Harnessing Flex Point Symmetry to Estimate Logistic Tumor Population Growth

• Published in: Bulletin of mathematical biology Vol. 86; no. 11; p. 135
• Main Authors: Pasetto, Stefano, Harshe, Isha, Brady-Nicholls, Renee, Gatenby, Robert. A., Enderling, Heiko
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2024; Springer Nature B.V
• Subjects: Animals; Artificial neural networks; Breast Neoplasms - pathology; Carrying capacity; Cell Biology; Computer Simulation; Data collection; Data points; Decision making; Demography; Evolution; Female; Growth rate; Humans; Life Sciences; Linguistics; Logistic Models; Mathematical and Computational Biology; Mathematical Concepts; Mathematics; Mathematics and Statistics; Models, Biological; Neoplasms - pathology; Neural networks; Oncology; Original Article; Population; Population growth; Symmetry; Tumor Burden; Tumors; Logistic function; Ghost symmetry; Tumor growth; Evolution forecasting; Mathematical oncology
• ISSN: 0092-8240; 1522-9602; 1522-9602
• DOI: 10.1007/s11538-024-01361-6

The observed time evolution of a population is well approximated by a logistic growth function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential, then decelerates as the population approaches its limit size, i.e., the carrying capacity. In mathematical oncology, the tumor carrying capacity has been postulated to be dynamically evolving as the tumor overcomes several evolutionary bottlenecks and, thus, to be patient specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against published pan-cancer animal and human breast cancer data, achieving a 30% to 40% reduction in the time at which subsequent data collection is necessary to estimate the logistic growth rate and carrying capacity correctly. These results could improve tumor dynamics forecasting and augment the clinical decision-making process.