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 / μ m 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.

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/β 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/β for all risks.

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" W_BE 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). W_BE was evaluated numerically for multiple values of d and r, and for different tumor and NT α/β-ratios. W_BE 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, W_BE decreases steeply initially for d > 2 Gy for late-reacting tissues with (α/β)_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/β-ratios for tumor and late-reacting NT of (α/β)_T  = 10 Gy and (α/β)_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 W_BE . Instead, clinical indications with more similar α/β-ratios of the tumor and dose-limiting NT toxicities [i.e., (α/β)_T  ≈ (α/β)_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 W_BE suggesting a possible benefit of strongly hypofractionated FLASH RT, even for generic α/β-ratios of (α/β)_T  = 10 Gy and (α/β)_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/β 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/β 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/β ratio. Therefore, this study attempted to estimate the α/β 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 β 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/β 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/β 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/β 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/β ratio should be used for calculation.

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/β-ratio of the tumor, (α/β)_T , and NT, (α/β)_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/β-ratios of (α/β)_T  = 10 Gy and (α/β)_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/β-ratios and D T = 2 ( α / β ) .

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.

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.

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

Simple Summary

This study proposes a novel strategy in brain cancer management. Stereotactic radiosurgery delivered by the Gamma Knife was combined with hyperthermia. For the radiobiological modelling of this synergistic treatment modality, we used the linear-quadratic model with temperature-dependent parameters to assess the potential enhancement of the therapeutic outcome. The results indicate that focused intracranial heating can be used to boost the dose to the target. Alternatively, one can conclude that for the same therapeutic effect, hyperthermia can help to minimize the dose undesirably delivered to healthy tissues. This study is also the first to advocate a combination of stereotactic radiosurgery with focused heating and motivates the future development of hyperthermia systems for brain cancer treatment.

Abstract

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.

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.

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 β 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.

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/β)_x and T_1/2 (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/β)_x and repair parameters ((α/β)_x  = 1-15 Gy, T_1/2  = 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 D_99% 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 T_1/2 range of 1-90 min when (α/β)_x is fixed as 10 Gy. It varied from 2.3% to 6.8% with an (α/β)_x range of 1-15 Gy for a fixed value of T_1/2  = 30 min. The decrease in biological D_99% 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 D_99% reduction was neither in the order of (α/β)_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/β=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 D_95% and D_98% 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.

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.

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/β 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.

Radiobiological considerations in combining doses from external beam radiotherapy and brachytherapy for cervical cancer

The recommended radio-therapeutic treatment for cervix cancer consists of a first phase of external beam radiotherapy (EBRT) plus a second phase of brachytherapy (BT), the combined treatment being delivered within 8 weeks. In order to assess a comprehensive dosimetry of the whole treatment, it is necessary to take into account that these two phases are characterized by different spatial and temporal dosimetric distributions, which complicates the task of the summation of the two contributions, EBRT and BT. Radiobiology allows to tackle this issue pragmatically by means of the LQ model and, in fact, this is the usual tool currently in use for this matter. In this work, we describe the rationale behind the summation of the dosimetric contributions of the two phases of the treatment, EBRT and BT, for cervix cancer, as carried out with the LQ model. Besides, we address, from a radiobiological point of view, several important considerations regarding the use of the LQ model for this task. One of them is the analysis of the effect of the overall treatment time in the result of the global treatment. Another important question considered is related to the fact that the capacity of LQ to predict the treatment outcomes is deteriorated when the dose per fraction of the radiotherapic scheme exceeds 6-10 Gy, which is a typical brachytherapy fractionation. Finally, we analyze the influence of the uncertainty and the variability of the main parameters utilized in the LQ model formulation in the assessment of the global dosimetry.

A radiobiological model of reoxygenation and fractionation effects

PURPOSE

The purpose of this study was to develop a radiobiological model of reoxygenation that fulfills the following goals: (a) Quantify the reoxygenation effect for different fractionations (b) Model the hypoxic fraction in tumors as a function of the number of radiation treatments. (c) Develop a simple analytical expression for a reoxygenation term in biological effect calculations.

METHOD

The model considers tumor cells in two compartments: an aerobic (or normoxic) population of cells and a hypoxic population including cells under a range of reduced oxygen concentrations. The surviving fraction is predicted using the linear-quadratic (LQ) model. A hypoxia reduction factor (HRF) is used to quantify reductions in radiosensitivity parameters α_A and β_A as cellular oxygen concentration decreases. The HRF is defined as the ratio of the dose at a specific level of hypoxia to the dose under fully aerobic conditions to achieve equal cell killing. The model assumes that a fraction of the hypoxic cells (Δ) moves from the hypoxic to the aerobic compartment after each daily fraction. As an example, we compare the effect of reoxygenation on biological response for a standard dose fractionation for nonsmall cell lung cancer (NSCLC) (d = 2 Gy, n = 33) to typical fractionations for stereotactic body radiotherapy (SBRT) and other nonstandard fractionations.

RESULTS

The reoxygenation effect is parameterized for biological effect calculations and an analytic expression for the surviving fraction after n daily treatments is derived. The hypoxic fraction either increases or decreases with n depending on the reoxygenation parameter Δ. For certain combinations of parameters, the biological effect of reoxygenation goes as -(n-1) · ln(1-Δ) providing a simple expression that can be introduced in biologically effective dose (BED) calculations. The model is used to compare fractionation schedules and quantitatively interpret results from molecular imaging studies of hypoxia. Based on the comparison of conventional fractionation and hypo- and hyper-fractionation for NSCLC, the value of Δ is estimated to be between 0.1 and 0.2 assuming plausible radiobiological parameters from the literature. This value is consistent with the preliminary analysis of the molecular imaging studies.

CONCLUSIONS

A novel radiobiological model was developed that can be used to evaluate the effect of reoxygenation in fractionated radiotherapy.

Comparison between model-predicted tumor oxygenation dynamics and vascular-/flow-related Doppler indices

PURPOSE

Mathematical modeling is a powerful and flexible method to investigate complex phenomena. It discloses the possibility of reproducing expensive as well as invasive experiments in a safe environment with limited costs. This makes it suitable to mimic tumor evolution and response to radiotherapy although the reliability of the results remains an issue. Complexity reduction is therefore a critical aspect in order to be able to compare model outcomes to clinical data. Among the factors affecting treatment efficacy, tumor oxygenation is known to play a key role in radiotherapy response. In this work, we aim at relating the oxygenation dynamics, predicted by a macroscale model trained on tumor volumetric data of uterine cervical cancer patients, to vascularization and blood flux indices assessed on Ultrasound Doppler images.

METHODS

We propose a macroscale model of tumor evolution based on three dynamics, namely active portion, necrotic portion, and oxygenation. The model parameters were assessed on the volume size of seven cervical cancer patients administered with 28 fractions of intensity modulated radiation therapy (IMRT) (1.8 Gy/fraction). For each patient, five Doppler ultrasound tests were acquired before, during, and after the treatment. The lesion was manually contoured by an expert physician using 4D View^® (General Electric Company - Fairfield, Connecticut, United States), which automatically provided the overall tumor volume size along with three vascularization and/or blood flow indices. Volume data only were fed to the model for training purpose, while the predicted oxygenation was compared a posteriori to the measured Doppler indices.

RESULTS

The model was able to fit the tumor volume evolution within 8% error (range: 3-8%). A strong correlation between the intrapatient longitudinal indices from Doppler measurements and oxygen predicted by the model (about 90% or above) was found in three cases. Two patients showed an average correlation value (50-70%) and the remaining two presented poor correlations. The latter patients were the ones featuring the smallest tumor reduction throughout the treatment, typical of hypoxic conditions. Moreover, the average oxygenation value predicted by the model was close to the average vascularization-flow index (average difference: 7%).

CONCLUSIONS

The results suggest that the modeled relation between tumor evolution and oxygen dynamics was reasonable enough to provide realistic oxygenation curves in five cases (correlation greater than 50%) out of seven. In case of nonresponsive tumors, the model failed in predicting the oxygenation trend while succeeded in reproducing the average oxygenation value according to the mean vascularization-flow index. Despite the need for deeper investigations, the outcomes of the present work support the hypothesis that a simple macroscale model of tumor response to radiotherapy is able to predict the tumor oxygenation. The possibility of an objective and quantitative validation on imaging data discloses the possibility to translate them as decision support tools in clinical practice and to move a step forward in the treatment personalization.

Radiobiology of hypofractionated stereotactic radiotherapy: what are the optimal fractionation schedules?

In hypofractionated stereotactic radiotherapy (SRT), high doses per fraction are usually used and the dose delivery pattern is different from that of conventional radiation. The daily dose is usually given intermittently over a longer time compared with conventional radiotherapy. During prolonged radiation delivery, sublethal damage repair takes place, leading to the decreased effect of radiation. In in vivo tumors, however, this decrease in effect may be counterbalanced by rapid reoxygenation. Another issue related to hypofractionated SRT is the mathematical model for dose evaluation and conversion. The linear-quadratic (LQ) model and biologically effective dose (BED) have been suggested to be incorrect when used for hypofractionation. The LQ model overestimates the effect of high fractional doses of radiation. BED is particularly incorrect when used for tumor responses in vivo, since it does not take reoxygenation into account. Correction of the errors, estimated at 5-20%, associated with the use of BED is necessary when it is used for SRT. High fractional doses have been reported to exhibit effects against tumor vasculature and enhance host immunity, leading to increased antitumor effects. This may be an interesting topic that should be further investigated. Radioresistance of hypoxic tumor cells is more problematic in hypofractionated SRT, so trials of hypoxia-targeted agents are encouraged in the future. In this review, the radiobiological characteristics of hypofractionated SRT are summarized, and based on the considerations, we would like to recommend 60 Gy in eight fractions delivered three times a week for lung tumors larger than 2 cm in diameter.

Applicability of the linear-quadratic model to single and fractionated radiotherapy schedules: an experimental study

The aim of this study was to examine the applicability of the linear-quadratic (LQ) model to single and fractionated irradiation in EMT6 cells. First, the α/β ratio of the cells was determined from single-dose experiments, and a biologically effective dose (BED) for 20 Gy in 10 fractions (fr) was calculated. Fractional doses yielding the same BED were calculated for 1-, 2-, 3-, 4-, 5-, 7-, 15- and 20-fraction irradiation using LQ formalism, and then irradiation with these schedules was actually given. Cell survival was determined by a standard colony assay. Differences in cell survival between pairs of groups were compared by t-test. The α/β ratio of the cells was 3.18 Gy, and 20 Gy in 10 fr corresponded to a BED3.18 of 32.6 Gy. The effects of 7-, 15- and 20-fraction irradiation with a BED3.18 of 32.6 Gy were similar to those of the 10-fraction irradiation, while the effects of 1- to 5-fraction irradiation were lower. In this cell line, the LQ model was considered applicable to 7- to 20-fraction irradiation or doses per fraction of 2.57 Gy or smaller. The LQ model might be applicable in the dose range below the α/β ratio.

Can the two mechanisms of tumor cell killing by radiation be exploited for therapeutic gain?

The radiation killing of tumor cells by ionizing radiation is best described by the linear-quadratic (LQ) model. Research into the underlying mechanisms of α- and β-inactivation has suggested that different molecular targets (DNA in different forms) and different microdosimetric energy deposits (spurs versus electron track-ends) are involved. Clinical protocols with fractionated doses of about 2.0 Gy/day were defined empirically, and we now know that they produce cancer cures mainly by the α-inactivation mechanism. Radiobiology studies indicate that α and β mechanisms exhibit widely different characteristics that should be addressed upfront as clinical fractionation schemes are altered. As radiation treatments attempt to exploit the advantages of larger dose fractions over shorter treatment times, the LQ model can be used to predict iso-effective tumor cell killing and possibly iso-effective normal tissue complications. Linking best estimates of radiobiology and tumor biology parameters with tumor control probability (TCP) and normal tissue complication probability (NTCP) models will enable us to improve and optimize cancer treatment protocols, delivering no more fractions than are strictly necessary for a high therapeutic ratio.

Critical dose and toxicity index of organs at risk in radiotherapy: analyzing the calculated effects of modified dose fractionation in non-small cell lung cancer

To increase the efficacy of radiotherapy for non-small cell lung cancer (NSCLC), many schemes of dose fractionation were assessed by a new "toxicity index" (I), which allows one to choose the fractionation schedules that produce less toxic treatments. Thirty-two patients affected by non resectable NSCLC were treated by standard 3-dimensional conformal radiotherapy (3DCRT) with a strategy of limited treated volume. Computed tomography datasets were employed to re plan by simultaneous integrated boost intensity-modulated radiotherapy (IMRT). The dose distributions from plans were used to test various schemes of dose fractionation, in 3DCRT as well as in IMRT, by transforming the dose-volume histogram (DVH) into a biological equivalent DVH (BDVH) and by varying the overall treatment time. The BDVHs were obtained through the toxicity index, which was defined for each of the organs at risk (OAR) by a linear quadratic model keeping an equivalent radiobiological effect on the target volume. The less toxic fractionation consisted in a severe/moderate hyper fractionation for the volume including the primary tumor and lymph nodes, followed by a hypofractionation for the reduced volume of the primary tumor. The 3DCRT and IMRT resulted, respectively, in 4.7% and 4.3% of dose sparing for the spinal cord, without significant changes for the combined-lungs toxicity (p < 0.001). Schedules with reduced overall treatment time (accelerated fractionations) led to a 12.5% dose sparing for the spinal cord (7.5% in IMRT), 8.3% dose sparing for V20 in the combined lungs (5.5% in IMRT), and also significant dose sparing for all the other OARs (p < 0.001). The toxicity index allows to choose fractionation schedules with reduced toxicity for all the OARs and equivalent radiobiological effect for the tumor in 3DCRT, as well as in IMRT, treatments of NSCLC.

Effectiveness of two different HDR brachytherapy regimens with the same BED value in cervical cancer

PURPOSE

To analyze the effectiveness of biologically effective dose (BED) in two different regimens of HDR brachytherapy keeping the same total BED to point A and to compare the relationship of overall treatment time in terms of local control and bladder and rectal complications.

MATERIAL AND METHODS

The study included two groups comprising a total of 90 cervical cancer patients who underwent external beam radiotherapy (EBRT) followed by HDR intracavitary brachytherapy (ICBT). EBRT treatment was delivered by a Co-60 teletherapy unit to a prescribed dose of 45 Gy with 1.8 Gy per fraction in 25 fractions over a period of five weeks. Parallel opposed anterior-posterior (AP/PA) fields with no central shielding were used, followed by the HDR ICBT dose, to point A, of either two fractions of 9.5 Gy with a gap of 10 days, or three fractions of 7.5 Gy with a gap of 7 days between the fractions. Gemcitabine (dose of 150 mg/m²) was given weekly to all the patients as a radiosensitizer. The calculate BED₃ to point A was almost the same in both groups to keep the same late complication rates. The doses, and BED₁₀ and BED₃, were calculated at different bladder and rectal point as well as at the lymphatic trapezoid points. During and after treatment patients were evaluated for local control and complications for 24 months.

RESULTS AND CONCLUSIONS

Doses and BEDs at different bladder, rectal and lymphatic trapezoid points, local control, and complications in both HDR ICBT groups did not have statistically significant differences (p > 0.05). Both HDR ICBT schedules are well tolerable and equally effective.