Please cite this article in press as: N. Filipovic, et al., Modeling of liver metastatic disease with applied drug therapy, Comput. Methods Programs Biomed. (2014), http://dx.doi.org/10.1016/j.cmpb.2014.04.013 ARTICLE IN PRESS COMM-3796; No. of Pages 9 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e x x x ( 2 0 1 4 ) xxx–xxx jo ur nal ho me p ag e: www.intl.elsevierhealt h.com/journals/cmpb Modeling of liver metastatic disease with applied drug therapy Nenad Filipovic a,b,c,* , Tijana Djukic a,b , Igor Saveljic b , Petar Milenkovic d,e , Gordana Jovicic a , Marija Djuric e a Faculty of Engineering, University of Kragujevac, 34000, Serbia b BioIRC R&D Bioengineering Center, Kragujevac, 34000, Serbia c Harvard University, Boston, USA d Institute for Oncology and Radiology of Serbia, 11000 Belgrade, Serbia e Laboratory for Anthropology, Institute of Anatomy, School of Medicine, University of Belgrade, 11000 Belgrade, Serbia a r t i c l e i n f o Article history: Received 21 August 2013 Received in revised form 18 February 2014 Accepted 15 April 2014 Keywords: Colorectal carcinoma Liver metastases Reaction-diffusion modeling Chemotherapy Cancer cell proliferation rate a b s t r a c t Colorectal carcinoma is acknowledged as the second leading cause of total cancer-related death in the European Region. The majority of deaths related to colorectal carcinoma are connected with liver metastatic disease. Approximately, in 25% of all patients, liver metastatic disease is diagnosed at the same time as the primary diagnosis, while up to a quarter of others would develop liver metastases in the course of the illness. In this study, we developed reaction-diffusion model and analyzed the effect of drug therapy on liver metastatic disease for a specific patient. Tumor volumes in specific time points were obtained using CT scan images. The nonlinear function for cell proliferation rate as well as data about clinically applied drug therapy was included in the model. Fitting procedure was used for parameter estimation. Good agreement of numerical and experimental results shows the feasibility and efficacy of the proposed system. © 2014 Elsevier Ireland Ltd. All rights reserved. 1. Introduction There are several theoretical methods that were developed to simulate tumor growth, such as several mathematical models [1–3], cellular automata [4], finite element methods [3–5] and angiogenesis-based methods [6]. Out of all mentioned math- ematical models, the reaction-diffusion model proposed by Swanson et al. [1] increased reliability of the tumor growth prediction process. Subsequently, in order to improve the ∗ Corresponding author at: Faculty of Engineering, Sestre Janjic 6, Kragujevac, Serbia. Tel.: +38 134334379; fax: +381 34333192. E-mail addresses: fica@kg.ac.rs (N. Filipovic), tijana@kg.ac.rs (T. Djukic), petar.milenkovic@gmail.com (P. Milenkovic), marijadjuric5@gmail.com (M. Djuric). reaction-diffusion model Clatz et al. [2] and Hoge et al. [3] introduced biomechanical deformation. Computer-aided systems have already been developed for automated detection and classification of cancer [7]. In these systems the computer analysis is performed using CT scan images [8], tumor markers [9], tissue microscopy [10] or sim- ilar. In this paper we present an approach to model tumor progression using numerical simulation. Computer model- ing of tumor progression based on new imaging techniques is essential to improve apprehension of metastases growth http://dx.doi.org/10.1016/j.cmpb.2014.04.013 0169-2607/© 2014 Elsevier Ireland Ltd. All rights reserved.