Detailed scientific description

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Project Summary

The key of scientific success in every field nowadays depends on interdisciplinary design. Medical treatment is not an exception either, engineers and doctors have to work together to find more effective solutions in healing. From the thirteen subdisciplines of biomedical engineering [1], physiological modelling, simulations and control represent the basic level: understand the physiological behavior, transform it into a model, and finally, design an automatic and (if possible) personalized drug-delivery treatment methodology for various diseases and injuries.

Cancer diseases are leading causes of death all around the world. In the EU, the total estimated number of cancer casualties for 2014 was 1.323 million [2]. In clinical practice there are general protocols for cancer therapies (like chemotherapy, radiotherapy); however, these treatments have a lot of side effects and tumor cells can become resistant to chemotherapy drugs, which makes the usage of new drugs necessary and from the other side increases the treatment cost.

Using control engineering methodologies (model identification and controller design) the protocols could become model-based and could lead to a personalized and optimal drug-delivery, decreasing the costs as well (Figure 1). The benefit of model-based healthcare applications could be adequately highlighted by diabetes, where research in artificial pancreas increased the quality of life of diabetic patients through the continuous glucose monitoring and insulin pump devices [3].

Figure 1. Basic idea of model-based cancer approach. Cancer treatments (surgical oncology, chemotherapy, radiotherapy and targeted molecular therapies) provide general protocols. Taking into account control engineering methodologies (model identification and controller design) the protocols could become model-based and the treatment could be personalized.

The aim of the current proposal originates from the artificial pancreas problem. Based on our expertise gained throughout the years in diabetes [4]-[8], the challenging inter-disciplinary research idea is to create a control engineering approach to stop vascular system development for the tumor by developing a continuous and auto-matic robust optimal drug delivery algorithm.

The proposed research brings novel approaches leading breakthrough results in cancer therapies. The corresponding medical treatment protocol (i.e. antiangiogenic targeted molecular therapy (ATMT) [9]) relies only on empirical scenarios. However, the corresponding drugs have high costs and lot of side effects; hence, its optimal usage is critical from both quality of life and treatment costs point of view. Our work would lead to personalized therapy possibility by the proposed model-based approach; hence, it would tame cancer effects by improving treatment efficiency, decreasing treatment cost and minimizing side effects of cancer therapy. The benefits and the concept of our innovative approach are summarized in Figure 2.

Figure 2. Benefits of Tamed Cancer. Conventional cancer therapies provide low costs due to the general mechanism of action; however, personalized level is poor in the lack of cancer specificity and personal parameters; side effects are frequent and serious. Using TMTs, high individualization level and limited side effects can be achieved due to specificity against different cancer mechanisms; however, the costs are high due to the expensive drug and empirical drug delivery. Tamed cancer personalizes administration of TMT drugs providing a) high individualization level due to cancer specificity and personalized treatment, b) virtually no side effect, c) low costs due to optimal drug delivery.


Our proposal focuses on modern robust control algorithm development in order to stop the angiogenesis process (i.e. vascular system development) of the tumor; hence, to stop tumor growth, maintaining it in a minimal, “tamed” form. We will refine the currently existing tumor growth model, design optimal control algorithm and guaranteeing its general applicability based on modern robust control methodology. The interdisciplinary nature of the research combines control engineering with computer science (computer simulations and modelling), mathematics (mostly biostatistical analysis) and medical sciences (ATMT). The proposal is structured in the following three objectives.

(Ob1) Tumor growth model identification

Mathematically, the tumor growth modeling question was analyzed in [11]-[12] from the appearance of the tumor growth model (so-called Hahnfeldt-model) [13]. The Hahnfeldt-model was based on the original concept of angiogenesis, i.e. endothelial sprouting (new blood vessels sprout from existing ones). However, newest medical results highlighted that antiangiogenic drugs have effect only in newly built vessels in tumors, but do not have effect on vessels which have already existed [14]. Consequently, there is a strong need to revise the existing tumor growth model, since according to the Hahnfeldt-model; every blood vessel can be eliminated by the drug.

A newly created and validated model [15] takes into account numerous effects, but with its 13 variables and 21 parameters it cannot be used for a further personalized protocol. A simplified model is needed, that is manageable for both real-life applicability and controller design. We have supporting data from our background results [16]-[17]; our proposal will create such a model.

(Ob2) Creating constant and variable quasi-continuous low-dosage therapy protocol

The effectiveness of a therapy strongly depends on the drug administration. While several studies have investigated the effectiveness of bevacizumab therapy according to different cancer types, but nowadays there is an intense debate on its utility. We have examined different methods to find the best tumor volume estimation since it creates the possibility for precise and effective drug administration with a much lower dose than in the protocol. We have found that the effectiveness of a constant lower dosage with a quasi-continuous therapy can be comparable with the protocol therapy or it is even better [18]. These first results show the outstanding opportunities of this research field: considering the possibility of precise tumor volume determination and the effective quasi-continuous drug administration, it brings a new treatment based on closed-loop control.

The usual (protocol-based) delivery of bevacizumab is via intravenous infusion, once every 2 or 3 weeks. The first step for more effective administration is to switch from bolus injection to daily, smaller amount of inhibitor delivery. In silico simulations and in vivo experiments will run separately but parallel. In the case of in silico simulations, administration will be based on the controller’s control signal; while in the case of in vivo experiments, delivery will be based on the previous in vivo results. This will be followed by investigation of variable quasi-continuous low-dosage therapy (i.e. case of time varying systems).

The aim of this objective is to create both constant and variable dose protocols where the administration is based on the prescribed dose, and delivered via injection. These protocols create the possibility of evidence-based personalized cancer therapy; however, this is an open loop control since there is no feedback in the system. Daily cancer therapy is not common since it worsen the quality of life of the patient because of the frequent hospital visits; however workaround for this issue in chemotherapy is already exist known as central venous catheter [19].

(Ob3) Design of optimal robust control algorithms for continuous low-dosage therapy

As it was mentioned above, most of the researchers applied the Hahnfeldt-model to design controller and perform simulations in the field of antiangiogenic control. The most relevant modifications of the original model were done by [20], and here bang-bang control was designed. Singular controls were designed in [21]; it discussed the optimal scheduling problem of a given amount of inhibitors in order to minimize the primary tumor volume. Suboptimal strategies (piecewise constant protocols) were investigated in [22], while [23] applied a set-valued control method. In [21]-[22] the control strategy is based on the tumor volume and the carrying capacity; however, in clinical practice only tumor volume can be measured. All these studies were only theoretical, the applied control strategies are nonlinear, and their practical feasibility was not discussed.

Our group has also analyzed the Hahnfeldt-model and we have designed several different control strategies. Linear Quadratic (LQ) method was used in [24], while linear model-based modern robust control method was applied in [25]. Feedback linearization was investigated for flat control in [26] and switching control in [27]. Comparison of the designed control strategies can be found in [28].

With our solid background in controller design for tumor growth model, our aim is to design optimal robust control algorithms for the newly created model, using the results of previously investigated control methods. Our strength – compared to the competitor researchers in this field – is that we have a very strong and well-functioning collaboration with medical expert and we have on-line developed the practical steps / feasibility questions of the artificial pancreas healthcare research problem [4]-[8]. Most of the researcher engineers and groups do not have the possibility to validate their model and revise the medical relevance of their results. Moreover, providing individualized solution for the patients, but guaranteeing robustness for a generalized medical model-based approach is a high risk challenge that needs adequate expertise. LPV technique [10] represents a postmodern modeling tool in order to treat nonlinear models as linear ones, without the approximation errors introduced by linearization [4], [6]. As a result, linear model-based modern robust control techniques can be applied directly on the original nonlinear model providing robustness in the largest possible way [4], [7]-[8].

[1] Bonzino J. The Biomedical Engineering Handbook. CRC with IEEE Press, 1995.
[2] Malvezzi M, Bertuccio P, Levi F, La Vecchia C, Negri E. European cancer mortality predictions for the year 2014. Ann Oncol, 00: 1-7, 2014.
[3] Cobelli C, Renard E, Kovatchev B. Artificial pancreas: Past, present and future. Diab, 60(11): 2672–2682, 2011.
[4] Kovács L, Benyó B, Bokor J, Benyó Z. Induced L2-norm Minimization of Glucose-Insulin System for Type I Diabetic Patients. Comp Meth Progr Biomed, 102(2): 105-118, 2011.
[5] Kovács L, Kulcsár B, György A, Benyó Z. Robust servo control of a novel type 1 diabetic model. Opt Contr Appl Meth, 32: 215-238, 2011.
[6] Szalay P, Eigner Gy, Kozlovszky M, Rudas I, Kovács L. The significance of LPV modeling of a widely used T1DM model. in Proc. 35th IEEE EMBS, Osaka, Japan, 3531-3534, July 2013.
[7] Kovács L, Szalay P, Almássy Zs, Barkai L. Applicability Results of a Nonlinear Model-Based Robust Blood Glucose Control Algorithm. J Diab Sci Techn, 7(3): 708-716, 2013.
[8] Szalay P, Eigner Gy, Kovács L. Linear Matrix Inequality-based Robust Controller design for Type-1 Diabetes Model. in Proc. 19th IFAC WC 2014, Cape Town, South Africa, 9247-9252, 2014.
[9] Bergers G, Benjamin LE. Tumorigenesis and the angiogenic switch. Nat Rev Cancer. 3(6): 401-410, 2003.
[10] Kosea I. Robust control of linear systems with real parametric uncertainty. Automatica. 35:679–687, 1999.
[11] Ledzewicz U, Schättler H. On an extension of a mathematical model for tumor anti-angiogenesis. Nonlin Analysis. 71: 2390-2397, 2009.
[12] Ledzewicz U, Schättler H. Optimal and suboptimal protocols for a class of mathematical models of tumor antiangiogenesis. J Theor Biol. 252: 295-312, 2008.
[13] Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L. Tumor Development under Angiogenic Signaling: A Dynamical Theory of Tumor Growth, Treatment Response, and Postvascular Dormancy. Cancer Res. 59: 4770-4775, 1999.
[14] Petersen I. Antiangiogenesis, anti-VEGF(R) and outlook. in: M. Dietel (Ed.), Recent Results in Cancer Research, Targeted Therapies in Cancer, Springer-Verlag Berlin-Heidelberg, 2007.
[15] Gevertz JL. Computational modeling of tumor response to vascular-targeting therapies – part I: validation. Comput Math Methods Med, 2011.
[16] Kiss B, Sápi J, Kovács L. Imaging method for model-based control of tumor diseases. in Proc. 11th IEEE SISY, Subotica, Serbia, 271-275, 2013.
[17] Sápi J, Drexler DA, Sápi Z, Kovács L. Identification of C38 colon adenocarcinoma growth under bevacizumab therapy and without therapy. in Proc. 15th IEEE CINTI, Budapest, Hungary, 443-448, 2014.
[18] Sápi J, Kovács L, Drexler DA, Kocsis P, Gajári D, Sápi Z. Tumor Volume Estimation and Quasi-Continuous Administration for Most Effective Bevacizumab Therapy, PLOS ONE, submitted, 2015.
[19] Galloway S, Bodenham A. Long‐term central venous access. Br J Anaesth. 2004; 92:722-34.
[20] D’Onofrio A, Gandolfi A. Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. Math Biosci, 191: 159-184, 2004.
[21] Ledzewicz U, Schättler H. Anti-angiogenic therapy in cancer treatment as an optimal control problem. SIAM J Contr Opt, 46: 1052-1079, 2007.
[22] Ledzewicz U, Marriott J, Maurer H, Schättler H. Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment. Math Med Biol, 27(2): 157-179, 2010.
[23] Kassara K, Moustafid A. Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method. Math Biosci, 231(2):1351-1343, 2011.
[24] Szeles A, Sápi J, Drexler DA, Harmati I, Sápi Z, Kovács L. Model-based angiogenic inhibition of tumor growth using modern robust control method. in Proc. 8th IFAC BMS, Budapest, Hungary, 113–118, 2012.
[25] L Kovács, A Szeles, J Sápi, DA Drexler, I Rudas, I Harmati, Z Sápi. Model-based Angiogenic Inhibition of Tumor Growth using Modern Robust Control Method. Comp Meth Prog Biomed, 114: 98-110, 2014.
[26] Drexler DA, Sápi J, Szeles A, Harmati I, Kovács A, Kovács L. Flat control of tumor growth with angiogenic inhibition. in Proc. 6th IEEE SACI, Timisoara, Romania, 179-183, 2012.
[27] Szeles A, Drexler DA, Sápi J, Harmati I, Sápi Z, Kovács L. Model-based Angiogenic Inhibition of Tumor Growth using Feedback Linearization. in Proc. 52nd IEEE CDC, Florence, Italy, 2054-2059, 2013.
[28] Szeles A, Drexler DA, Sápi J, Harmati I, Kovács L. Study of Modern Control Methodologies Applied to Tumor Growth under Angiogenic Inhibition. in Proc. 19th IFAC WC, Cape Town, South Africa, 9271-9276, 2014.

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