasize the potential value and feasibility of individualized model-suggested immunotherapy protocols.

Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics.

Glioblastoma (GBM), a highly aggressive (WHO grade IV) primary brain tumor, is refractory to traditional treatments, such as surgery, radiation or chemotherapy. This study aims at aiding in the design of more efficacious GBM therapies. We constructed a mathematical model for glioma and the immune system interactions, that may ensue upon direct intra-tumoral administration of ex vivo activated alloreactive cytotoxic-T-lymphocytes (aCTL). Our model encompasses considerations of the interactive dynamics of aCTL, tumor cells, major histocompatibility complex (MHC) class I and MHC class II molecules, as well as cytokines, such as TGF-beta and IFN-gamma, which dampen or increase the pro-inflammatory environment, respectively. Computer simulations were used for model verification and for retrieving putative treatment scenarios. The mathematical model successfully retrieved clinical trial results of efficacious aCTL immunotherapy for recurrent anaplastic oligodendroglioma and anaplastic astrocytoma (WHO grade III). It predicted that cellular adoptive immunotherapy failed in GBM because the administered dose was 20-fold lower than required for therapeutic efficacy. Model analysis suggests that GBM may be eradicated by new dose-intensive strategies, e.g., 3 x 10(8) aCTL every 4 days for small tumor burden, or 2 x 10(9) aCTL, infused every 5 days for larger tumor burden. Further analysis pinpoints crucial bio-markers relating to tumor growth rate, tumor size, and tumor sensitivity to the immune system, whose estimation enables regimen personalization. We propose that adoptive cellular immunotherapy was prematurely abandoned. It may prove efficacious for GBM, if dose intensity is augmented, as prescribed by the mathematical model. Re-initiation of clinical trials, using calculated individualized regimens for grade III-IV malignant glioma, is suggested.