State/Parameter Identification in Cancerous Models Using Unscented Kalman Filter

Abstract

Cancer is a disease affecting humans around the world. Exploring a deep understanding of the state/parameter estimation based on the drug prescription provides an awareness of the patient’s experience during the treatment. Applying controllers to such systems with the primary aim of reducing cancer cells with the fewest side effects is a very interesting field in the past decade. The usual assumptions followed when designing a controller are that all system parameters are constant and all states are measurable. However, this is not the case in reality. In this article, based on a five-states differential equation model, which models a combined therapy of chemotherapy and anti-angiogenic, the state and/or parameters are estimated using an unscented Kalman filter while a nonlinear adaptive controller produces drug injection rate as the control signals utilizing the estimated state/parameter. The advantage of this estimation method is that, unlike in the traditional extended Kalman filter, nonlinear dynamics can be used without any linearization. The results show that the state and parameter estimation with UKF was successful. This idea can be used to assign a mathematical cancer dynamic for any individual, and state/parameter estimation can be studied and verified throughout a patient’s treatment.