Hami Tourajizadeh - Department of Mechanical Engineering, Faculty of engineering, University of Kharazmi, Tehran, Iran
zahra zarandi - Department of Mechanical Engineering, Faculty of engineering, University of Kharazmi, Tehran, Iran
zakie farbodi - Department of Mechanical Engineering, Faculty of engineering, University of Kharazmi, Tehran, Iran
ehsan sadeghi - Departeman of Electrical Engineering, Sistan and Baluchestan University, Zahedan, Iran

In this paper, the analytic model of the mutation dynamics related to the cancer cells which is under the control of chemotherapy is developed and its corresponding metastasis is controlled using chemotherapy method.  The progress of a cancer tumours is contributed to two main factors including metastasis and mutation. It is observed that controlling the metastasis dynamic without considering the mutation phenomenon is doomed to fail. In this paper, the mathematical model of the cancer dynamic is improved considering the mutation of the stem cells and the effect of chemotherapy injection as the corresponding controlling signal is investigated in the extracted state space. Controlling the cancer growth and its mutation process is accomplished here using PID controller and State Feedback Control (SVFC) method. It is shown that by the aid of the proposed model of this paper, not only the number of the cancer cells can be converted to zero, but also the mutation process can be blocked since the feedback of the mutated cells are also engaged in the state space of the system. Verification of the model is conducted by the aid of simulation in the MATLAB and comparing the results with previous studies.

Cancer Modelling, Dynamics of mutation, Metastasis Controlling, Stem-cells