[C18] Biomathematics

[C18-04] Modeling Tumor Cell Proliferation from Biopsy Samples with an Extended Mean Field Approximation

*Siti Maghfirotul Ulyah¹, Ismaila Muhammed¹, Haralampos Hatzikirou¹ (1. Khalifa University (United Arab Emirates))

Keywords:

Tumor cell proliferation,Biopsy,Extended Mean Field Approximation,Logistic growth,Allee effect

A biopsy is a widely used diagnostic procedure for detecting conditions such as cancer, infections, and inflammatory diseases. In cell population studies, biopsy samples provide valuable insights into cellular growth, proliferation rates, and structural abnormalities—crucial factors in understanding disease progression. However, accurately estimating human cell proliferation rates remains a challenging task. To address this, we developed a method based on the birth-death Markov process to simulate logistic growth dynamics. Our approach leverages an extended Mean Field Approximation (MFA), which accounts for fluctuations in the evolution of observables such as statistical moments. By computing theoretical moments from the birth-death process, we solved the inverse problem to estimate the growth rate. We further validated the method using Markov Chain Monte Carlo (MCMC) simulations for both standard logistic growth and logistic growth with the Allee effect. The simulated population moments were then used in a regression model to predict growth rates, achieving low Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). When applied to real biopsy data, this approach enables more accurate estimation of human cell proliferation rates.