Time-dose Relationships Research Articles

Investigation of the Impact of Temporal Dose Delivery Patterns of Ion Irradiation with the Local Effect Model.

We present an extension of the Local Effect Model (LEM) to include time-dose relationships for predicting effects of protracted and split-dose ion irradiation at arbitrary LET. With this kinetic extension, the spatial and temporal induction and processing of DNA double strand breaks (DSB) in cellular nuclei can be simulated for a wide range of ion radiation qualities, doses and dose rates. The key concept of the extension is based on the joint spatial and temporal coexistence of initial DSB, leading to the formation of clustered DNA damage on the µm scale (as defined e.g., by the size scale of Mbp chromatin loops), which is considered to have an increased cellular lethality as compared to isolated, single DSB. By simulating the time dependent induction and repair of DSB and scoring of isolated and clustered DSB upon irradiation, the impact of dose rate and split dose on the cell survival probability can be computed. In a first part of this work, we systematically analyze the predicted impact of protraction in dependence of factors like dose, LET, ion species and radiosensitivity as characterized by the photon LQ-parameters. We establish links to common concepts that describe dose rate effects for low LET radiation. We also compare the model predictions to experimental data and find agreement with the general trends observed in the experiments. The relevant concepts of our approach are compared to other models suitable for predicting time effects. We investigate an apparent analogy between spatial and temporal concentration of radiation delivery, both leading to increased effectiveness, and discuss similarities and differences between the general dependencies of these clustering effects on their impacting factors. Finally, we conclude that the findings give additional support for the general concept of the LEM, i.e. the characterization of high LET radiation effects based on the distinction of just two classes of DSB (isolated DSB and clustered DSB).

Enhancing the Antimicrobial Effect of Ozone with Mentha piperita Essential Oil

This study aimed to obtain and analyse Mentha piperita essential oil (MpEO) for the prospect of being used as an enhancement agent for the antimicrobial potential of ozone against gram-positive and gram-negative bacteria and fungi. The research was done for different exposure times, and it gained time-dose relationships and time-effect correlations. Mentha piperita (Mp) essential oil (MpEO) was obtained via hydrodistillation and further analysed by using GC-MS. The broth microdilution assay was used to determine the strain inhibition/strain mass growth by using spectrophotometric optical density reading (OD). The bacterial/mycelium growth rates (BGR/MGR) and the bacterial/mycelium inhibition rates (BIR/MIR) after ozone treatment in the presence and absence of MpEO on the ATTC strains were calculated; the minimum inhibition concentration (MIC) and statistical interpretations of the time-dose relationship and specific t-test correlations were determined. The effect of ozone on the following tested strains at maximum efficiency was observed after 55 s of single ozone exposure, in order of effect strength: S. aureus > P. aeruginosa > E. coli > C. albicans > S. mutans. For ozone with the addition of 2% MpEO (MIC), maximum efficacy was recorded at 5 s for these strains, in order of effect strength: C. albicans > E. coli > P. aeruginosa > S. aureus > S. mutans. The results suggest a new development and affinity regarding the cell membrane of the different microorganisms tested. In conclusion, the use of ozone, combined with MpEO, is sustained as an alternative therapy in plaque biofilm and suggested as helpful in controlling oral disease-causing microorganisms in medicine.

Radiation-induced tissue damage and response.

Normal tissue responses to ionizing radiation have been a major subject for study since the discovery of X‐rays at the end of the 19th century. Shortly thereafter, time–dose relationships were established for some normal tissue endpoints that led to investigations into how the size of dose per fraction and the quality of radiation affected outcome. The assessment of the radiosensitivity of bone marrow stem cells using colony‐forming assays by Till and McCulloch prompted the establishment of in situ clonogenic assays for other tissues that added to the radiobiology toolbox. These clonogenic and functional endpoints enabled mathematical modeling to be performed that elucidated how tissue structure, and in particular turnover time, impacted clinically relevant fractionated radiation schedules. More recently, lineage tracing technology, advanced imaging and single cell sequencing have shed further light on the behavior of cells within stem, and other, cellular compartments, both in homeostasis and after radiation damage. The discovery of heterogeneity within the stem cell compartment and plasticity in response to injury have added new dimensions to the consideration of radiation‐induced tissue damage. Clinically, radiobiology of the 20th century garnered wisdom relevant to photon treatments delivered to a fairly wide field at around 2 Gy per fraction, 5 days per week, for 5–7 weeks. Recently, the scope of radiobiology has been extended by advances in technology, imaging and computing, as well as by the use of charged particles. These allow radiation to be delivered more precisely to tumors while minimizing the amount of normal tissue receiving high doses. One result has been an increase in the use of schedules with higher doses per fraction given in a shorter time frame (hypofractionation). We are unable to cover these new technologies in detail in this review, just as we must omit low‐dose stochastic effects, and many aspects of dose, dose rate and radiation quality. We argue that structural diversity and plasticity within tissue compartments provides a general context for discussion of most radiation responses, while acknowledging many omissions. © 2020 The Authors. The Journal of Pathology published by John Wiley & Sons Ltd on behalf of Pathological Society of Great Britain and Ireland.

Hydrogel-based diffusion chip with Electric Cell-substrate Impedance Sensing (ECIS) integration for cell viability assay and drug toxicity screening

In this study, we have provided a novel analytical integration between hydrogel-based cell chip and Electric Cell-substrate Impedance Sensing (ECIS) technique to apply to a high-throughput, real-time cell viability assay and drug screening. For simulating the drug diffusion model, we have developed a hydrogel-based tissue-mimicking structure with microfluidic channel, without unwanted flow, to generate a gradient concentration with long-term stability. Along the gradient line, four individual micro-electrodes were installed to record the impedance signal changes, which result from the cell viability under drug effects. By watching for cellular impedance changes, we successfully estimated the cytotoxicity of the treatment corresponding to the various concentration values of stimuli, generated by the diffusion process along the channel. Reliable IC50 values and time-dose relationships were also achieved. With the feature of real-time monitoring capability, the advantages of non-invasion, label-free detection, time saving and simple manipulation, our integrative device has become a promising high throughput cell-based on-chip platform for cell viability assay and drug screening.

Time and Dose Dependent Study of Doxorubicin Induced DU-145 Cytotoxicity

Doxorubicin is one of the most effective anti-tumour agent. To clarify whether a single dose produces its effects soon after dosing or only after hours or days and whether the effects are brief or prolonged, time-dose relationships were explored by calculating lethal time (LT(50)) values which is a statistical estimate of the time from dosage to death of 50% of the organisms/ or cells in a very large population subjected to a toxicant under specific conditions. This was achieved by the log-time log-dose curve which may be used to predict the proper doses to be used in long-term studies. Drug chemosensitivity using DU-145 cell lines have been investigated for this purpose. The results shows that the effects of doxorubicin started only after 24 hrs; however, resistance was developed, 40 hrs was the time required to kill 50% of cells , and post-incubation with fresh media (F.M.) exhibited more cell damages. It is concluded that doxorubicin is effective only after 24 hrs with resistance developed and post-incubation with F.M after treating cells with doxorubicin causes more damage than continuous incubation with the drug.

Dose-time relationships in fractionated radiotherapy for cancer

The irradiation time and the dose per fraction are two key parameters in the fractionated therapy of patients with cancer. Reduction of the total treatment time and the use of low doses per fraction lead to improvements in the therapeutic relationship in cancer of the head and neck and at other tumour localisations of epithelial origin. The introduction of the linear-quadratic model and the biologically effective dose concept into the clinical setting has enabled quantitative analysis of the biological effects of radiation on malignant tumours and on acutely and slowly responding tissues, notably enhancing the perception of relationships between basic phenomena and clinical data. As a result, new and better irradiation regimens have been developed for the treatment of patients with specific tumours.

Physical variables in experimental photocarcinogenesis and quantitative relationships between stages of tumor development

Solar ultraviolet (UV) radiation is a prominent environmental carcinogen, but it does not penetrate any deeper than the skin. The UV-related skin cancers are by far the most common form of cancer among white Caucasians in the USA and Australia, and this poses a serious public health problem. Chronic UV exposure of hairless mice is a well established model for squamous cell carcinomas in man. It is important to identify the essential physical variables, and explore fully how photocarcinogenesis evolves in dependence of these variables. The 3 main physical variables in photocarcinogenesis are (i) the wavelength of the radiation, (ii) the exposure and (iii) time. A good quantitative description of tumor induction and precursing stages can be given in terms of these variables. An analysis of this description shows us that the early induction of clusters of epidermal cells that over-express mutant p53 ('p53 patches') are closely and, most likely, causally linked to the eventual tumors. These p53 patches may thus serve as early indicators of tumor risk. The induction of an immune-tolerance toward the UV-induced tumors precedes the actual occurrence of the tumors at high daily doses, but extrapolation indicates that this order of events may be reversed at low daily doses. This disparity between the dose-time relationships for the tumor tolerance and the tumors needs to be investigated further. It could imply a shift to non-immunogenic tumors at low daily doses.

Physical variables in experimental photocarcinogenesis and quantitative relationships between stages of tumor development.

Solar ultraviolet (UV) radiation is a prominent environmental carcinogen, but it does not penetrate any deeper than the skin. The UV-related skin cancers are by far the most common form of cancer among white Caucasians in the USA and Australia, and this poses a serious public health problem. Chronic UV exposure of hairless mice is a well established model for squamous cell carcinomas in man. It is important to identify the essential physical variables, and explore fully how photocarcinogenesis evolves in dependence of these variables. The 3 main physical variables in photocarcinogenesis are (i) the wavelength of the radiation, (ii) the exposure and (iii) time. A good quantitative description of tumor induction and precursing stages can be given in terms of these variables. An analysis of this description shows us that the early induction of clusters of epidermal cells that over-express mutant p53 ('p53 patches') are closely and, most likely, causally linked to the eventual tumors. These p53 patches may thus serve as early indicators of tumor risk. The induction of an immune-tolerance toward the UV-induced tumors precedes the actual occurrence of the tumors at high daily doses, but extrapolation indicates that this order of events may be reversed at low daily doses. This disparity between the dose-time relationships for the tumor tolerance and the tumors needs to be investigated further. It could imply a shift to non-immunogenic tumors at low daily doses.

Time–dose relationships in radiation-enhanced integration

Purpose: We have shown that ionizing radiation increases recombination, as manifested by increased stable transduction of both plasmid and adenoviral vectors. This paper reports the duration of increased recombination after irradiation. Materials and methods: A549 or NIH/3T3 cells were transfected at various times after irradiation. Cells were also irradiated with several fractionation schemes and then transfected. Results: Enhanced integration (EI) is a very long-lived process, lasting at least 2-3 days after single radiation fractions. The duration of EI activation is radiation dose-dependent. The efficiency of EI is dependent on radiation dose and independent of fractionation, such that low dose-rate, fractionated and single radiation doses result in similar levels of EI when corrected for diverences in cytotoxicity. Conclusions: Radiation, given with fraction sizes and dose-rates used in clinical radiation therapy, induces a long-lived hyper-recombination state. Since radiotherapy is already a component of treatment for many malignancies and is integrated into radiation-gene therapy trials, an understanding of recombination events that improve gene delivery is important and timely.

Dosimetry calculation for a novel PHOSPHORUS-32- impregnated balloon angioplasty catheter for intravascular brachytherapy

Purpose. A phosphorus-32-impregnated balloon angioplasty catheter was used in a novel technique of simultaneous angioplasty and vessel irradiation. The 32P radionuclides were distributed on the surface of the balloon so that a certain amount of radiation was delivered while angioplasty was performed. Three-dimensional dosimetry and dose–time relationship needs to be established for the catheter so that quantitative dosimetric information is available for both clinical treatment and research investigation. Methods and Materials. The 32P-impregnated balloon of an angioplasty catheter was assumed to have a cylindrical shape, and the radionuclides were assumed to be distributed uniformly on the curved surface of the cylinder. The dose rate at a point in space was computed by integrating the point dose-rate kernel of 32P over the radioactive surface of the balloon. The point dose-rate kernel was computed with Monte Carlo simulation of radiation transport. The energy spectra of 32P based on a mathematical model was used in the calculations. The three-dimensional dose distributions and dose–time relationships were calculated for balloons of various lengths and radii. Results. At a short radial distance ( e.g., 0.2 mm) away from the balloon surface, the dose distribution was uniform across a large portion of the balloon along the longitudinal axis, and dropped off rapidly at both ends of the balloon. Uniformity became worse as the radial distance increased. Uniformity was almost independent of balloon radius. The underdosed length at each end of the balloon was also almost independent of balloon length. In the central transverse plane, the dose reached a maximum at the surface of the balloon and then dropped off rapidly as the distance increases. Relative dose coverage outside the balloon was approximately independent of balloon radius and length, and the absolute dose coverage was approximately inversely proportional to balloon radius and length, assuming same total activity. Conclusions. Point dose-rate kernel of 32P beta emitter and the three-dimensional dose distributions of a 32P-impregnated balloon from an novel angioplasty catheter were calculated. A rule of thumb for dose calculation and dose coverage was established for simultaneous angioplasty and vascular brachytherapy with a 32P-impregnated balloon catheter.

Radio-induced structural membrane modifications: a potential bioindicator of ionizing radiation exposure?

Purpose: This study focused on radio-induced membrane alterations in order to assess some related parameters as potential biological indicators of ionizing radiation effects in cases of accidental overexposure. Materials and methods: Radio-induced membrane alterations were assessed after gamma-irradiation of human blood. Biophysical techniques based on fluorescent probe incorporation into isolated living lymphocytes and erythrocytes membranes were applied. Results: Using the technique of fluorescence polarization, the lipophilic phase of the membrane was shown to be more fluid whereas the lipid-protein interface of the membrane was shown to be more rigid after gamma-irradiation. Fluorescent anisotropy modifications showed dose-time effect relationships after radiation exposure. Ionizing radiation induced a decrease in steadystate anisotropy values but did not affect the probe's lifetime as assessed by fluorescence lifetime distribution technique. These data suggest that the anisotropy variations are representative of the local properties of the fluorescent probe's micro-environment. However, the distribution width showed a decrease pointing towards radiation-induced changes of membrane domain organization, probably due not only to membrane water penetration related to lipoperoxidation, but also to compositional changes and redistribution of membrane components. In contrast, the lack of radiation effect observed using the lateral diffusion index technique may be related to the integrated overview of the radio-induced modifications of the membrane provided by this technique, which pointed out radio-induced damage to the membrane in micro-domains. Conclusion: These findings suggest the utility of structural membrane modification measurements as an early bio-indicator of ionizing radiation exposure.

Time- and dose-dependent development of potassium bromate-induced tumors in male Fischer 344 rats.

Potassium bromate (KBrO3) is a rodent carcinogen and a nephro- and neurotoxicant in humans. KBrO3 is used in cosmetics and food products and is a by-product of water disinfection by ozonization. KBrO3 is carcinogenic in the rat kidney, thyroid, and mesothelium and is a renal carcinogen in the male mouse. The present study was designed to investigate the relationship of time and dose to bromate-induced tumors in male Fischer 344 (F344) rats and to provide some insight into the development of these tumors. KBrO3 was dissolved in drinking water at nominal concentrations of 0, 0.02, 0.1, 0.2, and 0.4 g/L and administered to male F344 rats as the sole water source for 12, 26, 52, 78, or 100 wk. Renal cell tumors were present after 52 wk of treatment only in the high-dose group. Mesotheliomas developed after 52 wk of treatment on the tunica vaginalis. Mesotheliomas were present at sites other than the testicle after 78 wk of treatment, indicating that their origin was the testicular tunic. Thyroid follicular tumors were present as early as 26 wk in 1 rat each from the 0.1- and 0.2-g/L groups. The present study can be used as a basis for the determination of dose-time relationships of tumor development for a better understanding of KBrO3-induced cancer.

Medulloblastoma: time–dose relationship based on a 30-year review

Purpose: Time–dose relationships have proven important in many cancer sites. This study evaluates the time factors involved in the successful postoperative radiotherapy of medulloblastoma, based on a 30-year experience in a single institution. Methods and Materials: Fifty-three patients with medulloblastoma received postoperative craniospinal radiotherapy with curative intent between 1963 and 1993. Seven patients (13%) underwent biopsy alone, 28 patients (53%) had subtotal excision, and 18 patients (34%) had gross total excision. Eleven patients received adjuvant chemotherapy. The mean posterior fossa dose was 53.1 Gy; most patients received 54.0 Gy (range, 34.3 to 69.6 Gy). For 41 patients receiving once-a-day therapy, the mean dose was 50.6 Gy (range, 34.3 to 56.0 Gy). For 12 patients receiving twice-a-day therapy, the mean dose was 61.8 Gy (range, 52.6 to 69.6 Gy). Minimum follow-up was 2 years, and median follow-up was 10.7 years. Survival, freedom from relapse, and disease control in the posterior fossa were calculated using the Kaplan-Meier method, and multivariate analysis was performed for prognostic factors. Variables related to radiotherapy were examined, including dose to the craniospinal axis, dose to the posterior fossa, fractionation (once-a-day vs. twice-a-day), use of adjuvant chemotherapy, risk group [high (≥T3b or ≥M1) or low (≤T3a and M0-MX)], interval between surgery and radiotherapy (excluding patients receiving chemotherapy before radiotherapy), and duration of radiotherapy. Results: At 5 and 10 years, overall survival rates were 68 and 64%, respectively, and freedom-from-relapse rates were 61 and 52%, respectively. Rates of disease control in the posterior fossa at 5 and 10 years were 79 and 68%, respectively. At 5 years, absolute survival rates after biopsy alone, subtotal excision, and gross total excision were 43, 67, and 78%, respectively ( p = 0.04), and posterior fossa control rates were 27, 89, and 83%, respectively ( p = 0.004). Duration of the treatment course was the only radiotherapy-related variable with a significant impact on freedom from relapse and posterior fossa control. For patients whose radiation treatment duration was ≤45 days, posterior fossa control was 89% at 5 years, compared with 68% for those treated for >45 days ( p = 0.01). Duration of treatment also affected freedom from relapse at 5 years: ≤45 days (76%) compared with >45 days (43%), p = 0.004. Conclusion: Our study demonstrates that if adequate doses are used, then radiotherapy treatment duration will significantly affect the outcome in terms of control of disease in the posterior fossa and freedom from relapse. Fractions of at least 1.75 Gy given once a day, or a twice-a-day regimen should yield optimal local control results.

The Linear-Quadratic Model and Most Other Common Radiobiological Models Result in Similar Predictions of Time-Dose Relationships

One of the fundamental tools in radiation biology is a formalism describing time-dose relationships. For example, there is a need for reliable predictions of radiotherapeutic isoeffect doses when the temporal exposure pattern is changed. The most commonly used tool is now the linear-quadratic (LQ) formalism, which describes fractionation and dose-protraction effects through a particular functional form, the generalized Lea-Catcheside time factor, G. We investigate the relationship of the LQ formalism to those describing other commonly discussed radiobiological models in terms of their predicted time-dose relationships. We show that a broad range of radiobiological models are described by formalisms in which a perturbation calculation produces the standard LQ relationship for dose fractionation/protraction, including the same generalized time factor, G. This approximate equivalence holds not only for the formalisms describing binary misrepair models, which are conceptually similar to LQ, but also for formalisms describing models embodying a very different explanation for time-dose effects, namely saturation of repair capacity. In terms of applications to radiotherapy, we show that a typical saturable repair formalism predicts practically the same dependences for protraction effects as does the LQ formalism, at clinically relevant doses per fraction. For low-dose-rate exposure, the same equivalence between predictions holds for early-responding end points such as tumor control, but less so for late-responding end points. Overall, use of the LQ formalism to predict dose-time relationships is a notably robust procedure, depending less than previously thought on knowledge of detailed biophysical mechanisms, since various conceptually different biophysical models lead, in a reasonable approximation, to the LQ relationship including the standard form of the generalized time factor, G.

Time-dose relationships and brachytherapy in radiation oncology of head and neck cancer

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Intrathecal baclofen: does tolerance occur?

Concern over the development of tolerance in patients on continuous intrathecal baclofen therapy has arisen as this new form of treatment for spasticity has gained wider use. We have studied time-dose relationships in 18 spinal cord injured patients who have undergone intrathecal baclofen infusion pump implantation since February 1988 in our facility. Our data show that there was a significant increase in baclofen dosage needed to control spasticity during the first 12 months post implantation. After 12 months, however, no significant changes in dosage requirement was detected. In addition, there was no significant difference between completely and incompletely spinal cord injured patients with regard to both the initial dose and the tolerance trend.

Cellular and Molecular Changes in Mammary Epithelial Cells Following Irradiation

The present paper describes experiments conducted over the last several years which have focused primarily on the development of mammary tumors in BALB/c mice after neutron and gamma irradiation. Time-dose relationships for induction of mammary and lung tumors following irradiation with fission-spectrum neutrons and 137Cs gamma rays are described. Subsequent studies have used in vivo/in vitro approaches to characterize cellular and molecular changes. These studies suggest quantitative and qualitative differences in the effects of neutrons and gamma rays.

The effect of overall treatment time on local control in patients with adenocarcinoma of the prostate treated with radiation therapy

Studies of patients treated with radiation therapy for squamous cell carcinoma of the head and neck have demonstrated that when all other variables are constant, protraction of the overall treatment time leads to a decreased probability of local control. Few data exist on the effect of overall treatment time on local control following irradiation of tumors that are generally thought to be slowly proliferating, such as adenocarcinoma of the prostate. This analysis was undertaken to determine the time-dose relationships for local control of prostatic adenocarcinoma at the University of Florida. All patients were treated at least 5 years prior to the date of analysis. For patients with Stage A2 disease, a tumor dose of 6500 cGy in 7 to 7.5 weeks to 7000 cGy in 8 weeks resulted in local control in 1717 patients (100%). For patients with Stage B1 disease, the local control rate was 14/16 (88%) with an overall treatment time of ≤8 weeks versus 13 in patients who received split-course treatment in > 8 weeks (p = .097). For patients with Stage B2, C1, and C2 disease who received ≥6500 cGy, the 5-year rate of local control was lower when overall treatment time was protracted beyond 8 weeks. Results were as follows: B2 (62 patients), ≤8 weeks, 88%, versus > 8 weeks, 55%, p = .002; C1 (87 patients), ≤8 weeks, 88%, versus > 8 weeks, 73%, p = .052; C2 (33 patients), ≤8 weeks, 81%, versus > 8 weeks, 65%, p = .056. Stratification by tumor grade of patients with Stage B1, B2, C1, and C2 disease who received ≥6500 cGy demonstrated significantly lower local control rates for all grade categories when the overall treatment time was protracted beyond 8 weeks. Five-year local control rates (lifetable method) for overall treatment time ≤ 8 weeks versus > 8 weeks were as follows: well differentiated, 93% versus 73% (p = .003); moderately differentiated, 86% versus 69% (p = .017); and poorly differentiated, 75% versus 59% (p = .046). These data suggest that tumor repopulation during excessively protracted treatment may be a clinically significant factor in patients with adenocarcinoma of the prostate.

Dithiocarbamates and prevention of cadmium teratogenesis in the hamster

Certain dithiocarbamates (DTC) have been reported to protect against cadmium (Cd)-induced lethality and to decrease Cd body burden. The present study evaluated the influence of sodium N-benzyl-D-glucamine dithiocarbamate, sodium N-di(hydroxyethyl)amine dithiocarbamate, sodium 4-carboxyamidopiperidine-N-dithiocarbamate, and sodium N-methyl-D-glucamine dithiocarbamate on Cd-induced teratogenesis in the hamster. When given as a single ip injection at 2.2 mmol/kg 15 min prior to iv CdCl2 (2 mg/kg), all of the DTC afforded significant protection against Cd-induced developmental toxicity and reduced kidney [Cd] in the dam. Maternal liver [Cd] was reduced with the glucamine and dihydroxyethyl amine analogs, but treatment with the piperidine failed to influence hepatic [Cd]. Pretreatment of the dams with DTC 24 hr prior to Cd challenge failed to protect against Cd-induced embryotoxicity, and provided minimal, if any, reduction in renal or hepatic [Cd]. Pretreatment with the N-methyl-D-glucamine congener 24 hr prior to Cd exposure increased embryolethality. The dose-time relationships found here suggest that pharmacologically effective levels of these DTC decline within 24 hr of treatment and that induction of metallothionein does not play a major role in DTC antagonism of Cd poisoning.

Bone growth retardation induced by single and multifractionated irradiation

The right hind legs of 12- to 14-week-old mice were exposed to single and multifractionated courses of gamma-ray irradiation. The recovery curves, time-dose relationships, and fraction number-dose relationships were analyzed using femoral growth retardation as an endpoint. The bones grew 2 mm, about a 10% increase over their original lengths, in 12 months; and 63% and 85% in volume in 6 and 12 months, respectively. The ratio of the volume increase of the irradiated right leg per unit time, the actual growth, to the volume increase of the non-irradiated left leg, the potential growth, was calculated for each mouse. The doses necessary to produce a given degree of bone growth retardation in 50% of the tested animals were calculated for each treatment schedule. The isoeffect doses for a given degree of bone growth retardation after 2 and 4 equal fractionation exposure increased (peak at one day-interval) and decreased (trough at 2-day interval), and later increased additionally with increasing time intervals between doses.