Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method

Kassara, Khalid; MOUSTAFİD, Amine

doi:10.1016/j.mbs.2011.02.010

Cited by 20 publications

(28 citation statements)

References 22 publications

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“…The control input varies between 9 mg/kg and 50 mg/kg, and no saturation was needed to fulfill the physiological constraints opposed to the control inputs in [7,9]. In terms of daily and total inlet, adaptive fuzzy control outperformed the controllers presented in [6,8], and the plateau reached is far lower as well. The therapy presented in this paper causes less strain on the body since control input exceeds 40 mg/kg only for 7 days, not for 22 days as in [9].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The initial values of the consequent parts of the relations (the output membeship functions) are set based on a priori information, these are the additive inverses of the reasonable serum lev- els (50 mg/kg is the upper limit and 8.85 mg/kg is the lower limit according to [10]), the negative values are needed because the control design is carried out to determine −u according to (8).…”

Section: Simulation Parametersmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

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confidence: 99%

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

Szeles

Drexler

Sápi

et al. 2014

Per. Pol. Elec. Eng.

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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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Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Parametersmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Szeles

Drexler

Sápi

et al. 2014

Per. Pol. Elec. Eng.

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“…The term f (T ) in (1) describes the drug-free evolution of the tumor that can takes many forms in the literature (see for instance [8], [3], [6] and the references therein). The precise definition of this term is not necessary at this stage.…”

Section: Mathematical Modelmentioning

confidence: 99%

Observer-based efficiency enhancement in cell-cycle specific therapies

Alamir

Fiacchini

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-Cell-cycle specific drugs affect cells when they are in specific phases of their periodic cycle. However, injecting drug's strategy can only by global. This rises the problem of optimizing a global constrained decision variable (drug delivery profile with limited volume) when its effect depends on many local unknown characteristics (the individual cells phases). In this paper, an observer-based framework is proposed that enables a rational decision making in this particular circumstance. Simulation on a simple case are proposed to show the relevance of the proposed framework.

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Qualitative analysis of tumor growth model under antiangiogenic therapy - choosing the effective operating point and design parameters for controller design

Sápi

Drexler

Harmati

et al. 2015

Optim. Control Appl. Meth.

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SUMMARYEvery therapy that fights against cancer aims to reduce the tumor volume as far as possible. However, the price of low tumor volume has to be paid twice: as financial cost and also as side effect cost. In this article, we present qualitative correlation between the steady-state tumor volume and inhibitor serum concentration based on the tumor growth model. Assuming standard state feedback, we present qualitative correlation between the steady-state tumor volume and the parameters of the controller. In case of using an observer, we specify the steady-state tumor volume and the expression for determining the steady-state error of the state observer. We apply a limit for the state feedback to guarantee the stability of the closed-loop system and the positivity of the control signal. The controller parameters depend on the applied operation point where the nonlinear system was linearized. We have investigated the effect of the operation point via simulations, and we present a quantitative theory for choosing the effective operating point.

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Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method

Cited by 20 publications

References 22 publications

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

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

Observer-based efficiency enhancement in cell-cycle specific therapies

Qualitative analysis of tumor growth model under antiangiogenic therapy - choosing the effective operating point and design parameters for controller design

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