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Khajanchi2015 - The combined effects of optimal control in cancer remission

ABSTRACT: The combined effects of optimal control in cancer remission SubhasKhajanchi DibakarGhosh Abstract We investigate a mathematical model depicting the nonlinear dynamics of immunogenic tumors as envisioned by Kuznetsov et al. [1]. To understand the dynamics under what circumstances the cancer cells can be eliminated, we implement the theory of optimal control. We design two types of external treatment strategies, one is Adoptive Cellular Immunotherapy and another is interleukin-2. Our aim is to establish the treatment regimens that maximize the effector cell count and minimize the tumor cell burden and the deleterious effects of the total amount of drugs. We derive the existence of an optimal control by using the boundedness of solutions. We characterize the optimality system, in which the state system is coupled with co-states. The uniqueness of an optimal control of our problem is also analyzed. Finally, we demonstrate the numerical illustrations that the optimal regimens reduce the tumor burden under different scenarios.

SUBMITTER: Mohammad Umer Sharif Shohan

PROVIDER: BIOMD0000000897 | BioModels | 2020-01-03

REPOSITORIES: BioModels

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Project description:Predicting Outcomes of Prostate Cancer Immunotherapyby Personalized Mathematical Models Natalie Kronik1¤, Yuri Kogan1, Moran Elishmereni1, Karin Halevi-Tobias1, Stanimir Vuk-Pavlovic ́2.,Zvia Agur1*.1Institute for Medical BioMathematics, Bene Ataroth, Israel,2College of Medicine, Mayo Clinic, Rochester, Minnesota, United States of America Abstract 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 simplemathematical models.Methodology/Principal Findings:We developed a general mathematical model encompassing the basic interactions of avaccine, immune system and PCa cells, and validated it by the results of a clinical trial testing an allogeneic PCa whole-cellvaccine. For model validation in the absence of any other pertinent marker, we used the clinically measured changes inprostate-specific antigen (PSA) levels as a correlate of tumor burden. Up to 26 PSA levels measured per patient were dividedinto each patient’s training set and his validation set. The training set, used for model personalization, contained thepatient’s initial sequence of PSA levels; the validation set contained his subsequent PSA data points. Personalized modelswere 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 wasR2= 0.972). The model could notaccount for the inconsistent changes in PSA levels in 3 of the 15 responsive patients at the end of treatment. Each validatedpersonalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccinationregimens. 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 PCaimmunotherapy, which were retrospectively validated by clinical trial results. Our results emphasize the potential value andfeasibility of individualized model-suggested immunotherapy protocols.

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Khajanchi2015 - The combined effects of optimal control in cancer remission

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