Abstract
This paper deals with the applications of mathematical growth functions such as monomolecular, time delay logistic and Gompertz functions to describe the dynamics of avascular tumor growth. In this case we analyze the steady state of the modified systems of the model using Jacobean matrix to show that it is stable on the nontrivial stationary points of each applications. Numerical simulation of the growth functions is implemented by using “ode45” in MATLAB and graphical outputs are presented to show differences in evaluation of tumor sub-populations. We also find that the tumor cells increases with time so that the nutrient is disproportional to the number of cells and they transform in to quiescent and necrotic cells that cause cancer.
Highlights
The development of a solid tumor begins with a single cell that can be transformed as a result of mutation
Dynamics of growth of normal or malignant cells is in general described by the Gompertz function (Winsor, 1932) defined as %&'( )DKLM ( E:) with a rate of which is applied in the heterogeneous model on dynamics of avascular tumor growth so as to modify the proposed model leads to the following change for (1a)
Considering the three components of a tumor, the proliferating, quiescent and necrotic cells explicitly in its spheroidand our work deals on a three compartmental model
Summary
The development of a solid tumor begins with a single cell that can be transformed as a result of mutation. Growth and proliferation of the tumor leads to the development of an avascular tumors consisting of around 106cells which feed only on the nutrients available in the local environment [12]. As a starting point to minimize complexity of all stages of cancer, most literates agree that avascular tumor growth study is a basic foundation of the problem. Mathematical modeling and analysis of tumor growth processes give important insights on cancer growth situations. Mathematical models and numerical simulation with different approaches have been developed to describe features of avascular tumor growth. This work assess the application of monomolecular, time delay logistic, and Gompertz growth functions and their numerical analysis for dynamics of avascular tumor growth model. Numerical simulation of growth functions will be implemented by using MATLAB
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