Incorporating the field cancerization effect to improve modeling of untreated cancer growth

Understanding untreated cancer growth is important to improve mathematical descriptions of tumor progression and to examine interactions between tumor cells and surrounding tissue in the absence of therapy. Most mathematical models primarily represent cancer-cell populations and selected biochemical factors, without explicitly accounting for histologically normal but molecularly altered cells associated with the field cancerization effect. This study examines whether incorporating a population of normal preconditioned cells improves the representation of untreated tumor growth. Breast cancer is used as the main case study, based on longitudinal murine tumor-volume data, while datasets from additional cancer types are analyzed exploratorily to assess the descriptive flexibility of the framework. The model extends a logistic-type growth equation by coupling cancer-cell dynamics to a second equation for the normal preconditioned cell population. Parameters were estimated by minimizing the mean squared error after reparameterizing the model to remove structural redundancy among the original linear terms. The performance of the model was compared with the baseline formulation using the mean squared error, Akaike information criterion, and the Bayesian information criterion. The reparameterized extended model improved agreement with breast cancer data and retained better information-criterion values after accounting for model complexity. Exploratory applications to additional datasets and simulations under alternative initial conditions further characterized the descriptive behavior of the model. These findings suggest that coupling tumor growth to normal preconditioned-cell dynamics provides a useful phenomenological extension for untreated cancer modeling, while underscoring the need for direct biological validation, measurements of the preconditioned population, and further identifiability analysis.