Comparison of the induction of pulmonary neoplasms in Sprague-Dawley rats by fission neutrons and radon daughters

Pulmonary carcinomas were recorded in a life-span experiment of male Sprague-Dawley rats exposed to fission neutrons. Mortality-corrected prevalences are obtained by the method of isotonic regression. In a second part of the paper a comparison is made with data obtained earlier for radon-daughter inhalations in the same strain of rats. A simultaneous maximum likelihood analysis is applied jointly to all experimental groups from the radon inhalation and the fission neutron study. The dependence of the resulting coefficients for the different groups on absorbed dose or inhalation dose permits a derivation of equivalence ratios. At low doses the equivalence ratio is 3 WLM (working level months) of radon-daughter exposure to 1 mGy of fission neutrons. At higher doses the equivalence ratio decreases. The neutron data are also utilized to derive mortality-corrected lifetime incidences of pulmonary carcinomas in the exposed animals. At low doses the relation is consistent with linearity, but sublinearity (dose exponent less than 1) cannot be excluded.     

Neutron RBE for induction of tumors with high lethality in Sprague-Dawley rats

The effectiveness of fission neutrons is compared to that of gamma rays and X rays with regard to the induction of malignancies in male Sprague-Dawley rats. The analysis is based on autopsy results. It is focused on tumors that tend to be present in animals dying early, which is indicative of a high degree of lethality. The relative biological effectiveness (RBE) is deduced from a comparison of the cumulative hazard functions. Different nonparametric models-the constant relative risk model, a time shift model, and an acceleration model-are employed in the comparison, and the resulting values of RBE are seen to be substantially independent of the choice of model. The results are in good agreement with earlier studies of nonlethal lung tumors in the same series of experiments. At neutron doses of 20 to 60 mGy, the RBE of fission neutrons is about 50.     

Life shortening in mice exposed to fission neutrons and gamma rays. VII. Effects of 60 once-weekly exposures

A total of 6316 B6CF1 mice were exposed to 60 equal once-weekly doses of 0.85-MeV fission neutrons (0.033 to 0.67 cGy per weekly fraction) or 60Co gamma rays (1.67 to 10 cGy per weekly fraction) and were observed until they died. The mean aftersurvival times showed that the dose-response curves for both neutron and gamma-ray exposures were indistinguishable from linear over all doses except the highest neutron dose. The relative biological effectiveness (RBE) for neutrons, calculated as the ratio of the initial slopes of the dose-response curves, was about 20 for both males and females. Essentially the same value was obtained by a number of other analyses of the data. Virtually all of the radiation-specific excess mortality could be attributed to tumors; after decrementation of the population for nontumor deaths, the value of the RBE was not significantly changed.     

Relative biological effectiveness and tolerance dose of fission neutrons in canine skin for a potential combination of neutron capture therapy and fast-neutron therapy

To investigate the potential efficacy of fission neutrons from a fast-neutron reactor for the treatment of radioresistant tumors, the relative biological effectiveness (RBE) and tolerance dose of fission neutrons in canine skin were determined. The forelimbs of 34 healthy mongrel dogs received a single dose of fission neutrons (5.6, 6.8, 8.2, 9.6 or 11 Gy) or 137Cs gamma rays (10, 15, 20, 25 or 30 Gy). Based on observations of radiodermatitis for each radiation, the single-fraction RBE of fission neutrons in the sixth month was calculated as approximately 3. The tolerance doses of fission neutrons and gamma rays, defined as the highest doses giving no moist desquamation on the irradiated skin in the recovery phase, were estimated as 7.6 Gy and 20 Gy, respectively. The tolerance dose of 7.6 Gy of fission neutrons included 5.0 Gy of fast neutrons possessing high anti-tumor effects and 1.4 x 10(12) n/cm2 of thermal neutrons, which could be applicable to neutron capture therapy (NCT). The combination of fast-neutron therapy and NCT using a fast-neutron reactor might be useful for the treatment of radioresistant tumors.     

Lung cancer risk in mice: analysis of fractionation effects and neutron RBE with a biologically motivated model

Data from Argonne National Laboratory on lung cancer in 15,975 mice with acute and fractionated exposures to gamma rays and neutrons are analyzed with a biologically motivated model with two rate-limiting steps and clonal expansion. Fractionation effects and effects of radiation quality can be explained well by the estimated kinetic parameters. Both an initiating and a promoting action of neutrons and gamma rays are suggested. While for gamma rays the initiating event is described well with a linear dose-rate dependence, for neutrons a nonlinear term is needed, with less effectiveness at higher dose rates. For the initiating event, the neutron RBE compared to gamma rays is about 10 when the dose rate during each fraction is low. For higher dose rates this RBE decreases strongly. The estimated lifetime relative risk for radiation-induced lung cancers from 1 Gy of acute gamma-ray exposure at an age of 110 days is 1.27 for male mice and 1.53 for female mice. For doses less than 1 Gy, the effectiveness of fractionated exposure to gamma rays compared to acute exposure is between 0.4 and 0.7 in both sexes. For lifetime relative risk, the RBE from acute neutrons at low doses is estimated at about 10 relative to acute gamma-ray exposure. It decreases strongly with dose. For fractionated neutrons, it is lower, down to about 4 for male mice.     

Dose-response modeling of life shortening in a retrospective analysis of the combined data from the JANUS program at Argonne National Laboratory

Life shortening was investigated in both sexes of the B6CF1 (C57BL/6 x BALB/c) mouse exposed to fission neutrons and 60Co gamma rays. Three basic exposure patterns for both neutrons and gamma rays were compared: single exposures, 24 equal once-weekly exposures, and 60 equal once-weekly exposures. Ten different dose-response models were fitted to the data for animals exposed to neutrons. The response variable used for all dose-response modeling was mean after-survival. A simple linear model adequately described the response to neutrons for females and males at doses less than or equal to 80 cGy. At higher neutron dose levels a linear-quadratic equation was required to describe the life-shortening response. An effect of exposure pattern was observed prior to the detection of curvature in the dose response for neutrons and emerged as a potentially significant factor at neutron doses in the range of 40-60 cGy. Augmentation of neutron injury with dose protraction was observed in both sexes and began at doses as low as 60 cGy. The life-shortening response for all animals exposed to gamma rays (22-1918 cGy) was linear and inversely dependent upon the protraction period (1 day, 24 weeks, 60 weeks). Depending on the exposure pattern used for the gamma-ray baseline, relative biological effectiveness (RBE) values ranged from 6 to 43. Augmentation, because it occurred only at higher levels of neutron exposure, had no influence on the estimation of RBEm.     

Life shortening in mice exposed to fission neutrons and gamma rays. V. Further studies with single low doses

Data are presented on the mean after survival of female B6CF1 mice exposed to single doses of neutrons (1 to 40 rad) or gamma rays (22.5, 45, and 90 rad). For gamma-ray exposures and for neutron exposures up to 10 rad, the dose-response curves are indistinguishable from linear; higher neutron doses produce significant departures and linearity. Consequently, in these data, an upper limit of the relative biological effectiveness (RBE) exists for life shortening from all causes of death after single neutron exposures; this value is 15.0 +/- 5.1. The RBE depends on the cause of death, ranging from 2 to 5 for lymphoreticular tumors to 23-24 for lung tumors.     

A comparison of gamma and neutron irradiation on Raji cells: effects on DNA damage, repair, cell cycle distribution and lethality.

The Comet assay (microgel electrophoresis) was used to study DNA damage in Raji cells, a B-lymphoblastoid cell line, after treatment with different doses of neutrons (0.5 to 16 Gy) or gamma rays (1.4 to 44.8 Gy). A better growth recovery was observed in cells after gamma-ray treatments compared with neutron treatments. The relative biological effectiveness (RBE) of neutron in cell killing was determined to be 2.5. Initially, the number of damaged cells per unit dose was approximately the same after neutron and gamma-ray irradiation. One hour after treatment, however, the number of normal cells per unit dose was much lower for neutrons than for gamma rays, suggesting a more efficient initial repair for gamma rays. Twenty-four hours after treatment, the numbers of damaged cells per unit dose of neutrons or gamma rays were again at comparable level. Cell cycle kinetic studies showed a strong G2/M arrest at equivalent unit dose (neutrons up to 8 Gy; gamma rays up to 5.6 Gy), suggesting a period in cell cycle for DNA repair. However, only cells treated with low doses (up to 2 Gy) seemed to be capable of returning into normal cell cycle within 4 days. For the highest dose of neutrons, decline in the number of normal cells seen at already 3 days after treatment was deeper compared with equivalent unit doses of gamma rays. Our present results support different mechanisms of action by these two irradiations and suggest the generation of locally multiply damaged sites (LMDS) for high linear energy transfer (LET) radiation which are known to be repaired at lower efficiency.     

Neoplastic transformation is enhanced by multiple low doses of fission-spectrum neutrons

The neoplastic transformation of C3H mouse 10T1/2 cells was measured induced by fission-spectrum neutrons delivered at a high dose rate in five fractions over 4 days. The transformation frequency was significantly enhanced over that due to single equivalent total doses. These new data, in the low dose region, demonstrate an increased transformation frequency by fractionated versus single exposures of high-dose-rate fission-spectrum neutrons; an increase equal to that observed with low-dose-rate fission-spectrum neutrons (i.e., 0.086 rad/min). Estimates of the dose modifying factor (DMF), based upon the ratio of the initial linear portions of the induction curves for high and for low dose rates, suggest the same DMF (approximately 7.8) for both five daily fractions of high-dose-rate neutrons and for low-dose-rate neutrons. However, when these results are compared to those following high-dose-rate 60Co gamma rays (100 rad/min), the relative biological effectiveness (RBE) for low-dose-rate fission-spectrum neutrons based upon slope ratios is 19.6; similarly, the RBE relative to five daily fractions of 60Co gamma rays is 78.8.     

Neutron-energy-dependent oncogenic transformation of C3H 10T1/2 mouse cells

The relative biological effectiveness (RBE) of a range of neutron energies relative to 250-kVp X rays has been determined for oncogenic transformation and cell survival in the mouse C3H 10T 1/2 cell line. Monoenergetic neutrons at 0.23, 0.35, 0.45, 0.70, 0.96, 1.96, 5.90, and 13.7 MeV were generated at the Radiological Research Accelerator Facility of the Radiological Research Laboratories, Columbia University, and were used to irradiate asynchronous cells at low absorbed doses from 0.05 to 1.47 Gy. X irradiations covered the range 0.5 to 8 Gy. Over the more than 2-year period of this study, the 31 experiments provided comprehensive information, indicating minimal variability in control material, assuring the validity of comparisons over time. For both survival and transformation, a curvilinear dose response for X rays was contrasted with linear or nearly linear dose responses for the various neutron energies. RBE increased as dose decreased for both end points. Maximal RBE values for transformation ranged from 13 for cells exposed to 5.9-MeV neutrons to 35 for 0.35-MeV neutrons. This study clearly shows that over the range of neutron energies typically seen by nuclear power plant workers and individuals exposed to the atomic bombs in Japan, a wide range of RBE values needs to be considered when evaluating the neutron component of the effective dose. These results are in concordance with the recent proposals in ICRU 40 both to change upward and to vary the quality factor for neutron irradiations.     

Risk estimation for fast neutrons with regard to solid cancer.

In the absence of epidemiological information on the effects of neutrons, their cancer mortality risk coefficient is currently taken as the product of two low-dose extrapolations: the nominal risk coefficient for photons and the presumed maximum relative biological effectiveness of neutrons. This approach is unnecessary. Since linearity in dose is assumed for neutrons at low to moderate effect levels, the risk coefficient can be derived in terms of the excess risk from epidemiological observations at an intermediate dose of gamma rays and an assumed value, R(1), of the neutron RBE relative to this reference dose of gamma rays. Application of this procedure to the A-bomb data requires accounting for the effect of the neutron dose component, which, according to the current dosimetry system, DS86, amounts on average to 11 mGy in the two cities at a total dose of 1 Gy. With R(1) tentatively set to 20 or 50, it is concluded that the neutrons have caused 18% or 35%, respectively, of the total effect at 1 Gy. The excess relative risk (ERR) for neutrons then lies between 8 per Gy and 16 per Gy. Translating these values into risk coefficients in terms of the effective dose, E, requires accounting for the gamma-ray component produced by the neutron field in the human body, which will require a separate analysis. The risk estimate for neutrons will remain essentially unaffected by the current reassessment of the neutron doses in Hiroshima, because the doses are unlikely to change much at the reference dose of 1 Gy.     

Interpretation of cytogenetic damage induced in the germ line of male mice exposed for over 1 year to 239Pu alpha particles, fission neutrons, or 60Co gamma rays

The relative biological effectiveness (RBE) of 239Pu alpha particles, fission neutrons (0.85 MeV), and 60Co gamma rays has been evaluated for the induction of reciprocal chromosome translocations in spermatogonia and of chromosome/chromatid fragments and chromatid rearrangements in the primary spermatocyte of adult male B6CF1 mice. Age concurrency was maintained for both internal and external radiations which were delivered at about 1 rad/week for 239Pu (single intravenous dose of 10 microCi/kg), 0.67, 1.67, and 2.67 rad/week for neutrons, and 6.95, 17.4, and 32 rad/week for gamma rays for at least 60 weeks. In terms of frequency of translocations, the response to the alpha emitter was nonlinear (concave downward) with little dose-response predictability; to cumulative neutron exposures the response was linear, without evidence of a dose-rate effect; and to gamma radiation the responses were linear, and a significant dose-rate effect was seen. RBE estimates are variable. For translocations, the n/gamma ratio is between 10 and 24, depending upon weekly dose level, and the ratio is 1 or less for the alpha particle relative to the neutron. For fragments, the n/gamma ratio is 18 to 22, depending upon age factors, and alpha/n is 1.5. For chromatid rearrangements, n/gamma is 7 and alpha/n is essentially indeterminate, but much below one. The overall response to the alpha emitter is interpreted to be a complex function of (a) microdosimetric heterogeneity, (b) a nearly invariant deposition pattern in the gonad, (c) the high sensitivity of differentiating spermatogonia to cell killing, and (d) the capacity of stem cells in relatively radiation-free areas to progressively assume the major spermatogenic role.     

A radiobiological model for the relative biological effectiveness of high-dose-rate 252Cf brachytherapy

While there is significant clinical experience using both low- and high-dose-rate 252Cf brachytherapy, there are minimal data regarding values for the neutron relative biological effectiveness (RBE) with both modalities. The aim of this research was to derive a radiobiological model for 252Cf neutron RBE and to compare these results with neutron RBE values used clinically in Russia. The linear-quadratic (LQ) model was used as the basis to characterize cell survival after irradiation, with identical cell killing rates (S(N) = S(gamma)) between 252Cf neutrons and photons used for derivation of RBE. Using this equality, a relationship among neutron dose and LQ radiobiological parameter (i.e., alpha(N), beta(N), alpha(gamma), beta(gamma)) was obtained without the need to specify the photon dose. These results were used to derive the 252Cf neutron RBE, which was then compared with Russian neutron RBE values. The 252Cf neutron RBE was determined after incorporating the LQ radiobiological parameters obtained from cell survival studies with fast neutrons and teletherapy photons. For single-fraction high-dose-rate neutron doses of 0.5, 1.0, 1.5 and 2.0 Gy, the total biologically equivalent doses were 1.8, 3.4, 4.7 and 6.0 RBE Gy with 252Cf neutron RBE values of 3.2, 2.9, 2.7 and 2.5, respectively. Using clinical data for late-responding reactions from 252Cf, Russian investigators created an empirical model that predicted high-dose-rate 252Cf neutron RBE values ranging from 3.6 to 2.9 for similar doses and fractionation schemes and observed that 252Cf neutron RBE increases with the number of treatment fractions. Using these relationships, our results were in general concordance with high-dose-rate 252Cf RBE values obtained from Russian clinical experience.     

Biological effectiveness of neutrons from Hiroshima bomb replica: results of a collaborative cytogenetic study

The effectiveness of neutrons from a facsimile of the Hiroshima bomb was determined cytogenetically. The "Little-Boy" replica (LBR), assembled at Los Alamos as a controlled nuclear reactor for detailed physical dosimetry, was used. Of special interest, the neutron energy characteristics (including lineal energy) measured 0.74 m from the LBR were remarkably similar to those calculated for the 1945 Hiroshima bomb at 1 to 2 km from the hypocenter, as shown in a companion dosimetric paper (Straume, et al., Radiat. Res. 128, 133-142 (1991)). Thus we examine here the effectiveness of neutrons closely resembling those that the A-bomb survivors received at Hiroshima. Chromosome aberration frequencies were determined in human blood lymphocytes exposed in vitro to graded doses of LBR radiation (97% neutrons, 3% gamma rays). Vials of blood suspended in air at distances up to 2.10 m from the center of the LBR uranium core received doses ranging from 0.02 to 2.92 Gy. The LBR neutrons (E approximately 0.2 MeV) produced 1.18 dicentrics and rings per cell per Gy. They were more effective than the higher-energy fission neutrons (E approximately 1 MeV) commonly used in radiobiology. The maximum RBE (RBEM) of LBR neutrons at low doses is estimated to be 60 to 80 compared to 60Co gamma rays and 22 to 30 compared to 250-kVp X rays. These results provide a quantitative measurement of the biological effectiveness of Hiroshima-like neutrons.     

The relative biological effectiveness of 10B-neutron capture therapy for early skin reaction in the hamster

The relative biological effectiveness (RBE) of 10B-neutron capture therapy (BNCT) on skin was analyzed using hamsters. The Kyoto University Research Reactor, which has a very low contamination of gamma rays and fast neutrons, was used as a thermal neutron source. Boron-10-para-boronophenylalanine hydrochloride ([10B]BPA.HCl) was administered to the hamsters. The evolution and time course of early skin reactions were assessed. These reactions were compared with those produced by electron beams. The maximum safe skin doses (no more than moist desquamation) of BNCT and electron beams were established to be 11 and 21 Gy, respectively. The RBE at this single dose with BNCT was found to be 1.94, assuming that the RBE of the gamma rays was 1.0 and each component of BNCT (mixed radiations) was simply additive.     

Relative biological effectiveness measurements using murine lethality and survival of intestinal and hematopoietic stem cells after fermilab neutrons compared to JANUS reactor neutrons and 60Co gamma rays

The relative biological effectiveness (RBE) of the 25-MeV (average energy) neutron beam at the Fermi National Accelerator Laboratory was measured using murine bone marrow (LD50/30) and gut (LD50/6) lethality and killing of hematopoietic colony forming units (CFU-S) or intestinal clonogenic cells (ICC). The reference radiation was 60Co gamma rays. The LD50/30 and LD50/6 for mice exposed to the Fermilab neutron beam were 6.6 and 8.7 Gy, respectively, intermediate between those of JANUS neutrons and 60Co gamma rays. The D0 values for CFU-S and ICC were 47 cGy and 1.05 Gy, respectively, also intermediate between the lowest values found for JANUS neutrons and the highest values found after 60Co gamma rays. The split-dose survival ratios for CFU-S at intervals of 1-6 hr between doses were essentially 1.0 for both neutron sources, while the corresponding split-dose survival ratio for 60Co gamma rays was consistantly above 1, reaching a maximum of 1.7 with a 1-hr interval between doses. The 3-hr split-dose survival ratios for ICC were 1.0 for JANUS neutrons, 1.85 for Fermilab neutrons, and 6.5 for 60Co gamma rays. The RBE estimates for LD50/30 were 1.5 and 2.3 for Fermilab and JANUS neutrons, respectively. Based on LD50/6, the RBEs were 1.9 (Fermilab) and 3.0 (JANUS). The RBEs for CFU-S D0 were 1.4 (Fermilab) and 1.9 (JANUS) and for jejunal microcolony D0 1.4 (Fermilab) and 2.8 (JANUS).     

Absence of a dose-rate effect in the transformation of C3H 10T1/2 cells by alpha-particles

The findings of Hill et al. (1984) on the greatly enhanced transformation frequencies at very low dose rates of fission neutrons induced us to perform an analogous study with alpha-particles at comparable dose rates. Transformation frequencies were determined with gamma-rays at high dose rate (0.5 Gy/min), and with alpha-particles at high (0.2 Gy/min) and at low dose rates (0.83-2.5 mGy/min) in the C3H 10T1/2 cell system. alpha-particles were substantially more effective than gamma-rays, both for cell inactivation and for neoplastic transformation at high and low dose rates. The relative biological effectiveness (RBE) for cell inactivation and for neoplastic transformation was of similar magnitude, and ranged from about 3 at an alpha-particle dose of 2 Gy to values of the order of 10 at 0.25 Gy. In contrast to the experiments of Hill et al. (1984) with fission neutrons, no increased transformation frequencies were observed when the alpha-particle dose was protracted over several hours.     

Neutron RBEs and the radiosensitive target for mouse immature oocyte killing

The highly radiosensitive immature oocytes of mice were irradiated in vivo with graded doses of 252Cf fission radiation, 0.43- or 15-MeV neutrons, or 60Co gamma rays. Comparisons of oocyte survival for neutrons and for gamma rays demonstrate that neutron RBEs for the killing of these important cells do not reach the high values (30-50 or more) at low doses observed for several other biological end points. Rather, neutrons differ little in effectiveness from gamma rays in killing these extremely sensitive murine oocytes. For 0.43-MeV neutrons, RBEs obtained from fitted survival curves reach only 1.7 at 0.1 rad. For 15-MeV neutrons, they are not significantly different from 1 at any dose tested (lowest, 4.5 rad). For 252Cf fission neutrons (E = 2.15 MeV), RBEs are intermediate between those for 0.43- and 15-MeV neutrons. For all neutron energies tested, the RBEs are particularly low in the juvenile period, a time when murine immature oocytes are especially radiosensitive. With exposure just prior to birth, however, when these cells are much less easily killed, higher, more usual RBEs are found. The minimum size of the lethality target in mouse immature oocytes, estimated from the inactivation constant for 0.43-MeV neutrons and microdosimetric values, is larger than the nucleus but not larger than the cell. This and related analytical considerations suggest that the hypersensitive target in these particular oocytes is the plasma membrane, a finding which is in excellent accord with results from other experiments using different, contrasting radiations and dose deliveries (accelerated Si14+ ions, gamma rays, and beta rays from 3HOH compared with those from [3H]thymidine).     

Study of dose-rate effects of neutron radiation in a wild-type and a repair-deficient yeasts saccharomyces

We report here a comparative analysis of RBE for lethality of a single pulse (duration 65 micros) of fast neutron with ultra high dose rates (up to 6 x 10(6) Gy/s) and continuous neutron radiation (3.6 x 10(3) s) of the pulse reactor BARS-6. Three diploid strains, one haploid strain and three diploid repair-deficient strains (rad52-1/rad52-1; rad54/rad54; rad2/rad2) were used. The RBE values (D(0gamma)/1D(0n)) of a single pulse and continuous neutron irradiation were equal (1.7-1.8) with maximum RBE (4.1-3.1) in region of low doses (shoulder region). Haploid cells were found to be more (3 times) sensitive to both gamma-rays and neutrons than the wild type. There was no obvious decrease in the RBE of 1.9 in highly sensitive haploid cells as compared with highly resistant diploid cells. The repair-deficient strains (rad52-1/rad52-1; rad54/rad54) were more (up to 10 fold) sensitive to both neutrons and gamma-rays as compared with their parent line. The RBE values of 1.5-1.7 of neutrons for these mutants (independent by of the mode of irradiation) were found. The repair-deficient mutant rad2/rad2 had similar sensitivity as a wild type and a RBE value was 2.0. We have concluded that biological effectiveness of the neutrons of pulse reactor BARS-6 was independent of the dose-rate, differing up to 10(8) fold. The RBE didn't vary significantly with the capacity of cells to repair DNA damages.     

Comparison of recovery from potential mitotic abnormality in mitotically quiescent lens cells after X, neutron, and 56Fe irradiations

After exposure to various doses of 250 kVp X radiation, 0.85 Me V fission spectrum neutrons, or 600 MeV/A iron (Fe) particles, mitotically quiescent rat lens cells showed no visible evidence of radiation injury. However, following the mitogenic stimulus of wounding, mitotic abnormalities became evident when responding cells entered mitosis. Latent damage and recovery therefrom were monitored at 3, 7, 14, and 28 days after irradiation. Following doses of 1 to 10 Gy of X radiation, the recovery rate, indicated by a decrease in abnormalities with time, was proportional to dose, and the dose-effect slope decreased exponentially with time. Virtually no recovery occurred during the 28 days after 1.25 to 2.25 Gy of fission neutron radiation. After doses of 0.5 to 3.0 Gy of Fe particles, an increased expression of mitotic damage or recovery than recovery occurred. As a consequence of the differing patterns in time for expression of damage or recovery following X rays and the high-LET radiations, the relative biological effectiveness (RBE) increased from 3.6 to 16 for neutrons and from 2 to 10 for Fe particles over the 28-day observation period.