A framework for analysis of abortive colony size distributions using a model of branching processes in irradiated normal human fibroblasts

Modeling long-term tumor growth and kill after combinations of radiation and radiosensitizing agents

PURPOSE

Radiation therapy, whether given alone or in combination with chemical agents, is one of the cornerstones of oncology. We develop a quantitative model that describes tumor growth during and after treatment with radiation and radiosensitizing agents. The model also describes long-term treatment effects including tumor regrowth and eradication.

METHODS

We challenge the model with data from a xenograft study using a clinically relevant administration schedule and use a mixed-effects approach for model-fitting. We use the calibrated model to predict exposure combinations that result in tumor eradication using Tumor Static Exposure (TSE).

RESULTS

The model is able to adequately describe data from all treatment groups, with the parameter estimates taking biologically reasonable values. Using TSE, we predict the total radiation dose necessary for tumor eradication to be 110 Gy, which is reduced to 80 or 30 Gy with co-administration of 25 or 100 mg kg^-1 of a radiosensitizer. TSE is also explored via a heat map of different growth and shrinkage rates. Finally, we discuss the translational potential of the model and TSE concept to humans.

CONCLUSIONS

The new model is capable of describing different tumor dynamics including tumor eradication and tumor regrowth with different rates, and can be calibrated using data from standard xenograft experiments. TSE and related concepts can be used to predict tumor shrinkage and eradication, and have the potential to guide new experiments and support translations from animals to humans.

Simulating Space Radiation-Induced Breast Tumor Incidence Using Automata

Estimating cancer risk from space radiation has been an ongoing challenge for decades primarily because most of the reported epidemiological data on radiation-induced risks are derived from studies of atomic bomb survivors who were exposed to an acute dose of gamma rays instead of chronic high-LET cosmic radiation. In this study, we introduce a formalism using cellular automata to model the long-term effects of ionizing radiation in human breast for different radiation qualities. We first validated and tuned parameters for an automata-based two-stage clonal expansion model simulating the age dependence of spontaneous breast cancer incidence in an unexposed U.S.

POPULATION

We then tested the impact of radiation perturbation in the model by modifying parameters to reflect both targeted and nontargeted radiation effects. Targeted effects (TE) reflect the immediate impact of radiation on a cell's DNA with classic end points being gene mutations and cell death. They are well known and are directly derived from experimental data. In contrast, nontargeted effects (NTE) are persistent and affect both damaged and undamaged cells, are nonlinear with dose and are not well characterized in the literature. In this study, we introduced TE in our model and compared predictions against epidemiologic data of the atomic bomb survivor cohort. TE alone are not sufficient for inducing enough cancer. NTE independent of dose and lasting ∼100 days postirradiation need to be added to accurately predict dose dependence of breast cancer induced by gamma rays. Finally, by integrating experimental relative biological effectiveness (RBE) for TE and keeping NTE (i.e., radiation-induced genomic instability) constant with dose and LET, the model predicts that RBE for breast cancer induced by cosmic radiation would be maximum at 220 keV/μm. This approach lays the groundwork for further investigation into the impact of chronic low-dose exposure, inter-individual variation and more complex space radiation scenarios.

A mathematical model of tumor growth and its response to single irradiation

BACKGROUND

Mathematical modeling of biological processes is widely used to enhance quantitative understanding of bio-medical phenomena. This quantitative knowledge can be applied in both clinical and experimental settings. Recently, many investigators began studying mathematical models of tumor response to radiation therapy. We developed a simple mathematical model to simulate the growth of tumor volume and its response to a single fraction of high dose irradiation. The modelling study may provide clinicians important insights on radiation therapy strategies through identification of biological factors significantly influencing the treatment effectiveness.

METHODS

We made several key assumptions of the model. Tumor volume is composed of proliferating (or dividing) cancer cells and non-dividing (or dead) cells. Tumor growth rate (or tumor volume doubling time) is proportional to the ratio of the volumes of tumor vasculature and the tumor. The vascular volume grows slower than the tumor by introducing the vascular growth retardation factor, θ. Upon irradiation, the proliferating cells gradually die over a fixed time period after irradiation. Dead cells are cleared away with cell clearance time. The model was applied to simulate pre-treatment growth and post-treatment radiation response of rat rhabdomyosarcoma tumors and metastatic brain tumors of five patients who were treated with Gamma Knife stereotactic radiosurgery (GKSRS).

RESULTS

By selecting appropriate model parameters, we showed the temporal variation of the tumors for both the rat experiment and the clinical GKSRS cases could be easily replicated by the simple model. Additionally, the application of our model to the GKSRS cases showed that the α-value, which is an indicator of radiation sensitivity in the LQ model, and the value of θ could be predictors of the post-treatment volume change.

CONCLUSIONS

The proposed model was successful in representing both the animal experimental data and the clinically observed tumor volume changes. We showed that the model can be used to find the potential biological parameters, which may be able to predict the treatment outcome. However, there is a large statistical uncertainty of the result due to the small sample size. Therefore, a future clinical study with a larger number of patients is needed to confirm the finding.

Ionizing irradiation not only inactivates clonogenic potential in primary normal human diploid lens epithelial cells but also stimulates cell proliferation in a subset of this population

Over the past century, ionizing radiation has been known to induce cataracts in the crystalline lens of the eye, but its mechanistic underpinnings remain incompletely understood. This study is the first to report the clonogenic survival of irradiated primary normal human lens epithelial cells and stimulation of its proliferation. Here we used two primary normal human cell strains: HLEC1 lens epithelial cells and WI-38 lung fibroblasts. Both strains were diploid, and a replicative lifespan was shorter in HLEC1 cells. The colony formation assay demonstrated that the clonogenic survival of both strains decreases similarly with increasing doses of X-rays. A difference in the survival between two strains was actually insignificant, although HLEC1 cells had the lower plating efficiency. This indicates that the same dose inactivates the same fraction of clonogenic cells in both strains. Intriguingly, irradiation enlarged the size of clonogenic colonies arising from HLEC1 cells in marked contrast to those from WI-38 cells. Such enhanced proliferation of clonogenic HLEC1 cells was significant at ≥2 Gy, and manifested as increments of ≤2.6 population doublings besides sham-irradiated controls. These results suggest that irradiation of HLEC1 cells not only inactivates clonogenic potential but also stimulates proliferation of surviving uniactivated clonogenic cells. Given that the lens is a closed system, the stimulated proliferation of lens epithelial cells may not be a homeostatic mechanism to compensate for their cell loss, but rather should be regarded as abnormal. This is because these findings are consistent with the early in vivo evidence documenting that irradiation induces excessive proliferation of rabbit lens epithelial cells and that suppression of lens epithelial cell divisions inhibits radiation cataractogenesis in frogs and rats. Thus, our in vitro model will be useful to evaluate the excessive proliferation of primary normal human lens epithelial cells that may underlie radiation cataractogenesis, warranting further investigations.

A branching process model for the analysis of abortive colony size distributions in carbon ion-irradiated normal human fibroblasts

A single cell can form a colony, and ionizing irradiation has long been known to reduce such a cellular clonogenic potential. Analysis of abortive colonies unable to continue to grow should provide important information on the reproductive cell death (RCD) following irradiation. Our previous analysis with a branching process model showed that the RCD in normal human fibroblasts can persist over 16 generations following irradiation with low linear energy transfer (LET) γ-rays. Here we further set out to evaluate the RCD persistency in abortive colonies arising from normal human fibroblasts exposed to high-LET carbon ions (18.3 MeV/u, 108 keV/µm). We found that the abortive colony size distribution determined by biological experiments follows a linear relationship on the log-log plot, and that the Monte Carlo simulation using the RCD probability estimated from such a linear relationship well simulates the experimentally determined surviving fraction and the relative biological effectiveness (RBE). We identified the short-term phase and long-term phase for the persistent RCD following carbon-ion irradiation, which were similar to those previously identified following γ-irradiation. Taken together, our results suggest that subsequent secondary or tertiary colony formation would be invaluable for understanding the long-lasting RCD. All together, our framework for analysis with a branching process model and a colony formation assay is applicable to determination of cellular responses to low- and high-LET radiation, and suggests that the long-lasting RCD is a pivotal determinant of the surviving fraction and the RBE.

What are the intracellular targets and intratissue target cells for radiation effects?

Exactly a century after Röntgen's discovery of X rays, I entered a university to major in radiological sciences. At that time, I felt that, despite extensive use and indispensable roles of ionizing radiation in medicine and industry, many fascinating questions have yet to be answered concerning its biological mechanisms of action, and thus I decided to get into the field of radiation research. Fifteen years have passed since I started radiobiological studies in 1998, during which time various basic tenets I initially learned in my late teens and early twenties have been challenged by recent observations. Of these, this brief overview particularly focuses on the following five different albeit non mutually exclusive questions: (i) "Is nuclear DNA the only intracellular target for radiation effects?"; (ii) "What is the significance of delayed cell death in clonogenic survival?"; (iii) "Does an irradiated cell become a cancer cell?"; (iv) "Are cataracts tissue reactions?"; and (v) "Why is high-LET radiation biologically effective?".