Abstracts of the Association for Radiation Research Winter Meeting,Leeds, 6–8 January 1988

Summary

A sensitive experimental design and data analysis were used to test rigorously whether the repair capacity in the skin of the mouse foot changes during a course of repeated 240 k Vp X-ray doses. Any such changes might reflect saturation or induction of repair enzymes resulting from progressive radiation damage, but most importantly this assumption of equal effect per dose fraction is central to all analyses of multiple-fraction radiation treatments, and remained to be demonstrated conclusively in skin. An X-ray dose of 2·5 Gy was given two, eight, 14 or 20 times with an interfraction interval of 8 h. Individual skin reactions for each mouse were analysed separately, giving 139 estimates of the effectiveness of 2·5 Gy (～ 35 in each of the four fractionation schedules). Regression analysis of effect per fraction versus number of fractions showed that there was no significant trend, i.e. the damage per fraction was constant regardless of the number of fractions used. The mean damage per fraction was 3·75 ± 0·15 per cent (95 per cent CL) of the full underlying damage equivalent to transient moist desquamation, and the slope of this plot was 0·0075 per cent ± 0·022 per cent (95 per cent CL) per fraction. It was concluded that the assumption of equal effect per fraction was not invalidated in mouse skin. Shorter interfraction intervals would not allow full repair between fractions, and this could be misinterpreted as a progressive loss of repair capacity in this type of experiment. This was tested in skin by giving 2·5 Gy doses two, eight and 14 times with a 1-h interfraction interval. Effect per fraction increased with number of fractions, by an extra 37 per cent from two to eight fractions and by a further 14 per cent from eight to 14 fractions, giving the illusion of loss of repair as predicted. This confirms the need to check that where loss of repair capacity is suspected, this is not due artifactually to incomplete repair between fractions in slowly repairing systems.     

Recovery Kinetics of X-ray Damage in Mouse Skin: The Influence of Dose Per Fraction

Summary

The rate of recovery from radiation damage, as a function of dose per fraction, was investigated in mouse skin. Two different experimental designs were used, both incorporating the neutron top-up technique which enables the X-ray dose per fraction to be kept constant whilst changing the interfraction interval. Either equally space X-ray fractions (concertina design) or single or multiple pairs of X-ray doses (single and multiple split-dose designs) were given at varying intervals, followed by graded doses of neutrons. A wide range of X-ray doses per fraction were investigated (from 1 to 10·5 Gy) and the data were analysed using the Thames Incomplete Repair (IR) model modified for use with neutron top-up doses. Analyses of the data, obtained from five different experiments, indicate that the rate of recovery from radiation damage is significantly faster at doses per fraction between 1 and 4·4 Gy than at 10·5 Gy. These data appear not to support the assumption, made by most recovery models, that the rate of recovery is independent of dose.     

Repair kinetics in mouse lung after multiple X-ray fractions per day

The potential advantage for sparing normal tissue damage by hyperfractionation of low-LET radiation may be limited by the repair kinetics of tissues in the irradiated field. Tissues with slow repair kinetics will limit the number of fractions that may be given on the same day. Results are presented for mouse lung treated with a range of doses per fraction using either two or three fractions per day in multiple X-ray fractionation schedules. The results are analysed to determine whether the repair kinetics follow a single exponential function of time. The calculated repair rate (T1/2) was about 1.2 h for two fractions per day of 2 Gy (10F/5d) but slightly less (T1/2 = 0.8 h) for two fractions of 9 Gy (2F/1d). For smaller doses per fraction of 1.1 Gy, given three times per day (39F/13d), the T1/2 was not significantly less (T1/2 = 0.3-0.7 h). For three fractions per day of 1.1 Gy per fraction an unsatisfactory fit is achieved using a single exponential function of time, and a better fit is obtained using two components of repair. The repair kinetics are slow for lung, in comparison to acute reacting tissues (except skin), and may require that 6-8 h (i.e. four or five half-times) should be allowed between fractions on the same day so that more than 95 per cent of the repairable dose is repaired. At present the variation in repair kinetics with doses per fraction between 1.1 and 9 Gy are not significantly different, so no reduction of interfraction interval should be proposed.     

Does the repair capacity of skin change with repeated exposure to X-rays?

A sensitive experimental design and data analysis were used to test rigorously whether the repair capacity in the skin of the mouse foot changes during a course of repeated 240 kVp X-ray doses. Any such changes might reflect saturation or induction of repair enzymes resulting from progressive radiation damage, but most importantly this assumption of equal effect per dose fraction is central to all analyses of multiple-fraction radiation treatments, and remained to be demonstrated conclusively in skin. An X-ray dose of 2.5 Gy was given two, eight, 14 or 20 times with an interfraction interval of 8 h. Individual skin reactions for each mouse were analysed separately, giving 139 estimates of the effectiveness of 2.5 Gy (approximately 35 in each of the four fractionation schedules). Regression analysis of effect per fraction versus number of fractions showed that there was no significant trend, i.e. the damage per fraction was constant regardless of the number of fractions used. The mean damage per fraction was 3.75 +/- 0.15 per cent (95 per cent CL) of the full underlying damage equivalent to transient moist desquamation, and the slope of this plot was 0.0075 per cent +/- 0.022 per cent (95 per cent CL) per fraction. It was concluded that the assumption of equal effect per fraction was not invalidated in mouse skin. Shorter interfraction intervals would not allow full repair between fractions, and this could be misinterpreted as a progressive loss of repair capacity in this type of experiment. This was tested in skin by giving 2.5 Gy doses two, eight and 14 times with a 1-h interfraction interval. Effect per fraction increased with number of fractions, by an extra 37 per cent from two to eight fractions and by a further 14 per cent from eight to 14 fractions, giving the illusion of loss of repair as predicted. This confirms the need to check that where loss of repair capacity is suspected, this is not due artifactually to incomplete repair between fractions in slowly repairing systems.     

Study of Dose-rate and Split-dose Effects on the in Vitro Micronucleus Yield in Human Lymphocytes Exposed to X-rays

This paper reports the effects of changes in dose-rate and dose-fractionation on the micronucleus (MN) yield in human lymphocytes exposed to 250 kV X-rays. For the investigation of dose-rate effects whole blood samples of four healthy donors were irradiated with doses ranging from 1 to 4 Gy given at various dose-rates between 0·2 and 40 Gy/h. For the higher doses (3 and 4 Gy) a decline in the MN yield became apparent when the dose-rate was reduced below 1·6 Gy/h. This effect was enhanced systematically by a further lowering of the dose-rate. For lower doses (1 and 2 Gy) the reduction in the MN yield was less pronounced: only a small effect was observed for two donors when a dose of 2 Gy was administered at a dose-rate of 0·2 Gy/h. In the split-dose experiment a dose of 4 Gy was delivered either as a single exposure or in two fractions of 2 Gy, separated by time intervals ranging from 30 min to 10 h. A continuous decrease of the MN yield with increasing interfraction time is observed: after an initial fast decline a further slight reduction in the MN yield occurs. The observed dose-rate and split-dose effects on the MN yield can be attributed to repair of sublethal damage.     

Additivity of Type O and Type N Damage in Diploid Yeast

Summary

Idiopathic pneumonitis is a major cause of morbidity and mortality in patients with leukaemia undergoing total body irradiation (TBI) and bone marrow transplantation (BMT). The effect of variation in dose rate of TBI on the development of lethal and sublethal lung damage has been investigated in mice by measuring changes in carbon monoxide uptake. CBA mice were irradiated using a ⁶⁰Co source at 0·02, 0·05, 0·1, 0·2, 0·5 and 1·0 Gy min^?1 to a total dose of 15·5 Gy. A log–linear relationship between the severity of impairment of carbon monoxide uptake (V_CO) and dose rate was found. Ventilatory requirement (ventilation rate/V_CO) was raised 20 to 40 weeks after TBI at dose rates above 0·1 Gy min^?1. Time of onset and extent of elevation of ventilatory requirement were also dose-rate dependent. The implications of these findings for clinical practice are discussed.     

Repair kinetics in mouse lung: a fast component at 1.1 Gy per fraction

Four experiments to measure the half-time of repair of radiation damage in mouse lung are described. Three of these experiments used two or four doses per fraction of 3.6-9 Gy. Half-times of approximately 0.6 h were found. The fourth experiment investigated repair between the two doses in pairs of small doses given daily (26F x 1.1 Gy in 13 days). Evidence was obtained of more rapid repair between these small fractions, with a half-time of 0.30 h. Using the best methods of analysis appropriate to each experiment, the 95 per cent confidence limits for the T1/2 values at 1.1 Gy per fraction did not overlap with those for the large doses per fraction.     

The Circadian Rhythm for the Number and Sensitivity of Radiation-induced Apoptosis in the Crypts of Mouse Small Intestine

Summary

Apoptosis is a mode of cell death involving nuclear pycnosis, cytoplasmic condensation and karyorrhexis. Changes in the number of apoptotic cells at various times (3–12 h) after a single dose of either 0·5 or 9·0 Gy given at 09.00, 21.00 or 03.00 h were studied in histological sections of small intestinal crypts of mice. The incidences of apoptosis were examined 3 or 6 h after irradiation at different times of day with different doses of γ-rays ranging from 0·15 to 9·0 Gy. Survival curves were constructed from the dose–incidence curves for apoptosis, using the number of apoptotic cells after high doses (N_M) as the maximum cell population size. The mean lethal doses (D₀) for the dose range 0–0·5 Gy were calculated for each time of day. A circadian rhythm in both D₀ and N_M values was detected, indicating that both the number and sensitivity of radiation-induced apoptosis were changing throughout the day. A possible explanation based on the cell-cycle states of the target cell population for apoptosis (presumably functional stem cells) was drawn. Most of the target cells were assumed to be in an extended G₁ phase. Around 21.00 h a transition from G₁ to S phase takes place in some of these cells (approximately seven or eight cells per whole crypt). The S phase then lasts till around 06.00 h. They may be at G₂ and M around 06.00–09.00 h, and then they re-enter G₁. The circadian rhythm for the number and sensitivity of the cells susceptible to apoptosis obtained in the present report agrees well with this pattern of cell-cycle phases of target cells.     

Detection of Base Damage in DNA in Human Blood Exposed to Ionizing Radiation at Biologically Relevant Doses

Summary

The alkaline elution technique for the detection of DNA damage has been adapted to allow application on unlabelled blood cells. Both the induction and subsequent repair have been studied of two classes of DNA damage, viz. single-strand breaks and base damage recognized by the γ-endonuclease activity in a cell-free extract of Micrococcus luteus bacteria. The high sensitivity of the assay permitted the measurement of induction and repair of base damage after in vitro exposure of full blood under aerobic conditions to biologically relevant doses of γ-rays (1·5–4·5 Gy). After a radiation dose of 3 Gy about 50% of the base damage was removed within 1·5 h of repair. Base damage could still be detected at 24 h after exposure to 15 Gy.     

Alpha-particles Induce Preneoplastic Transformation of Rat Tracheal Epithelial Cells in Culture

Summary

To characterize the potential role of high-l.e.t. radiation in respiratory carcinogenesis, the cytotoxic and transforming potency of 5·5 MeV α-particles from electroplated sources of ²³⁸Pu were determined using primary cultures of rat tracheal epithelial cells. The α-particle response was compared to the effects of 280 kVp X-rays and of the direct-acting carcinogen N-methyl-N'-nitro-N-nitrosoguanidine. Increasing the α-particle dose caused an exponential decrease in survival with a D₃₇ of 1·6 Gy. X-rays also caused a dose-dependent decrease in survival (D₃₇ = 3·6 Gy) but the survival curve had a significant shoulder. The RBE for cell killing by α-particles versus X-rays varied with dose, and ranged between 4 and 1·5 for α doses in the range 0·2–4 Gy. At equally toxic doses (relative survival 0·18–0·2), all three agents induced similar frequencies of preneoplastic transformation. For preneoplastic transformation induced by doses of α- and X-radiations giving 80 per cent toxicity, an α RBE of 2·4 was derived. The similar RBEs for cell killing and for preneoplastic transformation suggest an association between the type or degree of radiation-induced damage responsible for both cell killing and cell transformation.     

Repair in mouse lung of multifraction X rays and neutrons: extension to 40 fractions

We have extended our previous multiple irradiations of mouse lung from 20 to 40 fractions of both X-ray and neutron radiation in order to test whether the repair parameters previously derived will hold for lower doses per fraction, down to 1.1 Gy of X rays and 0.18 Gy of 3 MeV neutrons per fraction. Repair parameters were calculated from measurements of breathing rate and lethality at monthly intervals up to 17 months after irradiation with 1, 10, 20 or 40 equal fractions. Sparing of neutron damage was negligible when the neutron dose was divided into multiple fractions, but progressively greater repair of lung damage was seen after increasing numbers of X-ray fractions. A significant increase in the iso-effect dose for 40 fractions of X rays was found compared with 20 fractions, even when two fractions per day were given at intervals of about 6 hours, as was the case in the 40 fraction experiment. The data were well fitted by the linear quadratic formula for response vs. dose per fraction and the ratio alpha/beta yielded values of approximately 3 Gy after X rays and 30 to 40 Gy after neutron irradiation; these values are not different from alpha/beta ratios found for up to 20 fractions. The single dose RBE was less than 2, increasing to about 6 at the lowest dose per fraction measured, in agreement with previous results. The ratio of the alpha component for neutrons to that for X rays was about 8, which is therefore the limiting RBE predicted for infinitely small doses per fraction.     

High Radiosensitivity of the MOLT-4 Leukaemic Cell Line

Summary

Radiation survival of MOLT-4, a leukaemic T-lymphocyte cell line, was measured by counting colonies formed in 0·8 per cent methyl cellulose. The survival curve was a simple exponential and showed the cells to be radiation sensitive, with D₀ = 0·49 ± 0·02 Gy and extrapolation number n = 0·92 ± 0·09. No increase in survival as measured by colony-forming ability or trypan blue dye exclusion was seen when the dose was split into two fractions, separated by a 5 h incubation period. Electron microscopy and trypan blue dye exclusion showed that 5 h after exposure to high doses, MOLT-4 cells began to die and displayed condensed, marginated chromatin and cellular vesticulation.     

Recovery kinetics of X-ray damage in mouse skin: the influence of dose per fraction.

The rate of recovery from radiation damage, as a function of dose per fraction, was investigated in mouse skin. Two different experimental designs were used, both incorporating the neutron top-up technique which enables the X-ray dose per fraction to be kept constant whilst changing the interfraction interval. Either equally spaced X-ray fractions (concertina design) or single or multiple pairs of X-ray doses (single and multiple split-dose designs) were given at varying intervals, followed by graded doses of neutrons. A wide range of X-ray doses per fraction were investigated (from 1 to 10.5 Gy) and the data were analysed using the Thames Incomplete Repair (IR) model modified for use with neutron top-up doses. Analyses of the data, obtained from five different experiments, indicate that the rate of recovery from radiation damage is significantly faster at doses per fraction between 1 and 4.4 Gy than at 10.5 Gy. These data appear not to support the assumption, made by most recovery models, that the rate of recovery is independent of dose.     

Murine Haemopoietic Stem Cells with Long-term Engraftment and Marrow Repopulating Ability are More Resistant to Gamma-radiation than are Spleen Colony Forming Cells

The radiation sensitivity of various subsets in the haemopoietic stem cell hierarchy was defined using a limiting dilution type long-term bone marrow culture technique that was previously shown to allow quantification of cells with spleen colony-forming potential (day-12 CFU-S) and in vivo marrow repopulating ability (MRA). Primitive stem cells that generate new in vitro clonable colony-forming cells (CFU-C) in the irradiated marrow (MRA) and have long-term repopulation ability (LTRA) in vitro (cobblestone area forming cell, CAFC day-28) had D₀ values of 1·25 and 1·38 Gy, respectively. A lower D₀ was found for the less primitive CFU-S day-12, CAFC day-12 and cells with erythroid repopulating ability (0·91, 1·08 and 0·97 Gy, respectively). CFU-S day-7 were the most radiosensitive (D₀ equalling 0·79 Gy), while CFU-C and CAFC day-5 were relatively resistant to irradiation (D₀ 1·33 and 1·77 Gy). Split-dose irradiation with a 6 h interval gave dose sparing for stem cells with MRA and even more with in vitro LTRA, less for CFU-S day-12 and CAFC day-10 and none for CFU-S day-7. The cell survival data of the specified stem cell populations were compared with the ability of a fixed number of B6-Gpi-1^a donor bone marrow cells to provide for short- and long-term engraftment in single- and split-dose irradiated cognenic B6-Gpi-1^b mice. Serial blood glucose phosphate isomerase (Gpi) phenotyping showed less chimerism in the split as compared to the single radiation dose groups beyond 4 weeks after transplant. Radiation dose-response curves corresponding to stable chimerism at 12 weeks for single and fractionated doses revealed appreciable split-dose recovery (D₂–D₁) in the order of 2 Gy. This was comparable to D₂–D₁ estimates for MRA and late-developing CAFC (1·27 and 1·43 Gy, respectively), but differed from the poor dose recovery in cells corresponding to the committed CFU-S day-7/12 and CAFC day-10 population (0·14–0·33 Gy). These data are together consistent with differential radiosensitivity and repair in the haemopoietic stem cell hierarchy, and provide a cellular basis for explaining the dose-sparing effect of fractionated total-body irradiation conditioning on long-term host marrow repopulation.     

Differential Response to Gamma Radiation of Human Stomach Cancer Cells in Vitro

Summary

In vitro effects of radiation were studied in two permanent cell lines (AGS and SII) from two patients with adenocarcinoma of the stomach and three permanent sublines from each cell line. Radiation survival parameters for AGS and SII parent cell lines and sublines were determined after in vitro irradiation of their cells with 0·5 to 10 Gy of ⁶⁰Co gamma rays. The AGS and SII cell lines had different growth properties, DNA contents and radiation survival curves. Surviving fractions of SII parent cells (76 chromosomes) after 2·0 and 10 Gy were 1·22 and 17·8 times greater, respectively, than values for AGS parent cells (47 chromosomes). Sensitivities (D₀) were 1·08 and 1·45 Gy for AGS and SII parent lines, respectively. The D₀ values for AGS parent cells and sublines were similar (1·01 to 1·08 Gy), but SII parent cells and sublines had D₀ values of 1·45, 1·36, 1·37 and 1·12 Gy (for SII-A). Also, the SII parent cells had survival fractions after 2·0 and 10 Gy that were 1·3 and 11·3 times greater, respectively, than values for the SII-A cells. These data show differences in radiation responses among stomach cancer cell lines and sublines that may relate to DNA content, but there was no consistent correlation between radiation response and a particular cell characteristic.     

Radiation Injury in Mouse Lung: Dependence on Oxygen Levels in the Inspired Gas

Summary

The relationship between radiosensitivity and the partial pressure of oxygen (PO₂) in the inspired gas has been established for radiation pneumonitis as a measure of lung damage following irradiation of the mouse thorax. The radiosensitivity at low PO₂ (0–1 per cent) fitted the linear transformation of the Alper, Howard-Flanders relationship giving a K value for lung tissue of 1·35 per cent oxygen with an oxygen enhancement ratio, m, of 2·13. The radiosensitivity at higher PO₂ (5–21 per cent) did not fit the Alper, Howard-Flanders relationship probably because the PO₂ of the inspired gas was greater than the PO₂ in the alveolus. At the low PO₂ levels in the inspired gas, back diffusion of oxygen from blood into the alveolus may lead to errors in the estimated value of K. If the low value of m is due to this ‘contaminating’ oxygen from blood then by taking a higher value for m, the amount of contaminating oxygen can be calculated (0·23 per cent) and a ‘true’ value for K (1·1 per cent) determined. Other uncertainties in this estimate of K due to the radiolytic consumption of oxygen and possible inadequacies in equilibration are discussed. Allowing for the uncertainties, it is concluded that the K value for lung damage lies towards the upper end of the range of K values measured for cells in vitro.     

Repair in mouse lung for up to 20 fractions of X rays or neutrons

Local irradiation of the mouse thorax followed by the measurement of lung damage up to 17 months after irradiation has been carried out with up to 20 fractions of 3 MeV neutrons or of 240 kV X rays. Doses per fraction down to 0.28 and 1.5 Gy respectively were used. Repair capacity and RBE values were assessed by measuring breathing rate and lethality at monthly intervals up to 17 months. Only a small sparing of neutron damage was found. Sparing with X rays continued to increase as the size of each fraction was decreased, and was the main influence on the RBE values. The single-dose RBE was approximately 1.8, increasing to approximately 5 at the lowest dose per fraction measured. Dose-response curves derived for each fraction were well fitted by the formula alpha d + beta d2 where the repair parameter alpha/beta has values of 2-4 Gy after X irradiation. A slight fall of alpha/beta with time after X irradiation was observed, from about 4 Gy for pneumonitis to about 2 Gy for late fibrosis. This was significant for lethality but not for the increase of breathing rate. With neutrons the value of alpha was much higher than with X rays and a trend of increasing value of alpha at later times after irradiation was seen. Use of the linear quadratic dose-response formula predicts a continuing increase in the sparing of X-ray damage in lung as doses per fraction are decreased below those used here, and a limiting low-dose RBE of about 7.     

正常肺组织大分割照射全肺平均耐受剂量与生物学效应研究

目的 建立正常组织分次照射基于肺纤维化影像学改变的全肺平均剂量-效应模型,定量分析分割照射相比单次照射的生物学效应及耐受剂量关系。方法 采用8~10周龄C57BL6雌性小鼠按随机数表法分组进行X射线全肺野照射,分别给予梯度剂量0、2.0 Gy×5次、4.0 Gy×5次、6.0 Gy×5次、7.0 Gy×5次、8.5 Gy×5次。照射后24周行CT扫描成像,CT图像三维重建后经三维分割算法获得肺部平均密度与肺部体积值,并分别据此进行Boltzmann模型放射生物学建模。结果 照射后24周CT图像三维重建冠状位图像提示剂量依赖的肺部影像学改变。同一时间点肺组织全基因组芯片与组织病理学研究均提示与影像学改变高度吻合。经放射生物学建模,分次照射诱导肺密度改变的全肺平均剂量（D_mean）中位剂量为（30.80±0.80）Gy（校正R²=0.97）;引起肺体积减小的中位剂量为（31.31±7.07）Gy（校正R²=0.92）。基于影像学参数的剂量-效应曲线提示,肺组织对分次照射的耐受性相比单次照射显著提高。结论 纤维化进展过程中,肺密度与肺体积改变对X射线的依赖性不仅取决于总剂量大小,也与分割次数、分次剂量存在一定关联。     

Cell Population Kinetics of the Rhabdomyosarcoma R1H of the Rat after Single Doses of X-rays

Summary

The kinetics of depopulation and repopulation of the solid transplantable rhabdomyosarcoma R1H of the rat following local irradiation with single subcurative X-ray doses of 7·5, 15 and 30 Gy was studied. Several parameters were sequentially measured over a time interval of 4 weeks after irradiation: the ratio of the number of tumour to host cells, and the cellular DNA content of tumour and host cells, were determined by flow cytometry; the amount of DNA per gram of tumour tissue was determined biochemically; the clonogenic fraction of tumour cells was obtained from in vitro colony assay; and the tumour volume was assessed by in situ caliper measurements. From the amount of DNA per gram and the average DNA content per cell, the total number of cells per gram of tumour tissue was obtained. From this and the other parameters measured, the number of clonogenic tumour cells, non-clonogenic tumour cells and nucleated host cells per tumour, as well as their variation with time and dose, could be derived. The results showed that there was a lag period prior to depopulation amounting to 3·8 ± 1·4, 1·4 ± 0·8 or 0 ± 0·7 days for 7·5, 15 or 30 Gy, respectively. The rate of depopulation of non-clonogenic tumour cells increased with dose; the halving times of non-clonogens were 4·7 ± 1·8, 2·6 ± 0·7 or 2·1 ± 0·4 days for the three doses applied. There were no indications that proliferation of doomed cells contributed significantly to tumour growth after irradiation. After lag periods that were similar in length to those prior to depopulation, a massive immigration of host cells was observed. Under certain conditions more than 97 per cent of the cells present in irradiated tumours were found to be of host origin. There was a lag period before the onset of repopulation by clonogenic tumour cells, the length of which increased from 2·7 ± 0·7 to 5·0 ± 0·8 or 6·3 ± 1·0 days for 7·5, 15 or 30 Gy, respectively. The initial rate of repopulation increased with radiation dose; after the end of the lag period the doubling time of clonogenic tumour cells (in controls amounting to 3·7 ± 0·2 days) was 3·1 ± 0·1, 2·1 ± 0·1 and 1·1 ± 0·1 days for the three doses applied. Nevertheless, all repopulation curves could be described by one particular Gompertz function (whose parameters also give a good fit to the volume growth of the undisturbed tumour), indicating that the rate of repopulation corresponds to the growth rate of untreated tumours that contain a comparable number of clonogens as are left in the irradiated tumours.