Modeling Physical and Chemical Growths of Avascular Tumor
نویسندگان
چکیده
Due to the avascular tumor growths were a complex activities that involved a chemical process and a physical process, a Finite Element Method (FEM) based mixture model was proposed in this paper. For the chemical process, the FEM was used to solve the reaction diffusion equations of three chemicals, which are the oxygen, glucose and GIF, under several specified boundary conditions. For the physical process, the FEM was used to solve the total energy equations which can be uniquely calculated as a function of the nodal displacements in the tumor. In each simulation step, we minimize the energy increment for all the tumor cells. The experiment results demonstrated that the proposed approach is quite efficient for the modeling of avascular tumor growth.
منابع مشابه
A stochastic mathematical model of avascular tumor growth patterns and its treatment by means of noises
Due to the rate increase in cancer incidence, many researchers in different fields have been conducting studies on cancer-related phenomena. Most studies are conducted to focus on cellular and molecular aspects of cancerous diseases and treatment strategies. Physicists have been using mathematical modeling and simulation to explain the growth pattern of tumors. Although most published studies i...
متن کاملMathematical Modeling and Analysis Simplified Mathematical Models of Avascular And Vascular Tumor Growth
Tumors become especially dangerous after they induce blood vessel growth, because the new blood vessels can not only carry oxygen and nutrition that further facilitate tumor growth but also act as passages for tumor cells to spread to other sites of the body. Thus tumor growth can be divided into two phases: avascular and vascular growth. We present two simple mathematical models, 1) to underst...
متن کاملTwo Dimensional Mathematical Model of Tumor Angiogenesis: Coupling of Avascular Growth and Vascularization
Introduction As a tumor grows, the demand for oxygen and nutrients increases and it grows further if acquires the ability to induce angiogenesis. In this study, we aimed to present a two-dimensional continuous mathematical model for avascular tumor growth, coupled with a discrete model of angiogenesis. Materials and Methods In the avascular growth model, tumor is considered as a single mass, wh...
متن کاملA chemical energy approach of avascular tumor growth: multiscale modeling and qualitative results.
In the present manuscript we propose a lattice free multiscale model for avascular tumor growth that takes into account the biochemical environment, mitosis, necrosis, cellular signaling and cellular mechanics. This model extends analogous approaches by assuming a function that incorporates the biochemical energy level of the tumor cells and a mechanism that simulates the behavior of cancer ste...
متن کاملThe protein profiles of primary tumors and their lung metastases.
of interest to the oncologist for some time, and several papers (1, 3, 4) have appeared relating to factors which modify metastases and the mode of cell transport. Little information, however, is available concerning the chemical nature of the cells which break free of the primary tumor mass and give rise to the secondary tumor growth. It is generally assumed that there are no chemical differen...
متن کامل