Therapeutic protocols in immunotherapy are usually proposed following the intuition and experience of the therapist. In order to deduce such protocols mathematical modeling, optimal control and simulations are used instead of the therapist's experience. Clinical efficacy of dendritic cell (DC) vaccines to cancer treatment is still unclear, since dendritic cells face several obstacles in the host environment, such as immunosuppression and poor transference to the lymph nodes reducing the vaccine effect. In view of that, we have created a mathematical murine model to measure the effects of dendritic cell injections admitting such obstacles. In addition, the model considers a therapy given by bolus injections of small duration as opposed to a continual dose. Doses timing defines the therapeutic protocols, which in turn are improved to minimize the tumor mass by an optimal control algorithm. We intend to supplement therapist's experience and intuition in the protocol's implementation. Experimental results made on mice infected with melanoma with and without therapy agree with the model. It is shown that the dendritic cells' percentage that manages to reach the lymph nodes has a crucial impact on the therapy outcome. This suggests that efforts in finding better methods to deliver DC vaccines should be pursued.

The infusion times and drug quantities are two primary variables to optimize when designing a therapeutic schedule. In this work, we test and analyze several extensions to the gradient descent equations in an optimal control algorithm conceived for therapy scheduling optimization. The goal is to provide insights into the best strategies to follow in terms of convergence speed when implementing our method in models for dendritic cell immunotherapy. The method gives a pulsed-like control that models a series of bolus injections and aims to minimize a cost a function, which minimizes tumor size and to keep the tumor under a threshold. Additionally, we introduce a stochastic iteration step in the algorithm, which serves to reduce the number of gradient computations, similar to a stochastic gradient descent scheme in machine learning. Finally, we employ the algorithm to two therapy schedule optimization problems in dendritic cell immunotherapy and contrast our method’s stochastic and non-stochastic optimizations.

Nowadays, immunotherapy has become an important alternative to fight cancer. One way in which biologists and medics use immunotherapy is by injecting antigen-incubated Dendritic Cells (DCs) into mice to stimulate an immune response. The DCs optimal quantities and infusion times for a successful cancer eradication are often unknown to the therapists; usually, these quantities are obtained by testing various protocols. The article shows a model of five differential equations which represents some interactions between some cells of the immune system and tumor cells which is used to test different infusion protocols of Dendritic Cells. This study aims to find operation ranges to DCs quantities and injection times for which the therapy reduces the tumor significantly. To that end, an exhaustive search of operative protocols is performed using simulations of a mathematical model. Furthermore, nonlinear analysis of the model reveals that without the DC therapy tumor cells cannot stay under non-lethal bounds. Finally, we show that a pulsed periodic therapy can prevent tumor relapsing when the doses and period times lie within a certain range.