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

Abstract

Fighting tumors is one of the most important problems of medical research. In this paper, antiangiogenic cancer therapy is investigated through its mathematical model. This tumor treatment method targets the endothelium of a growing tumor and belongs to the targeted molecular therapies. The aim of the IntroductionCancer treatment is one of the most rapidly developing research fields of medicine. Modern techniques including targeted molecular therapies target only cancerous cells opposed to conventional therapies, e.g. chemotherapy or radiotherapy where both tumorous and normal cells are affected by the applied drugs. In this paper, antiangiogenic therapy is investigated, this method inhibits the tumor from growing own blood vessel cappilaries which serve the tumor to nourish from the host body [1,2]. The most important advantage of the therapy is that patients do not have to suffer from severe side-effects during antiangiogenic treatment, and tumor cells do not develop intrinsic resistance to the angiogenic inhibitors.Philip Hahnfeldt et al. proposed a biologically validated, population based model described by ordinary differential equations in 1999 [3]. Since then, the mathematical model was modified and reformulated many times [4,5]. In this paper a simplified second order model is used to investigate adaptive fuzzy control methodology. For the same model, bang-singular-bang control was designed in [6] and optimal linear control was implemented in [7]. A set-valued protocol was elaborated in [8].More different approaches were used to handle the nonlinearity of the system. 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. Flatness based techniques were not efficient when nominal model parameters changed due to parametric uncertainties. In this paper, adaptive fuzzy control is designed, that can handle both the nonlinearity of the system and the effects of model parameter perturbations.Section 2 focuses on the biomedical background of tumor growth and applied treatments. Section 3 presents the nonlinear model of tumor growth under angiogenic inhibition. In Section 4, the theoretical background of fuzzy control is shortly in-

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Discrete time state feedback with setpoint control, actual state observer and load estimation for a tumor growth model

“…We investigated a well-known tumor growth model under antiangiogenic therapy [1] and designed several continuous time controllers like LQ control method and state observer [2][3][4], flat control [5][6][7], modern robust control method [8][9][10], feedback linearization method [11], and adaptive fuzzy techniques [12]. However, with the current scientific knowledge, there is no medical device which can handle continuous infusion cancer therapy [13]; hence we oriented in the current research work on discrete time control.…”

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.…”