Equivalent uniform RBE-weighted dose in eye plaque brachytherapy.

BACKGROUND: Brachytherapy for ocular melanoma is based on the application of eye plaques with different spatial dose nonuniformity, time-dependent dose rates and relative biological effectiveness (RBE). PURPOSE: We propose a parameter called the equivalent uniform RBE-weighted dose (EUDRBE) that can be used for quantitative characterization of integrated cell survival in radiotherapy modalities with the variable RBE, dose nonuniformity and dose rate. The EUDRBE is applied to brachytherapy with 125I eye plaques designed by the Collaborative Ocular Melanoma Study (COMS). METHODS: The EUDRBE is defined as the uniform dose distribution with RBE = 1 that causes equal cell survival for a given nonuniform dose distribution with the variable RBE > 1. The EUDRBE can be used for comparison of cell survival for nonuniform dose distributions with different RBE, because they are compared to the reference dose with RBE = 1. The EUDRBE is applied to brachytherapy with 125I COMS eye plaques that are characterized by a steep dose gradient in tumor base-apex direction, protracted irradiation during time intervals of 3-8 days, and variable dose-rate dependent RBE with a maximum of about 1.4. The simulations are based on dose of 85 Gy prescribed to the farthest intraocular extent of the tumor (tumor apex). To compute the EUDRBE in eye plaque brachytherapy and correct for protracted irradiation, the distributions of physical dose have been converted to non-uniform distributions of biologically effective dose (BED) to include the biological effects of sublethal cellular repair, Our radiobiological analysis considers the combined effects of different time-dependent dose rates, spatial dose non-uniformity, dose fractionation and different RBE and can be used to derive optimized dose regimens brachytherapy. RESULTS: Our simulations show that the EUDRBE increases with the prescription depths and the maximum increase may achieve 6% for the tumor height of 12 mm. This effect stems from a steep dose gradient within the tumor that increases with the prescription depth. The simulations also show that the EUDRBE increase may achieve 12% with increasing the dose rate when implant duration decreases. The combined effect of dose nonuniformity and dose rate may change the EUDRBE up to 18% for the same dose prescription of 85 Gy to tumor apex. The absolute dose range of 48-61 Gy (RBE) for the EUDRBE computed using 4 or 5 fractions is comparable to the dose prescriptions used in stereotactic body radiation therapy (SBRT) with megavoltage X-rays (RBE = 1) for different cancers. The tumor control probabilities in SBRT and eye plaque brachytherapy are very similar at the level of 80% or higher that support the hypothesis that the selected approximations for the EUDRBE are valid. CONCLUSIONS: The computed range of the EUDRBE in 125I COMS eye plaque brachytherapy suggests that the selected models and hypotheses are acceptable. The EUDRBE can be useful for analysis of treatment outcomes and comparison of different dose regimens in eye plaque brachytherapy.

Impact of radiation therapy on healthy and cancerous cell dynamics: a Mathematical analysis.

This study proposes a novel therapeutic model for cancer treatment with radiation therapy by analyzing the interactions among cancer, immune and healthy cells through a system of three ordinary differential equations. In this model, the natural influx rate of mature immune cells is assumed constant and is denoted by, a. The overall effect of radiation therapy on cancer cells is represented by a parameter, s; which is the surviving fraction of cells as determined by the Linear Quadratic (LQ) model. Conditions for the stability of equilibria in the interaction model modified to include the surviving fraction, are systematically established in terms of the dose and model parameters. Numerical simulations are performed in Wolfram MATHEMATICA software, investigating a spectrum of initial cell population values irradiated with 60Co γ-ray Low-LET radiation and High-LET 165 keV/µm Ni-ion radiation to facilitate improved visualization and in-depth analysis. By analyzing the model, this study identifies threshold values for the absorbed dose D for particular values of the model and radiation parameters for both High Linear Energy Transfer (high-LET) and Low Linear Energy Transfer (low-LET) radiations that ensure either eradication or minimization of cancer cells from a patient's body, providing valuable insights for designing effective cancer treatments.

Obtaining organ-specific radiobiological parameters from clinical data for radiation therapy planning of head and neck cancers.

Objective.Different radiation therapy (RT) strategies, e.g. conventional fractionation RT (CFRT), hypofractionation RT (HFRT), stereotactic body RT (SBRT), adaptive RT, and re-irradiation are often used to treat head and neck (HN) cancers. Combining and/or comparing these strategies requires calculating biological effective dose (BED). The purpose of this study is to develop a practical process to estimate organ-specific radiobiologic model parameters that may be used for BED calculations in individualized RT planning for HN cancers.Approach.Clinical dose constraint data for CFRT, HFRT and SBRT for 5 organs at risk (OARs) namely spinal cord, brainstem, brachial plexus, optic pathway, and esophagus obtained from literature were analyzed. These clinical data correspond to a particular endpoint. The linear-quadratic (LQ) and linear-quadratic-linear (LQ-L) models were used to fit these clinical data and extract relevant model parameters (alpha/beta ratio, gamma/alpha,dTand BED) from the iso-effective curve. The dose constraints in terms of equivalent physical dose in 2 Gy-fraction (EQD2) were calculated using the obtained parameters.Main results.The LQ-L and LQ models fitted clinical data well from the CFRT to SBRT with the LQ-L representing a better fit for most of the OARs. The alpha/beta values for LQ-L (LQ) were found to be 2.72 (2.11) Gy, 0.55 (0.30) Gy, 2.82 (2.90) Gy, 6.57 (3.86) Gy, 5.38 (4.71) Gy, and the dose constraint EQD2 were 55.91 (54.90) Gy, 57.35 (56.79) Gy, 57.54 (56.35) Gy, 60.13 (59.72) Gy and 65.66 (64.50) Gy for spinal cord, optic pathway, brainstem, brachial plexus, and esophagus, respectively. Additional two LQ-L parametersdTwere 5.24 Gy, 5.09 Gy, 7.00 Gy, 5.23 Gy, and 6.16 Gy, and gamma/alpha were 7.91, 34.02, 8.67, 5.62 and 4.95.Significance.A practical process was developed to extract organ-specific radiobiological model parameters from clinical data. The obtained parameters can be used for biologically based radiation planning such as calculating dose constraints of different fractionation regimens.

Radiobiological Meta-Analysis of the Response of Prostate Cancer to Different Fractionations: Evaluation of the Linear-Quadratic Response at Large Doses and the Effect of Risk and ADT.

The purpose of this work was to investigate the response of prostate cancer to different radiotherapy schedules, including hypofractionation, to evaluate potential departures from the linear-quadratic (LQ) response, to obtain the best-fitting parameters for low-(LR), intermediate-(IR), and high-risk (HR) prostate cancer and to investigate the effect of ADT on the radiobiological response. We constructed a dataset of the dose-response containing 87 entries/16,536 patients (35/5181 LR, 32/8146 IR, 20/3209 HR), with doses per fraction ranging from 1.8 to 10 Gy. These data were fit to tumour control probability models based on the LQ model, linear-quadratic-linear (LQL) model, and a modification of the LQ (LQmod) model accounting for increasing radiosensitivity at large doses. Fits were performed with the maximum likelihood expectation methodology, and the Akaike information criterion (AIC) was used to compare the models. The AIC showed that the LQ model was superior to the LQL and LQmod models for all risks, except for IR, where the LQL model outperformed the other models. The analysis showed a low α/ß for all risks: 2.0 Gy for LR (95% confidence interval: 1.7-2.3), 3.4 Gy for IR (3.0-4.0), and 2.8 Gy for HR (1.4-4.2). The best fits did not show proliferation for LR and showed moderate proliferation for IR/HR. The addition of ADT was consistent with a suppression of proliferation. In conclusion, the LQ model described the response of prostate cancer better than the alternative models. Only for IR, the LQL model outperformed the LQ model, pointing out a possible saturation of radiation damage with increasing dose. This study confirmed a low α/ß for all risks.

Active Immune Phenotype in Head and Neck Cancer: Reevaluating the Iso-Effect Fractionation Based on the Linear Quadratic (LQ) Model-A Narrative Review.

Altered fractionation concepts and especially moderate hypo-fractionation are evaluated as alternatives to standard treatment for head and neck squamous cell carcinoma (HNSCC), associated with or not concurrent with or sequential to chemotherapy. The calculation of the iso-equivalent dose regimens has as its starting point the linear quadratic (LQ) formalism traditionally based on the "4Rs" of radiobiology. The higher rates of therapeutic failure after radiotherapy of HNSCC are associated with the heterogeneity of radio-sensibility. The identification of genetic signatures and radio-resistance scores aims to improve the therapeutic ratio of radiotherapy and to conceptualize personalized fractionation schemes. The new data regarding the involvement of the sixth "R" of radiobiology in HNSCC, especially for the HPV-driven subtype, but also for the "immune active" minority of HPV-negative HNSCCs, bring to the fore a multifactorial variation of the α/ß ratio. The involvement of the antitumor immune response and the dose/fractionation/volume factors as well as the therapeutic sequence in the case of new multimodal treatments including immune checkpoint inhibitors (ICIs) could be included as an additional term in the quadratic linear formalism especially for hypo-fractionation regimens. This term should take into account the dual immunomodulatory effect (immunosuppressant and stimulator of antitumor immunity) of radiotherapy, which varies from case to case and can bring benefit or a detrimental effect.

The minimal FLASH sparing effect needed to compensate the increase of radiobiological damage due to hypofractionation for late-reacting tissues.

PURPOSE: Normal tissue (NT) sparing by ultra-high dose rate (UHDR) irradiations compared to conventional dose rate (CONV) irradiations while being isotoxic to the tumor has been termed "FLASH effect" and has been observed when large doses per fraction (d ≳ 5 Gy) have been delivered. Since hypofractionated treatment schedules are known to increase toxicities of late-reacting tissues compared to normofractionated schedules for many clinical scenarios at CONV dose rates, we developed a formalism based on the biologically effective dose (BED) to assess the minimum magnitude of the FLASH effect needed to compensate the loss of late-reacting NT sparing when reducing the number of fractions compared to a normofractionated CONV treatment schedule while remaining isoeffective to the tumor. METHODS: By requiring the same BED for the tumor, we derived the "break-even NT sparing weighting factor" WBE for the linear-quadratic (LQ) and LQ-linear (LQ-L) models for an NT region irradiated at a relative dose r (relative to the prescribed dose per fraction d to the tumor). WBE was evaluated numerically for multiple values of d and r, and for different tumor and NT α/ß-ratios. WBE was compared against currently available experimental data on the magnitude of the NT sparing provided by the FLASH effect for single fraction doses. RESULTS: For many clinically relevant scenarios, WBE decreases steeply initially for d > 2 Gy for late-reacting tissues with (α/ß)NT ≈ 3 Gy, implying that a significant NT sparing by the FLASH effect (between 15% and 30%) is required to counteract the increased radiobiological damage experienced by late-reacting NT for hypofractionated treatments with d < 10 Gy compared to normofractionated treatments that are equieffective to the tumor. When using the LQ model with generic α/ß-ratios for tumor and late-reacting NT of (α/ß)T  = 10 Gy and (α/ß)NT  = 3 Gy, respectively, most currently available experimental evidence about the magnitude of NT sparing by the FLASH effect suggests no net NT sparing benefit for hypofractionated FLASH radiotherapy (RT) in the high-dose region when compared with WBE . Instead, clinical indications with more similar α/ß-ratios of the tumor and dose-limiting NT toxicities [i.e., (α/ß)T  ≈ (α/ß)NT ], such as prostate treatments, are generally less penalized by hypofractionated treatments and need consequently smaller magnitudes of NT sparing by the FLASH effect to achieve a net benefit. For strongly hypofractionated treatments (>10-15 Gy/fraction), the LQ-L model predicts, unlike the LQ model, a larger WBE suggesting a possible benefit of strongly hypofractionated FLASH RT, even for generic α/ß-ratios of (α/ß)T  = 10 Gy and (α/ß)NT  = 3 Gy. However, knowledge on the isoeffect scaling for high doses per fraction (≳10 Gy/fraction) and its modeling is currently limited and impedes accurate and reliable predictions for such strongly hypofractionated treatments. CONCLUSIONS: We developed a formalism that quantifies the minimal NT sparing by the FLASH effect needed to compensate for hypofractionation, based on the LQ and LQ-L models. For a given hypofractionated UHDR treatment scenario and magnitude of the FLASH effect, the formalism predicts if a net NT sparing benefit is expected compared to a respective normofractionated CONV treatment.

Variability of α/ß ratios for prostate cancer with the fractionation schedule: caution against using the linear-quadratic model for hypofractionated radiotherapy.

BACKGROUND: Prostate cancer (PCa) is known to be suitable for hypofractionated radiotherapy due to the very low α/ß ratio (about 1.5-3 Gy). However, several randomized controlled trials have not shown the superiority of hypofractionated radiotherapy over conventionally fractionated radiotherapy. Besides, in vivo and in vitro experimental results show that the linear-quadratic (LQ) model may not be appropriate for hypofractionated radiotherapy, and we guess it may be due to the influence of fractionation schedules on the α/ß ratio. Therefore, this study attempted to estimate the α/ß ratio in different fractionation schedules and evaluate the applicability of the LQ model in hypofractionated radiotherapy. METHODS: The maximum likelihood principle in mathematical statistics was used to fit the parameters: α and ß values in the tumor control probability (TCP) formula derived from the LQ model. In addition, the fitting results were substituted into the original TCP formula to calculate 5-year biochemical relapse-free survival for further verification. RESULTS: Information necessary for fitting could be extracted from a total of 23,281 PCa patients. A total of 16,442 PCa patients were grouped according to fractionation schedules. We found that, for patients who received conventionally fractionated radiotherapy, moderately hypofractionated radiotherapy, and stereotactic body radiotherapy, the average α/ß ratios were 1.78 Gy (95% CI 1.59-1.98), 3.46 Gy (95% CI 3.27-3.65), and 4.24 Gy (95% CI 4.10-4.39), respectively. Hence, the calculated α/ß ratios for PCa tended to become higher when the dose per fraction increased. Among all PCa patients, 14,641 could be grouped according to the risks of PCa in patients receiving radiotherapy with different fractionation schedules. The results showed that as the risk increased, the k (natural logarithm of an effective target cell number) and α values decreased, indicating that the number of effective target cells decreased and the radioresistance increased. CONCLUSIONS: The LQ model appeared to be inappropriate for high doses per fraction owing to α/ß ratios tending to become higher when the dose per fraction increased. Therefore, to convert the conventionally fractionated radiation doses to equivalent high doses per fraction using the standard LQ model, a higher α/ß ratio should be used for calculation.

Heuristic estimation of the α/ß ratio for a cohort of Mexican patients with prostate cancer treated with external radiotherapy techniques.

BACKGROUND: The aim of the study was to Estimate and compare the radiobiological ratio α/ß with the heuristic method for a cohort of Mexican patients with prostate cancer (PCa) who were treated with external radiotherapy (RT) techniques at three Hospital Institutions in Mexico City. With the Kaplan-Meier technique and the Cox proportional hazards model, the biochemical relapse-free survival (bRFS) is determined and characterized for cohorts of Mexican patients with PCa who received treatment with external RT. Using these clinical outcomes, the radiobiological parameter α/ß is determined using the heuristic methodology of Pedicini et. al. MATERIALS AND METHODS: The α/ß is calculated from the survival curves for different treatment schemes implemented at three distinct hospitals. The Pedicini's techniques allow to determine the parameters α/ß, k and N 0 when treatments are not radiobiologically equivalent, therefore, are built up of a set of curved pairs for the biologically effective dose (BED) versus the ratio α/ß, where the ratio is given by the intersection for each pair of curves. RESULTS: Six different values of α/ß were found: the first α/ß = 2.46 Gy, the second α/ß = 3.30 Gy, the third for α/ß = 3.25 Gy, the fourth α/ß = 3.24 Gy, the fifth α/ß = 3.38 Gy and the last α/ß = 4.08 Gy. These values can be explained as follows: a) The bRFS of the schemes presents a statistical variation; b) The absorbed doses given to the patient present uncertainties on the physical dosimetry that are not on the modeling; c) Finally, in the model for the bRFS of Eq. (3), there are parameters that have to be considered, such as: the number of clonogenic tumor cells N 0 , the overall treatment time (OTT), the kick-off time for tumor repopulation T k and the repopulation doubling time. Therefore, the mean value to α/ß for all schemes has an average value of 3.29 (± 0.52) Gy. CONCLUSIONS: The value of α / ß ¯ = 3.29 ( ± 0.52 ) Gy is determined from cohorts of Mexican patients with PC a treated with external radiotherapy using the time-dependent LQ model, which is a higher value with respect to the "dogma" value of α/ß 1.5 Gy obtained with the LQ model without temporal dependence. Therefore, there is a possibility of optimizing treatments radiobiologically and improving the results of bRFS in Mexican patients with PCa treated with external radiotherapy.

Technical Note: Break-even dose level for hypofractionated treatment schedules.

PURPOSE: To derive the isodose line R relative to the prescription dose below which irradiated normal tissue (NT) regions benefit from a hypofractionated schedule with an isoeffective dose to the tumor. To apply the formalism to clinical case examples. METHODS: From the standard biologically effective dose (BED) equation based on the linear-quadratic (LQ) model, the BED of an NT that receives a relative proportion r of the prescribed dose per fraction for a given α/ß-ratio of the tumor, (α/ß)T , and NT, (α/ß)NT , is derived for different treatment schedules while keeping the BED to the tumor constant. Based on this, the "break-even" isodose line R is then derived. The BED of NT regions that receive doses below R decreases for more hypofractionated treatment schedules, and hence a lower risk for NT injury is predicted in these regions. To assess the impact of a linear behavior of BED for high doses per fraction (>6 Gy), we evaluated BED also using the LQ-linear (LQ-L) model. RESULTS: The formalism provides the equations to derive the BED of an NT as function of dose per fraction for an isoeffective dose to the tumor and the corresponding break-even isodose line R. For generic α/ß-ratios of (α/ß)T  = 10 Gy and (α/ß)NT  = 3 Gy and homogeneous dose in the target, R is 30%. R is doubling for stereotactic treatments for which tumor control correlates with the maximum dose of 100% instead of the encompassing isodose line of 50%. When using the LQ-L model, the notion of a break-even dose level R remains valid up to about 20 Gy per fraction for generic α/ß-ratios and D T = 2 ( α / ß ) . CONCLUSIONS: The formalism may be used to estimate below which relative isodose line R there will be a differential sparing of NT when increasing hypofractionation. More generally, it allows to assess changes of the therapeutic index for sets of isoeffective treatment schedules at different relative dose levels compared to a reference schedule in a compact manner.

Radiobiological Evaluation of Combined Gamma Knife Radiosurgery and Hyperthermia for Pediatric Neuro-Oncology.

Combining radiotherapy (RT) with hyperthermia (HT) has been proven effective in the treatment of a wide range of tumours, but the combination of externally delivered, focused heat and stereotactic radiosurgery has never been investigated. We explore the potential of such treatment enhancement via radiobiological modelling, specifically via the linear-quadratic (LQ) model adapted to thermoradiotherapy through modulating the radiosensitivity of temperature-dependent parameters. We extend this well-established model by incorporating oxygenation effects. To illustrate the methodology, we present a clinically relevant application in pediatric oncology, which is novel in two ways. First, it deals with medulloblastoma, the most common malignant brain tumour in children, a type of brain tumour not previously reported in the literature of thermoradiotherapy studies. Second, it makes use of the Gamma Knife for the radiotherapy part, thereby being the first of its kind in this context. Quantitative metrics like the biologically effective dose (BED) and the tumour control probability (TCP) are used to assess the efficacy of the combined plan.

Quantification of Differential Response of Tumour and Normal Cells to Microbeam Radiation in the Absence of FLASH Effects.

Microbeam radiotherapy (MRT) is a preclinical method of delivering spatially-fractionated radiotherapy aiming to improve the therapeutic window between normal tissue complication and tumour control. Previously, MRT was limited to ultra-high dose rate synchrotron facilities. The aim of this study was to investigate in vitro effects of MRT on tumour and normal cells at conventional dose rates produced by a bench-top X-ray source. Two normal and two tumour cell lines were exposed to homogeneous broad beam (BB) radiation, MRT, or were separately irradiated with peak or valley doses before being mixed. Clonogenic survival was assessed and compared to BB-estimated surviving fractions calculated by the linear-quadratic (LQ)-model. All cell lines showed similar BB sensitivity. BB LQ-model predictions exceeded the survival of cell lines following MRT or mixed beam irradiation. This effect was stronger in tumour compared to normal cell lines. Dose mixing experiments could reproduce MRT survival. We observed a differential response of tumour and normal cells to spatially fractionated irradiations in vitro, indicating increased tumour cell sensitivity. Importantly, this was observed at dose rates precluding the presence of FLASH effects. The LQ-model did not predict cell survival when the cell population received split irradiation doses, indicating that factors other than local dose influenced survival after irradiation.

Physical and biological beam modeling for carbon beam scanning at Osaka Heavy Ion Therapy Center.

We have developed physical and biological beam modeling for carbon scanning therapy at the Osaka Heavy Ion Therapy Center (Osaka HIMAK). Carbon beam scanning irradiation is based on continuous carbon beam scanning, which adopts hybrid energy changes using both accelerator energy changes and binary range shifters in the nozzles. The physical dose calculation is based on a triple Gaussian pencil-beam algorithm, and we thus developed a beam modeling method using dose measurements and Monte Carlo simulation for the triple Gaussian. We exploited a biological model based on a conventional linear-quadratic (LQ) model and the photon equivalent dose, without considering the dose dependency of the relative biological effectiveness (RBE), to fully comply with the carbon passive dose distribution using a ridge filter. We extended a passive ridge-filter design method, in which carbon and helium LQ parameters are applied to carbon and fragment isotopes, respectively, to carbon scanning treatment. We then obtained radiation quality data, such as the linear energy transfer (LET) and LQ parameters, by Monte Carlo simulation. The physical dose was verified to agree with measurements to within ±2% for various patterns of volume irradiation. Furthermore, the RBE in the middle of a spread-out Bragg peak (SOBP) reproduced that from passive dose distribution results to within ±1.5%. The developed carbon beam modeling and dose calculation program was successfully applied in clinical use at Osaka HIMAK.

Local Disease-Free Survival Rate (LSR) Application to Personalize Radiation Therapy Treatments in Breast Cancer Models.

Cancer heterogeneity represents the main issue for defining an effective treatment in clinical practice, and the scientific community is progressively moving towards the development of more personalized therapeutic regimens. Radiotherapy (RT) remains a fundamental therapeutic treatment used for many neoplastic diseases, including breast cancer (BC), where high variability at the clinical and molecular level is known. The aim of this work is to apply the generalized linear quadratic (LQ) model to customize the radiant treatment plan for BC, by extracting some characteristic parameters of intrinsic radiosensitivity that are not generic, but may be exclusive for each cell type. We tested the validity of the generalized LQ model and analyzed the local disease-free survival rate (LSR) for breast RT treatment by using four BC cell cultures (both primary and immortalized), irradiated with clinical X-ray beams. BC cells were chosen on the basis of their receptor profiles, in order to simulate a differential response to RT between triple negative breast and luminal adenocarcinomas. The MCF10A breast epithelial cell line was utilized as a healthy control. We show that an RT plan setup based only on α and ß values could be limiting and misleading. Indeed, two other parameters, the doubling time and the clonogens number, are important to finely predict the tumor response to treatment. Our findings could be tested at a preclinical level to confirm their application as a variant of the classical LQ model, to create a more personalized approach for RT planning.

Indirect cell death and the LQ model in SBRT and SRS.

High-dose hypofractionated SBRT and SRS indirectly kills substantial fractions of tumor cells via causing vascular damage. The LQ formula may work well for certain clinical cases of SBRT and SRS when the indirect/additional tumor cell death secondary to vascular damage is small. However, when the indirect cell death is extensive, the LQ model will underestimate the clinical outcome of SBRT and SRS.

The impact of dose delivery time on biological effectiveness in proton irradiation with various biological parameters.

PURPOSE: The purpose of this study is to evaluate the sublethal damage (SLD) repair effect in prolonged proton irradiation using the biophysical model with various cell-specific parameters of (α/ß)x and T1/2 (repair half time). At present, most of the model-based studies on protons have focused on acute radiation, neglecting the reduction in biological effectiveness due to SLD repair during the delivery of radiation. Nevertheless, the dose-rate dependency of biological effectiveness may become more important as advanced treatment techniques, such as hypofractionation and respiratory gating, come into clinical practice, as these techniques sometimes require long treatment times. Also, while previous research using the biophysical model revealed a large repair effect with a high physical dose, the dependence of the repair effect on cell-specific parameters has not been evaluated systematically. METHODS: Biological dose [relative biological effectiveness (RBE) × physical dose] calculation with repair included was carried out using the linear energy transfer (LET)-dependent linear-quadratic (LQ) model combined with the theory of dual radiation action (TDRA). First, we extended the dose protraction factor in the LQ model for the arbitrary number of different LET proton irradiations delivered sequentially with arbitrary time lags, referring to the TDRA. Using the LQ model, the decrease in biological dose due to SLD repair was systematically evaluated for spread-out Bragg peak (SOBP) irradiation in a water phantom with the possible ranges of both (α/ß)x and repair parameters ((α/ß)x  = 1-15 Gy, T1/2  = 0-90 min). Then, to consider more realistic irradiation conditions, clinical cases of prostate, liver, and lung tumors were examined with the cell-specific parameters for each tumor obtained from the literature. Biological D99% and biological dose homogeneity coefficient (HC) were calculated for the clinical target volumes (CTVs), assuming dose-rate structures with a total irradiation time of 0-60 min. RESULTS: The differences in the cell-specific parameters resulted in considerable variation in the repair effect. The biological dose reduction found at the center of the SOBP with 30 min of continuous irradiation varied from 1.13% to 14.4% with a T1/2 range of 1-90 min when (α/ß)x is fixed as 10 Gy. It varied from 2.3% to 6.8% with an (α/ß)x range of 1-15 Gy for a fixed value of T1/2  = 30 min. The decrease in biological D99% per 10 min was 2.6, 1.2, and 3.0% for the prostate, liver, and lung tumor cases, respectively. The value of the biological D99% reduction was neither in the order of (α/ß)x nor prescribed dose, but both comparably contributed to the repair effect. The variation of HC was within the range of 0.5% for all cases; therefore, the dose distribution was not distorted. CONCLUSION: The reduction in biological dose caused by the SLD repair largely depends on the cell-specific parameters in addition to the physical dose. The parameters should be considered carefully in the evaluation of the repair effect in prolonged proton irradiation.

Assessment of biological dosimetric margin for stereotactic body radiation therapy.

PURPOSE: To develop a novel biological dosimetric margin (BDM) and to create a biological conversion factor (BCF) that compensates for the difference between physical dosimetric margin (PDM) and BDM, which provides a novel scheme of a direct estimation of the BDM from the physical dose (PD) distribution. METHODS: The offset to isocenter was applied in 1-mm steps along left-right (LR), anterior-posterior (AP), and cranio-caudal (CC) directions for 10 treatment plans of lung stereotactic body radiation therapy (SBRT) with a prescribed dose of 48 Gy. These plans were recalculated to biological equivalent dose (BED) by the linear-quadratic model for the dose per fraction (DPF) of d = 3-20 Gy/fr and α / ß = 3 - 10 . BDM and PDM were defined so that the region that satisfied that the dose covering 95% (or 98%) of the clinical target volume was greater than or equal to the 90% of the prescribed PD and BED, respectively. An empirical formula of the BCF was created as a function of the DPF. RESULTS: There was no significant difference between LR and AP directions for neither the PDM nor BDM. On the other hand, BDM and PDM in the CC direction were significantly larger than in the other directions. BCFs of D95% and D98% were derived for the transverse (LR and AP) and longitudinal (CC) directions. CONCLUSIONS: A novel scheme to directly estimate the BDM using the BCF was developed. This technique is expected to enable the BED-based SBRT treatment planning using PD-based treatment planning systems.

Radio-thermo-sensitivity Induced by Gold Magnetic Nanoparticles in the Monolayer Culture of Human Prostate Carcinoma Cell Line DU145.

BACKGROUND AND OBJECTIVE: Prostate cancer is the second cause of death in men worldwide. In this study, the cytotoxic effects of PLGA polymer-coated gold Magnetic Nanoparticles (MGNPs), as a novel treatment to enhance radiation and thermal sensitivity in the presence of hyperthermia (43°C) and electron beam, on DU145 prostate cancer cells were investigated. METHODS: Nanoparticles were characterized using TEM, DLS, XRD and SAED methods. MGNPs entrance into the cells was determined using Prussian blue staining and TEM. Furthermore, the cytotoxic effects of combinatorial treatment modalities were assessed by applying colony and sphere formation assay. RESULTS: Our results revealed that the decrease of colony and sphere numbers after combinatorial treatment of hyperthermia and radiation in the presence of nanoparticles was significantly higher than the other treatment groups (P<0.05). This treatment method proved that it has the capability of eliminating most of the DU145 cells (80-100%), and increased the value of the linear parameter (α) to 4.86 times. CONCLUSION: According to the study, magnetic gold nanoparticles, in addition to having a high atomic number, can effectively transmit heat produced inside them to the adjacent regions under hyperthermia, which increases the effects of radio-thermosensitivity, respectively.

Comparison of hyper- and hypofractionated radiation schemes with IMRT technique in small cell lung cancer: Clinical outcomes and the introduction of extended LQ and TCP models.

PURPOSE: To evaluate the outcomes of 45 Gy/15 fractions/once-daily and 45 Gy/30 fractions/twice-daily radiation schemes utilizing intensity-modulated radiation therapy (IMRT) in extensive stage small cell lung cancer (SCLC), and to build up a new radiobiological model for tumor control probability (TCP) considering multiple biological effects. METHODS: Fifty-eight consecutive patients diagnosed with extensive stage SCLC, treated with chemotherapy and chest irradiation, were retrospectively reviewed. Thirty-seven received hyperfractionated IMRT (Hyper-IMRT, 45 Gy/30 fractions/twice-daily) and 21 received hypofractionated IMRT (Hypo-IMRT, 45 Gy/15 fractions/once-daily). Local progression-free survival (LPFS) and overall survival (OS) were calculated and compared. An extended linear-quadratic (LQ) model, LQRG, incorporating cell repair, redistribution, reoxygenation, regrowth and Gompertzian tumor growth was created based on the clinical data. The TCP model was reformulated to predict LPFS. The classical LQ and TCP models were compared with the new models. Akaike information criterion (AIC) was used to assess the quality of the models. RESULTS: The 2-year LPFS (34.1% vs 27.9%, p = 0.44) and OS (76.9% vs 76.9%, p = 0.26) were similar between Hyper- and Hypo-IMRT patients. According to the LQRG model, the α/ß calculated was 9.2 (95% confidence interval: 8.7-9.9) Gy after optimization. The average absolute and relative fitting errors for LPFS were 9.1% and 18.7% for Hyper-IMRT, and 8.8% and 16.2% for Hypo-IMRT of the new TCP model, compared with 29.1% and 62.3% for Hyper-IMRT, and 30.7% and 65.3% for Hypo-IMRT of the classical model. CONCLUSIONS: Hypo- and Hyper-IMRT resulted in comparable local control in the chest irradiation of extensive stage SCLC. The LQRG model has better performance in predicting the TCP (or LPFS) of the two schemes.

Research of Biological Dose Conversion Platform Based on a Modified Linear Quadratic Model.

The study aimed to develop a novel dose conversion platform by improving linear-quadratic (LQ) model to more accurately describe radiation response for high fraction/acute doses. This article modified the LQ model via piecewise fitting the biological dose curve using different fractionated dose and optimizing the consistency between mathematical model and experimental data to gain a more reasonable transform. That mathematical development of the LQ model further amended certain deviations of various cell curves with high doses and implied the rationality of the present model at low dose range. The modified biologically effective dose model that solved the dilemma of inaccurate LQ model had been used in comparing between hypofractionated and conventional fractioned dose. It has been verified that the calculated values are similar in the treatment of same efficacy, no matter what α/ß is, and provided a more rational explanation for significant differences among various hypofractionations. The equivalent uniform dose based on the subsection function could represent arbitrary inhomogeneous dose distributions including high-dose fractions, providing a foundation for the implementation of detailed evaluation of different cell dose effects.

Determining RBE for development of lung fibrosis induced by fractionated irradiation with carbon ions utilizing fibrosis index and high-LET BED model.

BACKGROUND AND PURPOSES: Carbon ion radiotherapy (CIRT) with raster scanning technology is a promising treatment for lung cancer and thoracic malignancies. Determining normal tissue tolerance of organs at risk is of utmost importance for the success of CIRT. Here we report the relative biological effectiveness (RBE) of CIRT as a function of dose and fractionation for development of pulmonary fibrosis using well established fibrosis index (FI) model. MATERIALS AND METHODS: Dose series of fractionated clinical quality CIRT versus conventional photon irradiation to the whole thorax were compared in C57BL6 mice. Quantitative assessment of pulmonary fibrosis was performed by applying the FI to computed tomography (CT) data acquired 24-weeks post irradiation. RBE was calculated as the ratio of photon to CIRT dose required for the same level of FI. Further RBE predictions were performed using the derived equation from high-linear energy transfer biologically effective dose (high-LET BED) model. RESULTS: The averaged lung fibrosis RBE of 5-fraction CIRT schedule was determined as 2.75 ±â€¯0.55. The RBE estimate at the half maximum effective dose (RBEED50) was estimated at 2.82 for clinically relevant fractional sizes of 1-6 Gy. At the same dose range, an RBE value of 2.81 ±â€¯0.40 was predicted by the high-LET BED model. The converted biologically effective dose (BED) of CIRT for induction of half maximum FI (BEDED50) was identified to be 58.12 Gy3.95. In accordance, an estimated RBE of 2.88 was obtained at the BEDED50 level. The LQ model radiosensitivity parameters for 5-fraction was obtained as αH = 0.3030 ±â€¯0.0037 Gy-1 and ßH = 0.0056 ±â€¯0.0007 Gy-2. CONCLUSION: This is the first report of RBE estimation for CIRT with the endpoint of pulmonary fibrosis in-vivo. We proposed in present study a novel way to mathematically modeling RBE by integrating RBEmax and α/ßL based on conventional high-LET BED conception. This model well predicted RBE in the clinically relevant dose range but is sensitive to the uncertainties of α/ß estimates from the reference photon irradiation (α/ßL). These findings will assist to eliminate current uncertainties in prediction of CIRT induced normal tissue complications and builds a solid foundation for development of more accurate in-vivo data driven RBE estimates.