Numerical modelling and control of tumour mutation using piecewise fuzzy approach

Abstract

Mutation dynamics of a cancer tumour is modelled here using numerical non-model-based approach of fuzzy and its metastasis is controlled using a closed loop controller. Cancer is the second cause of death in the world. Metastasis of the cancerous cells is the main source of its fatality and this phenomenon is extremely uncontrollable as a result of drug resistance.  Drug resistance itself is the consequence of the mutation of the cancerous stem cells. Thus modelling the metastasis without considering the effect of mutation is not practically efficient. Since, the exact analytic modelling of mutation is usually impossible, here a numeric approach is proposed toward modelling the cancer mutation using the fuzzy method.  As a result the number of the cancer cells and their related mutations are fuzzificated as the engaged states and their related performance subject to chemotherapy is predicted using the proposed fuzzy model. In order to increase the accuracy of the numerical modelling, the fuzzification process is modified using piecewise algorithm. Employing the mentioned numerical plant, it is possible to design and implement a closed loop controller using the feedback of the tumour, and consequently improve the schedule of chemotherapy in a way that the mutation and tumour growth would be blocked. State Vector Feedback Control (SVFC) is employed here to stabilize the mutation trigger and cancer development. Previous proposed analytic model of the studied cancer is employed here to provide the required data of fuzzy modelling instead of laboratory data and it is shown by the aid of MATLAB simulation that, using the proposed fuzzy model of cancer and mutation, the behaviour of the tumour can be predicted and its mutation and metastasis can be controlled successfully.