A diversity of responses displayed by a stochastic model of radiation carcinogenesis allowing for cell death

Yakovlev, Andrei; Polig, E.

doi:10.1016/0025-5564(95)00047-x

Cited by 47 publications

(30 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A rigorous treatment of the identifiability problem for the MVK model with constant parameters along the lines indicated in the previous section was first implemented by , and is presented below. shown by Heidenreich (1996) proposed by Yakovlev and Polig (1996). It is similar to the MVK model in that the survival function of time to tumor has the same general form (10).…”

Section: Identification Of Finite Parametric Modelsmentioning

confidence: 80%

See 1 more Smart Citation

Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology

Hanin

2002

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

A general framework for solving identification problem for a broad class of deterministic and stochastic models is discussed. This methodology allows for a unified approach to studying identifiability of various stochastic models arising in biology and medicine including models of spontaneous and induced carcinogenesis, tumor progression and detection, and randomized hit and target models of irradiated cell survival. A variety of known results on parameter identification for stochastic models is reviewed and several new results are presented with an emphasis on rigorous mathematical development.

show abstract

Section: Identification Of Finite Parametric Modelsmentioning

confidence: 80%

“…As shown by and Yakovlev and Polig (1996), under assumption (2) and for arbitrary promotion time distribution with CDF F, formation of clonogenic tumor cells is governed by a Poisson process with the integral rate…”

Section: Identification Of Finite Parametric Modelsmentioning

confidence: 99%

Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology

Hanin

2002

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

“…(Hanin et al, 2006;Heidenreich et al, 2004;Moolgavkar and Luebeck, 2003;Pierce, 2003;Yakovlev and Polig, 1996)] analyze the longer-time latency period in more detail. Such biologically based models usually do not assume or imply the product form, Eq.…”

Section: Err = Abmentioning

confidence: 99%

Second cancers after fractionated radiotherapy: Stochastic population dynamics effects

Sachs

Shuryak

Brenner

et al. 2007

Journal of Theoretical Biology

View full text Add to dashboard Cite

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.

show abstract

“…Much like the Moolgavkar-Venzon-Knudson model, this model describes and explains a wide range of experimental findings documented in the literature, and its structure renders the associated statistical problems tractable. The phenomenon of cell death plays a key role in the dose-rate effects observed in carcinogenesis studies (7,8). The model by Yakovlev and Polig provides a good description of various dose-rate effects in radiation and chemical carcinogenesis (9,10) while keeping parametric assumptions to a minimum as far as the dependence of its parameters on dose rate is concerned.…”

Section: Sectionmentioning

confidence: 99%

“…The derivation and biological substantiation of Eq. 1 are described at length by Yakovlev and Polig (7).…”

Section: Section 2: the Model And Estimation Proceduresmentioning

confidence: 99%

Estimating the probability of initiated cell death before tumor induction

Boucher

Yakovlev²

1997

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

The effects of cell toxicity are known to be inherent in carcinogenesis induced by radiation or chemical carcinogens. The event of cell death precludes tumor induction from occurring. A long standing problem is to estimate the proportion of initiated cells that die before tumor induction. No experimental techniques are currently available for directly gauging the rate of cell death over extended periods of time. The obstacle can be surmounted by newly developed theoretical methods of carcinogenesis modeling. In this paper, we apply such methods to published data on multiple lung tumors in mice receiving different schedules of urethane. Bioassays of this type play an important role in testing environmental chemicals for carcinogenic activity. Our estimates for urethane-induced carcinogenesis show that, unexpectedly, many initiated cells die early in the course of tumor promotion. We present numerical estimates for the probability of initiated cell death for different schedules (and doses) of urethane administration. Section 1As with many processes of carcinogenesis, the process of cell killing induced by a carcinogen is difficult to observe directly, and inferences rely on mathematical models. In a recent study (1), Moolgavkar et al. reported a statistical analysis of experimental data on enzyme-altered (ATPase-deficient) liver foci in rats induced by diethylnitrosamine. It is generally believed that these foci represent clones of initiated cells, and at least some of them eventually transform into malignant tumors. The authors used a two-stage birth-death-mutation model of carcinogenesis, usually referred to as the MoolgavkarVenzon-Knudson model (2, 3), to estimate the extinction probability for clones of altered cells in initiation-promotion experiments. In the absence of a promoter, the estimated extinction probability was higher than 0.99, and its value tended to decrease when two different promoters were applied; this effect can be attributed to stimulation of cell proliferation.The Moolgavkar-Venzon-Knudson model introduces the clonal expansion of initiated cells as the basic mechanism of tumor promotion. It is assumed that clonal growth begins immediately after initiation and can mathematically be described as a birth-and-death stochastic process. Under this model, the probability of a clone to become extinct is a natural summary characteristic of the susceptibility of initiated cells to death in the course of tumor development. However, there is experimental evidence that single initiated cells persist over an extended time period after the administration of a carcinogen. Using another biochemical marker (the placental form glutathione S-transferase) of cell initiation, Satoh et al. (4) have shown that single putative initiated cells (the placental form glutathione S-transferase-positive hepatocytes) and mini-foci consisting of such cells (2-10 cells) predominate in the preneoplastic liver within the first 12 weeks after a single exposure to diethylnitrosamine. Within 1 week after exposure, the e...

show abstract

A diversity of responses displayed by a stochastic model of radiation carcinogenesis allowing for cell death

Cited by 47 publications

References 48 publications

Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology

Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology

Second cancers after fractionated radiotherapy: Stochastic population dynamics effects

Estimating the probability of initiated cell death before tumor induction

Contact Info

Product

Resources

About