Non-Homogeneous Tumor Growth and Its Implications for Radiotherapy: A Phenomenological Approach.

Paolo Castorina,Gianluca Ferini,Luigi Castorina

doi:10.3390/jpm11060527

Abstract

Tumor regrowth and heterogeneity are important clinical parameters during radiotherapy, and the probability of treatment benefit critically depends on the tumor progression pattern in the interval between the fractional irradiation treatments. We propose an analytic, easy-to-use method to take into account clonal subpopulations with different specific growth rates and radiation resistances. The different strain regrowth effects, as described by Gompertz law, require a dose-boost to reproduce the survival probability of the corresponding homogeneous system and for uniform irradiation. However, the estimate of the survival fraction for a tumor with a hypoxic subpopulation is more reliable when there is a slow specific regrowth rate and when the dependence on the oxygen enhancement ratio of radiotherapy is consistently taken into account. The approach is discussed for non-linear two-population dynamics for breast cancer and can be easily generalized to a larger number of components and different tumor phenotypes.

Highlights

A quantitative understanding of tumor growth is crucial for the clinical management of disease, and tumor size is a main determinant of clinical severity and an important factor, among other criteria [1], to assess the staging criteria before and during radiotherapy (RT)
Tumor regrowth during radiotherapy is, an important clinical parameter [2] and, in particular, the dose-response relationship and, the probability of treatment benefit critically depend on the tumor heterogeneity and the regrowth pattern in the interval between the fractional irradiation treatments
Concerning the regrowth during radiotherapy, one has that: (a) the untreated tumor growth has been usually described by means of the Gompertz law (GL) [4,5,6,7,8], a non linear growth pattern previously proposed in actuarial mathematics [9]; (b) in a transplantable rat tumor, it was shown that control and regrowth curves after radiotherapy could be fitted by the same Gompertzian law, provided adjustments for the initial lag and the estimated number of clonogens immediately after irradiation were performed [10]; (c) Gompertzian growh has been assumed to describe human tumor repopulation during fractional radiotherapy by Hansen et al [11] and by O’Donougue [12]

Summary

Introduction

A quantitative understanding of tumor growth is crucial for the clinical management of disease, and tumor size is a main determinant of clinical severity and an important factor, among other criteria [1], to assess the staging criteria before and during radiotherapy (RT). Tumor regrowth during radiotherapy is, an important clinical parameter [2] and, in particular, the dose-response relationship and, the probability of treatment benefit critically depend on the tumor heterogeneity and the regrowth pattern in the interval between the fractional irradiation treatments. Concerning the regrowth during radiotherapy, one has that: (a) the untreated tumor growth has been usually described by means of the Gompertz law (GL) [4,5,6,7,8], a non linear growth pattern previously proposed in actuarial mathematics [9]; (b) in a transplantable rat tumor, it was shown that control and regrowth curves after radiotherapy could be fitted by the same Gompertzian law, provided adjustments for the initial lag and the estimated number of clonogens immediately after irradiation were performed [10]; (c) Gompertzian growh has been assumed to describe human tumor repopulation during fractional radiotherapy by Hansen et al [11] and by O’Donougue [12]

Methods

Results

Conclusion