Mathematical modelling of the distribution of tumor size in patient populations

Abstract

In radiation therapy tumor size, and thus also volume, has a significant impact on the local control of tumors. Moreover, tumor volume is a significant prognostic factor for modelling and predicting therapeutic outcomes in cancer treatment. In research, the distribution of tumor volumes in patient populations has so far remained widely unexplored. In this work, the frequency distributions of maximum diameter of tumors for various types of cancer was studied based on SEER data and it was explored if they can be modelled using Weibull distributions. Further, actual volume data were obtained directly from computer tomography (CT) datasets and the frequency distributions of tumor volumes and maximum diameters were explored and a link between them was found. In cancer research, tumors are often modelled as ellipsoids. In order to verify the appropriateness of using ellipsoids as a model, to the obtained three-dimensional data, ellipsoids were fitted and the resulting volumes and diameters analysed. Finally, NSCLC tumor diameters were Monte Carlo simulated using tumor growth and incidence models. A comparison of the simulated tumor diameter distributions with observed SEER data yielded the determination of tumor growth rates.