Logistic tumor-population growth and ghost-points symmetry.

The observed time evolution of a population is well approximated by a logistic function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential at a constant rate and capped at a limit size, i.e., the carrying capacity. In mathematical oncology, the carrying capacity has been postulated to be co-evolving and thus 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 a classic oncology database of logistic tumor growth, achieving a 30% to 40% reduction in the time necessary to correctly estimate the logistic growth rate and carrying capacity. Our results will improve tumor dynamics forecasting and augment the clinical decision-making process.

Predicting Patient-Specific Tumor Dynamics: How Many Measurements Are Necessary?

Acquiring sufficient data is imperative to accurately predict tumor growth dynamics and effectively treat patients. The aim of this study was to investigate the number of volume measurements necessary to predict breast tumor growth dynamics using the logistic growth model. The model was calibrated to tumor volume data from 18 untreated breast cancer patients using a varying number of measurements interpolated at clinically relevant timepoints with different levels of noise (0-20%). Error-to-model parameters and the data were compared to determine the sufficient number of measurements needed to accurately determine growth dynamics. We found that without noise, three tumor volume measurements are necessary and sufficient to estimate patient-specific model parameters. More measurements were required as the level of noise increased. Estimating the tumor growth dynamics was shown to depend on the tumor growth rate, clinical noise level, and acceptable error of the to-be-determined parameters. Understanding the relationship between these factors provides a metric by which clinicians can determine when sufficient data have been collected to confidently predict patient-specific tumor growth dynamics and recommend appropriate treatment options.