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

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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-\(4^{LUC+}\) cells into the right inguinal mammary fat pads of 6- to 8-week-old female Severe Combined Immuno-Deficient mice.

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Data Availibility

The data used in this study are published data and can be found in the work of Vaghi et al. (2020).

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Funding

No funding was received for conducting this study. The research does not include any human or animal participants.

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  1. Department of Mathematics, Augusta University, 1120 15th Str, GE 3018, Augusta, GA, 30912, USA

    Olusegun Michael Otunuga

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  1. Olusegun Michael Otunuga
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Correspondence to Olusegun Michael Otunuga.

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Appendices

Appendix A: Simulation results for the volume of tumor for remaining specimens using models A, B, C, D

Fig. 11
figure 11

Estimation of the volume of tumor using models A, B, C, and D using 100 sample paths

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Fig. 12
figure 12

Estimation of the volume of tumor using models A, B, C, and D using 100 sample paths

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Fig. 13
figure 13

Estimation of the volume of tumor using models A, B, C, and D using 100 sample paths

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Figures 11, 12 and 13 show the simulation results for the remaining mice specimens using models A, B, C, and D.

Appendix B: Table containing goodness of fit estimates for models A, B, C, and D for all 66 specimens

Table 5 Goodness of fit estimates for models A, B, C, and D for the remaining specimens
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Table 6 Goodness of fit estimates for models A, B, C, and D for the remaining specimens
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Here, we use \(L=100\) sample paths in the LS-LM estimation process to estimate the parameters in models A, B, C, D used in describing the volume of tumor for the remaining specimens not included in Fig. 10. The tumor growth for these specimens are reported in Figs. 11, 12 and 13, and their corresponding goodness-of-fit estimates reported on Tables 5 and 6.

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Otunuga, O.M. Tumor growth and population modeling in a toxicant-stressed random environment. J. Math. Biol. 88, 18 (2024). https://doi.org/10.1007/s00285-023-02035-y

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