Risk adaptive planning with biology-based constraints may lead to higher tumor control probability in tumors of the canine brain: A planning study.

BACKGROUND: Classical radiation protocols are guided by physical dose delivered homogeneously over the target. Protocols are chosen to keep normal tissue complication probability (NTCP) at an acceptable level. Organs at risk (OAR) adjacent to the target volume could lead to underdosage of the tumor and a decrease of tumor control probability (TCP). The intent of our study was to explore a biology-based dose escalation: by keeping NTCP for OAR constant, radiation dose was to be maximized, allowing to result in heterogeneous dose distributions. METHODS: We used computed tomography datasets of 25 dogs with brain tumors, previously treated with 10x4 Gy (40 Gy to PTV D50). We generated 3 plans for each patient: A) original treatment plan with homogeneous dose distribution, B) heterogeneous dose distribution with strict adherence to the same NTCPs as in A), and C) heterogeneous dose distribution with adherence to NTCP <5%. For plan comparison, TCPs and TCP equivalent doses (homogenous target dose which results in the same TCP) were calculated. To enable the use of the generalized equivalent uniform dose (gEUD) metric of the tumor target in plan optimization, the calculated TCP values were used to obtain the volume effect parameter a. RESULTS: As intended, NTCPs for all OARs did not differ from plan A) to B). In plan C), however, NTCPs were significantly higher for brain (mean 2.5% (SD±1.9, 95%CI: 1.7,3.3), p<0.001), optic chiasm (mean 2.0% (SD±2.2, 95%CI: 1.0,2.8), p=0.010) compared to plan A), but no significant increase was found for the brainstem. For 24 of 25 of the evaluated patients, the heterogenous plans B) and C) led to an increase in target dose and projected increase in TCP compared to the homogenous plan A). Furthermore, the distribution of the projected individual TCP values as a function of the dose was found to be in good agreement with the population TCP model. CONCLUSION: Our study is a first step towards risk-adaptive radiation dose optimization. This strategy utilizes a biologic objective function based on TCP and NTCP instead of an objective function based on physical dose constraints.

A concept for anisotropic PTV margins including rotational setup uncertainties and its impact on the tumor control probability in canine brain tumors.

Objective.In this modelling study, we pursued two main goals. The first was to establish a new CTV-to-PTV expansion which considers the closest and most critical organ at risk (OAR). The second goal was to investigate the impact of the planning target volume (PTV) margin size on the tumor control probability (TCP) and its dependence on the geometrical setup uncertainties. The aim was to achieve a smaller margin expansion close to the OAR while allowing a moderately larger expansion in less critical areas further away from the OAR and whilst maintaining the TCP.Approach.Imaging data of radiation therapy plans from pet dogs which had undergone radiation therapy for brain tumor were used to estimate the clinic specific rotational setup uncertainties. A Monte-Carlo methodology using a voxel-based TCP model was used to quantify the implications of rotational setup uncertainties on the TCP. A combination of algorithms was utilized to establish a computational CTV-to-PTV expansion method based on probability density. This was achieved by choosing a center of rotation close to an OAR. All required software modules were developed and integrated into a software package that directly interacts with the Varian Eclipse treatment planning system.Main results.Several uniform and non-isotropic PTVs were created. To ensure comparability and consistency, standardized RT plans with equal optimization constraints were defined, automatically applied and calculated on these targets. The resulting TCPs were then computed, evaluated and compared.Significance.The non-isotropic margins were found to result in larger TCPs with smaller margin excess volume. Further, we presented an additional application of the newly established CTV-to-PTV expansion method for radiation therapy of the spinal axis of human patients.

Tumour volume distribution can yield information on tumour growth and tumour control.

BACKGROUND: It is shown that tumour volume distributions can yield information on two aspects of cancer research: tumour induction and tumour control. MATERIALS AND METHODS: From the hypothesis that the intrinsic distribution of breast cancer volumes follows an exponential distribution, firstly the probability density function of tumour growth time was deduced via a mathematical transformation of the probability density functions of tumour volumes. In a second step, the distribution of tumour volumes was used to model the variation of the clonogenic cell number between patients in order to determine tumour control probabilities for radiotherapy patients. RESULTS: Distribution of lag times, i.e. the time from the appearance of the first fully malignant cell until a clinically observable cancer, can be used to deduce the probability of tumour induction as a function of patient age. The integration of the volume variation with a Poisson-TCP model results in a logistic function which explains population-averaged survival data of radiotherapy patients. CONCLUSIONS: The inclusion of tumour volume distributions into the TCP formalism enables a direct link to be deduced between a cohort TCP model (logistic) and a TCP model for individual patients (Poisson). The TCP model can be applied to non-uniform tumour dose distributions.

A Novel Analytical Population Tumor Control Probability Model Includes Cell Density and Volume Variations: Application to Canine Brain Tumor.

PURPOSE: Tumor control probability (TCP) models based on Poisson statistics characterize the distribution of surviving clonogens. Thus enabling the calculation of TCP for individuals. To mathematically describe clinically observed survival data of patient cohorts it is necessary to extend the Poisson TCP model. This is typically done by either incorporating variations of model parameters or by using an empirical logistic model. The purpose of this work is the development of an analytical population TCP model by mechanistic extension of the Possion model. METHODS AND MATERIALS: The frequency distribution of gross tumor volumes was used to incorporate tumor volume variations into the TCP model. Additionally the tumor cell density variation was incorporated. Both versions of the population TCP model were fitted to clinical data and compared to existing literature. RESULTS: It was shown that clinically observed brain tumor volumes of dogs undergoing radiotherapy are distributed according to an exponential distribution. The average gross tumor volume size was 3.37 cm3. Fitting the population TCP model including the volume variation using linear-quadratic and track-event model yieldedα=0.36Gy--1a, ß=0.045Gy--2, a=0.9yr--1, TD=5.0d,and p=.36Gy--1, q=0.48Gy--1, a=0.80yr--1, TD=3.0d, respectively. Fitting the population TCP model including both the volume and cell density variation yielded α=0.43Gy--1, ß=0.0537Gy--2, a=2.0yr--1, TD=3.0d, σ=2.5,and p=.43Gy--1, q=0.55Gy--1, a=2.0yr--1, TD=2.0d, σ=3.0,respectively. CONCLUSIONS: Two sets of radiobiological parameters were obtained which can be used for quantifying the TCP for radiation therapy of brain tumors in dogs. We established a mechanistic link between the poisson statistics based individual TCP model and the logistic TCP model. This link can be used to determine the radiobiological parameters of patient specific TCP models from published fits of logistic models to cohorts of patients.

Estimation of planning organ at risk volumes for ocular structures in dogs undergoing three-dimensional image-guided periocular radiotherapy with rigid bite block immobilization.

Planning organ at risk volume (PRV) estimates have been reported as methods for sparing organs at risk (OARs) during radiation therapy, especially for hypofractioned and/or dose-escalated protocols. The objectives of this retrospective, analytical, observational study were to evaluate peri-ocular OAR shifts and derive PRVs in a sample of dogs undergoing radiation therapy for periocular tumors. Inclusion criteria were as follows: dogs irradiated for periocular tumors, with 3D-image-guidance and at least four cone-beam CTs (CBCTs) used for position verification, and positioning in a rigid bite block immobilization device. Peri-ocular OARs were contoured on each CBCT and the systematic and random error of the shifts in relation to the planning CT position computed. The formula 1.3×Σ+0.5xσ was used to generate a PRV of each OAR in the dorsoventral, mediolateral, and craniocaudal axis. A total of 30 dogs were sampled, with 450 OARs contoured, and 2145 shifts assessed. The PRV expansion was qualitatively different for each organ (1-4 mm for the dorsoventral and 1-2 mm for the mediolateral and craniocaudal axes). Maximal PRV expansion was ≤4 mm and directional for the majority; most pronounced for corneas and retinas. Findings from the current study may help improve awareness of and minimization of radiation dose in peri-ocular OARs for future canine patients. Because some OARs were difficult to visualize on CBCTs and/ or to delineate on the planning CT, authors recommend that PRV estimates be institution-specific and applied with caution.

Reducing margins for abdominopelvic tumours in dogs: Impact on dose-coverage and normal tissue complication probability.

Image-guided, intensity modulated radiation therapy (IG-IMRT) reduces dose to pelvic organs at risk without losing dose coverage to the planning target volume (PTV) and might permit margin reductions potentially resulting in lower toxicity. Appropriate PTV margins have not been established for IG-IMRT in abdominopelvic tumours in dogs, and herein we explore if our usual PTV 5 mm margin can be reduced further. Datasets from dogs that underwent IG-IMRT for non-genitourinary abdominopelvic neoplasia with 5 mm-PTV expansion were included in this retrospective virtual study. The clinical target volumes and organs at risk (OAR) colon, rectum, spinal cord were adapted to each co-registered cone-beam computed tomography (CBCT) used for positioning. New treatment plans were generated and smaller PTV margins of 3 mm and 4 mm evaluated with respect to adequate dose coverage and normal tissue complication probability (NTCP) of OAR. Ten dogs with a total of 70 CBCTs were included. Doses to the OAR of each CBCT deviated mildly from the originally planned doses. In some plans, insufficient build-up of the high dose-area at the body surface was found due to inadequate or missing bolus placement. Overall, the margin reduction to 4 mm or 3 mm did not impair dose coverage and led to significantly lower NTCP in all OAR except for spinal cord delayed myelopathy. However, overall NTCP for spinal cord was very low (<4%). PTV-margins depend on patient immobilization and treatment technique and accuracy. IG-IMRT allows treatment with very small margins in the abdominopelvic region, ensuring appropriate target dose coverage, while minimizing NTCP.

A model of radiation action based on nanodosimetry and the application to ultra-soft X-rays.

A radiation action model based on nanodosimetry is presented. It is motivated by the finding that the biological effects of various types of ionizing radiation lack a consistent relation with absorbed dose. It is postulated that the common fundamental cause of these effects is the production of elementary sublesions (DSB), which are created at a rate that is proportional to the probability to produce more than two ionisations within a volume of 10 base pairs of the DNA. The concepts of nanodosimetry allow for a quantitative characterization of this process in terms of the cumulative probability F2. The induced sublesions can interact in two ways to produce lethal damage. First, if two or more sublesions accumulate in a locally limited spherical volume of 3-10 nm in diameter, clustered DNA damage is produced. Second, consequent interactions or rearrangements of some of the initial damage over larger distances (~ µm) can produce additional lethal damage. From the comparison of theoretical predictions deduced from this concept with experimental data on relative biological effectiveness, a cluster volume with a diameter of 7.5 nm could be determined. It is shown that, for electrons, the predictions agree well with experimental data over a wide energy range. The only free parameter needed to model cell survival is the intersection cross-section which includes all relevant cell-specific factors. Using ultra-soft X-rays it could be shown that the energy dependence of cell survival is directly governed by the nanodosimetric characteristics of the radiation track structure. The cell survival model derived in this work exhibits exponential cell survival at a high dose and a finite gradient of cell survival at vanishing dose, as well as the dependence on dose-rate.

Using biologically based objectives to optimize boost intensity-modulated radiation therapy planning for brainstem tumors in dogs.

Irradiated brain tumors commonly progress at the primary site, generating interest in focal dose escalation. The aim of this retrospective observational study was to use biological optimization objectives for a modeling exercise with simultaneously-integrated boost IMRT (SIB-IMRT) to generate a dose-escalated protocol with acceptable late radiation toxicity risk estimate and improve tumor control for brainstem tumors in dogs safely. We re-planned 20 dog brainstem tumor datasets with SIB-IMRT, prescribing 20 × 2.81 Gy to the gross tumor volume (GTV) and 20 × 2.5 Gy to the planning target volume. During the optimization process, we used biologically equivalent generalized equivalent uniform doses (gEUD) as planning aids. These were derived from human data, calculated to adhere to normal tissue complication probability (NTCP) ≤5%, and converted to the herein used fractionation schedule. We extracted the absolute organ at risk dose-volume histograms to calculate NTCP of each individual plan. For planning optimization, gEUD(a = 4)  = 39.8 Gy for brain and gEUD(a = 6.3)  = 43.8 Gy for brainstem were applied. Mean brain NTCP was low with 0.43% (SD ±0.49%, range 0.01-2.04%); mean brainstem NTCP was higher with 7.18% (SD ±4.29%, range 2.87-20.72%). Nevertheless, NTCP of < 10% in brainstem was achievable in 80% (16/20) of dogs. Spearman's correlation between relative GTV and NTCP was high (ρ = 0.798, P < .001), emphasizing increased risk with relative size even with subvolume-boost. Including biologically based gEUD values into optimization allowed estimating NTCP during the planning process. In conclusion, gEUD-based SIB-IMRT planning resulted in dose-escalated treatment plans with acceptable risk estimate of NTCP < 10% in the majority of dogs with brainstem tumors. Risk was correlated with relative tumor size.

A complication probability study for a definitive-intent, moderately hypofractionated image-guided intensity-modulated radiotherapy protocol for anal sac adenocarcinoma in dogs.

Previous trials showed the importance of administering radiation therapy (RT) with small doses per fraction in canine pelvic tumours to maintain acceptable toxicity levels. With increased accuracy/precision of RT, namely intensity-modulated RT (IMRT), this approach might be challenged. Theoretical toxicity calculations for a new definitive-intent moderately hypofractionated RT protocol for canine anal sac adenocarcinomas (ASAC) were performed, focussing on the risk of toxicity in pelvic organs at risk (OAR). Computed tomography datasets of 18 dogs with stage 3b ASAC were included. Re-planning with margins for daily image-guidance/IMRT was performed and a new protocol isoeffective to previously described definitive-intent protocols was computed. Dose-volume information were derived from individual plans and used for normal tissue complication probability (NTCP) computations. A 12 × 3.8 Gy protocol was computed for risk estimation. Tumour volumes ranged from 27.9 to 820.4 cm3 (mean 221.3 cm3 ± 188.9). For late rectal toxicity/bleeding ≥grade 2, median risk probability was 2.3% inter quartile range (IQR: 5.9; 95% confidence interval (CI): 1.2, 8.4) (rho = 0.436) and 3.4% (IQR: 0.96; 95%CI: 3.1, 4.0) (rho = 0.565), respectively. Median late toxicities in urinary bladder, kidneys and small bowel were <1%, except in one kidney. Myelopathy/myelonecrosis had a median risk probability of 4.1% (IQR: 23.5; 95%CI: 2.1, 25.2) (rho = 0.366) and 5.6% (IQR: 13.5; 95%CI: 3.1, 14.1) (rho = 0.363), respectively. However, graded risk showed a probability estimate for late spinal cord toxicity of ≥5% in 8/18 patients. The daily-imaging IMRT 12 × 3.8 Gy protocol for canine ASAC seems tolerable for most cases, even in advanced disease. Theoretical dose computations serve as estimate, but are safe measures before implementing new protocols into clinical use.

TRACK EVENT THEORY: A CELL SURVIVAL and RBE MODEL CONSISTENT WITH NANODOSIMETRY.

A simple model for cell survival which is valid also at high dose has been developed. The model parameters can be traced back to measurable quantities from nanodosimetry. It is assumed that a cell is killed by an event which is defined by two or more double strand breaks in differently sized lethal interaction volumes (LIVs). Two different mechanisms can produce events, one-track events by one-particle track and two-track events by two. One- and two-track events are statistically independent. From the stochastic nature of cell killing which is described by the Poisson distribution, the cell survival probability was derived. The ratio of the number of one- and two-track events can be directly expressed in terms of nanodosimetry by the probability F2 that at least two ionizations are produced in a basic interaction volume (5-10 base pairs). From the model, relative biological effectiveness (RBE) can be derived which depends only on F2 and the size of the LIV. The expression for RBE fits experimental data with satisfying quality.

Comparative evaluation of a novel, moderately hypofractionated radiation protocol in 56 dogs with symptomatic intracranial neoplasia.

BACKGROUND: Use of strongly hypofractionated radiation treatments in dogs with intracranial neoplasia did not improve outcomes and yielded increased rates of toxicosis. OBJECTIVES: To evaluate safety and efficacy of a new, moderately hypofractionated radiation protocol of 10 × 4 Gy compared to a standard protocol. ANIMALS: Convenience sample of 56 client-owned dogs with primary symptomatic brain tumors. METHODS: Retrospective observational study. Twenty-six dogs were assigned to the control standard protocol of 20 × 2.5 Gy (group A) and 30 dogs to the new protocol of 10 × 4 Gy (group B), assigned on owners' informed consent. Statistical analysis was conducted under the "as treated" regime, using Kaplan-Meier and Cox-regression analysis. Treatment was delivered with technically advanced image-guided radiation therapy. The 2 treatment groups were compared in terms of outcome and signs of toxicosis. RESULTS: Overall progression-free interval (PFI) and overall survival (OS) time were favorable, with 663 (95%CI: 497;828) and 637 (95%CI: 403;870) days, respectively. We found no significant difference between the two groups: PFI for dogs in group A vs B was 608 (95%CI: 437;779) days and mean (median not reached) 863 (95%CI: 644;1083) days, respectively (P = .89), and OS for dogs in group A vs B 610 (95%CI: 404;816) and mean (median not reached) 796 (95%CI: 586;1007) days (P = .83). CONCLUSION AND CLINICAL IMPORTANCE: In conclusion, 10 × 4 Gy is a safe and efficient protocol for treatment of primary intracranial neoplasia and future dose escalation can be considered.

The probabilities of one- and multi-track events for modeling radiation-induced cell kill.

In view of the clinical importance of hypofractionated radiotherapy, track models which are based on multi-hit events are currently reinvestigated. These models are often criticized, because it is believed that the probability of multi-track hits is negligible. In this work, the probabilities for one- and multi-track events are determined for different biological targets. The obtained probabilities can be used with nano-dosimetric cluster size distributions to obtain the parameters of track models. We quantitatively determined the probabilities for one- and multi-track events for 100, 500 and 1000 keV electrons, respectively. It is assumed that the single tracks are statistically independent and follow a Poisson distribution. Three different biological targets were investigated: (1) a DNA strand (2 nm scale); (2) two adjacent chromatin fibers (60 nm); and (3) fiber loops (300 nm). It was shown that the probabilities for one- and multi-track events are increasing with energy, size of the sensitive target structure, and dose. For a 2 × 2 × 2 nm3 target, one-track events are around 10,000 times more frequent than multi-track events. If the size of the sensitive structure is increased to 100-300 nm, the probabilities for one- and multi-track events are of the same order of magnitude. It was shown that target theories can play a role for describing radiation-induced cell death if the targets are of the size of two adjacent chromatin fibers or fiber loops. The obtained probabilities can be used together with the nano-dosimetric cluster size distributions to determine model parameters for target theories.

The Impact of the Geometrical Structure of the DNA on Parameters of the Track-Event Theory for Radiation Induced Cell Kill.

BACKGROUND AND PURPOSE: When fractionation schemes for hypofractionation and stereotactic body radiotherapy are considered, a reliable cell survival model at high dose is needed for calculating doses of similar biological effectiveness. An alternative to the LQ-model is the track-event theory which is based on the probabilities for one- and two two-track events. A one-track-event (OTE) is always represented by at least two simultaneous double strand breaks. A two-track-event (TTE) results in one double strand break. Therefore at least two two-track-events on the same or different chromosomes are necessary to produce an event which leads to cell sterilization. It is obvious that the probabilities of OTEs and TTEs must somehow depend on the geometrical structure of the chromatin. In terms of the track-event theory the ratio ε of the probabilities of OTEs and TTEs includes the geometrical dependence and is obtained in this work by simple Monte Carlo simulations. MATERIALS AND METHODS: For this work it was assumed that the anchors of loop forming chromatin are most sensitive to radiation induced cell deaths. Therefore two adjacent tetranucleosomes representing the loop anchors were digitized. The probability ratio ε of OTEs and TTEs was factorized into a radiation quality dependent part and a geometrical part: ε = εion ∙ εgeo. εgeo was obtained for two situations, by applying Monte Carlo simulation for DNA on the tetranucleosomes itself and for linker DNA. Low energy electrons were represented by randomly distributed ionizations and high energy electrons by ionizations which were simulated on rays. εion was determined for electrons by using results from nanodosimetric measurements. The calculated ε was compared to the ε obtained from fits of the track event model to 42 sets of experimental human cell survival data. RESULTS: When the two tetranucleosomes are in direct contact and the hits are randomly distributed εgeo and ε are 0.12 and 0.85, respectively. When the hits are simulated on rays εgeo and ε are 0.10 and 0.71. For the linker-DNA εgeo and ε for randomly distributed hits are 0.010 and 0.073, and for hits on rays 0.0058 and 0.041, respectively. The calculated ε fits the experimentally obtained ε = 0.64±0.32 best for hits on the tetranucleosome when they are close to each other both, for high and low energy electrons. CONCLUSIONS: The parameter εgeo of the track event model was obtained by pure geometrical considerations of the chromatin structure and is 0.095 ± 0.022. It can be used as a fixed parameter in the track-event theory.

A general model for stray dose calculation of static and intensity-modulated photon radiation.

PURPOSE: There is an increasing number of cancer survivors who are at risk of developing late effects caused by ionizing radiation such as induction of second tumors. Hence, the determination of out-of-field dose for a particular treatment plan in the patient's anatomy is of great importance. The purpose of this study was to analytically model the stray dose according to its three major components. METHODS: For patient scatter, a mechanistic model was developed. For collimator scatter and head leakage, an empirical approach was used. The models utilize a nominal beam energy of 6 MeV to describe two linear accelerator types of a single vendor. The parameters of the models were adjusted using ionization chamber measurements registering total absorbed dose in simple geometries. Whole-body dose measurements using thermoluminescent dosimeters in an anthropomorphic phantom for static and intensity-modulated treatment plans were compared to the 3D out-of-field dose distributions calculated by a combined model. RESULTS: The absolute mean difference between the whole-body predicted and the measured out-of-field dose of four different plans was 11% with a maximum difference below 44%. Computation time of 36 000 dose points for one field was around 30 s. By combining the model-calculated stray dose with the treatment planning system dose, the whole-body dose distribution can be viewed in the treatment planning system. CONCLUSIONS: The results suggest that the model is accurate, fast and can be used for a wide range of treatment modalities to calculate the whole-body dose distribution for clinical analysis. For similar energy spectra, the mechanistic patient scatter model can be used independently of treatment machine or beam orientation.

Concept for quantifying the dose from image guided radiotherapy.

BACKGROUND: Radiographic image guidance is routinely used for patient positioning in radiotherapy. All radiographic guidance techniques can give a significant radiation dose to the patient. The dose from diagnostic imaging is usually managed by using effective dose minimization. In contrast, image-guided radiotherapy adds the imaging dose to an already high level of therapeutic radiation which cannot be easily managed using effective dose. The purpose of this work is the development of a concept of IGRT dose quantification which allows a comparison of imaging dose with commonly accepted variations of therapeutic dose. METHODS: It is assumed that dose variations of the treatment beam which are accepted in the spirit of the ALARA convention can also be applied to the additional imaging dose. Therefore we propose three dose categories: Category I: The imaging dose is lower than a 2% variation of the therapy dose. Category II: The imaging dose is larger than in category I, but lower than the therapy dose variations between different treatment techniques. Category III: The imaging dose is larger than in Category II. For various treatment techniques dose measurements are used to define the dose categories. The imaging devices were categorized according to the measured dose. RESULTS: Planar kV-kV imaging is a category I imaging procedure. kV-MV imaging is located at the edge between category I and II and is for increasing fraction size safely a category I imaging technique. MV-MV imaging is for all imaging technologies a category II procedure. MV fan beam CT for localization is a category I technology. Low dose protocols for kV CBCT are located between category I and II and are for increasing fraction size a category I imaging technique. All other investigated Pelvis-CBCT protocols are category II procedures. Fan beam CT scout views are category I technology. Live imaging modalities are category III for conventional fractionation, but category II for stereotactic treatments. CONCLUSIONS: Dose from radiotherapy imaging can be categorized in terms of generally accepted dose variations of therapy dose. This concept allows the quantification of daily dose from image guided radiotherapy in the spirit of the ALARA convention.

Track-event theory of cell survival with second-order repair.

When fractionation schemes for hypofractionation and stereotactic body radiotherapy are considered, a reliable cell survival model at high dose is needed for calculating doses of similar biological effectiveness. In this work, a simple model for cell survival which is valid also at high dose is developed from Poisson statistics. It is assumed that a cell is killed by an event that is defined by two double-strand breaks on the same or different chromosomes. Two different mechanisms can produce events. A one-track event is always represented by two simultaneous double-strand breaks. A two-track event results in one double-strand break. Therefore, at least two two-track events on the same or different chromosomes are necessary to produce an event. It is assumed that two double-strand breaks can be repaired with a certain repair probability. Both the one-track events and the two-track events are statistically independent. From the stochastic nature of cell killing which is described by the Poisson distribution, the cell survival probability was derived. The model was fitted to experimental data. It was shown that a solution based on Poisson statistics exists for cell survival. It exhibits exponential cell survival at high dose and a finite gradient of cell survival at vanishing dose, which is in agreement with experimental cell studies. The model fits the experimental data as well as the LQ model and is based on two free parameters. It was shown that cell survival can be described with a simple analytical formula on the basis of Poisson statistics. This solution represents in the limit of large dose the typical exponential behavior and predicts cell survival as well as the LQ model.

A track-event theory of cell survival.

PURPOSE: When fractionation schemes for hypofractionation and stereotactic body radiotherapy are considered, a reliable cell survival model at high dose is needed for calculating doses of similar biological effectiveness. In this work a simple model for cell survival which is valid also at high dose is developed from Poisson statistics. MATERIALS AND METHODS: An event is defined by two double strand breaks (DSB) on the same or different chromosomes. An event is always lethal due to direct lethal damage or lethal binary misrepair by the formation of chromosome aberrations. Two different mechanisms can produce events: one-track events (OTE) or two-track-events (TTE). The target for an OTE is always a lethal event, the target for an TTE is one DSB. At least two TTEs on the same or different chromosomes are necessary to produce an event. Both, the OTE and the TTE are statistically independent. From the stochastic nature of cell kill which is described by the Poisson distribution the cell survival probability was derived. RESULTS: It was shown that a solution based on Poisson statistics exists for cell survival. It exhibits exponential cell survival at high dose and a finite gradient of cell survival at vanishing dose, which is in agreement with experimental cell studies. The model fits the experimental data nearly as well as the three-parameter formula of Hug-Kellerer and is only based on two free parameters. It is shown that the LQ formalism is an approximation of the model derived in this work. It could be also shown that the derived model predicts a fractionated cell survival experiment better than the LQ-model. CONCLUSIONS: It was shown that cell survival can be described with a simple analytical formula on the basis of Poisson statistics. This solution represents in the limit of large dose the typical exponential behavior and predicts cell survival after fractionated dose application better than the LQ-model.

Accuracy of out-of-field dose calculation of tomotherapy and cyberknife treatment planning systems: a dosimetric study.

PURPOSE: Late toxicities such as second cancer induction become more important as treatment outcome improves. Often the dose distribution calculated with a commercial treatment planning system (TPS) is used to estimate radiation carcinogenesis for the radiotherapy patient. However, for locations beyond the treatment field borders, the accuracy is not well known. The aim of this study was to perform detailed out-of-field-measurements for a typical radiotherapy treatment plan administered with a Cyberknife and a Tomotherapy machine and to compare the measurements to the predictions of the TPS. MATERIALS AND METHODS: Individually calibrated thermoluminescent dosimeters were used to measure absorbed dose in an anthropomorphic phantom at 184 locations. The measured dose distributions from 6 MV intensity-modulated treatment beams for CyberKnife and TomoTherapy machines were compared to the dose calculations from the TPS. RESULTS: The TPS are underestimating the dose far away from the target volume. Quantitatively the Cyberknife underestimates the dose at 40 cm from the PTV border by a factor of 60, the Tomotherapy TPS by a factor of two. If a 50% dose uncertainty is accepted, the Cyberknife TPS can predict doses down to approximately 10 mGy/treatment Gy, the Tomotherapy-TPS down to 0.75 mGy/treatment Gy. The Cyberknife TPS can then be used up to 10 cm from the PTV border the Tomotherapy up to 35 cm. CONCLUSIONS: We determined that the Cyberknife and Tomotherapy TPS underestimate substantially the doses far away from the treated volume. It is recommended not to use out-of-field doses from the Cyberknife TPS for applications like modeling of second cancer induction. The Tomotherapy TPS can be used up to 35 cm from the PTV border (for a 390 cm(3) large PTV).

Measurement of skin and target dose in post-mastectomy radiotherapy using 4 and 6 MV photon beams.

BACKGROUND: For patients with high risk breast cancer and mastectomy, radiotherapy is the treatment of choice to improve survival and local control. Target dose is mainly limited due to skin reactions. The feasibility of using 4 MV beams for chest wall treatment was studied and compared to standard 6 MV bolus radiotherapy. METHODS: Post-mastectomy IMRT was planned on an Alderson-phantom using 4 and 6 MV photon beams without/with a 0.5 cm thick bolus. Dose was measured using TLDs placed at 8 locations in 1 and 3 mm depth to represent skin and superficial target dose, respectively. RESULTS: 4 MV and 6 MV beams with bolus perform equally regarding target coverage. The minimum and mean superficial target dose for the 6 MV and 4 MV were 93.0% and 94.7%, and 93.1% and 94.4%, respectively. Regarding skin dose the 4 MV photon beam was advantageous. The minimum and mean skin dose for the 6 MV and 4 MV was 76.7% and 81.6%, and 69.4% and 72.9%, respectively. The TPS was able to predict dose in the build-up region with a precision of around 5%. CONCLUSIONS: The use of 4 MV photon beams are a good alternative for treating the thoracic wall without the need to place a bolus on the patient. The main limitation of 4 MV beams is the limited dose rate.