Lack of evidence for increased tolerance of rat spinal cord with decreasing fraction doses below 2 Gy

The radiation tolerance of the spinal cord, both in man and in rats, has been shown to depend strongly on the size of the dose per fraction. With fraction doses down to about 2 Gy, the spinal cord tolerance can be predicted by a modified Ellis formula: D approximately N0.43. More recently alternative isoeffect formulas were based on the linear-quadratic (LQ) model of cell survival where the effect of dose fractionation is characterized by the ratio alpha/beta which varies from tissue to tissue. For the spinal cord, as well as for other late responding tissues, the ratio alpha/beta is small, in contrast to most acutely responding tissues. Both the Ellis-type formula, and to a lesser extent the LQ-model, predict a continuously increasing tolerance dose with decreasing fraction size. From the LQ model, the concept of "flexure dose" has been derived, which proposes the limit of effective fractionation to be about 0.1 alpha/beta. At this dose per fraction no significant further gain in tolerance would be detected. From previous experiments on the rat cervical spinal cord with doses per fraction down to about 2 Gy, the ratio alpha/beta was determined to be 1.7 Gy, and the LQ-model would predict a rise in tolerance with a reduction in fraction size to far below 2 Gy. Based on these predictions clinical studies have been initiated assuming a significantly increased tolerance by reduction of fraction size to about 1 Gy. However, in the present experiments no evidence was found for such an increase in tolerance with fraction sizes below 2 Gy.     

Tumor radioresponsiveness versus fractionation sensitivity

Since the introduction of mammalian cell survival curves, the parameters D0 and N have been used as quantitative measures of inherent radiation sensitivity, as was the shoulder width Dq. These parameters are more generally applicable at high doses. We propose to introduce a measure of tumor radioresponsitivity that is more applicable to the clinical treatment schedules that employ small fractional doses (1-2 Gy), the ratio alpha/E, derived from the linear quadratic model for cell inactivation as the intercept on the reciprocal-dose plot. For tumor-control experiments this ratio is the reciprocal of the TCD50 when radiation is given in very small fractions or at low dose rates (assuming negligible clonogen proliferation). The rationales for this choice are: alpha is a measure of the steepness of the initial linear segment of the dose-survival curve. Accordingly, at doses per fraction of 1-2 Gy the observed effect increases with alpha. E is by definition a positive measure of the clonogen kill required for a specified tumor response, e.g., E = -log (surviving fraction of clonogens at the 50% control level). Therefore it is also a measure of the number of clonogens present at the time of inception of treatment, which for a given dose is a prime determinant of the probability of tumor control. This measure of radioresponsitivity is to be distinguished from the ratio alpha/beta, which is a measure of fractionation sensitivity. A survey of the literature indicates that these do not correlate, except in highly hypoxic tumors (e.g., clamped); such tumors are characterized by low radioresponsitivity as well as low fractionation sensitivity (high alpha/beta ratio). There are at present only limited data for determination of this ratio, however, since reciprocal-dose analysis requires tumor control doses for several different sizes of dose per fraction.     

Fractionation sensitivities and dose-control relations of head and neck carcinomas: analysis of the randomized hyperfractionation trials.

PURPOSE: A therapeutic benefit can be achieved by hyperfractionation (HF) if tumours have small fractionation sensitivities characterized by alpha/beta values greater than those for late effects of dose limiting normal tissues. It is the purpose of the present paper to estimate alpha/beta values for head and neck carcinomas from randomized HF trials. MATERIALS AND METHODS: Maximum likelihood estimates the alpha/beta ratio were obtained from tumour control data from the randomized HF trials using the LQ model and a logit or probit type dose-response curve. A joint analysis of five randomized HF trials for head and neck carcinomas was performed to estimate overall alpha/beta and gamma50 values for tumour control. In addition, alpha/beta ratios for the individual trials were estimated using fixed gamma50 values (characteristic quantifying the steepness of dose-response curves) between 1.4 and 5 for tumours. RESULTS: An overall gamma50 of 3.1 (1.5-4.7) was estimated for the dose-tumour control relation from the HF trials, assuming a logit or probit dose-response curve. The tumours showed small fractionation sensitivities characterized by an overall alpha/beta of 10.5 (6.5-29) Gy. One trial allowed quantitative estimation of the alpha/beta values for late normal tissue damage: The alpha/beta estimate for late effects of grade 2 + was 4.0 (3.3-5.0) Gy, assuming a fixed gamma50 of 5 and was even smaller for smaller gamma50 values. CONCLUSION: Head and neck carcinomas showed small fractionation sensitivities with alpha/beta values greater than those typical for bone, soft tissues, and skin, as well as steep dose response curves. Thus, important prerequisites for improving the therapeutic benefit of radiotherapy of head and neck carcinomas by HF are fulfilled for patients who met the accession criteria of the trials.     

Re-irradiation of mouse skin: similarity of dose reductions for healing and macrocolony endpoints

The amount of residual injury in mouse tail skin, assessed by the decrease in re-irradiation dose for equal effect, was similar whether assessed using healing or colony endpoints (17-21% after single priming doses). There were tendencies towards an increased sensitivity of the colony-forming cells by a factor of about 2, and less residual injury after multifractionated priming doses. These observations are compatible with a lower alpha/beta ratio characterising the response to dose fractionation for residual injury than for the acute healing response.     

Intrinsic radiosensitivity of human cell lines is correlated with radioresponsiveness of human tumors: analysis of 101 published survival curves

One hundred and one published survival curves for 92 human cell lines (including 64 tumor lines) have been analyzed in terms of several parameters that are supposed to characterize cell radiosensitivity. Values for n, Do, alpha and beta (from the linear quadratic model), D (Mean Inactivation Dose), and survivals at 2 Gy and 8 Gy have been obtained for each curve. It was found that: I. the initial part of the survival curve is specific to the corresponding cell line; II. this initial part is well characterized by the parameters alpha and D, the values of which can be used to compare intrinsic radiosensitivity among human cell lines; III. human tumor cell line radiosensitivity (expressed in terms of alpha, D and survival at 2 Gy) reflects the clinical radioresponsiveness of the tumors from which the cell lines are derived. Thus, cells from tumors with low radioresponsiveness (melanomas and glioblastomas) are the less radiosensitive. Furthermore, the range of survival at a dose of 2 Gy is broad enough to account, in large measure, for observed differences in clinical tumor radioresponsiveness.     

Rational dose fractionation schedule 1. Each fractional dose

The dose per fraction which will produce the maximum therapeutic ratio in clinical radiotherapy is discussed, using the data on the variation of the oxygen enhancement ratio with dose size and the difference in the dose response curves between tumor cell lines and late effects in normal tissues. Isoeffect doses for late injury increased more than that for tumor response with decreasing dose per fraction. When late effects in normal tissues are dose-limiting for radiotherapy, the highest therapeutic ratio (normal tissue tolerance dose/dose for a given probability of local tumor control) would be obtained when the dose/fraction is equal to the flexure dose. Lengthening the interfraction interval to allow complete repair of sublethal injury in the normal tissues responsible for late effects may allow some repopulation of tumor cells. In this case it may be necessary to increase the dose/fraction slightly above the flexure dose.     

Literature analysis of high dose rate brachytherapy fractionation schedules in the treatment of cervical cancer: is there an optimal fractionation schedule?

PURPOSE: A literature review and analysis was performed to determine whether or not efficacious high dose rate (HDR) brachytherapy fractionation schedules exist for the treatment of cervical cancer. METHODS AND MATERIALS: English language publications from peer reviewed journals were assessed to calculate the total contribution of dose to Point A from both the external and intracavitary portions of radiation for each stage of cervical cancer. Using the linear quadratic formula, the biologically effective dose to the tumor, using an alpha/beta = 10, was calculated to Point A (Gy10) in order to determine a dose response relationship for local control and survival. Significant complications were assessed by calculating the dose to the late-responding tissues at Point A using an alpha/beta = 3 (Gy3) as a surrogate for normal tissue tolerance, since few publications list the actual bladder and rectal doses. RESULTS: For all stages combined, the median external beam fractionation schedule to Point A was 40 Gy in 20 fractions, while the median HDR fractionation schedule was 28 Gy in 4 fractions. For stages IB, IIB, and IIIB the median biologically effective dose to Point A (Gy10) was 96, 96 and 100 Gy10s, respectively. No correlation was identified between Point A BED (Gy10s) to either survival or pelvic control. A dose response relationship could also not be identified when correlating Point A Gy3s to complications. CONCLUSION: A dose response relationship could not be identified for either tumor control nor late tissue complications. These findings do not necessarily question the validity of the linear quadratic model, as much as they question the quality of the current HDR brachytherapy literature as it is currently presented and reported. Most of the HDR publications report inadequate details of the dose fractionation schedules. Only a minority of publications report significant complications using the actuarial method. In the future, all HDR publications for the treatment of cervical cancer should provide accurate fractionation details for each stage of disease, while reporting actuarial complication rates. The optimal fractionation schedule for treating cervical cancer using HDR brachytherapy is still unknown, and presently can be based only on single institutions with significant experience.     

A review of alpha/beta ratios for experimental tumors: implications for clinical studies of altered fractionation

Clinical interest in the use of more and smaller dose fractions in radical radiotherapy has been stimulated by recent reviews of experimental results with normal tissues. It has been found that if the dose per fraction is reduced (i.e., in hyperfractionation) there is sparing of late responding normal tissues relative to those which respond early. This phenomenon can be understood in terms of the shapes of the underlying dose effect relationships, which can be described using the linear quadratic equation. The ratio (alpha/beta) of the linear (alpha) and quadratic (beta) terms is a useful measure of the curviness of such dose effect curves. Low alpha/beta values (1.5 to 5 Gy) have been observed for late responding normal tissues and indicate that radiation damage should be greatly spared by the use of dose fractions smaller than the 2 Gy used in conventional radiotherapy. By contrast the high alpha/beta values (6-14 Gy) observed for acutely responding normal tissues indicate that the response is relatively linear over the dose range of clinical interest. Hence less extra sparing effect is to be expected if lower doses per fraction are administered. If tumors respond in the same way as acutely responding normal tissues then hyperfractionation might confer a therapeutic gain relative to late responding normal tissues. We have reviewed published results for experimental tumors irradiated in situ and either assayed in situ or after excision. The alpha/beta ratios were usually at least as high as those for acutely responding normal tissues, and 36/48 tumors gave values greater than 8 Gy. Low values of less than 5 Gy were obtained for only 4/48 tumors. There are considerable technical problems in interpreting these experiments, but the results do suggest that hyperfractionation might confer therapeutic gain relative to late responding normal tissues on the basis of differences in repair capability. In clinical practice more efficient reoxygenation, cell cycle redistribution and decreased overall treatment time might also confer therapeutic gain.     

Epilation in mice after single and multifractionated irradiation

The response of the resting (fully formed) hair follicle to irradiation was studied using an arbitrary 6 unit scale of epilation as an endpoint. Dose-response curves for single and multifractionated irradiations were analyzed in terms of the dose that gave a certain response in 50% of the mice (HRD50). HRD50 values increased with decrease in dose per fraction even when changing from 1.6 Gy to 1.15 Gy per fraction. The plots of the reciprocal of isoeffective doses versus dose per fraction are nonlinear suggesting either inappropriateness of the linear-quadratic model over the whole range of doses, or incompleteness of repair given as they were, at 3-h intervals. Allowing for incomplete repair, estimates for the alpha/beta ratio were 3.1 Gy and 1.7 Gy for the complete data set or for doses less than 7 Gy, respectively. The steep slope of the isoeffect curve plotting total dose versus dose per fraction was comparable to late responding normal tissues like lung, kidney and spinal cord. Such a response is consistent with slow proliferation of the matrix cells of resting follicles. The same animals were kept to assess the effect of dose fractionation on lethal injury to the lung. Since epilation occurs well before death from lung injury, the data for the two responses were correlated to determine whether epilation might help in predicting the probability of the later development of lung injury: no association was found.     

Radiation effect in mouse skin: dose fractionation and wound healing

Radiation induced dermal injury was measured by the gain in the physical strength of healing wounds in mouse skin. A sigmoid dose response for the inhibition of wound healing 14 days after surgery was found for single doses of X rays. The sparing of dermal damage from fractionation of the X-ray dose was quantified in terms of the alpha/beta ratio in the linear-quadratic (LQ) model, at a wide range of doses per fraction reaching as low as about 1 Gy. The fit and the appropriateness of the LQ model for the skin wound healing assay was examined with the use of the Fe-plot in which inverse total dose is plotted versus dose per fraction for wound strength isoeffects. The alpha/beta ratio of the skin was about 2.5 Gy (95% confidence of less than +/- 1 Gy) and was appropriate over a dose range of 1 Gy to about 8 Gy. The low alpha/beta value is typical for a late responding tissue. This assay, therefore, has the advantage of measuring and forecasting late radiation responses of the dermis within a short time after irradiation.     

Isoeffect curves for radiation-induced cardiomyopathy in the dog

Canine hearts were irradiated with a range of total doses given in 2, 3, or 4 Gy per fraction. Echocardiography was done before irradiation and at 3 and 6 months after irradiation. Histologic analyses were done of tissues taken at necropsy 6 months after irradiation. The percentage vascular component in the ventricles decreased with increasing total doses. The connective tissue component increased at lower doses and then decreased at higher doses. There was more fibroblastic proliferation and collagen production in the lower dose range and there may have been more cell killing by the higher doses. There was some evidence of myocardial hypertrophy at higher doses, which would have caused an apparent decrease in the connective tissue component. In either case, surviving fibroblasts would be expected to continue proliferating and producing collagen. At longer time intervals after irradiation the connective tissue component would likely continue to increase as observed clinically. That increase would be proportional to dose, but might not be closely related to initial killing of fibroblasts. Many factors such as changes in blood supply, continued loss of myocardium, and other stresses on the heart could influence the degree of fibrosis at later times. A relationship of response to cell killing appeared to exist based on alpha/beta ratios that were less than 3 Gy whether determined at the mid-range or for the greatest response of vasculoconnective tissues. Alpha/beta ratios ranged from 2.7 to 5 Gy for increases in diastolic wall thickness of the left ventricle at 3 and 6 months after irradiation. The low alpha/beta ratios reflect relatively steep isoeffect curves and have important implications for use of coarser fractionation schedules for treatment volumes that include the heart. The risk of cardiac damage could be significantly increased.     

Recovery kinetics in mouse skin and CaNT tumours

Recovery kinetics and recovery capacity were studied in a fast proliferating normal tissue, skin, and in an anaplastic mouse mammary carcinoma, CaNT. Three fractions per day of X-rays, repeated over 5 days, were given at varying interfraction intervals from 0 to 8 h. The rate of recovery in tumours (t1/2 = 0.31 +/- 0.15 h for local control) was significantly faster than in skin (t1/2 = 0.96 +/- 0.10 h). By contrast, the fractionation sensitivity of CaNT tumours was less than that of skin (alpha/beta = 43.3 +/- 8.5 Gy vs. alpha/beta = 7.9 +/- 0.2 Gy). Tissues with recovery half-times similar to or longer than that determined for skin would be at risk if interfraction intervals less than 6 h are used in regimes which involve the use of two or more fractions per day. This would be especially true for tissues that show a greater sensitivity to dose fractionation, and hence more sparing of radiation damage with hyperfractionation.     

Is the α/β Value for Prostate Tumours Low Enough to be Safely Used in Clinical Trials?

There has been an intense debate over the past several years on the relevant alpha/beta value that could be used to describe the fractionation response of prostate tumours. Previously it has been assumed that prostate tumours have high alpha/beta values, similar to most other tumours and the early reacting normal tissues. However, the proliferation behaviour of the prostate tumours is more like that of the late reacting tissues, with slow doubling times and low alpha/beta values. The analyses of clinical results carried out in the past few years have indeed suggested that the alpha/beta value that characterises the fractionation response of the prostate is low, possibly even below the 3 Gy commonly assumed for most late complications, and hence that hypofractionation of the radiation treatment might improve the therapeutic ratio (better control at the same or lower complication rate). However, hypofractionation might also increase the complication rates in the surrounding late responding tissues and if their alpha/beta value is not larger that of prostate tumours it could even lead to a decrease in the therapeutic ratio. Therefore, the important question is whether the alpha/beta value for the prostate is lower than the alpha/beta values of the surrounding late responding tissues at risk. This paper reviews the clinical and experimental data regarding the radiobiological differential that might exist between prostate tumours and the late normal tissues around them. Several prospective hypofractionated trials that have been initiated recently in order to determine the alpha/beta value or the range of values that describe the fractionation response of prostate tumours are also reviewed. In spite of several confounding factors that interfere with the derivation of a precise value, it seems that most data support a trend towards lower alpha/beta values for prostate tumours than for rectum or bladder.     

The sensitivity of normal stroma to fractionated radiotherapy measured by a tumour growth rate assay

The growth rate of implanted tumours has been used as an assay for radiation injury in normal stroma. The subcutaneous tissue was irradiated in an unstimulated state and was then stimulated to produce new blood vessels by the inoculation of a syngeneic tumour 3 days after the last irradiation. Steep dose-response curves were obtained with a dose resolution of approximately 1 Gy. The time between irradiation and stimulation of the stroma by the tumour implant was shown to have no effect on tumour growth rate for times ranging from 1 h to 14 days after single doses. This functional assay of stromal damage has been used after irradiation with 1, 2, 5, 10 or 20 fractions of X-rays. Isoeffect data were well fitted by a linear-quadratic equation, for which the ratio of linear to quadratic coefficients (alpha/beta) was 6.2 +/- 0.6 Gy. This is on the high end of the range of published alpha/beta values for late reacting tissues and other stromal/vascular assays, but lower than those for all early reacting tissues. Overall treatment times ranging from 1 to 11 days were tested with the 2 and 5 fraction schedules. No effect attributable to slow repair or repopulation could be demonstrated over this period.     

Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord.

The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. This paper describes experiments in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spinal cord. The first group of rats were given doses in 1, 2, 4, 8 and 40 daily fractions. The second group of animals received three initial "top-up" doses of 9 Gy given once daily, representing three-quarters of tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 daily fractions. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of the forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 daily fractions (25.0-1.98 Gy per fraction) indicated consistency with the LQ model yielding an alpha/beta value of 2.41 Gy. Analysis of data from experiments in which the three "top-up" doses were followed by up to 10 fractions (10.0-1.64 Gy per fraction) gave an alpha/beta value of 3.41 Gy. However, data from "top-up" experiments with 20, 30 and 40 fraction (1.60-0.55 Gy per fraction) were inconsistent with the LQ model and gave a very small alpha/beta value of 0.48 Gy. It is concluded that the LQ model based on data from large doses per fraction underestimates the sparing effect of small doses per fraction provided sufficient time is allowed between each fraction for repair of sublethal damage.     

Hypofractionation for prostate cancer: a critical review

In ideal circumstances, the fractionation schedule of radiotherapy should match the fractionation sensitivity of the tumor relative to the nearby normal tissues. A number of recent publications have suggested that the alpha-beta ratio (alpha/beta) for prostate is low, in the range of 1 to 3 Gy. If alpha/beta is truly low, then hypofractionated schedules using fewer, larger fractions should improve the therapeutic ratio. This critical review examines the clinical experience with hypofractionation. Several prospective trials indicate that toxicity is limited with sophisticated dose delivery and compact clinical target volume to planning target volume margins, but the single-arm nature of these trials precludes definitive statements on efficacy. Several large randomized trials comparing conventional fractionation to hypofractionation are ongoing and are described. Until these trials are completed and the results submitted for rigorous peer review, the notion that alpha/beta for prostate cancer is low remains an unconfirmed hypothesis.     

Regional perfusion treatment with melphalan for melanoma in a limb: an evaluation of drug kinetics

The time course of tissue levels of melphalan during normothermic isolated limb perfusion, and the overall tissue levels per 60 min of perfusion, were estimated from the known pharmacokinetic parameters for a fixed dose of drug per liter of tissue (Benckhuijsen et al., J. Pharmacol Exp Ther 1986; 237: 583-8). The application of differing total doses of drug resulted in varying concentrations in the perfusate plasma. Above a certain plasma level, uptake into the bulk of the tissues did not increase with the area under the plasma concentration vs time curve or its beta-phase. Similar tissue levels were found after perfusion of regions of less than three and a half liter with 13 mg/l as in regions of 5 to 16 liter after perfusion with 10 mg of melphalan per liter. It cannot be predicted from the available data whether the extent of uptake of melphalan into the tumour tissue is equal to or greater than that into the bulk of the tissues. The estimated uptake of drug into the tissues confirms the validity of the dose calculation per liter of tissue. On the basis of the present results, a refined dosimetric formula will be obtainable that includes the desired area under the plasma concentration vs time curve as a determinant for an optimal dose.     

Deterministic rather than stochastic factors explain most of the variation in the expression of skin telangiectasia after radiotherapy.

BACKGROUND: The large patient-to-patient variability in the grade of normal tissue injury after a standard course of radiotherapy is well established clinically. A better understanding of this individual variation may provide valuable insights into the pathogenesis of radiation damage and the prospects of predicting the outcome. PURPOSE: To estimate the relative importance of the stochastic vs. patient-related components of variability in the expression of radiation-induced normal tissue damage. METHODS AND MATERIALS: The study data were selected from the dose fractionation studies of Turesson in Gothenburg. Patients treated with bilateral internal mammary fields, who completed at least 10 years of follow-up, were included. The material included 22 different fractionation schedules (11 on each side). Telangiectasia was graded on an arbitrary 6-point scale using clinical photographs of the irradiated fields. For each field, in each patient, a curve showing the grade of telangiectasia as a function of time was constructed. A measure of radioresponsiveness was obtained from the difference between the area under the curve (AUC) for a specific field in an individual patient minus the mean AUC of fields receiving the same dose fractionation schedule. As a confirmatory procedure, the same analysis was repeated with a weighted area under the curve (WAUC) approach, in which the time spent at or above each of the 5 nonzero grades was calculated for each field in each patient. These times were used as explanatory variables in a linear regression analysis of biological equivalent dose to establish statistically the weight of each grade providing the optimal relationship between dose and effect. Using these regression coefficients, the weighted area under the grade-time curve (WAUC) was estimated. RESULTS: The AUC was significantly correlated with the isoeffective dose in 2-Gy fractions (ID2). An analysis of variance components, using the maximum likelihood method, showed that 90% (with 95% confidence limits 65% and 100%) of the variance in radioresponsiveness in the right-sided field was explained by the radioresponsiveness on the left-sided field. Through the linear regression analysis between the AUC and the ID2, it was estimated that patients with a reaction that is 1 SD from the population mean would require a dose modification of approximately 23 Gy (from the group mean of 56 Gy) to give them a level of reaction similar to the group average. Similarly, the WAUC was significantly correlated with the ID2, and 81% (with 95% confidence limits 49% and 100%) of the variance in radioresponsiveness in the right-sided field was explained by the radioresponsiveness on the left-sided field. Patients with a reaction that is 1 SD from the population mean would require a dose modification of approximately 21 Gy (from the group mean of 56 Gy) to give them a level of reaction similar to the group average. CONCLUSION: For a given fractionation schedule, patient-related factors explain 81-90% of the patient-to-patient variation in telangiectasia level seen after radiotherapy. The remaining 10-19% are explained by stochastic effects. This observation encourages further research into genetic or phenotypic assays of normal tissue radioresponsiveness.     

Changes in early and late radiation responses with altered dose fractionation: Implications for dose-survival relationships

Clinical and experimental evidence for divergent changes in early and late radiation responses in normal tissues after changes in dose fractionation indicate a greater sensitivity of late responses to changes in dose per fraction. In experimental studies of the effect of dose per fraction on early and late isoeffects, a larger number-of-fractions exponent for the late responses is the rule. These findings imply that the shape of the dose-survival curve for the target cells whose depletion results in late effects is different from that for target cells for acute effects: as the dose increases the contribution to cell killing from accumulated sublethal injury, relative to killing from single hit events, increases more rapidly in the target cells for late effects. In other words, the survival curve for the target cells for late injury must be “curvier” than that for acute effects. Although such survival curve characteristics are independent of the survival curve model chosen to describe them, they would represent, in terms of the parameters of the linear quadratic model, S = e^?αD?βD², a higher $\text{β}\text{α}$ ratio for late effects. If the dose survival characteristics of tumor clonogens resemble those of the target cells in acutely responding normal tissues, and if late injury in normal tissues is dose-limiting, then a therapeutic gain would result from reducing the size of dose per fraction by hyperfractionation. Conversely, increasing the size of dose per fraction should reduce the therapeutic differential.     

Alpha/beta ratio: A dose range dependence study

PURPOSE: To investigate the dependence of the alpha/beta ratio determined from in vitro survival curves on the dose ranges. METHODS: Detailed clonogenic cell survival experiments were used to determine the least squares estimators for the linear quadratic model for different dose ranges. The cell lines used were CHO AA8, a Chinese hamster fibroblast cell line; U-373 MG, a human glioblastoma cell line; and CP3 and DU-145, two human prostate carcinoma cell lines. The alpha, beta, and alpha/beta ratio behaviors, combined with a goodness-of-fit analysis and Monte Carlo simulation of the experiments, were assessed within different dose regions. RESULTS: Including data from the low-dose region has a significant influence on the determination of the alpha, beta, and alpha/beta ratio from in vitro survival curve data. In this region, the values are poorly determined and have significant variability. The mid-dose region is characterized by more precise and stable values and is in agreement with the linear quadratic model. The high-dose region shows relatively small statistical error in the fitted parameters but the goodness-of-fit and Monte Carlo analyses showed poor quality fits. CONCLUSION: The dependence of the fitted alpha and beta on the dose range has an impact on the alpha/beta ratio determined from the survival data. The low-dose region had a significant influence that could be a result of a strong linear, rather than quadratic, component, hypersensitivity, and adaptive responses. This dose dependence should be interpreted as a caution against using inadequate in vitro cell survival data for alpha/beta ratio determination.