Second cancers after fractionated radiotherapy: Stochastic population dynamics effects

Abstract

When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well characterized doses of a well studied carcinogen, followed by long-term monitoring.In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze if radiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this IIP model. Combining Monte Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance ≫ mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; b) weekend treatment gaps during radiotherapy, apart from decreasing the probability of eradicating the primary cancer, substantially increase the risk of later second cancers.

Clinical Features of Patients with Esophageal and Second Primary Cancers

“…Previous studies had revealed the most common SPCs were neoplasms of upper aerodigestive organs, lung and thyroid gland in the EC patients (Matsubara et al, 2003;Das et al, 2006). This phenomenon could be interpreted as radiotherapy for esophageal cancers enhanced the risk of developing a second malignancy in nearby organs (Sachs et al, 2007). These results were partially inconsistent with our clinical data because HCC was also shown as one of the most common SPCs in the EC patients in our study.…”

Malignant induction probability maps for radiotherapy using X-ray and proton beams

“…Many mathematical models have been proposed to describe the dose-response relationship for radiationinduced cancer [2][3][4]. Some models are applicable in low-dose regions and have to be extrapolated to higher doses relevant for radiotherapy [5].…”

“…This study has not considered the effect of cell repopulation during treatment as, in most instances, the radiation cancer and sarcoma induction will occur in very slowly dividing cell systems such as basal cells of skin, connective tissues, meninges, glial tissues, thyroid and prostate, which emerge from very stable tissues and are associated with low repopulation rates. For tissues that repopulate during radiotherapy, such as bronchial and buccal mucosa and even breast epithelium, an additional time factor may be required [4].…”

A Rapid-Mutation Approximation for Cell Population Dynamics

“…A partial justification for this deterministic approach is that the phenomenon of subpopulation extinction, which is often the main reason for replacing a deterministic by a more detailed stochastic analysis (e.g. Tan, 2002;Sachs et al, 2007), is not as important in the present context as in many other population dynamics models, because on the present picture rapid alterations can rapidly resurrect an extinct subpopulation. We will assume the time-development of the cell population is governed by the following proliferation-alteration system of ordinary differential equations:…”