Estimating the Growth Rate of Tumor Cells from Biopsy Samples Using an Extended Mean Field Approximation

Siti MaghfirotulUlyah

Khalifa University, Abu Dhabi, United Arab Emirates

"Estimating the Growth Rate of Tumor Cells from Biopsy Samples Using an Extended Mean Field Approximation"

A biopsy is a common procedure used to diagnose diseases like cancer, infections, or inflammatory conditions. In cell population studies, biopsy samples provide valuable data to analyze cellular growth, proliferation rates, and structural abnormalities, which are essential for understanding disease progression. Estimating the growth (proliferation) rate of human cells is a challenging task. To address this, we have developed a method based on the birth-death Markov process to simulate the logistic growth model. We applied an extended Mean Field Approximation (MFA) for birth-death Markov processes, which accounts for fluctuations in the evolution of observables, such as moments. By calculating the theoretical moments from the birth-death process, we solved the inverse problem and estimated the growth rate. Additionally, we performed Markov Chain Monte Carlo (MCMC) simulations for both logistic growth and logistic growth with the Allee effect. The moments of the simulated population were used to predict the growth rate through regression analysis, achieving a high R-squared value. Finally, by applying this approach to biopsy data, one can estimate the proliferation rate of human cells with greater accuracy.
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