Modeling of cancer growth considering the dynamics of mutation and controlling the cell proliferation of cancer in the presence of mutation using adaptive control

Cancer is a prevalent disease nowadays, and its mortal and incurable entity makes its treatment a challenging process. The main obstacle to the treatment of this disease, however, is the so-called mutation phenomenon. In this paper, the dynamics of this phenomenon are estimated as an independent state and are coupled to the dynamics of the other cancer states which makes the behavior of the cancer more predictable. As a result, with the aid of this modified nonlinear dynamics, a properly closed-loop controller is designed and implemented on the cancer system by which both metastasis and mutation can be controlled simultaneously by extracting the time-dependent dosage of the chemotherapy according to the cancerous cell population. On the other hand, taking into account that the engaged parameters in mutation dynamics cannot be perfectly approximated as an unknown phenomenon, an adaptive controller is designed which makes the treatment even more robust against the parametric uncertainties contributed to the mutation dynamics. The modified state space, including mutation as an independent state, is first developed, and two controllers of feedback linearization and an adaptive controller are designed. With the aid of some analytic and comparative simulations, the necessity of modeling mutation and the efficiency of the proposed controllers are analyzed and compared. It is shown that taking into account the mutation dynamics in the designed controller of the cancer increases the speed of the cancer treatment and decreases its relapse.