The Abundance of Available Precursor Cells Can Drive Pediatric Cancer Incidence: Insights From an Algebraic Model.

Abstract

Cancers in children show incidence distributions by age that cannot be explained by mathematical models designed to understand carcinogenesis in adults. Unlike carcinomas that tend to increase in incidence with age, pediatric cancers demonstrate unique phases of increasing incidence with a peak age of incidence followed by declining incidence. To date, mathematical models of this phenomenon are limited to statistical representations describing the frequency of oncogenic second genetic alterations in genetically susceptible individuals. To develop a mathematical description of pediatric cancer incidence, we created an algebraic model based on the concept that a limited cell population is available to become Ewing sarcoma. Our algebraic models for the incidence of Ewing sarcoma express incidence as a function of both the risk of oncogenic genetic events and the number of available cells capable of becoming Ewing sarcoma. Our models allow predictions about changes in the abundance of available cells capable of undergoing oncogenesis. This concept can explain the anatomic distribution and incidence of Ewing sarcoma by age. We believe that this concept also explains how the same genetic alterations can be seen in diverse cancer types. Verification of our models for Ewing sarcoma with experimental data can predict how the risk of oncogenic events for pediatric cancers changes with age. Our algebraic model is a novel articulation of the biological concepts that drive pediatric oncogenesis and can be applied to the observed age distributions of nearly all pediatric cancer types.