Graduation Year

2022

Date of Submission

4-2022

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Biophysics

Reader 1

Adam Landsberg

Reader 2

Scot Gould

Rights Information

© 2022 Garegin Soghomonyan

Abstract

Abstract

Statistical mechanical approaches to modeling tumor growth have opened the door for new approaches to managing clinical dosing regimens and procedures in cancer patients to slow the proliferation of tumors 1,2,3. In single tumors, as the tumor grows larger, the dynamics of the system create a hypoxic boundary in the center of the tumor which is also starved of nutrients. This causes cell death and the creation of a non-proliferating necrotic core. Previous models have sought to incorporate this phenomenon by using logarithmic functions which decay either as a function of time or as the surface area to volume ratio decreases with size. I propose that the necrotic core needs to be viewed separately from the proliferating outer shell of a tumor. I used a Gompertzian growth formula for the entire tumor, and then subtracted the inner necrotic core from this growth rate as a harvested Bertalanffy model (in essence treating the proliferating and non-proliferating regions separately). The formula is presented below:

The rate of the population growth, dN, in this model is dependent on multiple coefficients. The first coefficient K is a constant that comes from the integration of the Gompertzian model. NP and CP are the populations of the total tumor, and the necrotic core, respectfully. The coefficient a is representative of the percentage of the total tumor that is hypoxic

DigitizeIt was used to extract real tumor growth data from previous cancer research, and then Mathematica was used to nonlinearly fit the proposed formula to the data, and graph the data. The R2 value or the fit was 0.81, suggesting a strong correlation. With more research, these models could help create personalized patient dosing regimens and predict how much of a tumor needs to be removed (when full excision is not possible) to minimize future growth. One problem which should be addressed in the future when applying such mathematical models to data is that even with strong predictive accuracy, the constants governing the curves are mathematically optimized, and the underlying theory is still unknown. Having a deeper understanding of the factors influencing tumor growth would lead to targeted strategies at cancer treatment designed to slow tumor cell proliferation itself, rather than just map and predict the rate of tumor growth.

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