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Radiobiological modelling of the risk of radiation-induced tumours following high dose radiation implies a general form for the dose-response relationship. Generally, risk will rise with radiation dose at low doses, reach a maximum value and then decline with further increase in dose. The magnitude of risk and the dose at which this risk is maximum are strongly dependent on the kinetics of repopulation by surviving normal and mutant cells and on genetic factors likely to differ between tissues and between individuals. The most reliable way to reduce the risk of second tumours is to reduce radiation dose further at sites where the dose is already low. These sites are usually distant from the primary treatment volume. For illustrative purposes, we have compared the predicted relative risks of second tumours at "distant sites" for treatment plans giving similar dose distributions (dose volume histograms) at the primary site. We suggest that dose reduction to distant sites could be of significant benefit in reducing the risk of second tumours. Further improvement will require more detailed knowledge of the radiation sensitivities and mutagenicities, together with the repopulation kinetics of the various cell lineages within the treatment volume.

Purpose: To investigate the role of cellular repopulation in the dose-response relationship for radiation carcinogenesis resulting from high doses of radiation., Method: A two-stage mathematical model of radiation carcinogenesis was developed and used to explore the effects of differing assumptions about repopulation by surviving normal stem cells and by one-stage mutants., Results: Characteristically, cancer incidence at any fixed time after irradiation increases with radiation dose, reaches a peak and then declines with dose (the decline reflecting radiation cell-killing). The optimal dose for cancer incidence, and the incidence level at this dose, are strongly influenced by repopulation kinetics. If repopulation does not occur, or is impaired owing to radiation damage to tissues, the highest value of cancer incidence is reduced, and this value occurs at a lower dose than if repopulation had been complete. A similar result is found if repopulation by one-stage mutants is impaired relative to unmutated cells, or if tissue recovery is assisted by immigration of unirradiated cells., Conclusions: Differing repopulation kinetics can account for differing dose-response relationships after large doses of radiation. These findings are relevant to the occurrence of 'second tumours' following radiotherapy and to the interaction of radiation with other agents.

A stochastic process model for one-, two-, and three-stage malignant transformation has been developed for embryonic and adult mice. The model has been used to study the influence of mutation rate, number of stages required for transformation, and number of stem cells at risk on the kinetics of spontaneous appearance of malignant tumors. As expected, tumors appeared earlier with fewer required mutational stages, higher mutation rate, and greater number of stem cells at risk. However, a notable observation was that tumor latency was more strongly influenced by number of stages and by stem cell number at lower mutation rates than at higher rates. This implies that tumor latency may be a less useful observation when the spontaneous mutation rate is high. In the future, the model will be applied to analysis of tumorigenesis experiments in transgenic mice with p53 genetic abnormalities, subjected to irradiation or chemical tumorigenesis at different stages of development.

Purpose: A model is presented for calculating combinations of targeted 131I and total body irradiation, followed by bone marrow rescue, in the treatment of tumors of different radiosensitivity. The model is used to evaluate the role of the total body irradiation component in the optimal combination regime as a function of the radiosensitivity of the tumor cells., Methods and Materials: A microdosimetric model was used to calculate absorbed dose in small tumors and micrometastases when uniformly targeted by the radionuclide 131I. Cell kill was calculated from absorbed dose using an extended version of the linear quadratic model. The addition of varying total doses of total body irradiation, assuming 2 Gy fractions, was also calculated using the linear quadratic model. The net cell kill from combined modality (targeted 131I and total body irradiation) was computed for varying proportions of the two components, for a range of tumor sizes, restricting the total radiation dose to within tolerance for a full-course TBI regime (approximately 14 Gy total) in all cases. The calculations were repeated for a range of presumed tumor uptakes of the targeting agent and for a range of tumor radiosensitivities, typical of those reported for tumor cells of differing type in culture. Optimal regimes were identified as those predicted to yield a high probable tumor cure rate (evaluated using a Poisson statistical model) for all tumor sizes., Results: The analysis supports earlier model studies which predicted that systemic combination treatment with targeted 131I and total body irradiation would be superior to either component used alone. The intrinsic tumor radiosensitivity is found to be a factor which influences the optimal combination of the 131I and external beam total body irradiation components. The total body irradiation component is greater in optimal regimes treating radio-resistant than radiosensitive tumors. However, an obligatory total body irradiation component is also predicted for more radiosensitive tumors; the analysis suggests that the total body irradiation component should in no circumstances be less than 2 x 2 Gy, whilst practical arguments exist in favor of higher doses., Conclusion: Total body irradiation is an obligatory component for effective systemic treatment of disseminated malignant tumors to which 131I can be selectively targeted. Clinical studies applying this strategy to the treatment of neuroblastoma by 131I targeted by meta-iodo-benguanidine (mIBG), total body irradiation and bone marrow rescue are now in progress.

Neuraxis radiotherapy of radiosensitive tumours such as medulloblastoma is usually carried out using conventionally sized fractions and a shrinking field technique. Plowman and Doughty (Br. J. Radiol., 64 (1991) 603-607) have proposed a partial transmission block (PTB) technique which entails the use of small daily doses over a conventional time period. Radiobiological analysis suggests that, although the PTB technique may be adequate for slowly growing tumours, therapeutic efficacy is likely to be compromised where the tumour doubling time is short. Accelerated hyperfractionation (twice daily fractions) provides a possible alternative to both conventional scheduling and the PTB technique. Direct measurement of the kinetics of tumour cells in CSF, where possible, may provide useful guidance in the choice of regimes.

In tumour regrowth-delay experiments, the analysis of results in the higher dose ranges may be complicated by a dose-dependent proportion of non-recurrent (cured) tumours, whose inclusion in the analysis is not straightforward. A study of the relation of growth delay to cure has been carried out using a model of tumour response which assumes Poisson (single-cell) cure statistics and exponential regrowth kinetics of recurrent tumours, and which makes use of Monte Carlo simulation techniques to represent the effects of inter-tumour heterogeneity. This approach yields correction factors compensating for tumour cures in growth-delay experiments. For homogeneous tumour systems (all tumours and treatments identical) these corrections are small and not significantly different from corrections obtained using the "long delay" procedure suggested previously (Denekamp, 1980; Fowler et al., 1980). For heterogeneous systems, however, correction factors increase with the heterogeneity of the system, and may become quite large. It is concluded that the quantitative assessment of heterogeneity is required, and a possible approach to this is suggested. Should evaluation of heterogeneity prove feasible, it will allow more efficient use of tumour-response data, and may permit realistic estimates of clonogenic cell survival in situ.

The primary effect of irradiation on self-renewing normal tissues is sterilisation of their proliferative cells, but how this translates into failure of tissue function depends on the mode of organisation of the tissue concerned. It has recently been suggested (Michalowski, 1981) that proliferative normal tissues may be classed as "hierarchical" (like haemopoietic tissues) or as "flexible" (like liver parenchyma) and that radiation injury to tissue function develops by different pathways in these tissues. Mathematical model studies confirm the different radiation responses of differently organized tissues. Tissues of the "flexible" or "F-type" category display a variety of novel radiobiological properties, different from those of the more familiar "hierarchical" or "H-type" tissues. The "F-type" responses are strongly influenced by radiation-sterilised ("doomed") cells, and it is suggested that the rôle of "doomed" cells has been undervalued relative to that of clonogenic survivors. Since "F-type" tissues have characteristically low rates of cell renewal, it is possible that these tissues are preferentially responsible for late effects of irradiation in clinical radiotherapy.

It is proposed that tumour progression results from the increased mutability of tumour cells and that this mutability leads to the acquisition of a large number of 'neutral' mutations having no significant effects under physiological conditions but capable of lethal expression under different conditions. High temperatures often lead to expression of neutral mutations and this could provide a mechanism for the observed thermosensitivity of tumour cells, and a rational basis for the use of hyperthermia in cancer treatment.