Research Article Dynamic Modeling of the Angiogenic Switch and Its Inhibition by Bevacizumab Dávid Csercsik 1,2 and Levente Kovács 1 1 Physiological Controls Research Center, University Research, Innovation and Service Center, ´ Obuda University, Budapest, Hungary 2 P´ azm´ any P´ eter Catholic University, Faculty of Information Technology and Bionics, P.O. Box 278, 1444 Budapest, Hungary Correspondence should be addressed to D´ avid Csercsik; csercsik@itk.ppke.hu Received 10 September 2018; Revised 12 November 2018; Accepted 12 December 2018; Published 3 January 2019 Guest Editor: Alejandro F. Villaverde Copyright © 2019 D´ avid Csercsik and Levente Kov´ acs. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We formulate a dynamic model of vascular tumor growth, in which the interdependence of vascular dynamics with tumor volume is considered. Te model describes the angiogenic switch; thus the inhibition of the vascularization process by antiangiogenic drugs may be taken into account explicitly. We validate the model against volume measurement data originating from experiments on mice and analyze the model behavior assuming diferent inputs corresponding to diferent therapies. Furthermore, we show that a simple extension of the model is capable of considering cytotoxic and antiangiogenic drugs as inputs simultaneously in qualitatively diferent ways. 1. Introduction Neovascularization means the formation of new blood ves- sels. Angiogenesis, an important form of neovascularization, is characterized by hypoxia-driven sprouting of new capil- laries from postcapillary venules. Tis mechanism plays an important role in many physiological (e.g., wound healing [1]) and pathological (e.g., macular degeneration [2]) pro- cesses. In the development of tumors, angiogenesis plays an exceptionally important role [3, 4]. In the beginning, when the tumorous cells form a small plaque, the tumor cells are well supported with metabolites by difusion from the environment. However, as the size of the tumor increases, cells in the inside become insufciently supported. Tumor- induced angiogenesis is the process of blood vessel formation, in which new vasculature is formed in order to support these insufciently supported tumor cells. Lately, much has been revealed about the details of tumor- induced angiogenesis and the underlying biochemical and biomechanical regulatory processes. Tese studies served as basis for the development of targeted molecular therapies [5]. Te aim of these therapies is to inhibit tumor-related angiogenesis, thus cutting the tumor from metabolic support. Bevacizumab (Avastin) is a pharmacotherapeutic antian- giogenic agent developed to withhold pathological angiogen- esis [6] via the inhibition of the tumor angiogenic factor VEGF (vascular endothelial growth factor) [7]. VEGF may be considered as a representative member of the family of biochemical agents promoting angiogenesis, called tumor angiogenic factors (TAFs). In [8], two diferent dosage protocols of bevacizumab were compared. In the case of the frst protocol, experimental animals (mice) received one high dose according to the generally accepted medical principle, while in the case of the second protocol (quasi-continuous therapy), a much lower dose was delivered every day of the therapy. Results have shown that the quasi-continuous protocol was more efective, while the total injected amount of the drug was signifcantly less. As antiangiogenic agents are expensive, the total used drug amount is an important aspect to consider in therapeutic design. In addition, reduction of therapeutic doses is also desirable to minimize drug side efects. Te result described in [8] underlines the importance of therapy optimization in the case of the application of antiangiogenic drugs and shows that computational methods may help to exploit the potentials of this approach. Hindawi Complexity Volume 2019, Article ID 9079104, 18 pages https://doi.org/10.1155/2019/9079104