Linear-quadratic Equation Research Articles

A mathematical model of brain tumour response to radiotherapy and chemotherapy considering radiobiological aspects

Glioblastoma is the most frequent and malignant brain tumour. For many years, the conventional treatment has been maximal surgical resection followed by radiotherapy (RT), with a median survival time of less than 10 months. Previously, the use of adjuvant chemotherapy (given after RT) has failed to demonstrate a statistically significant survival advantage. Recently, a randomized phase III trial has confirmed the benefit of temozolomide (TMZ) and has defined a new standard of care for the treatment of patients with high-grade brain tumours. The results showed an increase of 2.5 months in median survival, and 16.1% in 2 year survival, for patients receiving RT with TMZ compared with RT alone. It is not clear whether the major benefit of TMZ comes from either concomitant administration of TMZ with RT, or from six cycles of adjuvant TMZ, or both. The objectives were to develop our original model, which addressed survival after RT, to construct a new module to assess the potential role of TMZ from clinical data, and to explore its synergistic contribution in addition to radiation. The model has been extended to include radiobiological parameters. The addition of the linear quadratic equation to describe cellular response to treatment has enabled us to quantify the effects of radiation and TMZ in radiobiological terms. The results indicate that the model achieves an excellent fit to the clinical data, with the assumption that TMZ given concomitantly with RT synergistically increases radiosensitivity. The alternative, that the effect of TMZ is due only to direct cell killing, does not fit the clinical data so well. The addition of concomitant TMZ appears to change the radiobiological parameters. This aspect of our results suggests possible treatment developments. Our observations need further evaluations in real clinical trials, may suggest treatment strategies for new trials, and inform their design.

PCR-based Analysis of Radiation-induced Chromosome Aberrations

The majority of radiation-induced toxicity in carcinoma is linked to aberrant mitoses, a “mitotic catastrophe” driven by chromosomal aberrations, such as dicentrics. Cell survival analysis modeled the production of these rearrangements using a linear quadratic equation with two coefficients, α and β. In this widely used interpretation of cell survival curves, the α (linear) coefficient relates to damage affecting chromosomes simultaneously while the β (square) term describes chromosome damage separated in time.

The relationship between altitude of meteorological stations and average monthly and annual precipitation

The aim of this study was to prove that altitudinal variability of average monthly and annual precipitation is better summarised when the altitude observed within a radius of several kilometres around a meteorological station is taken into consideration, instead of the altitude of the station itself. The use of the variable Z′, which combines the altitude of the closest mountain with its distance from the station, is compared against the use of altitude alone in simple linear and multiple quadratic regression equations for the altitudinal interpolation of precipitation over Greece. The data-set comprised precipitation observations from 516 meteorological stations. The comparison between the two variables is discussed on the basis of the resulting determination coefficients (R2) and standard errors of estimate (S). For all seasons, except summer, it was found that the variable Z′ improves the predictive ability of the regression equations, thus showing its potential for further use in interpolation procedures.

SU‐FF‐T‐492: Mechanistic Formulation of a Lineal‐Quadratic‐Linear (LQL) Model: Split‐Dose Experiments and Exponentially Decaying Sources

Purpose: In recent years, several models were proposed that modify the standard linear‐quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. We consider a mechanistic formulation of a LQL model in the case of split‐dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose‐rate and fractionation with only one additional parameter. Method and Materials: We use a compartmental formulation of the LQL model from the literature. We analytically solve the model's differential equations for the case of a split‐dose experiment and for an exponentially decaying source. We compare the solutions of the survival fraction with the standard LQ equations and with the Lethal‐Potentially Lethal (LPL) model. Results: In the case of the split‐dose experiment, the LQL model predicts a recovery ratio (RR) as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter β. The LQL solution for the split‐dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half‐life of the source is much larger than the characteristic repair time, which is the clinically relevant case. Conclusion: The compartmental formulation of the LQL model can be used for arbitrary dose‐rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split‐doses is also predicted.

Does Three-Dimensional External Beam Partial Breast Irradiation Spare Lung Tissue Compared With Standard Whole Breast Irradiation?

To determine whether three-dimensional conformal partial breast irradiation (3D-PBI) spares lung tissue compared with whole breast irradiation (WBI) and to include the biologically equivalent dose (BED) to account for differences in fractionation. Radiotherapy treatment plans were devised for WBI and 3D-PBI for 25 consecutive patients randomized on the NSABP B-39/RTOG 0413 protocol at Mayo Clinic in Jacksonville, Florida. WBI plans were for 50 Gy in 25 fractions, and 3D-PBI plans were for 38.5 Gy in 10 fractions. Volume of ipsilateral lung receiving 2.5, 5, 10, and 20 Gy was recorded for each plan. The linear quadratic equation was used to calculate the corresponding dose delivered in 10 fractions and volume of ipsilateral lung receiving these doses was recorded for PBI plans. Ipsilateral mean lung dose was recorded for each plan and converted to BED. There was a significant decrease in volume of lung receiving 20 Gy with PBI (median, 4.4% vs. 7.5%; p < 0.001), which remained after correction for fractionation (median, 5.6% vs. 7.5%; p = 0.02). Mean lung dose was lower for PBI (median, 3.46 Gy vs. 4.57 Gy; p = 0.005), although this difference lost significance after conversion to BED (median, 3.86 Gy(3) vs 4.85 Gy(3), p = 0.07). PBI plans exposed more lung to 2.5 and 5 Gy. 3D-PBI exposes greater volumes of lung tissue to low doses of radiation and spares the amount of lung receiving higher doses when compared with WBI.

Late chest wall toxicity after MammoSite ® breast brachytherapy

Purpose Accelerated partial breast irradiation (APBI) with the MammoSite ® breast brachytherapy (MBB) system is being investigated as an alternative to whole breast radiation in breast conservation therapy (BCT) at multiple centers worldwide. The newness of MBB means a complete understanding of long-term toxicity, particularly involving the chest wall, has yet to be completely articulated. We report the first pathologic rib fractures associated with MBB and dosimetric analysis of the original treatment plans. Methods and Materials As part of ongoing quality assurance, we reviewed the records of 129 sequential patients who underwent MBB for breast cancer and identified those who subsequently had clinically significant and radiographically documented rib fracture(s) involving the ipsilateral chest wall. Equivalent tolerance doses yielding a 5% and 50% risk of rib toxicity within 5 years from treatment with 10 fractions (as with MBB) were previously calculated using the linear quadratic equation based on 2 Gy per fraction treatments delivered to one-third of the rib volume (TD5/5 = 37 Gy; TD50/5 = 44 Gy). The original radiation therapy plans were evaluated vis-à-vis the plane films or PET/CT images documenting the osseous abnormalities and presenting complaints to find the specific fractured ribs. The specific effected ribs were contoured on the planning CT in “bone windows” using the Nucletron MicroSelectron-classic V2 (Nucletron B.V., Veenendaal, The Netherlands) for this analysis and the original patient treatments. With these datasets, we determined the dose–volume characteristics of the effected ribs including maximal dose encompassing the entire rib on one CT slice, V 20Gy, V 30Gy, V 37Gy, V 44Gy , D 50, D 25, and D 5 (the mean dose to 50%, 25%, and 5% of the rib). Results Between May 2002 and August 2007, three of 105 patients with a minimum of 6-months follow-up who underwent adjuvant APBI by MBB were found to have a total of five treatment-related rib fractures. The average dose–volume characteristics from the original plans were as follows: D 50 = 22.1 Gy, D 25 = 32.2 Gy, D 5 = 41.6 Gy, max dose to 1 cc = 34.8, D max (to 0.1 cc) = 45.6 Gy, V 20 Gy = 57.4%, V 30 Gy = 30.8%, V 37 Gy = 15.9%, V 44 Gy = 6.6%, and max dose through rib = 35.8 Gy. Two patients sustained two rib fractures and 1 patient had a single rib fracture. Four of five fractures occurred in postmenopausal patients and two of five fractures occurred in a patient with a history of osteoporosis and exposure to adjuvant chemotherapy. Conclusions Fractures occurred in ribs with V 37 Gy and V 44 Gy each well below 33%. As long-term toxicity data accrue from APBI series, the traditional models for estimating the biologic equivalent dose may benefit from refinements that specifically address the unique radiobiologic and physical properties intrinsic to high-dose-rate brachytherapy for breast conservation therapy.

General properties of different models used to predict normal tissue complications due to radiation

In the current study the author analyzes general properties of three different models used to predict normal tissue complications due to radiation: (1) Surviving fraction of normal cells in the framework of the linear quadratic (LQ) equation for cell kill, (2) the Lyman-Kutcher-Burman (LKB) model for normal tissue complication probability (NTCP), and (3) generalized equivalent uniform dose (gEUD). For all considered cases the author assumes fixed average dose to an organ of interest. The author's goal is to establish whether maximizing dose uniformity in the irradiated normal tissues is radiobiologically beneficial. Assuming that NTCP increases with increasing overall cell kill, it is shown that NTCP in the LQ model is maximized for uniform dose. Conversely, NTCP in the LKB and gEUD models is always smaller for a uniform dose to a normal organ than that for a spatially varying dose if parameter n in these models is small (i.e., n <1). The derived conflicting properties of the considered models indicate the need for more studies before these models can be utilized clinically for plan evaluation and/or optimization of dose distributions. It is suggested that partial-volume irradiation can be used to establish the validity of the considered models.

A simple algebraic approximation to the Erlang loss system

We use Palm calculus to derive a simple, intuitive system of two linear-quadratic equations and two unknowns, whose algebraic solution yields Harel’s (1988) upper bound to the Erlang loss probability. We then derive a sequence of progressively stronger systems of equations, which eventually become exact. We provide two example applications.

In vitro study of cell survival following dynamic MLC intensity‐modulated radiation therapy dose deliverya)

The possibility of reduced cell kill following intensity-modulated radiation therapy (IMRT) compared to conventional radiation therapy has been debated in the literature. This potential reduction in cell kill relates to prolonged treatment times typical of IMRT dose delivery and consequently increased repair of sublethal lesions. While there is some theoretical support to this reduction in cell kill published in the literature, direct experimental evidence specific to IMRT dose delivery patterns is lacking. In this study we present cell survival data for three cell lines: Chinese hamster V79 fibroblasts, human cervical carcinoma, SiHa and colon adenocarcinoma, WiDr. Cell survival was obtained for 2.1 Gy delivered as acute dose with parallel-opposed pair (POP), irradiation time 75 s, which served as a reference; regular seven-field IMRT, irradiation time 5 min; and IMRT with a break for multiple leaf collimator (MLC) re-initialization after three fields were delivered, irradiation time 10 min. An actual seven-field dynamic MLC IMRT plan for a head and neck patient was used. The IMRT plan was generated for a Varian EX or iX linear accelerator with 120 leaf Millenium MLC. Survival data were also collected for doses 1X, 2X, 3X, 4X, and 5x 2.1 Gy to establish parameters of the linear-quadratic equation describing survival following acute dose delivery. Cells were irradiated inside an acrylic cylindrical phantom specifically designed for this study. Doses from both IMRT and POP were validated using ion chamber measurements. A reproducible increase in cell survival was observed following IMRT dose delivery. This increase varied from small for V79, with a surviving fraction of 0.8326 following POP vs 0.8420 following uninterrupted IMRT, to very pronounced for SiHa, with a surviving fraction of 0.3903 following POP vs 0.5330 for uninterrupted IMRT. When compared to IMRT or IMRT with a break for MLC initialization, cell survival following acute dose delivery was significantly different, p < 0.05, in three out of six cases. In contrast, when cell survival following IMRT was compared to that following IMRT with a break for MLC initialization the difference was always statistically insignificant. When projected to a 30 fraction treatment, dose deficit to bring cell survival to the same value as in POP was calculated as 4.1, 24.9, and 31.1 Gy for V79, WiDr, and SiHa cell lines, respectively. The dose deficit did not relate to the alpha/beta ratio obtained in this study for the three cell lines. Clinical data do not show reduction in local control following IMRT. Possible reasons for this are discussed. The obtained data set can serve as a test data set for models designed to explore the effect of dose delivery prolongation/fractionation in IMRT on radiation therapy outcome.

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.

Hypofractionated stereotactic radiotherapy combined with topotecan in recurrent malignant glioma

Purpose: To assess hypofractionated stereotactic radiotherapy (H-SRT) with concurrent topotecan in patients with recurrent malignant glioma. Methods and Materials: Between February 1998 and December 2001, 25 patients with recurrent malignant glioma were treated in a phase I-II study (8 females and 17 males; median age, 45 years; range, 11–66 years; median Karnofsky performance status, 80%, range, 50–100%; median Mini Mental Standard Examination score, 25 points; range, 10–30 points). Of the 25 patients, 20% had World Health Organization Grade III and 80% World Health Organization Grade IV glioma. All patients had been treated previously by external beam radiotherapy with 54.4 Gy in 34 fractions twice daily, at least 6 h apart, within 3.5 weeks or 60 Gy in 30 fractions within 6 weeks. In addition, 84% had already received at least one chemotherapy regimen for recurrence. The median H-SRT dose at the 80% isodose was 25 Gy, and the maximal dose was 30 Gy delivered in five to six fractions on consecutive days. Topotecan (1.1 mg/m 2 /d) was given as a continuous i.v. infusion during H-SRT. Depending on the toxicity and compliance, patients received an additional 48 topotecan courses. Results: For all patients, the actuarial median progression-free survival was 10.5 months (range, 1.4–47.8 months), the median functional survival was 12.6 months (range, 1.6–49.5 months), and the median overall survival was 14.5 months (range, 3–56.4 months). Twelve percent of patients developed presumed adverse radiation effects (Radiation Therapy Oncology Group Grade 2). According to the Common Toxicity Criteria, version 2.0, no topotecan-related Grade 4 toxicity was noted. Grade 3 neutropenia was documented after 14 and Grade 3 thrombopenia after 12 courses. Conclusion: H-SRT with topotecan is feasible and well-tolerated in patients with recurrent high-grade glioma and results in similar survival compared with other repeat treatment modalities.

Dynamic Simulation of Multibody Systems Using a New State-Time Methodology

This paper presents a new methodology demonstrating the feasibility and advantages of a state-time formulation for dynamic simulation of complex multibody systems which shows potential advantages for exploiting massively parallel computing resources. This formulation allows time to be discretized and parameterized so that it can be treated as a variable in a manner similar to the system state variables. As a consequence of such a state-time discretization scheme, the system of governing equations yields to a set of loosely coupled linear-quadratic algebraic equations that is well-suited in structure for some families of nonlinear algebraic equations solvers. The goal of this work is to develop efficient multibody dynamics algorithm that is extremely scalable and better able to fully exploit anticipated immensely parallel computing machines (tera flop, peta flop and beyond) made available to it.

Re-Irradiation of Brain Metastases and Metastatic Spinal Cord Compression: Clinical Practice Suggestions

The recent improvements of therapeutic approaches in oncology have allowed a certain number of patients with advanced disease to survive much longer than in the past. So, the number of cases with brain metastases and metastatic spinal cord compression has increased, as has the possibility of developing a recurrence in areas of the central nervous system already treated with radiotherapy. Clinicians are reluctant to perform re-irradiation of the brain, because of the risk of severe side effects. The tolerance dose for the brain to a single course of radiotherapy is 50-60 Gy in 2 Gy daily fractions. New metastases appear in 22-73% of the cases after whole brain radiotherapy, but the percentage of reirradiated patients is 3-10%. An accurate selection must be made before giving an indication to re-irradiation. Patients with Karnofsky performance status > 70, age < 65 years, controlled primary and no extracranial metastases are those with the best prognosis. The absence of extracranial disease was the most significant factor in conditioning survival, and maximum tumor diameter was the only variable associated with an increased risk of unacceptable acute and/or chronic neurotoxicity. Re-treatment of brain metastases can be done with whole brain radiotherapy, stereotactic radiosurgery or fractionated stereotactic radiotherapy. Most patients had no relevant radiation-induced toxicity after a second course of whole brain radiotherapy or stereotactic radiosurgery. There are few data on fractionated stereotactic radiotherapy in the re-irradiation of brain metastases. In general, the incidence of an "in-field" recurrence of spinal metastasis varies from 2.5-11% of cases and can occur 2-40 months after the first radiotherapy cycle. Radiation-induced myelopathy can occur months or years (6 months-7 years) after radiotherapy, and the pathogenesis remains obscure. Higher radiotherapy doses, larger doses per fraction, and previous exposure to radiation could be associated with a higher probability of developing radiation-induced myelopathy. Experimental data indicate that also the total dose of the first and second radiotherapy, interval to re-treatment, length of the irradiated spinal cord, and age of the treated animals influence the risk of radiation-induced myelopathy. An alpha/beta ratio of 1.9-3 Gy could be generally the reference value for fractionated radiotherapy. However, when fraction sizes are up to 5 Gy, the linear-quadratic equation become a less valid model. The early diagnosis of relapse is crucial in conditioning response to re-treatment.

SU-FF-T-379: Biological Radial Dose Functions for Brachytherapy Sources

Purpose: Brachytherapy is often used in combination with external-beam-radiotherapy to deliver a tumoricidal dose, while respecting critical organ tolerances. Its biological equivalence to an external beam dose fractionation has conventionally been considered via only the prescribed dose, preventing the 3D summation of brachytherapy and external beam dose distributions. We investigate a methodology that calculates a brachytherapy dose distribution biologically equivalent to an external beam dose fractionation schedule using a commercial treatment-planning system that has only conventional brachytherapy dose calculation models. Method and Materials: Dose distributions from high-dose-rate (HDR) brachytherapy treatments, including point-source, line-source, planar, and intracavitary gynecological implants were converted to their biological equivalents for corresponding external beam dose fractionations using the linear quadratic equation and an α/β ratio of 10. The radial-dose-function (RDF) values of an Ir-192 source were modified (BRDF) to yield these biologically-equivalent dose distributions using the conventional dose calculation formalism. Use of this formalism was demonstrated by planning an IMRT treatment of cervical cancer constrained by delivered HDR dose distributions. Results: The BRDFs of HDR Ir-192 treatments vary as a function of external beam dose fractionations, the α/β ratio used, and implant geometry. BRDF's dependence on implant geometry is due to the nonlinearity of the linear-quadratic equation. BRDF's have non-unitary values at 1 cm from the source, depending on the equivalence of prescribed external beam and brachytherapy doses. Comparisons between the biological-equivalent dose distributions and the approximations obtained using BRDF showed excellent agreement. Conclusion: A method is proposed to allow calculation of biologically-equivalent brachytherapy dose distribution in commercial treatment planning systems. Preliminary studies using the BRDF demonstrated its usefulness in the IMRT treatment planning when constrained by delivered brachytherapy dose distribution. The process can also be used to review brachytherapy implant dose distributions at conventional external-beam fractionation schedules.

WE-E-T-617-04: IMRT and Brachytherapy for Cervical Cancer

Purpose: Radiotherapy of cervical cancer is usually delivered through a combination of external-beam and intracavitary-brachytherapy treatments. A portion of the external-beam treatment is often delivered with a midline block, either straight or tapered at the edges, to avoid overdosing the brachytherapy dose distribution. This study investigates the replacement of the midline block with intensity-modulated-radiation-therapy (IMRT), matching the IMRT dose to the biologically-equivalent brachytherapy dose distribution, while additionally achieving optimized target coverage and minimized critical organ doses. Method and Materials: CT scans of a female pelvic phantom were imported into a commercial treatment planning system (TPS) to calculate the dose distribution of a high-dose-rate (HDR) tandem and ovoid treatment delivering 650cGy to point A. A planning target volume (PTV), the rectum, and the bladder were segmented. The brachytherapy dose distribution was converted to its biologically-equivalent dose distribution, at 180cGy daily fractions, using the linear-quadratic equation and an α/β ratio of 10, by modifying the HDR source's radial-dose function (RDF) values. A set of IMRT fields, at 180cGy/fraction, was planned to deliver a dose of 720cGy to the target for each HDR fraction while accounting for implant dose. The IMRT fields geometry included two scenarios; AP/PA parallel-opposed fields, mimicking the conventional split-field pelvis treatments with a midline block, and a 5-field coplanar beam arrangement that had the potential to improve target coverage and reduce critical-organ doses. Results: The single-source RDF values were successfully modified to compute the biologically-equivalent dose distribution of the HDR treatment. The TPS was able to calculate IMRT field fluence maps, in both scenarios, to obtain dose volume histograms of the target and the critical organs as prescribed. Conclusion: It was demonstrated that IMRT doses distributions for cervical cancer treatment can be biologically matched to brachytherapy dose distributions, thus improving target coverage and sparing critical structures.

Chest wall dose in MammoSite™ breast brachytherapy: Radiobiologic estimations of late complication risk based on dose–volume considerations

Purpose To estimate the risk of late effects in women treated with MammoSite™ brachytherapy (MBT), the balloon catheters of which were placed near the ribs. Methods and Materials Upon reviewing 93 plans, 16 patients (17%) treated with MBT were considered to have received a high chest wall dose (≥120% isodose line in contact with a rib). A dose–volume histogram was generated for this rib, and its distance from the MBT balloon measured. Using the linear quadratic equation, the equivalent dose, delivered in 10 fractions, to the dose that causes a 5% and 50% risk of rib late effects at 5 years using 2 Gy per fraction, was calculated to be 37 and 44 Gy, respectively. The rib volume receiving greater than or equal to these doses (V37 and V44) was correlated to the balloon-to-rib distance. Chest wall signs, symptoms, and radiologic findings for all 16 patients were recorded. Results The median balloon-to-rib distance was 4.8 mm. The median values of V37 and V44 were 13.5% and 3.3%, respectively. All patients with a V37 ≥ 15% and V44 ≥ 5% had a minimum balloon-to-rib distance of <5 mm. Two patients reported treatment-related chest wall tenderness (both had balloons placed <5 mm from the chest wall), but neither presented with radiologic complications. Conclusions Sixteen patients considered to receive relatively high chest wall doses had less than one-third of their primary rib volume being exposed to the estimated TD 5/5 and TD 50/5 doses. Therefore, we estimate the risk of late effects in women treated with MBT, the balloon catheters of which placed near the ribs were negligible, and believe that MBT remains a safe and effective treatment for selected patients with early stage breast cancer.

Influence of overall treatment time and radiobiological parameters on biologically effective doses in cervical cancer patients treated with radiation therapy alone

The aim of the study was to examine the influence of overall treatment time (OTT) on the value of calculated biological effective doses (BEDs) for different biological variables. These variables were: tumour proliferation rate, different cell radiosensitivity (α=0.2, 0.3, and 0.4 /Gy), and different start time for repopulation (Tk=21, 28, and 35 days). Also the influence of age (≤50 years >), Hb level (≤116 g/l>), tumor proliferation rate (bromodeoxyuridine labelling index; BrdUrdLI), and DNA ploidy on survival after shorter (≤60 days) or longer (>60 days) OTT was investigated. The study included 229 patients with cervix carcinoma treated entirely by standard radiotherapy (RT) (external beam RT plus low-medium dose-rate (LDR/MDR) brachytherapy (BT) at the Center of Oncology in Krakow. The linear quadratic equation was used to calculate BED, which is proportional to log cell kill. BEDs 10 (for tumours) were calculated with consideration of OTT for each patient and tumour proliferation rate (standardized potential doubling time; standardized Tpot) based on BrdUrdLI assessed on biopsy material before RT. Median OTT was 90 days (range 30–210). The mean calculated total BED for point A for tumour and ‘early reactions’ was equal to 103.0 Gy10. The longest median survival time—52 months—was seen for patients treated with OTT ≤60 days. If OTT exceeded 90 days to more than 120 days, loss in BED10 for relatively radiosensitive tumours (α=0.3–0.4/Gy and Tk=28 days) was equal to 0.37–0.26 Gy/day. However, for radioresistant tumours (α=0.2/Gy) it was 0.6 Gy/day. For fast proliferating tumours (BrdUrdLI >8.8%) BED loss was 1.4 Gy/day and for slowly proliferating tumours (BrdUrdLI ≤8.8%) it was 0.2 Gy/day. Assuming shorter (21 days) or longer (35 days) periods for Tk and relatively radiosensitive tumours similar BED loss of 0.38 Gy/day was observed. Kaplan–Meier analysis revealed that OTT ≤60 days was a significant prognostic factor for overall survival (OS) (p=0.019), disease-free survival (DFS) (p=0.0173), and local control (LC) (p=0.011). BED10 had significant influence on survival (p=0.047). Cox multivariate analysis revealed that for OTT shorter than 60 days the only favourable significant parameters were: age >50 years (p=0.003) and high Hb level (>116 g/l) (p=0.041). For longer treatments (OTT >60 days) the unfavourable parameters were: age ≤50 years (p=0.037), BrdUrdLI ≤8.8% (p=0.003), tumour aneuploidy (p=0.043), and BED10 ≤103 Gy (p=0.017). The examined tumour biological parameters should be taken into account for RT and provide a basis for adjuvant RT.

Does the dose protraction inherent to IMRT decreases tumor cell killing in vitro

To determine whether protracted dose delivery inherent to IMRT treatments results in decreased tumor cell killing. IMRT aims to improve the therapeutic ratio of conventional radiotherapy by optimizing the delivery of ionizing radiation (IR) using a multileaf-collimator (MLC), tailoring radiation fluence to patient treatment fields. In comparison to 3D-CRT, IMRT treatment times are prolonged (10–40 minutes) depending on the hardware, software, and planning systems employed. Previously reported data predict a decrease in the biologically effective dose (BED) of IMRT due to such factors as decreased dose rate (5cGy - 100cGy/minute) when compared with 3D-CRT (200–800cGy/min) and partial shielding of the target volume during IMRT. Herein we describe an in vitro system that allows delivery of an IMRT head and neck plans from patients using SQ-20b human tumor cells to compare clonogenic survival after radiotherapy delivered via conventional or IMRT plans. From our data, a predictive model of tumor cell death was designed. An IMRT phantom was designed to mimic a previously treated patient with head and neck cancer. The phantom was constructed to accommodate a 150mm tissue culture flask (T-150) which was located so as to act as a surrogate for the patients gross tumor volume (GTV). 24 hours prior to the first fractionated treatment (Fx), SQ-20B tumor cells (D0 = 2.3 Gy) were plated at varying densities in T-150 flasks which were filled with media to approximately 80% capacity. 7-Field IMRT plans were designed that varied only in lead movement delay to vary treatment times from 10–40 minutes. Opposed lateral plans (OLp) with similar DVHs were designed and were delivered at 400cGy/min. Treatments to the cells were delivered in 180cGy daily Fx for a total of 5 Fx with both the IMRT and OLp for comparison purposes. TLDs verified that all plans delivered dose to within a 5% error. Seven days after the last fractionated treatment, crystal violet stained colonies >100 cells were scored as viable. At least 1200 colonies were collected per time point. Initial in-vitro survival data demonstrates that survival of tumor cells was increased 30% (p < 0.02 Mann-Whitney Rank Sum Test) with IMRT treatments of 40 minutes (41% survival) compared with opposed lateral treatment (33%) with little change when treatments were reduced to 10 minutes. The linear-quadratic equation was modified to account for repair of sublethal damage between the delivery of individual fields: S(D) = exp[-n(αd+βG(t)d2)+γT] where, α,β characterize cell radiosensitivity, γ - effective repopulation rate, T-duration of treatment, G(t) -dose protraction factor, n - # of fractions (5). Using the model, prolonged treatments (>20 minutes) decrease cell killing by 1–3% /Fx. When coupled with Fx therapy, a 50–140% (α/β dependent) decrease in cell kill is observed (Table). IMRT plans that protract treatment times beyond 10–15 minutes significantly decrease tumor cell killing in Fx therapy. Protracted dose delivery coupled with shielding of some areas of the tumor from dose during the treatment may account for these experimental observations. Current studies are attempting to optimize the gantry angles and fields utilized in order to maximize tumor cell killing.

Accelerated IMRT with concomitant boost after breast-conserving therapy (BCT): Preliminary clinical results and dose volume histogram (DVH) analysis

Accelerated IMRT with concomitant boost after breast-conserving therapy (BCT): Preliminary clinical results and dose volume histogram (DVH) analysis

Alteration of cellular DNA-repair by interferon-beta

Type I interferons have been investigated as radiosensitizer over a long time. Recent clinical data in pancreatic cancer are suggesting an enhanced efficacy of radiation (XRT) and chemotherapy by the simultaneous application with IFN-alpha. On the other hand, a randomized clinical study on the addition of IFN-beta to XRT for the treatment of lung cancer showed a negative result. These observations are suggesting, that the interaction of XRT with type I interferons might be determined by the genetic background of the treated tumors. Since the enhancement of radiation by IFN-beta is associated with an increase of the alpha-component of the survival curves; we assumed that the interaction of IFN-beta with ionizing irradiation is characterized by interference with DNA repair. A number of cell lines representing normal tissue and different tumor types and with known genetic alterations in DNA repair (DNA-PK and Brca2) or cell cycle control (TP53, RB) were used. Cellular repair capacity was modulated by wortmannin (WMN) treatment (in M059K cells) or PRCDK gene transfection (in M059J cells). For experiments, cells were incubated with natural IFN-beta (IFN) (0, 300 I.U./ml or 3000 I.U./ml) 24 h before irradiation. Cycling or confluent cell cultures were used. We measured cellular survival after graded single dose irradiation, split dose (SD), and low dose rate irradiation (LDR), with colony formation as an endpoint. Survival curves were fitted according to the linear-quadratic equation. Sensitizer enhancement ratios were calculated at the 37% survival level, and isobologram analysis was applied to test the IFN-radiation interactions. Apoptosis and DNA-rejoining were measured by standard assays. On the survival level, additive as well as supraadditive interactions of IFN and XRT were observed, depending on the cell lines used. The IFN effectiveness was more pronounced in cycling compared to resting cells. The expression of mutated TP53 or RB did not influence the IFN-induced radiation cytotoxicity. Incubation with 3000 I.U./ml IFN could induce apoptosis, but it did sparsely account for increased radiation toxicity. Supraadditivity of IFN and XRT was always accompanied by increased alpha-values of the respective survival curves. The involvement of repair processes in the IFN effectiveness was supported by the results of the SD and LDR experiments, indicating an inhibition of sublethal damage repair. Initial DSBs or DNA rejoining were not altered by IFN-treatment. DNA-PK deficient M059J cells were radiosensitive and showed a supraadditive IFN-XRT interaction that could be abrogated by the re-transfection of a functional PRKDC gene (M059J-Fus1 cells). DNA-PK proficient M059K cells were radioresistant and showed a solely additive IFN-XRT interaction, which could be converted into supraadditivity by repair-inhibition with WMN. Brca2-deficient CAPAN-1 pancreatic tumor cells were extremely IFN sensitive but showed additive IFN-XRT interaction, while Brca2 proficient pancreatic tumor cells were less IFN sensitive and showed a supraadditive IFN-XRT interaction. Our results are pointing towards an interaction of IFN with the regulation of the repair of radiation-induced damage as the predominant mechanism of IFN-related radiosensitization. Inhibition of the Non-Homologous-End-Joining repair (NHEJ) pathway, as shown in MO59J cells and WMN inhibited MO59K-cells, led to a supraadditive interaction of IFN and XRT, whereas cells with intact NHEJ (MO59K-cells) showed an additive interaction of IFN and XRT. Likely IFN is interfering with the second major pathway of double strand break repair, homologous recombination (HR). This was supported by the observation that mutation in the Brca2-gene in CAPAN-1 cells, which is already associated with impaired HR, did not alter the interaction of IFN with radiation repair