Model-based angiogenic inhibition of tumor growth using feedback linearization

Abstract

In the last decades beside conventional cancer treatment methods, molecular targeted therapies show prosperous results. These therapies have limited side-effects, and in comparison to chemotherapy, tumorous cells show lower tendency of becoming resistant to the applied antiangiogenic drugs. In clinical research, antiangiogenic therapy is one of the most promising cancer treatment methods. Using a simplified model of the reference dynamical model for tumor growth under angiogenic inhibition from the literature, exact linearization is performed in the paper to handle the nonlinear behavior of the model. Two different control methods are applied on the linearized model: flat control and switching control. Simulations are performed on the nonlinear model to show the characteristics of the therapies carried out using the presented control methods.

Model-based Angiogenic Inhibition of Tumor Growth using Adaptive Fuzzy Techniques

“…However, the controller was not able to reach the minimal volume (1 mm 3 ) in 50 days as controllers in [11,12]; the plateau can be attained after 100 days. The effects of model parameter perturbations were investigated, since the advantage of adaptive fuzzy methodology is that controller design can be carried out without knowing the exact model formulation using appropriate estimation.…”

“…The constraint is fulfilled, related calculations were published in [12]. The notations are the following: n is the differential order of the system (n = 2), f (x) ∈ R, g(x) ∈ R (since the controlled system is a single-input single-output system), and g(x) > 0.…”

“…The adaptation law and the supervisory control related parameters were set according to results of exact linearization [12]. The real-valued functions of the system transformed into the form of (7) are…”

“…Working point linearization was performed to design and analyze state-space and robust control in former papers [7,9,10], flatness based technique was proposed in [11] for the original model using constant Hurwitz polinomial,and in [12] for the simplified model using tumor volume dependent Hurwitz polinomials. Linear controllers could not handle the nonlinearity of the system appropriately, since the magnitude of the control input was infeasible, and the avascular state of the tumor was not attained.…”

Potential Benefits of Discrete-Time Controller-based Treatments over Protocol-based Cancer Therapies

“…We investigated a well-known tumor growth model under antiangiogenic therapy [6] and designed several continuous-time controllers like an LQ control method and state observer [7][8][9], flat control [10][11][12], modern robust control method [13][14][15], feedback linearization method [16] and adaptive fuzzy techniques [17]. However, with the current scientific knowledge, there is no medical device which can handle continuous infusion cancer therapy [18]; hence we designed a discretetime control herein.…”