Modelling of carcinogenesis and low-dose hypersensitivity: an application to lung cancer incidence among atomic bomb survivors

Lung cancer incidence among the atomic bomb survivors from Hiroshima and Nagasaki was analysed with the two-step clonal expansion (TSCE) model of carcinogenesis. For the baseline incidence, a new set of model parameters is introduced, which can be determined with a higher precision than the parameter sets previously used. The effect of temporal changes in the smoking behaviour on the lung cancer incidence is modelled by allowing initiation, inactivation and division rates of intermediate cells to depend on the year of birth. The TSCE model is further developed by implementing low-dose hypersensitivity in the survival of lung epithelial cells. According to the model fit to the data, the acute gamma exposure of the atomic bomb survivors does not only result in the conventional initiating effect, but also in a promoting effect for lung cancer. Compared to the model in which radiation acts merely on initiation, the new model is in better agreement with the age-at-exposure dependence in the data, and it does not predict an unexpected increase of the excess relative risk (ERR) at 40 years after exposure. According to the new model, the ERR at low doses increases non-linearly with dose, especially during the first 10 years after exposure to older persons.     

Testing goodness of fit for stochastic models of carcinogenesis.

This paper considers the utility of statistical goodness of fit testing in the context of mechanistic models of carcinogenesis. Two stochastic models of carcinogenesis were tested with several sets of experimental and epidemiological data using a formal goodness of fit test specially designed to accommodate censored observations: these were the two-stage model allowing for clonal expansion of initiated cells and its simpler version with gamma distributed promotion time. The results of this application, supplemented by visual examination of local likelihood kernel estimates of the hazard function and the corresponding model-based estimates, show that mechanistic models of carcinogenesis provide a good fit to the data in the majority of cases under study.     

On the parameters of the clonal expansion model

The exact hazard function of the clonal expansion model was analyzed, and it was shown that only three of its four parameters can be determined by fitting to the age dependence of spontaneous tumor incidence rates. The same holds for the survival function.     

A model for hepatocarcinogenesis with clonal expansion of three successive phenotypes of preneoplastic cells

The two-stage model with clonal expansion of intermediate cells has often been used to describe the carcinogenesis process. The model hypothesizes that cells have to undergo two mutations on their way from the normal to the malignant stage. Biological experiments indicate the existence of three types of preneoplastic cells in hepatocarcinogenesis representing three successive intermediate stages in the development of malignant cells from normal cells. This finding suggests that hepatocarcinogenesis should be described by a multi-stage model with three intermediate stages, leading to a four-stage mutation model with clonal expansion of all types of intermediate cells. This model is presented and mathematical approximations for the number and size of nonextinct premalignant clones of the different cell types are derived. The model is applied to focal lesion data from a rat hepatocarcinogenesis experiment.     

A multi-step kinetic model for substrate assimilation and bacterial growth: application to benzene biodegradation

A multi-step kinetic model based on the concept of synthesizing unit (SU) was developed for describing benzene biodegradation in Pseudomonas putida F1. The model herein presented considered substrate arrival rates to the SU rather than concentrations, and provided a reasonable good fit of the dynamics of both catechol and biomass concentrations experimentally determined. It was based on very general assumptions and could be applied to any process accumulating metabolic intermediates. Conventional growth models considering a single step can be regarded as a particular case of this multi-step model. Despite the merits of this model, its applicability strongly depends on the knowledge of the complex induction-repression and inhibition mechanisms governing the different catabolic steps of the degradation pathway, which in most cases are difficult to elucidate experimentally and/or to model mathematically. In this particular case repression of benzene oxidation by catechol and self-inhibition of catechol transformation were experimentally confirmed and considered in the simulation, resulting in a good fit (relative average error of 6%) of the experimental data.     

Promotion of initiated cells by radiation-induced cell inactivation

Cells on the way to carcinogenesis can have a growth advantage relative to normal cells. It has been hypothesized that a radiation-induced growth advantage of these initiated cells might be induced by an increased cell replacement probability of initiated cells after inactivation of neighboring cells by radiation. Here Monte Carlo simulations extend this hypothesis for larger clones: The effective clonal expansion rate decreases with clone size. This effect is stronger for the two-dimensional than for the three-dimensional situation. The clones are irregular, far from a circular shape. An exposure-rate dependence of the effective clonal expansion rate could come in part from a minimal recovery time of the initiated cells for symmetric cell division.     

Bone cancer risk in mice exposed to 224Ra: protraction effects from promotion

This paper analyzes data for the osteosarcoma incidence in life-time experiments of (224)Ra injected mice with respect to the importance of initiating and promoting action of ionizing high LET-radiation. This was done with the biologically motivated two step clonal expansion (TSCE) model of tumor induction. Experimentally derived osteosarcoma incidence in 1,194 mice following exposure to (224)Ra with different total radiation doses and different fractionation patterns were analyzed together with incidence data from 1,710 unirradiated control animals. Effects of radiation on the initiating event and on the clonal expansion rate, i.e. on promotion were found to be necessary to explain the observed patterns with this model. The data show a distinct inverse protraction effect at high doses, whereas at lower doses this effect becomes insignificant. Such a behavior is well reproduced in the proposed model: At dose rates above 6 mGy/day a longer exposure produces higher ERR per dose, while for lower rates the reverse is the case. The TSCE model permits the deduction of several kinetic parameters of a postulated two-step bone tumorigenesis process. Mean exposure rates of 0.13 mGy/day are found to double the baseline initiation rate. At rates above 100 mGy/day, the initiation rate decreases. The clonal expansion rate is doubled at 8 mGy/day, and it levels out at rates beyond 100 mGy/day.     

Estimating the proportion cured of cancer: Some practical advice for users

BackgroundCure models can provide improved possibilities for inference if used appropriately, but there is potential for misleading results if care is not taken. In this study, we compared five commonly used approaches for modelling cure in a relative survival framework and provide some practical advice on the use of these approaches.Patients and methodsData for colon, female breast, and ovarian cancers were used to illustrate these approaches. The proportion cured was estimated for each of these three cancers within each of three age groups. We then graphically assessed the assumption of cure and the model fit, by comparing the predicted relative survival from the cure models to empirical life table estimates.ResultsWhere both cure and distributional assumptions are appropriate (e.g., for colon or ovarian cancer patients aged <75 years), all five approaches led to similar estimates of the proportion cured. The estimates varied slightly when cure was a reasonable assumption but the distributional assumption was not (e.g., for colon cancer patients ≥75 years). Greater variability in the estimates was observed when the cure assumption was not supported by the data (breast cancer).ConclusionsIf the data suggest cure is not a reasonable assumption then we advise against fitting cure models. In the scenarios where cure was reasonable, we found that flexible parametric cure models performed at least as well, or better, than the other modelling approaches. We recommend that, regardless of the model used, the underlying assumptions for cure and model fit should always be graphically assessed.     

Calorimetric vs. van't Hoff binding enthalpies from isothermal titration calorimetry: Ba2+-crown ether complexation

The 1:1 complexation reaction between Ba(2+) and 18-crown-6 ether is re-examined using isothermal titration calorimetry (ITC), with the goal of clarifying previously reported discrepancies between reaction enthalpies estimated directly (calorimetric) and indirectly, from the temperature dependence of the reaction equilibrium constant K (van't Hoff). The ITC thermograms are analyzed using three different non-linear fit models based on different assumptions about the data error: constant, proportional to the heat and proportional but correlated. The statistics of the fitting indicate a preference for the proportional error model, in agreement with expectations for the conditions of the experiment, where uncertainties in the delivered titrant volume should dominate. With attention to proper procedures for propagating statistical error in the van't Hoff analysis, the differences between Delta H(cal) and Delta H(vH) are deemed statistically significant. In addition, statistically significant differences are observed for the Delta H(cal) estimates obtained for two different sources of Ba(2+), BaCl(2) and Ba(NO(3))(2). The effects are tentatively attributed to deficiencies in the standard procedure in ITC of subtracting a blank obtained for pure titrant from the thermogram obtained for the sample.     

The linear no-threshold model does not hold for low-dose ionizing radiation

Almost all of the data on the biological effects of ionizing radiation come from studies of high doses. However, the human population is unlikely to be exposed to such doses. Regulatory limits for radiation exposure are based on the linear no-threshold model, which predicts that the relationship between biological effects and radiation dose is linear, and that any dose has some effect. Chromosomal changes are an important effect of ionizing radiation because of their role in carcinogenesis. Here we exposed pKZ1 mice to single whole-body X-radiation doses as low as 1 microGy. We observed three different phases of response: (1) an induction of inversions at ultra-low doses, (2) a reduction below endogenous inversion frequency at low doses, and (3) an induction of inversions again at higher doses. These results do not fit a linear no-threshold model, and they may have implications for the way in which regulatory standards are presently set and for understanding radiation effects.     

Lung tumour risk in radon-exposed rats from different experiments: comparative analysis with biologically based models

Data sets of radon-exposed male rats from Wistar and Sprague-Dawley strains have been investigated with two different versions of the two-step clonal expansion (TSCE) model of carcinogenesis. These so-called initiation-promotion (IP) and initiation-transformation (IT) models are named after the cell-based processes that are assumed to be induced by radiation. The analysis was done with all malignant lung tumours taken to be incidental and with fatal tumours alone. For all tumours treated as incidental, both models could explain the tumour incidence data equally well. Owing to its better fit, only the IP model was applied in the analysis of fatal tumours that carry additional information on the time when they cause death. A statistical test rejected the hypothesis that a joint cohort of Wistar and Sprague-Dawley rats can be described with the same set of model parameters. Thus, the risk analysis has been carried out for the Wistar rats and the Sprague-Dawley rats separately and has been restricted to fatal tumours alone because of their similar effect in humans. Using a refined technique of age-adjustment, the lifetime excess absolute risk has been standardised with the survival function from competing risks in the control population. The age-adjusted excess risks for both strains of rats were of similar size, for animals with first exposure later in life they decreased markedly. For high cumulative exposure the excess risk increased with longer exposure duration, for low cumulative exposure it showed the opposite trend. In addition, high cumulative exposure exerted lethal effects other than lung cancer on the rats.     

A review of the evidence from in vitro and in vivo studies for a role for phorbol ester tumour promoters from the Euphorbiales in the selection and clonal expansion of specific cell populations

Review of the evidence from in vitro and in vivo studies for a role for phorbol ester tumour promoters from the Euphorbiales in the selection and clonal expansion of specific cell populations. The identification of the active principle of croton oil as 12-0-tetradecanoylphorbol-13-acetate (TPA) and the advent of in vitro studies, facilitated the identification of a plethora of biochemical effects, certain of which could be correlated with biological and differentiation end points. Evidence is presented for the ability of TPA to select and expand specific cell populations in two different cell culture systems. The roles of differentiation state and second messenger systems will be discussed in relation to models of multi-step carcinogenesis.     

Concepts of association between cancer and ionising radiation: accounting for specific biological mechanisms

The probability that an observed cancer was caused by radiation exposure is usually estimated using cancer rates and risk models from radioepidemiological cohorts and is called assigned share (AS). This definition implicitly assumes that an ongoing carcinogenic process is unaffected by the studied radiation exposure. However, there is strong evidence that radiation can also accelerate an existing clonal development towards cancer. In this work, we define different association measures that an observed cancer was newly induced, accelerated, or retarded. The measures were quantified exemplarily by Monte Carlo simulations that track the development of individual cells. Three biologically based two-stage clonal expansion (TSCE) models were applied. In the first model, radiation initiates cancer development, while in the other two, radiation has a promoting effect, i.e. radiation accelerates the clonal expansion of pre-cancerous cells. The parameters of the TSCE models were derived from breast cancer data from the atomic bomb survivors of Hiroshima and Nagasaki. For exposure at age 30, all three models resulted in similar estimates of AS at age 60. For the initiation model, estimates of association were nearly identical to AS. However, for the promotion models, the cancerous clonal development was frequently accelerated towards younger ages, resulting in associations substantially higher than AS. This work shows that the association between a given cancer and exposure in an affected person depends on the underlying biological mechanism and can be substantially larger than the AS derived from classic radioepidemiology.

     

Lung cancer in Mayak workers: interaction of smoking and plutonium exposure

Lung cancer mortality among 5058 male workers of the Mayak Production Association has been analyzed with emphasis on the interaction of smoking and radiation exposure by using the two-step clonal expansion (TSCE) model of carcinogenesis. The cohort consists of all Mayak workers with known smoking status, who were employed in the period 1948–1972, and who either had the plutonium concentration in urine measured or who worked in the reactors, where plutonium exposure was negligible. Those who died during the first two years after the first urine sampling were excluded. The follow-up extended until the end of 1998. During this time, 2176 workers died, including 244 lung cancer cases. Mayak workers were exposed to external (gamma and neutron) radiation, and in the radiochemical and plutonium plants to plutonium. In the preferred TSCE model, internal radiation and smoking act on the clonal expansion of pre-carcinogenic clones. Assuming a plutonium radiation weighting factor of 20, the excess relative risk per lung dose was estimated to be 0.11 (95% CI: 0.08; 0.17) Sv⁻¹. Most of the lung cancer deaths are found to be due to smoking. The second main factor is the interaction of smoking and internal radiation. The model is sub-multiplicative in relative risks due to smoking and radiation. In a multiplicative version of the TSCE model, internal radiation acts on initiation and transformation rates. This model version agrees with conventional epidemiological risk models, because it also suggests a higher risk estimate than the preferred TSCE model. However, it fits the data less well than the preferred model. An erratum to this article can be found at     

Evaluating automated parameter constraining procedures of neuron models by experimental and surrogate data

Neuron models, in particular conductance-based compartmental models, often have numerous parameters that cannot be directly determined experimentally and must be constrained by an optimization procedure. A common practice in evaluating the utility of such procedures is using a previously developed model to generate surrogate data (e.g., traces of spikes following step current pulses) and then challenging the algorithm to recover the original parameters (e.g., the value of maximal ion channel conductances) that were used to generate the data. In this fashion, the success or failure of the model fitting procedure to find the original parameters can be easily determined. Here we show that some model fitting procedures that provide an excellent fit in the case of such model-to-model comparisons provide ill-balanced results when applied to experimental data. The main reason is that surrogate and experimental data test different aspects of the algorithm’s function. When considering model-generated surrogate data, the algorithm is required to locate a perfect solution that is known to exist. In contrast, when considering experimental target data, there is no guarantee that a perfect solution is part of the search space. In this case, the optimization procedure must rank all imperfect approximations and ultimately select the best approximation. This aspect is not tested at all when considering surrogate data since at least one perfect solution is known to exist (the original parameters) making all approximations unnecessary. Furthermore, we demonstrate that distance functions based on extracting a set of features from the target data (such as time-to-first-spike, spike width, spike frequency, etc.)—rather than using the original data (e.g., the whole spike trace) as the target for fitting—are capable of finding imperfect solutions that are good approximations of the experimental data.     

A mathematical and statistical framework for modelling dispersal

Mechanistic and phenomenological dispersal modelling of organisms has long been an area of intensive research. Recently, there has been an increased interest in intermediate models between the two. Intermediate models include major mechanisms that affect dispersal, in addition to the dispersal curve of a phenomenological model. Here we review and describe the mathematical and statistical framework for phenomenological dispersal modelling. In the mathematical development we describe modelling of dispersal in two dimensions from a point source, and in one dimension from a line or area source. In the statistical development we describe applicable observation distributions, and the procedures of model fitting, comparison, checking, and prediction. The procedures are also demonstrated using data from dispersal experiments. The data are hierarchically structured, and hence, we fit hierarchical models. The Bayesian modelling approach is applied, which allows us to show the uncertainty in the parameter estimates and in predictions. Finally, we show how to account for the effect of wind speed on the estimates of the dispersal parameters. This serves as an example of how to strengthen the coupling in the modelling between the phenomenon observed in an experiment and the underlying process – something that should be striven for in the statistical modelling of dispersal.