Investigation Of The Tumor Growth Dynamics

Cancer threatens people health so its pathogenesis and clinical research have attracted widely attention.This paper studies the prostate tumor growth dynamics under intermittent androgen suppression by simulating.The aim is to obtain the optimal thresholds ranges of intermittent androgen suppression,reveal the competition mechanism about the relapse and explore the different ways to control the androgen level intermittently and study the process of tumor genesis of the cancer stem cell.The main work of this paper has been shown as follow.Firstly,the paper simulates the tumor growth by using the model of prostate tumor growth under intermittent androgen suppression with different thresholds.Based on the simulation results,this paper analyzes the influence of the thresholds on the effects of the control then builds the object function to judge the best value ranges of the thresholds.Secondly,this paper considers the competition between the androgen dependent cell and the androgen independent cell to propose a competitive model.For the competition model,the intermittent androgen suppression can realize the successful control and avoid the androgen independent relapse even though the net growth rate of androgen independent cells is positive for any androgen level.Furthermore the paper proposes a competitive model in the environment with a finite carrying capacity considering the nutrients and inhibitors.The results show that the tumor does not grow infinitely with the net growth rate of androgen independent cells being androgen independent even though the competitive strength between androgen dependent and androgen independent cells is weak.But the tumor goes through the primary oscillating period which is sensitive to androgen suppression,then the rise period which is not sensitive to androgen suppression,and th e eventual stable period.Intriguingly,if the limited factors are strengthened,the stable state value will decline leading to that the rise period shortens and even more disappears.Thirdly,this paper presents a new model in which the androgen is suppressed or not based on the number of androgen independent cells and another new model in which the androgen is suppressed or not directly.The simulations show that the dynamic behaviors of the tumor growth may be divergence or oscillation in different androgen suppression forms.Fourthly,based on the cancer stem cell theory,this paper puts forward a prostate cancer stem cell model under the intermittent androgen suppression and simulates the tumor development in natural condition and in the intermittent androgen suppression therapy.The obtaining of the optimal thresholds ranges of intermittent androgen suppression provides suggestions for the medical experiments or clinical treatments and it also offers a possible way to determine a suitable scheme.The numerical simulations of the competition model and the limited model give new ideas in tumor growth control.The tumor growth models with different control forms present the analytic equation to describe the intermittent treatment.The cancer stem cell model shows the cancer stem cell mechanism of the tumor development.