title: Modeling and simulation of a low-grade urinary bladder carcinoma.
abstract: In this work, we present a mathematical model of the initiation and progression of a low-grade urinary bladder carcinoma. We simulate the crucial processes affecting tumor growth, such as oxygen diffusion, carcinogen penetration, and angiogenesis, within the framework of the urothelial cell dynamics. The cell dynamics are modeled using the discrete technique of cellular automata, while the continuous processes of carcinogen penetration and oxygen diffusion are described by nonlinear diffusion-absorption equations. As the availability of oxygen is necessary for tumor progression, processes of oxygen transport to the tumor growth site seem most important. Our model yields a theoretical insight into the main stages of development and growth of urinary bladder carcinoma with emphasis on the two most common types: bladder polyps and carcinoma in situ. Analysis of histological structure of bladder tumor is important to avoid misdiagnosis and wrong treatment. We expect our model to be a valuable tool in the study of bladder cancer progression due to the exposure to carcinogens and the oxygen dependent expression of genes promoting tumor growth. Our numerical simulations have good qualitative agreement with in vivo results reported in the corresponding medical literature.
authors: Department of Computer Science and Mathematics, Ariel University, Ariel 40700, Israel. Electronic address: svetlanabu@ariel.ac.il.
authors: Svetlana
authors: S
authors: Bunimovich-Mendrazitsky
authors: V.A. Negovsky Research Institute for General Reanimatology, 25 Petrovka, Bldg. 2, Moscow 107035, Russian Federation; D. Rogachev Federal Clinical Research Center for Children Hematology, Oncology and Immunology, 1 Samory Mashela St., Moscow 117198, Russian Federation; University of Nebraska Medical Center, Omaha, NE 68198, USA. Electronic address: vpisarev@gmail.com.
authors: Vladimir
authors: V
authors: Pisarev
authors: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland. Electronic address: ekashdan@maths.ucd.ie.
authors: Eugene
authors: E
authors: Kashdan
mesh_terms: D019295:Computational Biology; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D001743:Urinary Bladder / Q000166:cytology / Q000502:physiology; D001749:Urinary Bladder Neoplasms
keywords: Angiogenesis; Bladder cancer; Cellular automata; Hybrid model; Nonlinear diffusion‐absorption equation