Radiation Treatment Schedules Research Articles

The Effect of Biologically Effective Dose and Radiation Treatment Schedule on Overall Survival in Stage I Non-Small Cell Lung Cancer Patients Treated With Stereotactic Body Radiation Therapy

To determine the effect of biologically effective dose (BED10) and radiation treatment schedule on overall survival (OS) in patients with early-stage non-small cell lung cancer (NSCLC) undergoing stereotactic body radiation therapy (SBRT). Using data from 65 treatment centers in the United States, we retrospectively reviewed the records of T1-2 N0 NSCLC patients undergoing SBRT alone from 2006 to 2014. Biologically relevant covariates, including dose per fraction, number of fractions, and time between fractions, were used to quantify BED10 and radiation treatment schedule. The linear-quadratic equation was used to calculate BED10 and to generate a dichotomous dose variable of <105Gy versus ≥105Gy BED10. The primary outcome was OS. We used the Kaplan-Meier method, the log-rank test, and Cox proportional hazards regression with propensity score matching to determine whether prescription BED10 was associated with OS. We identified 747 patients who met inclusion criteria. The median BED10 was 132Gy, and 59 (7.7%) had consecutive-day fractions. Median follow-up was 41months, and 452 patients (60.5%) had died by the conclusion of the study. The 581 patients receiving ≥105Gy BED10 had a median survival of 28months, whereas the 166 patients receiving <105Gy BED10 had a median survival of 22months (log-rank, P=.01). Radiation treatment schedule was not a significant predictor of OS on univariable analysis. After adjusting for T stage, sex, tumor histology, and Eastern Cooperative Oncology Group performance status, BED10 ≥105Gy versus <105Gy remained significantly associated with improved OS (hazard ratio 0.78, 95% confidence interval 0.62-0.98, P=.03). Propensity score matching on imbalanced variables within high- and low-dose cohorts confirmed a survival benefit with higher prescription dose. We found that dose escalation to 105Gy BED10 and beyond may improve survival in NSCLC patients treated with SBRT.

Technical Note: Partial body irradiation of mice using a customized PMMA apparatus and a clinical 3D planning/LINAC radiotherapy system.

In vivo radiobiology experiments involving partial body irradiation (PBI) of mice are of major importance because they allow for the evaluation of individual organ tolerance; overcoming current limitations of experiments using lower dose, whole body irradiation. In the current study, the authors characterize and validate an effective and efficient apparatus for multiple animal PBI, directed to the head, thorax, or abdomen of mice. The apparatus is made of polymethylmethacrylate and consists of a rectangular parallelepiped prism (40 cm × 16 cm × 8 cm), in which five holes were drilled to accomodate standard 60 ml syringes, each housing an unanesthetized, fully immobilized mouse. Following CT-scanning and radiotherapy treatment planning, radiation fields were designed to irradiate the head, thorax, or abdomen of the animal. Thermoluminescent dosimeters (TLDs) were used to confirm the treatment planning dosimetry for primary beam and scattered radiation. Mice are efficiently placed into 60 ml syringes and immobilized, without the use of anesthetics. Although partial rotational movement around the longitudinal axis and a minor 2 mm forward/backward movement are permitted, this does not compromise the irradiation of the chosen body area. TLDs confirmed the dose values predicted by the treatment planning dosimetry, both for primary beam and scattered radiation. The customized PMMA apparatus described and validated is cost-effective, convenient to use, and efficient in performing PBI without the use of anesthesia. The developed apparatus permits the isolated irradiation of the mouse head, thorax, and abdomen. Importantly, the apparatus allows the delivery of PBI to five mice, simultaneously, representing an efficient way to effectively expose a large number of animals to PBI through multiple daily fractions, simulating clinical radiotherapy treatment schedules.

Within the next five years, most radiotherapy treatment schedules will be designed using spatiotemporal optimization.

Within the next five years, most radiotherapy treatment schedules will be designed using spatiotemporal optimization.

At the Crossroads of Cancer Stem Cells, Radiation Biology, and Radiation Oncology.

Reports that a small subset of tumor cells initiate and sustain tumor growth, are resistant to radiation and drugs, and bear specific markers have led to an explosion of cancer stem cell research. These reports imply that the evaluation of therapeutic response by changes in tumor volume is misleading, as volume changes reflect the response of the sensitive rather than the resistant tumorigenic cell population. The reports further suggest that the marker-based selection of the tumor cell population will facilitate the development of radiation treatment schedules, sensitizers, and drugs that specifically target the resistant tumorigenic cells that give rise to treatment failure. This review presents evidence that contests the observations that cancer stem cell markers reliably identify the subset of tumor cells that sustain tumor growth and that the marker-identified population is radioresistant relative to the marker-negative cells. Experimental studies show that cells and tumors that survive large radiation doses are not more radioresistant than unirradiated cells and tumors, and also show that the intrinsic radiosensitivity of unsorted colony-forming tumor cells, in combination with the fraction of unsorted tumor cells that are tumor initiating, predicts tumor radiocurability.

Boosting Response: The Impact of Immune Checkpoint Inhibitors on Radiation Treatment Schedules

1Department of Radiation Oncology, Christiana Care Health Services Inc., Newark DE 19713, USA 2Center for Translational Cancer Research, Helen F Graham Cancer Center and Research Institute, Christiana Care Health Services Inc., Newark DE 19713, USA 3Department of Radiation Oncology, Kimmel Cancer Center, Thomas Jefferson University, Philadelphia, PA 19107, USA 4Department of Radiation Physics, MD Anderson Cancer Center, Houston, TX 77030, USA 5Departments of Biological Sciences and Medical Laboratory Sciences, University of Delaware, Newark DE 19713, USA *Corresponding author Jennifer Sims-Mourtada, PhD Senior Clinical Scientist Center for Translational Cancer Research Helen F Graham Cancer Center and Research Institute Christiana Care Health Services Inc. Newark DE 19713, USA; Departments of Biological Sciences and Medical Laboratory Sciences University of Delaware Newark DE 19713, USA Tel. 302-623-4648 Fax: 1-302623 -4314 E-mail: jsimsmourtada@christianacare.org

Treatment of Breast and Prostate Cancer by Hypofractionated Radiotherapy: Potential Risks and Benefits

Breast cancer and prostate cancer are the most common cancers diagnosed in women and men, respectively, in the UK, and radiotherapy is used extensively in the treatment of both. In vitro data suggest that tumours in the breast and prostate have unique properties that make a hypofractionated radiotherapy treatment schedule advantageous in terms of therapeutic index. Many clinical trials of hypofractionated radiotherapy treatment schedules have been completed to establish the extent to which hypofractionation can improve patient outcome. Here we present a concise description of hypofractionation, the mathematical description of converting between conventional and hypofractionated schedules, and the motivation for using hypofractionation in the treatment of breast and prostate cancer. Furthermore, we summarise the results of important recent hypofractionation trials and highlight the limitations of a hypofractionated treatment regimen.

Role of Palliative Radiotherapy for Bone Metastasis

With approximately 50-70% of patients with advanced cancer developing bone metastases during the course of their disease, treatment of bone metastases depends on many factors including performance status, pathology, site of disease, and neurologic status [1]. Radiotherapy has become highly precise, improving local control and facilitating minimally invasive treatment, and has attracted attention as a curative treatment method comparable to surgery. On the other hand, radiotherapy also plays an extremely important role in palliative treatment for advanced cancer patients [2]. Palliative care and treatment is aimed at providing relief from pain and other symptoms. Curative and palliative radiotherapies differ in the radiation field size, dose fraction, and treatment schedule. We review the role of radiotherapy in palliative treatment for patients with symptomatic bone metastases.

Short course high dose radiotherapy in the treatment of anaplastic thyroid carcinoma.

Purpose. Anaplastic thyroid carcinoma (ATC) is a rare but aggressive tumor with limited survival. To date, the ideal radiation treatment schedule, one that balances limited survival with treatment efficacy, remains undefined. In this retrospective series we investigate the effectiveness and tolerability of hypofractionated radiation therapy in the treatment of ATC. Methods. 17 patients with biopsy proven ATC treated between 2004 and 2012 were reviewed for outcomes and toxicity. All patients received short course radiation. Results. The most commonly prescribed dose was 54 Gy in 18 fractions. Median survival was 9.3 months. 47% of patients were metastatic at diagnosis and the majority of patients (88%) went on to develop metastasis. Death from local progression was seen in 3 patients (18%), 41% experienced grade 3 toxicity, and there were no grade 4 toxicities. Conclusions. Here we demonstrated the safety and feasibility of hypofractionated radiotherapy in the treatment of ATC. This approach offers shorter treatment courses (3-4 weeks) compared to traditional fractionation schedules (6-7 weeks), comparable toxicity, local control, and the ability to transition to palliative care sooner. Local control was dependent on the degree of surgical debulking, even in the metastatic setting.

Is excision alone adequate for low-risk DCIS of the breast treated with breast conserving therapy

Ductal carcinoma in situ (DCIS) represents a quarter of newly diagnosed breast neoplasms, with the majority of cases detected on routine screening mammography in asymptomatic women. Currently, most women with newly diagnosed DCIS are eligible for breast conserving therapy (BCT); however, significant controversy exists regarding whether or not to add radiation treatment (RT) after surgical excision in low-risk patients. While four older prospective randomized clinical trials have shown that the addition of RT after lumpectomy reduces the risk of ipsilateral breast tumor recurrence (IBTR) by approximately 50 %, recent studies have continued to attempt to identify a subset of patients with favorable risk DCIS who are at a sufficiently low-risk of IBTR that omitting RT might be reasonable. While a number of smaller studies have shown promising results, recent prospective data have consistently affirmed the increased risk of IBTR with the omission of RT, with no subset of patients consistently identified that can be safely observed without RT. While radiation after lumpectomy remains the “standard of care,” even in these low-risk patients, future directions include improvements in genetic assays to better identify low-risk patients and new RT techniques and schedules that can potentially reduce the duration of therapy and toxicity while improving quality of life for patients. Based on the data available, we continue to recommend radiation therapy for low-risk patients with DCIS as no discernible subset has been identified that does not benefit from radiation therapy.

S95 SOCCAR: Internationally Resonant Results from a Randomised Trial Based on UK Clinical Practise

Concurrent chemoradiation is now recognised as a standard of care for patients with inoperable Stage III NSCLC and good Performance Status. Two year survival rates in published trials ranges from...

TH-A-BRB-02: Mechanistic Linear-Quadratic-Linear (LQL) Model for Large Doses Per Fraction

The Linear-Quadratic (LQ) model has been successfully used for at least two decades to quantify radiation effects at standard (1.2-3Gy) doses. The validity of the standard LQ model for larger doses per fraction has been called into question by many authors, in part due to the continuous bending of the cell survival curve at large doses, contrary to results from in-vitro experiments. In recent years, Stereotactic Body Radiation Therapy (SBRT) treatments with large fraction doses have become more common, making the modeling for large doses per fraction of significant clinical relevance. Many authors have proposed extensions of the LQ model to address the shape of the cell survival curve at larger doses by arbitrary adding a phenomenological parameter to the LQ model. In this work, we discuss a Linear-Quadratic-Linear (LQL) model with a mechanistic formulation. This LQL model has one additional parameter with respect to the standard LQ model and can be derived by mechanistic arguments. The additional parameter makes the survival curve linear at high doses and has been estimated using in-vivo and in-vitro data. The advantage of a mechanistic model is that it allows for modeling of radiation effects for any given dose- rate and fractionation scheme. As an example, we present the LQL prediction for split dose experiments and low-dose-rate (LDR) prostate brachytherapy. The LQL model is equivalent to other mechanistic models like the Lethal-Potentially-Lethal model (LPL) but it retains the well-known parameters from the standard LQ model. As a clinical application, using estimated values of the additional parameter, we investigate the impact on the biologically effective dose (BED) for clinical SBRT treatment schedules of various cancer sites. Learning Objectives: 1. Understand the limitations of the standard LQ model for large doses per fraction. 2. Understand the mechanistic formulation of the proposed LQL. 3. Understand how the LQL can be used to calculate the BED for SBRT radiation treatment schedules and compare them with standard fractionation.

Mast Cells Are an Essential Component of Human Radiation Proctitis and Contribute to Experimental Colorectal Damage in Mice

Radiation proctitis is characterized by mucosal inflammation followed by adverse chronic tissue remodeling and is associated with substantial morbidity and mortality. Mast cell hyperplasia has been associated with diseases characterized by pathological tissue remodeling and fibrosis. Rectal tissue from patients treated with radiotherapy shows mast cell hyperplasia and activation, suggesting that these cells play a role in the development of radiation-induced sequelae. To investigate the role of mast cells in radiation damage, experimental radiation proctitis was induced in a mast cell-deficient (W(sh)/W(sh)) mouse model. The colon and rectum of W(sh)/W(sh) and wild-type mice were exposed to 27-Gy single-dose irradiation and studied after 2 and 14 weeks. Irradiated rodent rectum showed mast cell hyperplasia. W(sh)/W(sh) mice developed less acute and chronic rectal radiation damage than their control littermates. Tissue protection was associated with increased tissue neutrophil influx and expression of several inflammatory mediators immediately after radiation exposure. It was further demonstrated that mast cell chymase, tryptase, and histamine could change human muscularis propria smooth muscle cells into a migrating/proliferating and proinflammatory phenotype. These data show that mast cells have deleterious effects on both acute and chronic radiation proctitis, possibly by limiting acute tissue neutrophil influx and by favoring phenotypic orientation of smooth muscle cells, thus making them active participants in the radiation-induced inflammatory process and dystrophy of the rectal wall.

The initial experience of electronic brachytherapy for the treatment of non-melanoma skin cancer

BackgroundMillions of people are diagnosed with non-melanoma skin cancers (NMSC) worldwide each year. While surgical approaches are the standard treatment, some patients are appropriate candidates for radiation therapy for NMSC. High dose rate (HDR) brachytherapy using surface applicators has shown efficacy in the treatment of NMSC and shortens the radiation treatment schedule by using a condensed hypofractionated approach. An electronic brachytherapy (EBT) system permits treatment of NMSC without the use of a radioactive isotope.MethodsData were collected retrospectively from patients treated from July 2009 through March 2010. Pre-treatment biopsy was performed to confirm a malignant cutaneous diagnosis. A CT scan was performed to assess lesion depth for treatment planning, and an appropriate size of surface applicator was selected to provide an acceptable margin. An HDR EBT system delivered a dose of 40.0 Gy in eight fractions twice weekly with 48 hours between fractions, prescribed to a depth of 3-7 mm. Treatment feasibility, acute safety, efficacy outcomes, and cosmetic results were assessed.ResultsThirty-seven patients (mean age 72.5 years) with 44 cutaneous malignancies were treated. Of 44 lesions treated, 39 (89%) were T1, 1 (2%) Tis, 1 (2%) T2, and 3 (7%) lesions were recurrent. Lesion locations included the nose for 16 lesions (36.4%), ear 5 (11%), scalp 5 (11%), face 14 (32%), and an extremity for 4 (9%). Median follow-up was 4.1 months. No severe toxicities occurred. Cosmesis ratings were good to excellent for 100% of the lesions at follow-up.ConclusionsThe early outcomes of EBT for the treatment of NMSC appear to show acceptable acute safety and favorable cosmetic outcomes. Using a hypofractionated approach, EBT provides a convenient treatment schedule.

Radioprotection: the non-steroidal anti-inflammatory drugs (NSAIDs) and prostaglandins.

Clinical and experimental studies of the acute and late effects of radiation on cells have enhanced our knowledge of radiotherapy and have led to the optimisation of radiation treatment schedules and to more precise modes of radiation delivery. However, as both normal and cancerous tissues have similar response to radiation exposure, radiation-induced injury on normal tissues may present either during, or after the completion of, the radiotherapy treatment. Studies on both NSAIDs and prostaglandins have indeed shown some evidence of radioprotection. Both have the potential to increase the survival of cells but by entirely different mechanisms. Studies of cell kinetics reveal that cells in the mitotic (M) and late G2 phases of the cell cycle are generally most sensitive to radiation compared with cells in the early S and G1/G0 phases. Furthermore, radiation leads to a mitotic delay in the cell cycle. Thus, chemical agents that either limit the proportion of cells in the M and G2 phases of the cell cycle or enhance rapid cell growth could in principle be exploited for their potential use as radioprotectors to normal tissue during irradiation. NSAIDs have been shown to exert anti-cancer effects by causing cell-cycle arrest, shifting cells towards a quiescence state (G0/G1). The same mechanism of action was observed in radioprotection of normal tissues. An increase in arachidonic acid concentrations after exposure to NSAIDs also leads to the production of an apoptosis-inducer ceramide. NSAIDs also elevate the level of superoxide dismutase in cells. Activation of heat shock proteins by NSAIDs increases cell survival by alteration of cytokine expression. A role for NSAIDs with respect to inhibition of cellular proliferation possibly by an anti-angiogenesis mechanism has also been suggested. Several in-vivo studies have provided evidence suggesting that NSAIDs may protect normal tissues from radiation injury. Prostaglandins do not regulate the cell cycle, but they do have a variety of effects on cell growth and differentiation. PGE(2) mediates angiogenesis, increasing the supply of oxygen and nutrients, essential for cellular survival and growth. Accordingly, PGE(2) at sufficiently high plasma concentrations enhances cellular survival by inhibiting pro-inflammatory cytokines such as TNF-alpha and IL-1beta. Thus, PGE(2) acts as a modulator, rather than a mediator, of inflammation. Prospective studies have suggested the potential use of misoprostol, a PGE(1) analogue, before irradiation, in prevention of radiation-induced side effects. The current understanding of the pharmacology of NSAIDs and prostaglandins shows great potential to minimise the adverse effects of radiotherapy on normal tissue.

SORS: A New Software for the Simulation of Radiotherapy Schedule

We present a software for choosing the best radiotherapy treatment schedule for head and neck cancers as a beginning radiotherapy plan or a temporarily interrupted plan. Its application occurs according to two modalities: the first adopts the best estimates for model parameters; the second takes into account the parameters' uncertainty too. In both cases, the choice becomes the schedule with the highest uncomplicated tumor control probability (UTCP). In the UTCP valuation, the normal tissue complication probability (NTCP) of each organ is related to the gravity of its possible late injury. For NTCP calculation, it has been adopted the empirical LKB (Lyman-Kutcher-Burman) model corrected for dose/fraction via linear-quadratic model and the incomplete repair effect. The tumor control probability (TCP) model is Poisson based and contains corrections for dose/fraction and regrowth effect; optionally, it can be accounted for the incomplete repair effect as well. At the end of processing, a detailed file with all informations about UTCP, TCP and single organ NTCP is furnished for every examined schedule. Moreover, a useful 3-D graphic representation of the schedule's UTCP is available, allowing the physician to easily understand the schedules with the highest radiotherapeutic efficacy. The open source characteristic allows the program to adapt to the individual clinical case as well as to be a valid support in radiobiological research.

Feasibility of using administrative claims data for cost-effectiveness analysis of a clinical trial

Objective: This study was performed retrospectively to determine if Medicare claims data could be used to evaluate the cost effectiveness, from a payer perspective, of different radiation treatment schedules evaluated in a national clinical trial.Methods: Medicare costs from all providers and all places of service were obtained from the Centers for Medicare & Medicaid Services for patients treated in the period 1992–1996 on Radiation Therapy Oncology Group 90-03, and combined with data on outcomes from the trial.Results: Of the 1,113 patients entered, Medicare cost data and clinical outcomes were available for 187 patients. Significant differences in tolerance of treatment and outcome were noted between patients with Medicare data included in the study and patients without Medicare data, and non-Medicare patients excluded from it. Ninety-five percent confidence ellipses on the incremental cost-effectiveness scatterplots crossed both axes, indicating non-significant differences in cost effectiveness between radiation treatment schedules.Conclusions: Claims data permit estimation of cost effectiveness, but Medicare data provide inadequate representation of results applicable to patients from the general population.Keywords:

Palliative Radiotherapy Tailored to Live Expectancy in Terminally Ill Cancer Patients: Reality or Myth?

About 50% of patients referred to radiotherapy are treated with palliative intent. Treatment and fractionation schedules must be tailored to the survival time and the risk of late sequelae. However, prognostic estimates are usually obtained by an informal decision process incompatible with evidence based standards. In fact, little is known about the adequacy of palliative radiation treatment schedules in end-stage cancer patients.

Clinical significance of cumulative biological effective dose and overall treatment time in the treatment of carcinoma cervix

The purpose of this retrospective study is to report the radiotherapy treatment response of, and complications in, patients with cervical cancer on the basis of cumulative biologic effective dose (BED) and overall treatment time (OTT).Sixty-four (stage II - 35/64; stage III - 29/64) patients of cervical cancer were treated with combination of external beam radiotherapy (EBRT) and low dose rate intracavitary brachytherapy (ICBT). The cumulative BED was calculated at Point A (BED10); and bladder, rectal reference points (BED2,5) using the linear-quadratic BED equations.The local control (LC) rate and 5-year disease-free survival (DFS) rate in patients of stage II were comparable for BED10 <84.5 and BED10 >84.5 but were much higher for BED10 >84.5 than BED10 <84.5 (P< 0.01) in stage III patients. In the stage II patients, The LC rate and 5-year DFS rate were comparable for OTT <50 days and for OTT >50 days but were much higher in stage III patients with OTT < 50 than OTT >50 days (P< 0.001). It was also observed that patients who received BED2.5 <105 had lesser rectal (P< 0.001) and bladder complications than BED2.5 >105. Higher rectal complication-free survival (CFSR) rate, bladder complication-free survival (CFSB) rate and all-type late complication-free survival rate were observed in patients who received BED2.5 < 105 than BED2.5 >105.A balanced, optimal and justified radiotherapy treatment schedule to deliver higher BED10 (>84.5) and lower BED2.5 (< 105) in lesser OTT (< 50 days) is essential in carcinoma cervix to expect a better treatment outcome in all respects.

Preoperative chemoradiation for locally advanced carcinoma of the vulva

Objective. A twice daily (BID) radiation treatment schedule (interval of 4–6 h) delivered concurrent with chemotherapy for advanced or critically located carcinoma of the vulva was modeled on the schema developed by the Gynecology Oncology Group (GOG). Inguinal nodes were included in the treatment fields even if clinically negative. This review analyzed the outcomes using this approach. Methods. A retrospective review was conducted of the records of 18 patients with vulvar cancer. Patients were treated with a modified GOG schema using 5-fluorouracil (5FU) and cisplatin with BID radiation treatments during the first and last weeks of treatment and seven daily radiation treatments in between. The regional nodes and primary tumor were prescribed 44.6 Gy. Resection of the primary tumor bed and inguinal dissection was planned at 4–6 weeks post-treatment. Clinical and pathological responses as well as locoregional control and toxicity were assessed. Results. All patients responded. There were 13/18 complete clinical responses (cCR), of whom 12 remained NED at 25 months. Of the five partial clinical response (cPR) patients, two have suffered local recurrences, despite surgical resection in one and electron boost in the other. All patients developed a desquamative perineal skin reaction necessitating a mean treatment break of 15 days. No severe hematological toxicity was encountered, and only one patient had grade 3 small bowel toxicity. One patient required surgical debridement for groin wound breakdown. Conclusion. The use of BID chemoradiation resulted in complete or partial responses in all cases. Post-treatment groin dissection can be performed without significant post-operative complications.

The effect of fraction time in intensity modulated radiotherapy: theoretical and experimental evaluation of an optimization problem (the real conclusions): in regard to Mu et al. Radiotherapy on Oncology 2003; 68: 181?87

Mu and colleagues have studied the effect of prolongation of fraction delivery time using Chinese hamster fibroblasts (V79-379-A) by subdividing the total dose per fraction into a number equal sub-fractions separated by fixed time intervals. We agree with their general conclusions that the prolongation of fraction time may spare tissues with a fast DNA repair and that there is a risk for sparing tumors. We also agree that this should be considered when IMRT is applied in the clinic. When we read their paper in greater detail we asked ourselves two questions: first, why do the theoretical predictions given in their paper not match the observed experimental data? Secondly, can we provide a theoretical model using the same assumptions about incomplete repair as Mu et al. that does indeed match the data? We believe we have come up with answers to both questions. Which are, first that Mu et al. have used an inappropriate theoretical model to describe their experiment (see Eq. (2) below), and secondly that if one uses an appropriate theoretical model (see Eq. (5) below) this model predicts the experimental results obtained by Mu et al. very well indeed for doses per fraction used in conventional radiotherapy. To show these points we start by stating the problem, the Linear Quadratic formalism including incomplete repair between fractions states that the surviving fraction, SFnd, of cells after n fractions of dose d can be described as follows (Eq. (3) in the Mu et al. paper):(1)SFnd=exp(−nαd−Gnβd2)where G is the correction for incomplete repair between fractions. In what follows, we will use for G the expressions given by Mu et al. (Eqs. (4) and (5)) to describe the incomplete repair between fractions. If one sets n=1 in Eq. (1)(2)SFd=exp(−ad−Gβd2),as one would think is applicable for one fraction of dose d and calculates using Mu et al.'s data (α=0.16Gy−1,β=0.016Gy−2, an acute surviving fraction for a fraction of 2Gy delivered continuously over 1 min SF2=0.68, and an acute surviving fraction for a fraction of 8Gy delivered continuously over 4 min SF8=0.10) then one obtains the ratios of surviving fractions of prolonged irradiation to the surviving fraction for acute irradiation shown in the fourth and fifth column of Table 1 which are the same as the theoretical values given in Table 2 of Mu et al.'s paper. However, this is incorrect, since in their experimental design Mu et al. have chosen to subdivide each treatment fraction into m subfractions of dose Δ separated by a time interval δT, such that the dose per fraction is given by d=mΔ and the overall treatment time is given by T=(m−1)δT. Now using Eq. (2) for a subfraction of dose Δ we find:(3)SFΔδT=exp(−αΔ−GβΔ2),Then the surviving fraction of cells after delivering m subfractions separated by time intervals δT is simply given by:(4)SFmΔδT=(SFΔδT)m=exp(−αmΔ−GβmΔ2),Using the fact that the dose per fraction is given by d=mΔ, (Eq. (4)) can be rewritten as follows:(5)SFdδT=exp−α(mΔ)−Gβm(mΔ)2=exp−αd−Gβmd2Eq. (5) instead of Eq. (2), as used by Mu et al., represents the correct theoretical model to describe their experiment. Now making use of Eq. (5) and either a mono-exponential repair model with T1/2=0.4h or a bi-exponential repair model with a 60% fast component, T1/2=0.4h, and a 40% slow component, T1/2=4h, one obtains the ratios of surviving fractions of prolonged irradiation to the surviving fraction for acute irradiation shown in the sixth, seventh, eighth, and ninth column of Table 1, respectively. As one can see from Table 1 using Eq. (5) yields excellent agreement between theoretical predicted and experimental observed ratios of surviving fractions of prolonged irradiation to the surviving fraction for acute irradiation for conventional doses per fraction and significantly over predicts for large doses per fraction using either a mono-exponential or bi-exponential repair model. Therefore, the real conclusions of the study by Mu et al. are that the tumorcidal effect of a radiotherapy treatment schedule can be adversely affected significantly by prolonging the delivery time per fraction to 40 min as could be possible for some complex IMRT plans, and furthermore that this effect is well predicted by current biological repair models in the range of conventional doses per fraction.