Tumor growth and population modeling in a toxicant-stressed random environment.

Abstract

When examining some factors that contribute to the growth or decline of a population or tumor, it is essential to consider a random hypothesis. By analyzing the effects of stress on a population (or volume of tumor growth) in a random environment, we develop stochastic models describing the dynamics of the population (or tumor growth) based on random adjustments to the population's intrinsic growth rate, carrying capacity, and harvesting efforts (or tumor treatments). Apart from the models' ability to capture fluctuations, the availability of a shape parameter in the models gives it the flexibility to describe a variety of population/tumor data with different shapes. The distribution of the stressed population size with or without harvesting (or treatments) is derived and used to calculate the maximum expected amount of harvests that can be taken from the population without depleting resources in the long run (or the minimum amount of chemotherapy needed to cause shrinkage or eradication of a tumor). The work done is applied to analyze tumor growth using published data comprising of the volume of breast tumor obtained by orthotopically implanting LM2-[Formula: see text] cells into the right inguinal mammary fat pads of 6- to 8-week-old female Severe Combined Immuno-Deficient mice.