Sorting lung tumor volumes from 4D-MRI data using an automatic tumor-based signal reduces stitching artifacts.

PURPOSE: To investigate whether a novel signal derived from tumor motion allows more precise sorting of 4D-magnetic resonance (4D-MR) image data than do signals based on normal anatomy, reducing levels of stitching artifacts within sorted lung tumor volumes. METHODS: (4D-MRI) scans were collected for 10 lung cancer patients using a 2D T2-weighted single-shot turbo spin echo sequence, obtaining 25 repeat frames per image slice. For each slice, a tumor-motion signal was generated using the first principal component of movement in the tumor neighborhood (TumorPC1). Signals were also generated from displacements of the diaphragm (DIA) and upper and lower chest wall (UCW/LCW) and from slice body area changes (BA). Pearson r coefficients of correlations between observed tumor movement and respiratory signals were determined. TumorPC1, DIA, and UCW signals were used to compile image stacks showing each patient's tumor volume in a respiratory phase. Unsorted image stacks were also built for comparison. For each image stack, the presence of stitching artifacts was assessed by measuring the roughness of the compiled tumor surface according to a roughness metric (Rg). Statistical differences in weighted means of Rg between any two signals were determined using an exact permutation test. RESULTS: The TumorPC1 signal was most strongly correlated with superior-inferior tumor motion, and had significantly higher Pearson r values (median 0.86) than those determined for correlations of UCW, LCW, and BA with superior-inferior tumor motion (p < 0.05). Weighted means of ratios of Rg values in TumorPC1 image stacks to those in unsorted, UCW, and DIA stacks were 0.67, 0.69, and 0.71, all significantly favoring TumorPC1 (p = 0.02-0.05). For other pairs of signals, weighted mean ratios did not differ significantly from one. CONCLUSION: Tumor volumes were smoother in 3D image stacks compiled using the first principal component of tumor motion than in stacks compiled with signals based on normal anatomy.

ImmunoChemoradiation for Non-Small Cell Lung Cancer: A Meta-Analysis of Factors Influencing Survival Benefit in Combination Trials.

PURPOSE: Adding immune checkpoint blockade (ICB) to concurrent chemoradiotherapy (cCRT) has improved overall survival (OS) for inoperable locally advanced non-small cell lung cancer. Trials of cCRT-ICB are heterogeneous for factors such as tumor stage and histology, programmed cell death ligand-1 (PDL-1) status, and cCRT-ICB schedules. We therefore aimed to determine the ICB contribution to survival across studies and identify factors associated with survival gain. METHODS AND MATERIALS: Data were collated from cCRT-ICB clinical studies published 2018 to 2022 that treated 2196 patients with non-small cell lung cancer (99% stage 3). Associations between 2-year OS and ICB, CRT, patient and tumor factors were investigated using metaregression. A published model of survival after radiation therapy (RT) or CRT was extended to include ICB effects. The model was fitted simultaneously to the cCRT-ICB data and data previously compiled for RT/CRT treatments alone. The net ICB contribution (OS gain) and its associations with factors were described by fitted values of ICB terms added to the model. Statistical significance was determined by likelihood-ratio testing. RESULTS: The gain in 2-year OS from ICB was 9.9% overall (95% CI, 7.6%, 12.2%; P = .018). Both OS gain and 2-year OS itself rose with increasing planned ICB duration (P = .008, .002, respectively) and with tumor PDL-1 ≥ 1% (P = .034, .023). Fitted OS gains were also greater for patients with stage 3B/C disease (P = .021). OS gain was not associated with tumor histology, patient performance status, radiation therapy dose, ICB drug type (anti-PDL-1 vs anti-programmed cell death-1), or whether ICB began concurrently with or after cCRT. CONCLUSIONS: Fitted gains in 2-year OS due to ICB were higher in cohorts with greater fractions of stage 3B/C patients and patients with tumor PDL-1 ≥ 1%. OS gain was also significantly higher in a single cohort with a planned ICB duration of 2 years rather than 1, but was not associated with whether ICB treatment began during versus after CRT.

A Biomathematical Model of Tumor Response to Radioimmunotherapy With αPDL1 and αCTLA4.

There is evidence of synergy between radiotherapy and immunotherapy. Radiotherapy can increase liberation of tumor antigens, causing activation of antitumor T-cells. This effect can be boosted with immunotherapy. Radioimmunotherapy has potential to increase tumor control rates. Biomathematical models of response to radioimmunotherapy may help on understanding of the mechanisms affecting response, and assist clinicians on the design of optimal treatment strategies. In this work we present a biomathematical model of tumor response to radioimmunotherapy. The model uses the linear-quadratic response of tumor cells to radiation (or variation of it), and builds on previous developments to include the radiation-induced immune effect. We have focused this study on the combined effect of radiotherapy and αPDL1/ αCTLA4 therapies. The model can fit preclinical data of volume dynamics and control obtained with different dose fractionations and αPDL1/ αCTLA4. A biomathematical study of optimal combination strategies suggests that a good understanding of the involved biological delays, the biokinetics of the immunotherapy drug, and the interplay between them, may be of paramount importance to design optimal radioimmunotherapy schedules. Biomathematical models like the one we present can help to interpret experimental data on the synergy between radiotherapy and immunotherapy, and to assist in the design of more effective treatments.

Roadmap for precision preclinical x-ray radiation studies.

This Roadmap paper covers the field of precision preclinical x-ray radiation studies in animal models. It is mostly focused on models for cancer and normal tissue response to radiation, but also discusses other disease models. The recent technological evolution in imaging, irradiation, dosimetry and monitoring that have empowered these kinds of studies is discussed, and many developments in the near future are outlined. Finally, clinical translation and reverse translation are discussed.

Tomotherapy-like versus VMAT-like treatments: a multicriteria comparison for a prostate geometry.

PURPOSE: To perform a methodological comparison of volumetric modulated arc therapy (VMAT)-like and tomotherapy-like techniques for a prostate geometry, exploring the dependence on machine, delivery, and optimization parameters of cost function values optimized for each technique. METHODS: A gradient-descent algorithm is used to optimize tomotherapy-like treatments, while VMAT-like optimization is carried out using a direct-aperture simulated annealing algorithm with 180 control points equispaced at 2° angles. Dose distributions are linked to fluences via a three-dimensional double-gaussian pencil beam model. Plans are optimized for a prostate geometry, outlined according to the CHHiP protocol. The cost function used for optimization contains ten simple functions, each of which describes a single planning objective. These functions are split into three structure groups according to whether they are used to control PTV, rectal or bladder dose levels. Different optimizations have been performed by varying the relative weights of each of these structure groups, exploring in this way a three-dimensional Pareto front. Plan quality is studied according to the value of the optimized cost function and the relative Euclidean distance between the components of the cost function and those of the nearest plan lying on a reference Pareto front obtained for tomotherapy-like plans generated using a 1 cm fan-beam width and 1/3 pitch. RESULTS: The quality of tomotherapy-like optimization depends on the fan-beam width, s, and rotation pitch, p, used to deliver the treatment. These values together define the effective longitudinal resolution with which fluence can be modulated, and lower cost function values are obtained for treatments optimized with tighter pitches and narrower fan-beam widths (higher modulation resolution). On the other hand, the cost function values of VMAT-like optimizations depends on the optimization running time, leaf displacement constraints, and number of arcs employed, as well as on the size of the beamlets used in the optimization (a change in leaf width from 5 to 10 mm clearly worsens the value of the objective function, but only a marginal improvement is observed when the leaf movement discretization step is reduced from 5 to 5/3 mm). However, for no combination of these parameter values did VMAT-like optimizations match the cost function values of optimized tomo-like plans obtained for s = 1 cm and p = 1∕3 (or 1/2). This is the case all across the Pareto front. On the other hand, cost function values of VMAT-like plans are generally lower than those of optimized tomotherapy-like plans obtained for s = 2.5 cm. CONCLUSIONS: Tomotherapy-like plans created for the prostate geometry using a 1 cm fan-beam width and pitches of 1/3 or 1/2 have lower cost function values than VMAT-like plans, although the associated dosimetric improvements are quite small, both techniques generating very good dose distributions. When a 2.5 cm wide fan-beam is used for tomotherapy-like treatments the pattern is reversed, the tomotherapy-like plans having higher cost functions than the VMAT-like ones.

Collection efficiencies of ionization chambers in pulsed radiation beams: an exact solution of an ion recombination model including free electron effects.

Objective.Boaget al(1996) formulated a key model of collection efficiency for ionization chambers in pulsed radiation beams, in which some free electrons form negatively charged ions with a density that initially varies exponentially across the chamber. This non-uniform density complicates ion recombination calculations, in comparison with Boag's 1950 work in which a collection efficiency formula,f, was straightforwardly obtained assuming a uniform negative ion cloud. Boaget al(1996) therefore derived collection efficiency formulaef',f″ andf'″ based on three approximate descriptions of the exponentially-varying negative ion cloud, each uniform within a region. Collection efficiencies calculated by Boaget al(1996) using these formulae differed by a maximum of 5.1% relative (at 144 mGy dose-per-pulse with 212 V applied over a 1 mm electrode separation) and all three formulae are often used together. Here an exact solution of the exponentially-varying model is obtained.Approach.The exact solution was derived from a differential equation relating the number of negative ions collected from within some distance of the anode to numbers of ions initially located within that region. Using the resulting formula,fexp, collection efficiencies were calculated for a range of ionization chamber properties and doses-per-pulse, and compared withf,f',f″ andf″' values and results from an ion transport code.Main results.fexpvalues agreed to 5 decimal places with ion transport code results. The maximum relative difference betweenfexpandf″', which was often closest tofexp, was 0.78% for the chamber properties and doses-per-pulse studied by Boaget al(1996), rising to 6.1% at 1 Gy dose-per-pulse and 2 mm electrode separation.Significance.Use offexpshould reduce ambiguities in collection efficiencies calculated using the approximate formulae, although like themfexpdoes not account for electric field distortion, which becomes substantial at doses-per-pulse ≥100 mGy.

Dose-Response Analysis Describes Particularly Rapid Repopulation of Non-Small Cell Lung Cancer during Concurrent Chemoradiotherapy.

(1) Purpose: We analysed overall survival (OS) rates following radiotherapy (RT) and chemo-RT of locally-advanced non-small cell lung cancer (LA-NSCLC) to investigate whether tumour repopulation varies with treatment-type, and to further characterise the low α/ß ratio found in a previous study. (2) Materials and methods: Our dataset comprised 2-year OS rates for 4866 NSCLC patients (90.5% stage IIIA/B) belonging to 51 cohorts treated with definitive RT, sequential chemo-RT (sCRT) or concurrent chemo-RT (cCRT) given in doses-per-fraction ≤3 Gy over 16-60 days. Progressively more detailed dose-response models were fitted, beginning with a probit model, adding chemotherapy effects and survival-limiting toxicity, and allowing tumour repopulation and α/ß to vary with treatment-type and stage. Models were fitted using the maximum-likelihood technique, then assessed via the Akaike information criterion and cross-validation. (3) Results: The most detailed model performed best, with repopulation offsetting 1.47 Gy/day (95% confidence interval, CI: 0.36, 2.57 Gy/day) for cCRT but only 0.30 Gy/day (95% CI: 0.18, 0.47 Gy/day) for RT/sCRT. The overall fitted tumour α/ß ratio was 3.0 Gy (95% CI: 1.6, 5.6 Gy). (4) Conclusion: The fitted repopulation rates indicate that cCRT schedule durations should be shortened to the minimum in which prescribed doses can be tolerated. The low α/ß ratio suggests hypofractionation should be efficacious.

Quantitative Analysis of Radiation-Associated Parenchymal Lung Change.

We present a novel classification system of the parenchymal features of radiation-induced lung damage (RILD). We developed a deep learning network to automate the delineation of five classes of parenchymal textures. We quantify the volumetric change in classes after radiotherapy in order to allow detailed, quantitative descriptions of the evolution of lung parenchyma up to 24 months after RT, and correlate these with radiotherapy dose and respiratory outcomes. Diagnostic CTs were available pre-RT, and at 3, 6, 12 and 24 months post-RT, for 46 subjects enrolled in a clinical trial of chemoradiotherapy for non-small cell lung cancer. All 230 CT scans were segmented using our network. The five parenchymal classes showed distinct temporal patterns. Moderate correlation was seen between change in tissue class volume and clinical and dosimetric parameters, e.g., the Pearson correlation coefficient was ≤0.49 between V30 and change in Class 2, and was 0.39 between change in Class 1 and decline in FVC. The effect of the local dose on tissue class revealed a strong dose-dependent relationship. Respiratory function measured by spirometry and MRC dyspnoea scores after radiotherapy correlated with the measured radiological RILD. We demonstrate the potential of using our approach to analyse and understand the morphological and functional evolution of RILD in greater detail than previously possible.

Numbers of beam angles required for near-optimal IMRT: theoretical limits and numerical studies.

PURPOSE: To derive limits on the numbers of beams needed to deliver near-optimal IMRT, and to assess the accuracy of the limits. METHODS: The authors four different limits have been derived. One, K(A), has been obtained by coupling Fourier techniques with a proof used to obtain Bortfeld's limit, K, that if all the cross-profiles of a many-field plan can be represented as polynomials of order (K-1) over the range [-R, + R], then within the radius R circle an identical dose-distribution can be created using just K fields. Two further limits, K(H) and K(N), have been obtained using sampling theory, the K(N) limit describing fields spaced at the Nyquist frequency. K(N) can be generalized to K(N,Fbeamlet), a limit that accounts for the finite size of the beamlets from which modulated fields are constructed. Using Bortfeld's theoretical framework, the accuracy of the limits has been explored by testing how well the cross-profiles of an 8 MV double-Gaussian pencil beam and of 1 and 4 cm wide fields can be approximated by polynomials of orders equal to the different limits minus one. The dependence of optimized cost function values of IMRT plans, generated for a simple geometry and for a head-and-neck (oropharynx) case, on the numbers of beams used to construct the plans has also been studied. RESULTS: The limits are all multiples of R/W (W being the 20%-80% penumbra-width of a broad field) and work out at K = 27, K(A) = 43, K(H) = 34, and K(N) = 68 fields for R = 10 cm and W = 5.3 mm. All and none of the cross-profiles are approximated well by polynomials of order K(N)-1 and K-1, respectively, suggesting some inaccuracy in the assumptions used to derive the limit K. Order K(A)-1 polynomials cannot accurately describe the pencil beam profile, but do approximate the 1- and 4-cm profiles reasonably well because higher spatial frequencies are attenuated in these wider fields. All the profiles are represented well by polynomials of order K(N,Fbeamlet(-1)), which decreases from K(N) as beamlet width increases. Cost functions generated in the IMRT planning study fall as greater numbers of fields are used, before plateauing out around K(N,Fbeamlet) fields. CONCLUSIONS: Numerical calculations suggest that the minimum number of fields required for near-optimal IMRT lies around the generalized Nyquist limit K(N,Fbeamlet). For a clinically realistic 20%-80% penumbra-width of 5.3 mm and a radius of interest of 10 cm, K(N,Fbeamlet) falls from 68 to 47 fields as the beamlet width rises from 0 to 1 cm.

Classification of tolerable/intolerable mucosal toxicity of head-and-neck radiotherapy schedules with a biomathematical model of cell dynamics.

PURPOSE: The purpose of this study is to present a biomathematical model based on the dynamics of cell populations to predict the tolerability/intolerability of mucosal toxicity in head-and-neck radiotherapy. METHODS AND MATERIALS: Our model is based on the dynamics of proliferative and functional cell populations in irradiated mucosa, and incorporates the three As: Accelerated proliferation, loss of Asymmetric proliferation, and Abortive divisions. The model consists of a set of delay differential equations, and tolerability is based on the depletion of functional cells during treatment. We calculate the sensitivity (sen) and specificity (spe) of the model in a dataset of 108 radiotherapy schedules, and compare the results with those obtained with three phenomenological classification models, two based on a biologically effective dose (BED) function describing the tolerability boundary (Fowler and Fenwick) and one based on an equivalent dose in 2 Gy fractions (EQD2 ) boundary (Strigari). We also perform a machine learning-like cross-validation of all the models, splitting the database in two, one for training and one for validation. RESULTS: When fitting our model to the whole dataset, we obtain predictive values (sen + spe) up to 1.824. The predictive value of our model is very similar to that of the phenomenological models of Fowler (1.785), Fenwick (1.806), and Strigari (1.774). When performing a k = 2 cross-validation, the specificity and sensitivity in the validation dataset decrease for all models, from ˜1.82 to Ëœ1.55-1.63. For Fowler, the worsening is higher, down to 1.49. CONCLUSIONS: Our model has proved useful to predict the tolerability/intolerability of a dataset of 108 schedules. As the model is more mechanistic than other available models, it could prove helpful when designing unconventional dose fractionations, schedules not covered by datasets to which phenomenological models of toxicity have been fitted.

The PTW microSilicon diode: Performance in small 6 and 15 MV photon fields and utility of density compensation.

PURPOSE: We have experimentally and computationally characterized the PTW microSilicon 60023-type diode's performance in 6 and 15 MV photon fields ≥5 × 5 mm2 projected to isocenter. We tested the detector on- and off-axis at 5 and 15 cm depths in water, and investigated whether its response could be improved by including within it a thin airgap. METHODS: Experimentally, detector readings were taken in fields generated by a Varian TrueBeam linac and compared with doses-to-water measured using Gafchromic film and ionization chambers. An unmodified 60023-type diode was tested along with detectors modified to include 0.6, 0.8, and 1.0 mm thick airgaps. Computationally, doses absorbed by water and detectors' sensitive volumes were calculated using the EGSnrc/BEAMnrc Monte Carlo radiation transport code. Detector response was characterized using k Q c l i n , 4 cm f c l i n , 4 cm , a factor that corrects for differences in the ratio of dose-to-water to detector reading between small fields and the reference condition, in this study 5 cm deep on-axis in a 4 × 4 cm2 field. RESULTS: The greatest errors in measurements of small field doses made using uncorrected readings from the unmodified 60023-type detector were over-responses of 2.6% ± 0.5% and 5.3% ± 2.0% determined computationally and experimentally, relative to the reading-per-dose in the reference field. Corresponding largest errors for the earlier 60017-type detector were 11.9% ± 0.6% and 11.7% ± 1.4% over-responses. Adding even the thinnest, 0.6 mm, airgap to the 60023-type detector over-corrected it, leading to under-responses of up to 4.8% ± 0.6% and 5.0% ± 1.8% determined computationally and experimentally. Further, Monte Carlo calculations indicate that a detector with a 0.3 mm airgap would read correctly to within 1.3% on-axis. The ratio of doses at 15 and 5 cm depths in water in a 6 MV 4 × 4 cm2 field was measured more accurately using the unmodified 60023-type detector than using the 60017-type detector, and was within 0.3% of the ratio measured using an ion chamber. The 60023-type diode's sensitivity also varied negligibly as dose-rate was reduced from 13 to 4 Gy min-1 by decreasing the linac pulse repetition frequency, whereas the sensitivity of the 60017-type detector fell by 1.5%. CONCLUSIONS: The 60023-type detector performed well in small fields across a wide range of beam energies, field sizes, depths, and off-axis positions. Its response can potentially be further improved by adding a thin, 0.3 mm, airgap.

Associations between cardiac irradiation and survival in patients with non-small cell lung cancer: Validation and new discoveries in an independent dataset.

INTRODUCTION: In 'IDEAL-6' patients (N = 78) treated for locally-advanced non-small-cell lung cancer using isotoxically dose-escalated radiotherapy, overall survival (OS) was associated more strongly with VLAwall-64-73-EQD2, the left atrial (LA) wall volume receiving 64-73 Gy equivalent dose in 2 Gy fractions (EQD2), than with whole-heart irradiation measures. Here we test this in an independent cohort 'OX-RT' (N = 64) treated routinely. METHODS: Using Cox regression analysis we assessed how strongly OS was associated with VLAwall-64-73-EQD2, with whole-heart volumes receiving 64-73 Gy EQD2 or doses above 10-to-70 Gy thresholds, and with principal components of whole-heart dose-distributions. Additionally, we tested associations between OS and volumes of cardiac substructures receiving dose-ranges described by whole-heart principal components significantly associated with OS. RESULTS: In univariable analyses of OX-RT, OS was associated more strongly with VLAwall-64-73-EQD2 than with whole-heart irradiation measures, but more strongly still with VAortV-29-38-EQD2, the volume of the aortic valve region receiving 29-38 Gy EQD2. The best multivariable OS model included LA wall and aortic valve region mean doses, and the aortic valve volume receiving ≥38 Gy EQD2, VAortV-38-EQD2. In a subsidiary analysis of IDEAL-6, the best multivariable model included VLAwall-64-73-EQD2, VAortV-29-38-EQD2, VAortV-38-EQD2 and mean aortic valve dose. CONCLUSION: We propose reducing heart mean doses to the lowest levels possible while meeting protocol dose-limits for lung, oesophagus, proximal bronchial tree, cord and brachial plexus. This in turn achieves large reductions in VAortV-29-38-EQD2 and VLAwall-64-73-EQD2, and we plan to closely monitor patients with values of these measures still >0% (their median value in OX-RT) following reduction.

Cardiac-sparing radiotherapy for locally advanced non-small cell lung cancer.

BACKGROUND: We have carried out a study to determine the scope for reducing heart doses in photon beam radiotherapy of locally advanced non-small cell lung cancer (LA-NSCLC). MATERIALS AND METHODS: Baseline VMAT plans were created for 20 LA-NSCLC patients following the IDEAL-CRT isotoxic protocol, and were re-optimized after adding an objective limiting heart mean dose (MDHeart). Reductions in MDHeart achievable without breaching limits on target coverage or normal tissue irradiation were determined. The process was repeated for objectives limiting the heart volume receiving ≥ 50 Gy (VHeart-50-Gy) and left atrial wall volume receiving ≥ 63 Gy (VLAwall-63-Gy). RESULTS: Following re-optimization, mean MDHeart, VHeart-50-Gy and VLAwall-63-Gy values fell by 4.8 Gy and 2.2% and 2.4% absolute respectively. On the basis of associations observed between survival and cardiac irradiation in an independent dataset, the purposefully-achieved reduction in MDHeart is expected to lead to the largest improvement in overall survival. It also led to useful knock-on reductions in many measures of cardiac irradiation including VHeart-50-Gy and VLAwall-63-Gy, providing some insurance against survival being more strongly related to these measures than to MDHeart. The predicted hazard ratio (HR) for death corresponding to the purposefully-achieved mean reduction in MDHeart was 0.806, according to which a randomized trial would require 1140 patients to test improved survival with 0.05 significance and 80% power. In patients whose baseline MDHeart values exceeded the median value in a published series, the average MDHeart reduction was particularly large, 8.8 Gy. The corresponding predicted HR is potentially testable in trials recruiting 359 patients enriched for greater MDHeart values. CONCLUSIONS: Cardiac irradiation in RT of LA-NSCLC can be reduced substantially. Of the measures studied, reduction of MDHeart led to the greatest predicted increase in survival, and to useful knock-on reductions in other cardiac irradiation measures reported to be associated with survival. Potential improvements in survival can be trialled more efficiently in a population enriched for patients with greater baseline MDHeart levels, for whom larger reductions in heart doses can be achieved.

Report of AAPM Task Group 155: Megavoltage photon beam dosimetry in small fields and non-equilibrium conditions.

Small-field dosimetry used in advance treatment technologies poses challenges due to loss of lateral charged particle equilibrium (LCPE), occlusion of the primary photon source, and the limited choice of suitable radiation detectors. These challenges greatly influence dosimetric accuracy. Many high-profile radiation incidents have demonstrated a poor understanding of appropriate methodology for small-field dosimetry. These incidents are a cause for concern because the use of small fields in various specialized radiation treatment techniques continues to grow rapidly. Reference and relative dosimetry in small and composite fields are the subject of the International Atomic Energy Agency (IAEA) dosimetry code of practice that has been published as TRS-483 and an AAPM summary publication (IAEA TRS 483; Dosimetry of small static fields used in external beam radiotherapy: An IAEA/AAPM International Code of Practice for reference and relative dose determination, Technical Report Series No. 483; Palmans et al., Med Phys 45(11):e1123, 2018). The charge of AAPM task group 155 (TG-155) is to summarize current knowledge on small-field dosimetry and to provide recommendations of best practices for relative dose determination in small megavoltage photon beams. An overview of the issue of LCPE and the changes in photon beam perturbations with decreasing field size is provided. Recommendations are included on appropriate detector systems and measurement methodologies. Existing published data on dosimetric parameters in small photon fields (e.g., percentage depth dose, tissue phantom ratio/tissue maximum ratio, off-axis ratios, and field output factors) together with the necessary perturbation corrections for various detectors are reviewed. A discussion on errors and an uncertainty analysis in measurements is provided. The design of beam models in treatment planning systems to simulate small fields necessitates special attention on the influence of the primary beam source and collimating devices in the computation of energy fluence and dose. The general requirements for fluence and dose calculation engines suitable for modeling dose in small fields are reviewed. Implementations in commercial treatment planning systems vary widely, and the aims of this report are to provide insight for the medical physicist and guidance to developers of beams models for radiotherapy treatment planning systems.

An approach to multiobjective optimization of rotational therapy. II. Pareto optimal surfaces and linear combinations of modulated blocked arcs for a prostate geometry.

PURPOSE: The purpose of this work is twofold: To further develop an approach to multiobjective optimization of rotational therapy treatments recently introduced by the authors [J. Pardo-Montero and J. D. Fenwick, "An approach to multiobjective optimization of rotational therapy," Med. Phys. 36, 3292-3303 (2009)], especially regarding its application to realistic geometries, and to study the quality (Pareto optimality) of plans obtained using such an approach by comparing them with Pareto optimal plans obtained through inverse planning. METHODS: In the previous work of the authors, a methodology is proposed for constructing a large number of plans, with different compromises between the objectives involved, from a small number of geometrically based arcs, each arc prioritizing different objectives. Here, this method has been further developed and studied. Two different techniques for constructing these arcs are investigated, one based on image-reconstruction algorithms and the other based on more common gradient-descent algorithms. The difficulty of dealing with organs abutting the target, briefly reported in previous work of the authors, has been investigated using partial OAR unblocking. Optimality of the solutions has been investigated by comparison with a Pareto front obtained from inverse planning. A relative Euclidean distance has been used to measure the distance of these plans to the Pareto front, and dose volume histogram comparisons have been used to gauge the clinical impact of these distances. A prostate geometry has been used for the study. RESULTS: For geometries where a blocked OAR abuts the target, moderate OAR unblocking can substantially improve target dose distribution and minimize hot spots while not overly compromising dose sparing of the organ. Image-reconstruction type and gradient-descent blocked-arc computations generate similar results. The Pareto front for the prostate geometry, reconstructed using a large number of inverse plans, presents a hockey-stick shape comprising two regions: One where the dose to the target is close to prescription and trade-offs can be made between doses to the organs at risk and (small) changes in target dose, and one where very substantial rectal sparing is achieved at the cost of large target underdosage. Plans computed following the approach using a conformal arc and four blocked arcs generally lie close to the Pareto front, although distances of some plans from high gradient regions of the Pareto front can be greater. Only around 12% of plans lie a relative Euclidean distance of 0.15 or greater from the Pareto front. Using the alternative distance measure of Craft ["Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization," Phys. Medica (to be published)], around 2/5 of plans lie more than 0.05 from the front. Computation of blocked arcs is quite fast, the algorithms requiring 35%-80% of the running time per iteration needed for conventional inverse plan computation. CONCLUSIONS: The geometry-based arc approach to multicriteria optimization of rotational therapy allows solutions to be obtained that lie close to the Pareto front. Both the image-reconstruction type and gradient-descent algorithms produce similar modulated arcs, the latter one perhaps being preferred because it is more easily implementable in standard treatment planning systems. Moderate unblocking provides a good way of dealing with OARs which abut the PTV. Optimization of geometry-based arcs is faster than usual inverse optimization of treatment plans, making this approach more rapid than an inverse-based Pareto front reconstruction.

Homogenized blocked arcs for multicriteria optimization of radiotherapy: analytical and numerical solutions.

PURPOSE: Homogenized blocked arcs are intuitively appealing as basis functions for multicriteria optimization of rotational radiotherapy. Such arcs avoid an organ-at-risk (OAR), spread dose out well over the rest-of-body (ROB), and deliver homogeneous doses to a planning target volume (PTV) using intensity modulated fluence profiles, obtainable either from closed-form solutions or iterative numerical calculations. Here, the analytic and iterative arcs are compared. METHODS: Dose-distributions have been calculated for nondivergent beams, both including and excluding scatter, beam penumbra, and attenuation effects, which are left out of the derivation of the analytic arcs. The most straightforward analytic arc is created by truncating the well-known Brahme, Roos, and Lax (BRL) solution, cutting its uniform dose region down from an annulus to a smaller nonconcave region lying beyond the OAR. However, the truncation leaves behind high dose hot-spots immediately on either side of the OAR, generated by very high BRL fluence levels just beyond the OAR. These hot-spots can be eliminated using alternative analytical solutions "C" and "L," which, respectively, deliver constant and linearly rising fluences in the gap region between the OAR and PTV (before truncation). RESULTS: Measured in terms of PTV dose homogeneity, ROB dose-spread, and OAR avoidance, C solutions generate better arc dose-distributions than L when scatter, penumbra, and attenuation are left out of the dose modeling. Including these factors, L becomes the best analytical solution. However, the iterative approach generates better dose-distributions than any of the analytical solutions because it can account and compensate for penumbra and scatter effects. Using the analytical solutions as starting points for the iterative methodology, dose-distributions almost as good as those obtained using the conventional iterative approach can be calculated very rapidly. CONCLUSIONS: The iterative methodology is appropriate and useful for computing homogenized blocked arcs, as it produces better dose-distributions than the analytic approaches and their obvious extensions, and can more straightforwardly be used to generate homogenized arcs for concave OARs. However, the analytical solutions provide promising starting points for the iterative algorithm, leading to fast convergence.

A mathematical model of dynamics of cell populations in squamous epithelium after irradiation.

PURPOSE: To develop multi-compartment mechanistic models of dynamics of stem and functional cell populations in epithelium after irradiation. Methods and materials: We present two models, with three (3C) and four (4C) compartments respectively. We use delay differential equations, and include accelerated proliferation, loss of division asymmetry, progressive death of abortive stem cells, and turnover of functional cells. The models are used to fit experimental data on the variations of the number of cells in mice mucosa after irradiation with 13 Gy and 20 Gy. Akaike information criteria (AIC) was used to evaluate the performance of each model. RESULTS: Both 3C and 4C models provide good fits to experimental data for 13 Gy. Fits for 20 Gy are slightly poorer and may be affected by larger uncertainties and fluctuations of experimental data. Best fits are obtained by imposing constraints on the fitting parameters, so to have values that are within experimental ranges. There is some degeneration in the fits, as different sets of parameters provide similarly good fits. CONCLUSIONS: The models provide good fits to experimental data. Mechanistic approaches like this can facilitate the development of mucositis response models to nonstandard schedules/treatment combinations not covered by datasets to which phenomenological models have been fitted. Studying the dynamics of cell populations in multifraction treatments, and finding links with induced toxicity, is the next step of this work.

Chemoradiotherapy of locally-advanced non-small cell lung cancer: Analysis of radiation dose-response, chemotherapy and survival-limiting toxicity effects indicates a low α/ß ratio.

PURPOSE: To analyse changes in 2-year overall survival (OS2yr) with radiotherapy (RT) dose, dose-per-fraction, treatment duration and chemotherapy use, in data compiled from prospective trials of RT and chemo-RT (CRT) for locally-advanced non-small cell lung cancer (LA-NSCLC). MATERIAL AND METHODS: OS2yr data was analysed for 6957 patients treated on 68 trial arms (21 RT-only, 27 sequential CRT, 20 concurrent CRT) delivering doses-per-fraction ≤4.0 Gy. An initial model considering dose, dose-per-fraction and RT duration was fitted using maximum-likelihood techniques. Model extensions describing chemotherapy effects and survival-limiting toxicity at high doses were assessed using likelihood-ratio testing, the Akaike Information Criterion (AIC) and cross-validation. RESULTS: A model including chemotherapy effects and survival-limiting toxicity described the data significantly better than simpler models (p < 10-14), and had better AIC and cross-validation scores. The fitted α/ß ratio for LA-NSCLC was 4.0 Gy (95%CI: 2.8-6.0 Gy), repopulation negated 0.38 (95%CI: 0.31-0.47) Gy EQD2/day beyond day 12 of RT, and concurrent CRT increased the effective tumour EQD2 by 23% (95%CI: 16-31%). For schedules delivered in 2 Gy fractions over 40 days, maximum modelled OS2yr for RT was 52% and 38% for stages IIIA and IIIB NSCLC respectively, rising to 59% and 42% for CRT. These survival rates required 80 and 87 Gy (RT or sequential CRT) and 67 and 73 Gy (concurrent CRT). Modelled OS2yr rates fell at higher doses. CONCLUSIONS: Fitted dose-response curves indicate that gains of ~10% in OS2yr can be made by escalating RT and sequential CRT beyond 64 Gy, with smaller gains for concurrent CRT. Schedule acceleration achieved via hypofractionation potentially offers an additional 5-10% improvement in OS2yr. Further 10-20% OS2yr gains might be made, according to the model fit, if critical normal structures in which survival-limiting toxicities arise can be identified and selectively spared.

Density compensated diodes for small field dosimetry: comprehensive testing and implications for design.

PURPOSE: In small megavoltage photon fields, the accuracies of an unmodified PTW 60017-type diode dosimeter and six diodes modified by adding airgaps of thickness 0.6-1.6 mm and diameter 3.6 mm have been comprehensively characterized experimentally and computationally. The optimally thick airgap for density compensation was determined, and detectors were micro-CT imaged to investigate differences between experimentally measured radiation responses and those predicted computationally. METHODS: Detectors were tested on- and off-axis, at 5 and 15 cm depths in 6 and 15 MV fields ≥ 0.5 × 0.5 cm2. Computational studies were carried out using the EGSnrc/BEAMnrc Monte Carlo radiation transport code. Experimentally, radiation was delivered using a Varian TrueBeam linac and doses absorbed by water were measured using Gafchromic EBT3 film and ionization chambers, and compared with diode readings. Detector response was characterized via the [Formula: see text] formalism, choosing a 4 × 4 cm2 reference field. RESULTS: For the unmodified 60017 diode, the maximum error in small field doses obtained from diode readings uncorrected by [Formula: see text] factors was determined as 11.9% computationally at +0.25 mm off-axis and 5 cm depth in a 15 MV 0.5 × 0.5 cm2 field, and 11.7% experimentally at -0.30 mm off-axis and 5 cm depth in the same field. A detector modified to include a 1.6 mm thick airgap performed best, with maximum computationally and experimentally determined errors of 2.2% and 4.1%. The 1.6 mm airgap deepened the modified dosimeter's effective point of measurement by 0.5 mm. For some detectors significant differences existed between responses in small fields determined computationally and experimentally, micro-CT imaging indicating that these differences were due to within-tolerance variations in the thickness of an epoxy resin layer. CONCLUSIONS: The dosimetric performance of a 60017 diode detector was comprehensively improved throughout 6 and 15 MV small photon fields via density compensation. For this approach to work well with good detector-to-detector reproducibility, tolerances on dense component dimensions should be reduced to limit associated variations of response in small fields, or these components should be modified to have more water-like densities.