Studying the importance of regulatory T cells in chemoimmunotherapy mathematical modeling and proposing new approaches for developing a mathematical dynamic of cancer.

Studying the mathematical dynamics of cancer has gained the attention of bioengineers in the past three decades. Different kinds of modelling considering various aspects of treatment have been proposed. In this paper, the key role of Regulatory T cells is discussed and a model in ordinary differential equation (ODE) form is proposed by adding this state to the system dynamics considering chemoimmunotherapy treatment. Regulatory T cells are considered as one of the main tumor cells' tactics to deceive the body's immune system. The improved model is verified mathematically and biologically and fits all criteria in both fields. The results show that entering Regulatory T cells state on cancer mathematical modelling for simulating body cells for chemoimmunotherapy provides a way to identify critical cases more carefully, which a simplified model is unable to accomplish. This point emphasizes the fact that this state must be present in cancer modelling to anticipate immune response more accurately. The advanced system fixed points are obtained by the Newton method and bifurcation diagrams are derived and discussed. New features and remarks are proposed during the journey of developing more accurate models that have the best fit with laboratory data. The sensitivity chart of the model is illustrated and novel aspects of discussions are made with the aim of personalizing a model for a patient and identifying critical conditions based on the chart before any treatment begins. This point enables physicians to determine whether critical conditions have occurred for a patient in a specific treatment or not.

Optimal control design for drug delivery of immunotherapy in chemoimmunotherapy treatment.

BACKGROUND AND OBJECTIVE: There are various approaches to control a mathematical dynamic of cancer, each of which is suitable for a special goal. Optimal control is considered as an applicable method to calculate the minimum necessary drug delivery in such systems. METHODS: In this paper, a mathematical dynamic of cancer is proposed considering tumor cells, natural killer cells, CD8+T cells, circulating lymphocytes, IL-2 cytokine and Regulatory T cells as the system states, and chemotherapy, IL-2 and activated CD8+T cells injection rate as the control signals. After verifying the proposed mathematical model, the importance of the drug delivery timing and the effect of cancer cells initial condition are discussed. Afterwards, an optimal control is designed by defining a proper cost function with the goal of minimizing the number of tumor cells, and two immunotherapy drug amounts during treatment CONCLUSIONS: Results show that inappropriate injection of immunotherapy time schedule and the number of initial conditions of cancer cells might result in chemoimmunotherapy failure and auxiliary treatment must be prescribed to decrease tumor size before any treatment takes place. The obtained optimal control signals show that with lower amount of drug delivery and a suitable drug injection time schedule, tumor cells can be eliminated while a fixed immunotherapy time schedule protocol fails with larger amount of drug injection. This conclusion can be utilized with the aim of personalizing drug delivery and designing more accurate clinical trials based on the improved model simulations in order to save cost and time.

Subcutaneous insulin administration by deep reinforcement learning for blood glucose level control of type-2 diabetic patients.

BACKGROUND: Type-2 diabetes mellitus is characterized by insulin resistance and impaired insulin secretion in the human body. Many endeavors have been made in terms of controlling and reducing blood glucose via the medium of automated controlling tools to increase precision and efficiency and reduce human error. Recently, reinforcement learning algorithms are proved to be powerful in the field of intelligent control, which was the motivation for the current study. METHODS: For the first time, a reinforcement algorithm called normalized advantage function (NAF) algorithm has been applied as a model-free reinforcement learning method to regulate the blood glucose level of type-2 diabetic patients through subcutaneous injection. The algorithm has been designed and developed in a model-free approach to avoid additional inaccuracies and parameter uncertainty introduced by the mathematical models of the glucoregulatory system. Insulin doses constitute the control action that is designed to be stated directly in clinical language with the unit IU. In this regard, a new environment state is considered in addition to the glucose level to take into account the delayed effect of insulin elimination under the skin. Finally, a simple but practical reward function is developed to be used with the NAF algorithm to correct the glucose level and maintain it in the desired range. RESULTS: The simulation environment was set up to imitate the basal-bolus process accurately. Results for 30 days of simulation of the designed controller on three different average virtual patients verify the feasibility and effectiveness of the method and reveal our proposed controller's learning ability. Moreover, as the insulin elimination dynamic was taken into account, a more complete and more realistic model than the previously studied models has emerged. CONCLUSION: NAF has proved a promising control approach, able to successfully regulate and significantly reduce the fluctuation of the blood glucose without meal announcements, compared to standard optimized open-loop basal-bolus therapies. The method and its results, which are directly in the clinical language, are applicable in real-time clinical situations.

Optimal control methods for drug delivery in cancerous tumour by anti-angiogenic therapy and chemotherapy.

There are numerous mathematical models simulating the behaviour of cancer by considering variety of states in different treatment strategies, such as chemotherapy. Among the models, one is developed which is able to consider the blood vessel-production (angiogenesis) in the vicinity of the tumour and the effect of anti-angiogenic therapy. In the mentioned-model, normal cells, cancer cells, endothelial cells, chemotherapy and anti-angiogenic agents are taking into account as state variables, and the rate of injection of the last two are considered as control inputs. Since controlling the cancerous tumour growth is a challenging matter for patient's life, the time schedule design of drug injection is very significant. Two optimal control strategies, an open-loop (calculus of variations) and a closed-loop (state-dependent Riccati equation), are applied on the system in order to find an optimal time scheduling for each drug injection. By defining a proper cost function, an optimal control signal is designed for each one. Both obtained control inputs have reasonable answers, and the system is controlled eventually, but by comparing them, it is concluded that both methods have their own benefits which will be discussed in details in the conclusion section.

Nonlinear adaptive control of tuberculosis with consideration of the risk of endogenous reactivation and exogenous reinfection.

Tuberculosis is one of deadly diseases in many countries that attacks to the human body and causes damage to the lung, causing bloody coughing and if left untreated, it will kill half of the affected people. Tuberculosis bacteria can stay latent and reactivate after passing appropriate conditions. For this reason, control of this disease and treatment of infected people has a significant importance, and observing health issues can prevent the spread of it. In this paper, a nonlinear adaptive control method is proposed for the first time in order to control and treat tuberculosis outbreak subjected to the modeling uncertainty. To design a control system being robust against uncertainties, an adaptation law is defined to update values of estimated parameters and ensures the whole system stability. The treatment achievement and stability of the closed-loop system is proved by the Lyapunov theorem and confirmed by some simulations. The proposed strategy has the capability to control the tuberculosis outbreak by reducing the numbers of active infectious and persistent latent individuals based on their desired values in the society.

Derivation of an optimal trajectory and nonlinear adaptive controller design for drug delivery in cancerous tumor chemotherapy.

Numerous models have investigated cancer behavior by considering different factors in chemotherapy. The subject of a controller design approach for these models in order to find the best rate of drug injection during the course of treatment has recently attracted much attention. The rate of drug injections is very important in chemotherapy, as it not only causes cancer cells to die, but also kills healthy cells. On the other hand, by modeling tumor growth behavior in each patient, different parameters for the dynamics of the system should be considered. In this study, optimal control signals were obtained for the most recent model of chemotherapy, using the steepest descent method. The logic of the solution was biologically compared to the experimental results. Then an adaptive controller, considering this path as the desired optimal trajectory, directs the system towards it. The global stability of the closed-loop system is achieved by means of the Lyapunov stability theory and Barbalat lemma. It is worth noting that some of the system parameters are estimated using an online recursive estimation method. Simulation results indicate the performance and effectiveness of the designed controller. The estimation parameters are also verified using experimental data from available studies.

Optimal sliding mode control of drug delivery in cancerous tumour chemotherapy considering the obesity effects.

Different control strategies have been proposed for drug delivery in chemotherapy during recent years. These control algorithms are designed based on dynamic models of various orders. The order of the model depends on the number of effects considered in the model. In a recent model, the effect of obesity on the tumour progression and optimal control strategy in chemotherapy have been investigated in a fifth-order state-space model. However, the optimal controller is open loop and not robust to the common uncertainties of such biological system. Here, the sliding surface is obtained by the optimal trajectory and by considering uncertainties of some parameters, the robust-sliding control law is formulated in a way to slid on the optimal surface. Then, a sliding mode controller is designed to determine the drug dose rate such that the system follows the optimal desired trajectory. The stability of the control system is proved and the simulation results indicate that three states track the trajectory and the remaining two states satisfy the constraints.

Optimal neuro-fuzzy control of hepatitis C virus integrated by genetic algorithm.

Hepatitis C blood born virus is a major cause of liver disease that more than three per cent of people in the world is dealing with, and the spread of hepatitis C virus (HCV) infection in different populations is one of the most important issues in epidemiology. In the present study, a new intelligent controller is developed and tested to control the hepatitis C infection in the population which the authors refer to as an optimal adaptive neuro-fuzzy controller. To design the controller, some data is required for training the employed adaptive neuro-fuzzy inference system (ANFIS) which is selected by the genetic algorithm. Using this algorithm, the best control signal for each state condition is chosen in order to minimise an objective function. Then, the prepared data is utilised to build and train the Takagi-Sugeno fuzzy structure of the ANFIS and this structure is used as the controller. Simulation results show that there is a significant decrease in the number of acute-infected individuals by employing the proposed control method in comparison with the case of no intervention. Moreover, the authors proposed method improves the value of the objective function by 19% compared with the ordinary optimal control methods used previously for HCV epidemic.