Model-based optimal control method for cancer treatment using model predictive control and robust fixed point method

Abstract

Cancerous diseases are being responsible for the death of many around the globe. Treating these illnesses pose a significant challenge to the medical professionals. While conventional methods, chemotherapy or radiotherapy for example, provide a remedy to the issue their side effects are not negligible. In the past few decades new methods have emerged, which could hinder the strength of the side effects and most remarkably, antiangiogenic therapy can make a notable difference in every day cancer treatment. While the technique has many advantages the cost of treatments are often expensive due to the non-personalized administration medical protocols. In this paper a model based solution is provided which aims to lower the medical expenses during the treatment by creating personalized administration plans with the help of control engineering.

The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer

“…After every measurement, the optimal next step in the adaptive therapeutic protocol could be calculated and used to stabilize the tumor burden, or may even be steered to create a pathway toward cure. To compare different mathematical models and seek the optimal cancer treatment, an optimal control theory approach may suffice [7,47,54,57,133,134,160]. Additionally, model predictive control (MPC) can use real-time monitored data to update the optimal cancer treatment.…”

Nonlinear Model Predictive Control Using Robust Fixed Point Transformation-Based Phenomena for Controlling Tumor Growth

“…The tumor reduces under 10 (mm 3 ) volume in 31 (days), with an inhibitor concentration of 765.7 (mg/kg). Compared to the results in [10] this is clearly an improve in terms of concentration during the transient phase, i.e., the amount of medication given to the patient until the tumor volume reaches 10 (mm 3 ). Nominal trajectory Figure 2.…”

“…In spite of these facts, a novel approach is presented in this paper, which combines the optimal behaviour of the Nonlinear Model Predictive Control (NMPC) in conjunction with the error insensitive traits of the Robust Fixed Point Transformation (RFPT) based nonlinear adaptive control. In a previous work, the NMPC architecture was deployed in order to tackle the optimization issue [10]. However as it was indicated in [11], the states of the system are not measurable due to large parameter uncertainties and model imperfections; therefore, an adaptive approach is suggested.…”

The contribution of evolutionary game theory to understanding and treating cancer

“…After every measurement, the optimal next step in the adaptive therapeutic protocol could be calculated and used to stabilize the tumor burden, or might even be steered to create a pathway towards cure. To compare different mathematical models and seek the optimal cancer treatment, an optimal control theory approach may suffice [7,40,46,49,113,114,133]. Additionally, model predictive control (MPC) can use real-time monitored data to update the optimal cancer treatment.…”