Bi-compartmental modelling of tumor and supporting vasculature growth dynamics for cancer treatment optimization purpose D´ avid Csercsik, Johanna S´ api, Tam´ as G¨ onczy and Levente Kov´ acs Abstract— We introduce a nonlinear bi-compartmental dy- namic tumor cell and supporting vasculature volume growth model which takes into account nutrient and cell proliferation, necrosis and angiogenesis. Validation of the model requires measurement data on tumor volume during the therapy; for explicit identification of vasculature growth dynamic, in vivo measurement data on vasculature volume during the therapy are required as well. We show that the model can be used for the evaluation of drug dosage protocols. I. I NTRODUCTION Recently it has been shown by [1] that innovative dosage delivery methods of anti-angiogenic drugs may be more effective for treating tumors, compared to conventional anti- angiogenic dosage protocols. In order to optimize such therapies with computer methods, we need a computational model, which is on the one hand capable of the integration of pathophysiological knowledge and measurement data. On the other hand, its computational complexity should be at a tractable level regarding optimization and controller design purposes. Controller design methodology is unavoidable if we wish to develop closed loop devices in the future for personalized tumor treatment purposes [2]. The drawbacks and shortcomings of models which are suitable for controller design are summarized in [3]. A common feature of these models is that either they do not explicitly consider angio- genesis, or they are far too complex for controller design [4]. For a recent review of integrative models of vascular remodeling during tumor growth see [5]. The Hahnfeldt model [6] considers vasculature volume changes during tumor growth; however, its validity has been already questioned by new biological results [7]. The model of Yang [8] considers basic angiogenic processes as well on a physical basis; however, since the proposed model is based on concentrations as state-variables, it is unable to describe tumor geometry and spatial aspects, which are, nevertheless, the most easiest aspects to measure. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 679681). D. Csercsik is with the Faculty of Information Technology and Bion- ics, P´ azm´ any P´ eter Catholic University, Budapest, Hungary and with the Physiological Controls Research Center, Research and Innovation Center of ´ Obuda University, ´ Obuda University, Budapest, Hungary (e-mail: cserc- sik@itk.ppke.hu) T. G¨ onczy is with the Faculty of Information Technology and Bion- ics, P´ azm´ any P´ eter Catholic University, Budapest, Hungary (e-mail: gontom93@gmail.com) J. S´ api and L. Kov´ acs are with the Physiological Controls Research Center, Research and Innovation Center of ´ Obuda University, ´ Obuda University, Budapest, Hungary (e-mails: sapi.johanna@nik.uni-obuda.hu, kovacs.levente@nik.uni-obuda.hu ) In this article we propose a new model which explicitly considers angiogenic processes and the effect of vasculature volume in the tumor. We suppose that vasculature con- centration feeds back to tumor development by affecting the nutrition concentration in the tumor. As the proposed model takes into account exact geometrical aspect, viz. tumor volume is calculated, we are able to compare it with experimental results. Furthermore, we validate the behavior of the model via its response to various dosage protocols of anti-angiogenic drug. The paper is organized as follows. In Section II, we present the modelling assumptions based on the newest biological findings; after that the model equations are discussed, par- ticularly the choice of the variables. In Section III, first model calibration results based on experimental tumor volume data are presented, and then the response of the model to different delivery methods of antiangiogenic drugs are examined. The paper ends with the conclusions and future works in Section IV. II. MATERIAL AND METHODS A. Modelling Assumptions Based on the newest biological findings [5], [7], and in accordance with our previous results [9], modelling assump- tions are the following: • We assume spherical tumor geometry, composed of a core and of a periphery layer. • Living tumor cells of the periphery proliferate (cellular mitosis) on a rate which depends on the level of nutrient reaching them, and on the level of their actual concentration. • Tumor cells of the core produce tumor angiogenic factor (TAF), if the nutrient concentration in the core is low. • Tumor cells of the core necrotize, if the nutrient con- centration in the core is too low. • TAF stimulates new blood vessel formation and vascu- lature growth in the periphery. • We assume that processes of cellular responses and synthesis of various factors (as TAF) are much faster than growth-related mechanisms. • As the tumor grows and makes contact with external vasculature, blood vessels are accumulated in the pe- riphery and they are partially incorporated from the environment to the tumor periphery, and then from tumor periphery to the tumor core. • We assume that tumor cells basically stay in the same place; however, as the tumor grows, the same geo- 2017 IEEE 56th Annual Conference on Decision and Control (CDC) December 12-15, 2017, Melbourne, Australia 978-1-5090-2872-6/17/$31.00 ©2017 IEEE 4698