Tumor microenvironmental influences on tumor growth using non-extensive entropy
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ORIGINAL PAPER
Tumor microenvironmental influences on tumor growth using nonextensive entropy H R Rastegar Sedehi1*
, R Khordad2 and B Vaseghi2
1
Department of Physics, College of Sciences, Jahrom University, Jahrom 74137-66171, Iran 2
Department of Physics, College of Sciences, Yasouj University, Yasouj 75914-353, Iran Received: 02 July 2019 / Accepted: 16 September 2020
Abstract: We have used non-extensive entropy to study the influence of the non-immunogenic tumor microenvironmental effects on dynamics of tumor growth. For this purpose, we have first employed the Tsallis and Abe entropies with different parameters. Then, we have applied the phenomenological model equation to determine the steady-state distribution for investigating tumor growth. Numerical results show that the steady-state distribution can change with some factors. We also plot this quantity versus the tumor population for studying the properties of steady state of tumor growth. Keywords: Non-extensive entropy; Tumor growth; Microenvironmental factors
1. Introduction Numerous complex systems have been introduced in the literature over the past five decades [1, 2]. Complex system is of interest to engineers, physicists, biologist, mathematicians and many other scientists. The study of dynamics of complex systems under random environmental factors has attracted much attention among researchers. The exact prediction of dynamical behavior of complex systems may be sought through analysis of a chaotic mathematical model or through analytical techniques [3–5]. In the literature, scientists have tried to control the behavior of complex systems. Hitherto, several techniques have been devised for such control such as stochastic method. This method has a key role in studying the behavior of complex systems. Scientists have successfully used the stochastic approach as a trustworthy method with application in many areas such as biology, physics and chemistry. When the complex system is under noise, the stochastic method can be also employed to investigate the system behavior. Examples of such systems are bistable system, mode laser system, genotype selection, genetic transcription regulation and tumor growth [6–8]. The theory of dynamical systems provides a description of the deterministic dynamics of a complex system, and it
explains the microscopic movements of the particles. The stochastic Langevin equation is one of the most widely known mathematical models for the phenomenon of Brownian motion. Correlation between noises can change the system dynamics, and thereby we can apply the Langevin-type description for describing the dynamic system. The Langevin equation can describe systems in the nonequilibrium state. The correlation time of the noise in real physics should be nonzero, and it is characterized as colored or non-white [9–11]. Tumors are tissues growing under special conditions, and it is a complex process. Tissue growth is originated by external factors and lead to chains of reaction, which may be identical, or at least similar, even in
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