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Objective. Modern radiotherapy stands to benefit from the ability to efficiently adapt plans during treatment in response to setup and geometric variations such as those caused by internal organ deformation or tumor shrinkage. A promising strategy is to develop a framework, which given an initial state defined by patient-attributes, can predict future states based on pre-learned patterns from a well-defined patient population. Approach. Here, we investigate the feasibility of predicting patient anatomical changes, defined as a joint state of volume and daily setup changes, across a fractionated treatment schedule using two approaches. The first is based on a new joint framework employing quantum mechanics in combination with deep recurrent neural networks, denoted QRNN. The second approach is developed based on a classical framework, which models patient changes as a Markov process, denoted MRNN. We evaluated the performance characteristics of these two approaches on a dataset of 125 head and neck cancer patients, which was supplemented by synthetic data generated using a generative adversarial network. Model performance was evaluated using area under the receiver operating characteristic curve (AUC) scores. Main results. The MRNN framework had slightly better performance than the QRNN framework, with MRNN (QRNN) validation AUC scores of 0.742±0.021 (0.675±0.036), 0.709±0.026 (0.656±0.021), 0.724±0.036 (0.652±0.044), and 0.698±0.016 (0.605±0.035) for system state vector sizes of 4, 6, 8, and 10, respectively. Of these, only the results from the two higher order states had statistically significant differences(p<0.05).A similar trend was also observed when the models were applied to an external testing dataset of 20 patients, yielding MRNN (QRNN) AUC scores of 0.707 (0.623), 0.687 (0.608), 0.723 (0.669), and 0.697 (0.609) for states vectors sizes of 4, 6, 8, and 10, respectively. Significance. These results suggest that both stochastic models have potential value in predicting patient changes during the course of adaptive radiotherapy., (© 2021 Institute of Physics and Engineering in Medicine.)

Purpose: Modern inverse radiotherapy treatment planning requires nonconvex, large-scale optimizations that must be solved within a clinically feasible timeframe. We have developed and tested a quantum-inspired, stochastic algorithm for intensity-modulated radiotherapy (IMRT): quantum tunnel annealing (QTA). By modeling the likelihood probability of accepting a higher energy solution after a particle tunneling through a potential energy barrier, QTA features an additional degree of freedom (the barrier width, w) not shared by traditional stochastic optimization methods such as Simulated Annealing (SA). This additional degree of freedom can improve convergence rates and achieve a more efficient and, potentially, effective treatment planning process., Methods: To analyze the character of the proposed QTA algorithm, we chose two stereotactic body radiation therapy (SBRT) liver cases of variable complexity. The "easy" first case was used to confirm functionality, while the second case, with a more challenging geometry, was used to characterize and evaluate the QTA algorithm performance. Plan quality was assessed using dose-volume histogram-based objectives and dose distributions. Due to the stochastic nature of the solution search space, extensive tests were also conducted to determine the optimal smoothing technique, ensuring balance between plan deliverability and the resulting plan quality. QTA convergence rates were investigated in relation to the chosen barrier width function, and QTA and SA performances were compared regarding sensitivity to the choice of solution initializations, annealing schedules, and complexity of the dose-volume constraints. Finally, we investigated the extension from beamlet intensity optimization to direct aperture optimization (DAO). Influence matrices were calculated using the Eclipse scripting application program interface (API), and the optimizations were run on the University of Michigan's high-performance computing cluster, Flux., Results: Our results indicate that QTA's barrier-width function can be tuned to achieve faster convergence rates. The QTA algorithm reached convergence up to 46.6% faster than SA for beamlet intensity optimization and up to 26.8% faster for DAO. QTA and SA were ultimately found to be equally insensitive to the initialization process, but the convergence rate of QTA was found to be more sensitive to the complexity of the dose-volume constraints. The optimal smoothing technique was found to be a combination of a Laplace-of-Gaussian (LOG) edge-finding filter implemented as a penalty within the objective function and a two-dimensional Savitzky-Golay filter applied to the final iteration; this achieved total monitor units more than 20% smaller than plans optimized by commercial treatment planning software., Conclusions: We have characterized the performance of a stochastic, quantum-inspired optimization algorithm, QTA, for radiotherapy treatment planning. This proof of concept study suggests that QTA can be tuned to achieve faster convergence than SA; therefore, QTA may be a good candidate for future knowledge-based or adaptive radiation therapy applications., (© 2019 American Association of Physicists in Medicine.)

Purpose: Individualization of therapeutic outcomes in NSCLC radiotherapy is likely to be compromised by the lack of proper balance of biophysical factors affecting both tumor local control (LC) and side effects such as radiation pneumonitis (RP), which are likely to be intertwined. Here, we compare the performance of separate and joint outcomes predictions for response-adapted personalized treatment planning., Methods: A total of 118 NSCLC patients treated on prospective protocols with 32 cases of local progression and 20 cases of RP grade 2 or higher (RP2) were studied. Sixty-eight patients with 297 features before and during radiotherapy were used for discovery and 50 patients were reserved for independent testing. A multiobjective Bayesian network (MO-BN) approach was developed to identify important features for joint LC/RP2 prediction using extended Markov blankets as inputs to develop a BN predictive structure. Cross-validation (CV) was used to guide the MO-BN structure learning. Area under the free-response receiver operating characteristic (AU-FROC) curve was used to evaluate joint prediction performance., Results: Important features including single nucleotide polymorphisms (SNPs), micro RNAs, pretreatment cytokines, pretreatment PET radiomics together with lung and tumor gEUDs were selected and their biophysical inter-relationships with radiation outcomes (LC and RP2) were identified in a pretreatment MO-BN. The joint LC/RP2 prediction yielded an AU-FROC of 0.80 (95% CI: 0.70-0.86) upon internal CV. This improved to 0.85 (0.75-0.91) with additional two SNPs, changes in one cytokine and two radiomics PET image features through the course of radiotherapy in a during-treatment MO-BN. This MO-BN model outperformed combined single-objective Bayesian networks (SO-BNs) during-treatment [0.78 (0.67-0.84)]. AU-FROC values in the evaluation of the MO-BN and individual SO-BNs on the testing dataset were 0.77 and 0.68 for pretreatment, and 0.79 and 0.71 for during-treatment, respectively., Conclusions: MO-BNs can reveal possible biophysical cross-talks between competing radiotherapy clinical endpoints. The prediction is improved by providing additional during-treatment information. The developed MO-BNs can be an important component of decision support systems for personalized response-adapted radiotherapy., (© 2018 American Association of Physicists in Medicine.)

Background: In non-small-cell lung cancer radiotherapy, radiation pneumonitis≥grade 2 (RP2) depends on patients' dosimetric, clinical, biological and genomic characteristics., Methods: We developed a Bayesian network (BN) approach to explore its potential for interpreting biophysical signaling pathways influencing RP2 from a heterogeneous dataset including single nucleotide polymorphisms, micro RNAs, cytokines, clinical data, and radiation treatment plans before and during the course of radiotherapy. Model building utilized 79 patients (21 with RP2) with complete data, and model testing used 50 additional patients with incomplete data. A developed large-scale Markov blanket approach selected relevant predictors. Resampling by k-fold cross-validation determined the optimal BN structure. Area under the receiver-operating characteristics curve (AUC) measured performance., Results: Pre- and during-treatment BNs identified biophysical signaling pathways from the patients' relevant variables to RP2 risk. Internal cross-validation for the pre-BN yielded an AUC=0.82 which improved to 0.87 by incorporating during treatment changes. In the testing dataset, the pre- and during AUCs were 0.78 and 0.82, respectively., Conclusions: Our developed BN approach successfully handled a high number of heterogeneous variables in a small dataset, demonstrating potential for unraveling relevant biophysical features that could enhance prediction of RP2, although the current observations would require further independent validation., (Copyright © 2017 Elsevier B.V. All rights reserved.)

Purpose: To quantify lung perfusion changes after breast/chest wall radiation therapy (RT) using pre- and post-RT single photon emission computed tomography/computed tomography (SPECT/CT) attenuation-corrected perfusion scans; and correlate decreased perfusion with adjuvant RT dose for breast cancer in a prospective clinical trial., Methods and Materials: As part of an institutional review board-approved trial studying the impact of RT technique on lung function in node-positive breast cancer, patients received breast/chest wall and regional nodal irradiation including superior internal mammary node RT to 50 to 52.2 Gy with a boost to the tumor bed/mastectomy scar. All patients underwent quantitative SPECT/CT lung perfusion scanning before RT and 1 year after RT. The SPECT/CT scans were co-registered, and the ratio of decreased perfusion after RT relative to the pre-RT perfusion scan was calculated to allow for direct comparison of SPECT/CT perfusion changes with delivered RT dose. The average ratio of decreased perfusion was calculated in 10-Gy dose increments from 0 to 60 Gy., Results: Fifty patients had complete lung SPECT/CT perfusion data available. No patient developed symptoms consistent with pulmonary toxicity. Nearly all patients demonstrated decreased perfusion in the left lung according to voxel-based analyses. The average ratio of lung perfusion deficits increased for each 10-Gy increment in radiation dose to the lung, with the largest changes in regions of lung that received 50 to 60 Gy (ratio 0.72 [95% confidence interval 0.64-0.79], P<.001) compared with the 0- to 10-Gy region. For each increase in 10 Gy to the left lung, the lung perfusion ratio decreased by 0.06 (P<.001)., Conclusions: In the assessment of 50 patients with node-positive breast cancer treated with RT in a prospective clinical trial, decreased lung perfusion by SPECT/CT was demonstrated. Our study allowed for quantification of lung perfusion defects in a prospective cohort of breast cancer patients for whom attenuation-corrected SPECT/CT scans could be registered directly to RT treatment fields for precise dose estimates., Competing Interests: The remaining authors report no conflicts of interest., (Copyright © 2016 Elsevier Inc. All rights reserved.)

Purpose: Limits on mean lung dose (MLD) allow for individualization of radiation doses at safe levels for patients with lung tumors. However, MLD does not account for individual differences in the extent or spatial distribution of pulmonary dysfunction among patients, which leads to toxicity variability at the same MLD. We investigated dose rearrangement to minimize the radiation dose to the functional lung as assessed by perfusion single photon emission computed tomography (SPECT) and maximize the target coverage to maintain conventional normal tissue limits., Methods and Materials: Retrospective plans were optimized for 15 patients with locally advanced non-small cell lung cancer who were enrolled in a prospective imaging trial. A staged, priority-based optimization system was used. The baseline priorities were to meet physical MLD and other dose constraints for organs at risk, and to maximize the target generalized equivalent uniform dose (gEUD). To determine the benefit of dose rearrangement with perfusion SPECT, plans were reoptimized to minimize the generalized equivalent uniform functional dose (gEUfD) to the lung as the subsequent priority., Results: When only physical MLD is minimized, lung gEUfD was 12.6 ± 4.9 Gy (6.3-21.7 Gy). When the dose is rearranged to minimize gEUfD directly in the optimization objective function, 10 of 15 cases showed a decrease in lung gEUfD of >20% (lung gEUfD mean 9.9 ± 4.3 Gy, range 2.1-16.2 Gy) while maintaining equivalent planning target volume coverage. Although all dose-limiting constraints remained unviolated, the dose rearrangement resulted in slight gEUD increases to the cord (5.4 ± 3.9 Gy), esophagus (3.0 ± 3.7 Gy), and heart (2.3 ± 2.6 Gy)., Conclusions: Priority-driven optimization in conjunction with perfusion SPECT permits image guided spatial dose redistribution within the lung and allows for a reduced dose to the functional lung without compromising target coverage or exceeding conventional limits for organs at risk.

Although large volumes of information are entered into our electronic health care records, radiation oncology information systems and treatment planning systems on a daily basis, the goal of extracting and using this big data has been slow to emerge. Development of strategies to meet this goal is aided by examining issues with a data farming instead of a data mining conceptualization. Using this model, a vision of key data elements, clinical process changes, technology issues and solutions, and role for professional societies is presented. With a better view of technology, process and standardization factors, definition and prioritization of efforts can be more effectively directed.

Purpose: To introduce a hybrid volumetric modulated arc therapy/intensity modulated radiation therapy (VMAT/IMRT) optimization strategy called FusionArc that combines the delivery efficiency of single-arc VMAT with the potentially desirable intensity modulation possible with IMRT., Methods: A beamlet-based inverse planning system was enhanced to combine the advantages of VMAT and IMRT into one comprehensive technique. In the hybrid strategy, baseline single-arc VMAT plans are optimized and then the current cost function gradients with respect to the beamlets are used to define a metric for predicting which beam angles would benefit from further intensity modulation. Beams with the highest metric values (called the gradient factor) are converted from VMAT apertures to IMRT fluence, and the optimization proceeds with the mixed variable set until convergence or until additional beams are selected for conversion. One phantom and two clinical cases were used to validate the gradient factor and characterize the FusionArc strategy. Comparisons were made between standard IMRT, single-arc VMAT, and FusionArc plans with one to five IMRT∕hybrid beams., Results: The gradient factor was found to be highly predictive of the VMAT angles that would benefit plan quality the most from beam modulation. Over the three cases studied, a FusionArc plan with three converted beams achieved superior dosimetric quality with reductions in final cost ranging from 26.4% to 48.1% compared to single-arc VMAT. Additionally, the three beam FusionArc plans required 22.4%-43.7% fewer MU∕Gy than a seven beam IMRT plan. While the FusionArc plans with five converted beams offer larger reductions in final cost--32.9%-55.2% compared to single-arc VMAT--the decrease in MU∕Gy compared to IMRT was noticeably smaller at 12.2%-18.5%, when compared to IMRT., Conclusions: A hybrid VMAT∕IMRT strategy was implemented to find a high quality compromise between gantry-angle and intensity-based degrees of freedom. This optimization method will allow patients to be simultaneously planned for dosimetric quality and delivery efficiency without switching between delivery techniques. Example phantom and clinical cases suggest that the conversion of only three VMAT segments to modulated beams may result in a good combination of quality and efficiency.

Purpose: To study the impact of daily rotations and translations of the prostate on dosimetric coverage during radiation therapy (RT)., Methods and Materials: Real-time tracking data for 26 patients were obtained during RT. Intensity modulated radiation therapy plans meeting RTOG 0126 dosimetric criteria were created with 0-, 2-, 3-, and 5-mm planning target volume (PTV) margins. Daily translations and rotations were used to reconstruct prostate delivered dose from the planned dose. D95 and V79 were computed from the delivered dose to evaluate target coverage and the adequacy of PTV margins. Prostate equivalent rotation is a new metric introduced in this study to quantify prostate rotations by accounting for prostate shape and length of rotational lever arm., Results: Large variations in prostate delivered dose were seen among patients. Adequate target coverage was met in 39%, 65%, and 84% of the patients for plans with 2-, 3-, and 5-mm PTV margins, respectively. Although no correlations between prostate delivered dose and daily rotations were seen, the data showed a clear correlation with prostate equivalent rotation., Conclusions: Prostate rotations during RT could cause significant underdosing even if daily translations were managed. These rotations should be managed with rotational tolerances based on prostate equivalent rotations., (Copyright © 2013 Elsevier Inc. All rights reserved.)

Purpose: Apertures obtained during volumetric modulated arc therapy (VMAT) planning can be small and irregular, resulting in dosimetric inaccuracies during delivery. Our purpose is to develop and integrate an aperture-regularization objective function into the optimization process for VMAT, and to quantify the impact of using this objective function on dose delivery accuracy and optimized dose distributions., Methods: An aperture-based metric ("edge penalty") was developed that penalizes complex aperture shapes based on the ratio of MLC side edge length and aperture area. To assess the utility of the metric, VMAT plans were created for example paraspinal, brain, and liver SBRT cases with and without incorporating the edge penalty in the cost function. To investigate the dose calculation accuracy, Gafchromic EBT2 film was used to measure the 15 highest weighted apertures individually and as a composite from each of two paraspinal plans: one with and one without the edge penalty applied. Films were analyzed using a triple-channel nonuniformity correction and measurements were compared directly to calculations., Results: Apertures generated with the edge penalty were larger, more regularly shaped and required up to 30% fewer monitor units than those created without the edge penalty. Dose volume histogram analysis showed that the changes in doses to targets, organs at risk, and normal tissues were negligible. Edge penalty apertures that were measured with film for the paraspinal plan showed a notable decrease in the number of pixels disagreeing with calculation by more than 10%. For a 5% dose passing criterion, the number of pixels passing in the composite dose distributions for the non-edge penalty and edge penalty plans were 52% and 96%, respectively. Employing gamma with 3% dose/1 mm distance criteria resulted in a 79.5% (without penalty)/95.4% (with penalty) pass rate for the two plans. Gradient compensation of 3%/1 mm resulted in 83.3%/96.2% pass rates., Conclusions: The use of the edge penalty during optimization has the potential to markedly improve dose delivery accuracy for VMAT plans while still maintaining high quality optimized dose distributions. The penalty regularizes aperture shape and improves delivery efficiency.

Purpose: Inverse planned intensity modulated radiation therapy (IMRT) has helped many centers implement highly conformal treatment planning with beamlet-based techniques. The many comparisons between IMRT and 3D conformal (3DCRT) plans, however, have been limited because most 3DCRT plans are forward-planned while IMRT plans utilize inverse planning, meaning both optimization and delivery techniques are different. This work avoids that problem by comparing 3D plans generated with a unique inverse planning method for 3DCRT called inverse-optimized 3D (IO-3D) conformal planning. Since IO-3D and the beamlet IMRT to which it is compared use the same optimization techniques, cost functions, and plan evaluation tools, direct comparisons between IMRT and simple, optimized IO-3D plans are possible. Though IO-3D has some similarity to direct aperture optimization (DAO), since it directly optimizes the apertures used, IO-3D is specifically designed for 3DCRT fields (i.e., 1-2 apertures per beam) rather than starting with IMRT-like modulation and then optimizing aperture shapes. The two algorithms are very different in design, implementation, and use. The goals of this work include using IO-3D to evaluate how close simple but optimized IO-3D plans come to nonconstrained beamlet IMRT, showing that optimization, rather than modulation, may be the most important aspect of IMRT (for some sites)., Methods: The IO-3D dose calculation and optimization functionality is integrated in the in-house 3D planning/optimization system. New features include random point dose calculation distributions, costlet and cost function capabilities, fast dose volume histogram (DVH) and plan evaluation tools, optimization search strategies designed for IO-3D, and an improved, reimplemented edge/octree calculation algorithm. The IO-3D optimization, in distinction to DAO, is designed to optimize 3D conformal plans (one to two segments per beam) and optimizes MLC segment shapes and weights with various user-controllable search strategies which optimize plans without beamlet or pencil beam approximations. IO-3D allows comparisons of beamlet, multisegment, and conformal plans optimized using the same cost functions, dose points, and plan evaluation metrics, so quantitative comparisons are straightforward. Here, comparisons of IO-3D and beamlet IMRT techniques are presented for breast, brain, liver, and lung plans., Results: IO-3D achieves high quality results comparable to beamlet IMRT, for many situations. Though the IO-3D plans have many fewer degrees of freedom for the optimization, this work finds that IO-3D plans with only one to two segments per beam are dosimetrically equivalent (or nearly so) to the beamlet IMRT plans, for several sites. IO-3D also reduces plan complexity significantly. Here, monitor units per fraction (MU/Fx) for IO-3D plans were 22%-68% less than that for the 1 cm × 1 cm beamlet IMRT plans and 72%-84% than the 0.5 cm × 0.5 cm beamlet IMRT plans., Conclusions: The unique IO-3D algorithm illustrates that inverse planning can achieve high quality 3D conformal plans equivalent (or nearly so) to unconstrained beamlet IMRT plans, for many sites. IO-3D thus provides the potential to optimize flat or few-segment 3DCRT plans, creating less complex optimized plans which are efficient and simple to deliver. The less complex IO-3D plans have operational advantages for scenarios including adaptive replanning, cases with interfraction and intrafraction motion, and pediatric patients., (© 2012 American Association of Physicists in Medicine.)

Purpose: Although previous work demonstrated superior dose distributions for left-sided breast cancer patients planned for intensity-modulated radiation therapy (IMRT) at deep inspiration breath hold compared with conventional techniques with free-breathing, such techniques are not always feasible to limit the impact of respiration on treatment delivery. This study assessed whether optimization based on multiple instance geometry approximation (MIGA) could derive an IMRT plan that is less sensitive to known respiratory motions., Methods and Materials: CT scans were acquired with an active breathing control device at multiple breath-hold states. Three inverse optimized plans were generated for eight left-sided breast cancer patients: one static IMRT plan optimized at end exhale, two (MIGA) plans based on a MIGA representation of normal breathing, and a MIGA representation of deep breathing, respectively. Breast and nodal targets were prescribed 52.2 Gy, and a simultaneous tumor bed boost was prescribed 60 Gy., Results: With normal breathing, doses to the targets, heart, and left anterior descending (LAD) artery were equivalent whether optimizing with MIGA or on a static data set. When simulating motion due to deep breathing, optimization with MIGA appears to yield superior tumor-bed coverage, decreased LAD mean dose, and maximum heart and LAD dose compared with optimization on a static representation., Conclusions: For left-sided breast-cancer patients, inverse-based optimization accounting for motion due to normal breathing may be similar to optimization on a static data set. However, some patients may benefit from accounting for deep breathing with MIGA with improvements in tumor-bed coverage and dose to critical structures.

Inverse-planned intensity modulated radiation therapy (IMRT) is often able to achieve complex treatment planning goals that are unattainable with forward three-dimensional (3D) conformal planning. However, the common use of IMRT has introduced several new challenges. The potentially high degree of modulation in IMRT beams risks the loss of some advantages of 3D planning, such as excellent target coverage and high delivery efficiency. Previous attempts to reduce beam complexity by smoothing often result in plan degradation because the smoothing algorithm cannot distinguish between areas of desirable and undesirable modulation. The purpose of this work is to introduce and evaluate adaptive diffusion smoothing (ADS), a novel procedure designed to preferentially reduce IMRT beam complexity. In this method, a discrete diffusion equation is used to smooth IMRT beams using diffusion coefficients, automatically defined for each beamlet, that dictate the degree of smoothing allowed for each beamlet. This yields a method that can distinguish between areas of desirable and undesirable modulation. The ADS method has been incorporated into our optimization system as a weighted cost function penalty, with two diffusion coefficient definitions designed to promote: (1) uniform smoothing everywhere or (2) smoothing based on cost function gradients with respect to the plan beamlet intensities. The ADS method (with both coefficient types) has been tested in a phantom and in two clinical examples (prostate and head/neck). Both types of diffusion coefficients produce plans with reduced modulation and minimal dosimetric impact, but the cost function gradient-based coefficients show more potential for reducing beam modulation without affecting dosimetric plan quality. In summary, adaptive diffusion smoothing is a promising tool for ensuring that only the necessary amount of beam modulation is used, promoting more efficient and accurate IMRT planning, QA, and delivery.

Optimization problems in IMRT inverse planning are inherently multicriterial since they involve multiple planning goals for targets and their neighbouring critical tissue structures. Clinical decisions are generally required, based on tradeoffs among these goals. Since the tradeoffs cannot be quantitatively determined prior to optimization, the decision-making process is usually indirect and iterative, requiring many repetitive optimizations. This situation becomes even more challenging for cases with a large number of planning goals. To address this challenge, a multicriteria optimization strategy called lexicographic ordering (LO) has been implemented and evaluated for IMRT planning. The LO approach is a hierarchical method in which the planning goals are categorized into different priority levels and a sequence of sub-optimization problems is solved in order of priority. This prioritization concept is demonstrated using two clinical cases (a simple prostate case and a relatively complex head and neck case). In addition, a unique feature of LO in a decision support role is discussed. We demonstrate that a comprehensive list of planning goals (e.g., approximately 23 for the head and neck case) can be optimized using only a few priority levels. Tradeoffs between different levels have been successfully prohibited using the LO method, making the large size problem representations simpler and more manageable. Optimization time needed for each level was practical, ranging from approximately 26 s to approximately 217 s. Using prioritization, the LO approach mimics the mental process often used by physicians as they make decisions handling the various conflicting planning goals. This method produces encouraging results for difficult IMRT planning cases in a highly intuitive manner.

The purpose of this study was to investigate the number of intermediate states required to adequately approximate the clinically relevant cumulative dose to deforming/moving thoracic anatomy in four-dimensional (4D) conformal radiotherapy that uses 6 MV photons to target tumors. Four patients were involved in this study. For the first three patients, computed tomography images acquired at exhale and inhale were available; they were registered using B-spline deformation model and the computed transformation was further used to simulate intermediate states between exhale and inhale. For the fourth patient, 4D-acquired, phase-sorted datasets were available and each dataset was registered with the exhale dataset. The exhale-inhale transformation was also used to simulate intermediate states in order to compare the cumulative doses computed using the actual and the simulated datasets. Doses to each state were calculated using the Dose Planning Method (DPM) Monte Carlo code and dose was accumulated for scoring on the exhale anatomy via the transformation matrices for each state and time weighting factors. Cumulative doses were estimated using increasing numbers of intermediate states and compared to simpler scenarios such as a "2-state" model which used only the exhale and inhale datasets or the dose received during the average phase of the breathing cycle. Dose distributions for each modeled state as well as the cumulative doses were assessed using dose volume histograms and several treatment evaluation metrics such as mean lung dose, normal tissue complication probability, and generalized uniform dose. Although significant "point dose" differences can exist between each breathing state, the differences decrease when cumulative doses are considered, and can become less significant yet in terms of evaluation metrics depending upon the clinical end point. This study suggests that for certain "clinical" end points of importance for lung cancer, satisfactory predictions of accumulated total dose to be received by the distorting anatomy can be achieved by calculating the dose to but a few (or even simply the average) phases of the breathing cycle.

Purpose: To investigate methods of reporting and analyzing statistical uncertainties in doses to targets and normal tissues in Monte Carlo (MC)-based treatment planning., Methods and Materials: Methods for quantifying statistical uncertainties in dose, such as uncertainty specification to specific dose points, or to volume-based regions, were analyzed in MC-based treatment planning for 5 lung cancer patients. The effect of statistical uncertainties on target and normal tissue dose indices was evaluated. The concept of uncertainty volume histograms for targets and organs at risk was examined, along with its utility, in conjunction with dose volume histograms, in assessing the acceptability of the statistical precision in dose distributions. The uncertainty evaluation tools were extended to four-dimensional planning for application on multiple instances of the patient geometry. All calculations were performed using the Dose Planning Method MC code., Results: For targets, generalized equivalent uniform doses and mean target doses converged at 150 million simulated histories, corresponding to relative uncertainties of less than 2% in the mean target doses. For the normal lung tissue (a volume-effect organ), mean lung dose and normal tissue complication probability converged at 150 million histories despite the large range in the relative organ uncertainty volume histograms. For "serial" normal tissues such as the spinal cord, large fluctuations exist in point dose relative uncertainties., Conclusions: The tools presented here provide useful means for evaluating statistical precision in MC-based dose distributions. Tradeoffs between uncertainties in doses to targets, volume-effect organs, and "serial" normal tissues must be considered carefully in determining acceptable levels of statistical precision in MC-computed dose distributions.

Radiotherapy treatment plans that are optimized to be highly conformal based on a static patient geometry can be degraded by setup errors and/or intratreatment motion, particularly for IMRT plans. To achieve improved plans in the face of geometrical uncertainties, direct simulation of multiple instances of the patient anatomy (to account for setup and/or motion uncertainties) is used within the inverse planning process. This multiple instance geometry approximation (MIGA) method uses two or more instances of the patient anatomy and optimizes a single beam arrangement for all instances concurrently. Each anatomical instance can represent expected extremes or a weighted distribution of geometries. The current implementation supports mapping between instances that include distortions, but this report is limited to the use of rigid body translations/ rotations. For inverse planning, the method uses beamlet dose calculations for each instance, with the resulting doses combined using a weighted sum of the results for the multiple instances. Beamlet intensities are then optimized using the inverse planning system based on the cost for the composite dose distribution. MIGA can simulate various types of geometrical uncertainties, including random setup error and intratreatment motion. A limited number of instances are necessary to simulate Gaussian-distributed errors. IMRT plans optimized using MIGA show significantly less degradation in the face of geometrical errors, and are robust to the expected (simulated) motions. Results for a complex head/neck plan involving multiple target volumes and numerous normal structures are significantly improved when the MIGA method of inverse planning is used. Inverse planning using MIGA can lead to significant improvements over the use of simple PTV volume expansions for inclusion of geometrical uncertainties into inverse planning, since it can account for the correlated motions of the entire anatomical representation. The optimized plan results reflect the differing patient geometry situations which can be important near the surface or heterogeneities. For certain clinical situations, the MIGA optimization approach can correct for a significant part of the degradation of the plan caused by the setup uncertainties.

Purpose: A mechanism has been developed to evaluate the influence of random setup variations on dose during treatment planning. The information available for studying these factors shifts from population-based models toward patient-specific data as treatment progresses and setup measurements for an individual patient become available. This study evaluates the influence of population as well as patient-specific setup distributions on treatment plans for focal liver tumors., Methods and Materials: Eight patients with focal liver tumors were treated on a protocol that involved online setup measurement and adjustment, as well as ventilatory immobilization. Summary statistics from these three-dimensional conformal treatments yielded individual and population distributions of position at initial setup for each fraction. A convolution model for evaluation of the influence of random setup variation on calculated dose distributions has been previously described and investigated for application to focal liver radiotherapy by our department. Individual patient doses based on initial setup positions were calculated by convolving the calculated dose distribution with an anisotropic probability distribution function representing the individual patient's random variations. A separate convolution using population-averaged random variations was performed. Individual beam apertures were then adjusted to provide plans that ensured proper dose to the clinical target volume following convolution with population distributions, as well as individual patient position uncertainty models., Results: Individual patient setup distributions for the course of treatment had random setup variations (sigma) that ranged from 2.5 to 5.7 mm (left-right), 2.1 to 8.3 mm (anterior-posterior), and 4.1 to 10.8 mm (cranial-caudal). The population random components were 4.2 mm (left-right), 4.1 mm (anterior-posterior), and 7.0 mm (cranial-caudal) at initial setup. The initial static planned dose distribution overestimated the volume of liver irradiated to high doses, because inclusion of setup uncertainties generally blurred the resulting doses, shifting the higher-dose region of normal liver dose-volume histograms to lower doses. Furthermore, the population-based dose convolution tended to predict a higher risk of radiation damage to the liver (based on an in-house parameterization of the Lyman normal tissue complication probability model) than the individual patient calculations. For an individual plan, application of different individual random variations yielded change in effective volume differences with a 3% range. Plan adjustment to account for random setup variations generally resulted in a lower change in effective volume than initial planning using a planning target volume followed by calculation of delivered dose based on random offsets., Conclusion: This study hints at the factors that most strongly influence planning of liver treatments taking into account geometric variations. Given a setup verification methodology that rapidly reduces systematic offsets, the importance of realistic incorporation of geometric variations as an initial step in treatment planning, as well as possible plan refinement, is demonstrated.

Despite the well-known benefits of positron emission tomography (PET) imaging in lung cancer diagnosis and staging, the poor spatial resolution of PET has limited its use in radiotherapy planning. Methods used for segmenting tumor from normal tissue, such as threshold boundaries using a fraction of the standardized uptake value (SUV), are subject to uncertainties. The issue of respiratory motion in the thorax confounds the problem of accurate target definition. In this work, we evaluate how changing the PET-defined target volume by varying the threshold value in the segmentation process impacts target and normal lung tissue doses. For each of eight lung cancer patients we retrospectively generated multiple PET-target volumes; each target volume corresponds to those voxels with intensities above a given threshold level, defined by a percentage of the maximum voxel intensity. PET-defined targets were compared to those from CT; CT targets comprise a composite volume generated from breath-hold inhale and exhale datasets; the CT dataset therefore also includes the extents of tumor motion. Treatment plans using Monte Carlo dose calculation were generated for all targets; the dose uniformity was approximately 100+/-5% within the internal target volume (ITV) (formed by a uniform 8-mm expansion of the composite gross target volume (GTV)). In all cases differences were observed in the generalized equivalent uniform doses (gEUDs) to the targets and in the mean lung doses (MLDs) and normal tissue complication probabilities (NTCPs) to the normal lung tissues. The magnitudes of the dose differences were found to depend on the target volume, location, and amount of irradiated normal lung tissue, and in many instances were clinically meaningful (greater than a single 2 Gy fraction). For those patients studied, results indicate that accurate dosimetry using PET volumes is highly dependent on accurate target segmentation. Further study with correlation to clinical outcome will be helpful in determining how to apply these various PET and CT volumes in treatment planning, to potentially improve local tumor control and reduce normal tissue toxicities.

In this study we investigated the accumulation of dose to a deforming anatomy (such as lung) based on voxel tracking and by using time weighting factors derived from a breathing probability distribution function (p.d.f.). A mutual information registration scheme (using thin-plate spline warping) provided a transformation that allows the tracking of points between exhale and inhale treatment planning datasets (and/or intermediate state scans). The dose distributions were computed at the same resolution on each dataset using the Dose Planning Method (DPM) Monte Carlo code. Two accumulation/interpolation approaches were assessed. The first maps exhale dose grid points onto the inhale scan, estimates the doses at the "tracked" locations by trilinear interpolation and scores the accumulated doses (via the p.d.f.) on the original exhale data set. In the second approach, the "volume" associated with each exhale dose grid point (exhale dose voxel) is first subdivided into octants, the center of each octant is mapped to locations on the inhale dose grid and doses are estimated by trilinear interpolation. The octant doses are then averaged to form the inhale voxel dose and scored at the original exhale dose grid point location. Differences between the interpolation schemes are voxel size and tissue density dependent, but in general appear primarily only in regions with steep dose gradients (e.g., penumbra). Their magnitude (small regions of few percent differences) is less than the alterations in dose due to positional and shape changes from breathing in the first place. Thus, for sufficiently small dose grid point spacing, and relative to organ motion and deformation, differences due solely to the interpolation are unlikely to result in clinically significant differences to volume-based evaluation metrics such as mean lung dose (MLD) and tumor equivalent uniform dose (gEUD). The overall effects of deformation vary among patients. They depend on the tumor location, field size, volume expansion, tissue heterogeneity, and direction of tumor displacement with respect to the beam, and are more likely to have an impact on serial organs (such as esophagus), rather than on large parallel organs (such as lung).

In this study, we show that beam model differences play an important role in the comparison of does calculated with various algorithms for lung cancer treatment planning. These differences may impact the accurate correlation of dose with clinical outcome. To accomplish this, we modified the beam model penumbral parameters in an equivalent path length (EPL) algorithm and subsequently compared the EPL doses with those generated with Monte Carlo (MC). A single AP beam was used for beam fitting. Two different beam models were generated for EPL calculations: (1) initial beam model (init&#95;fit) and (2) optimized beam model (best&#95;fit) , with parameters optimized to produce the best agreement with MC calculated profiles at several depths in a water phantom. For the 6 MV, AP beam, EPL(init&#95;fit) calculations were on average within 2%/2 mm (1.4 mm max.) agreement with MC; the agreement for EPL(best&#95;fit) was 2%/1.0 mm (1.3 mm max.) for EPL(best&#95;fit). Treatment planning was performed using a realistic lung phantom using 6 and 15 MV photons. In all homogeneous phantom plans, EPL(best&#95;fit) calculations were in better agreement with MC. In the heterogeneous 6 MV plan, differences between EPL(best&#95;fit and init&#95;fit) and MC were significant for the tumour. The EPL(init&#95;fit), unlike the EPL(best&#95;fit) calculation, showed large differences in the lung relative to MC. For the 15 MV heterogeneous plan, clinically important differences were found between EPL(best&#95;fit or init&#95;fit) and MC for tumour and lung, suggesting that the algorithmic difference in inhomogeneous cases, differences between EPL(best&#95;fit) and MC for lung tissues were smaller compared to those between EPL(init&#95;fit) and MC. Although the extent to which beam model differences impact the dose comparisons will be dependent upon beam parameters (orientation, field size and energy), and the size and location of the tumour, this study shows that failing to correctly account for beam model differences will lead to biased comparisons between dose algorithms. This may ultimately hinder our ability to accurately correlate dose with clinical outcome.

The advent of dynamic radiotherapy modeling and treatment techniques requires an infrastructure to weigh the merits of various interventions (breath holding, gating, tracking). The creation of treatment planning models that account for motion and deformation can allow the relative worth of such techniques to be evaluated. In order to develop a treatment planning model of a moving and deforming organ such as the lung, registration tools that account for deformation are required. We tested the accuracy of a mutual information based image registration tool using thin-plate splines driven by the selection of control points and iterative alignment according to a simplex algorithm. Eleven patients each had sequential CT scans at breath-held normal inhale and exhale states. The exhale right lung was segmented from CT and served as the reference model. For each patient, thirty control points were used to align the inhale CT right lung to the exhale CT right lung. Alignment accuracy (the standard deviation of the difference in the actual and predicted inhale position) was determined from locations of vascular and bronchial bifurcations, and found to be 1.7, 3.1, and 3.6 mm about the RL, AP, and IS directions. The alignment accuracy was significantly different from the amount of measured movement during breathing only in the AP and IS directions. The accuracy of alignment including thin-plate splines was more accurate than using affine transformations and the same iteration and scoring methodology. This technique shows promise for the future development of dynamic models of the lung for use in four-dimensional (4-D) treatment planning.

We have applied convolution methods to account for some of the effects of respiratory induced motion in clinical treatment planning of the lung. The 3-D displacement of the GTV center-of-mass (COM) as determined from breath-hold exhale and inhale CT scans was used to approximate the breathing induced motion. The time-course of the GTV-COM was estimated using a probability distribution function (PDF) previously derived from diaphragmatic motion [Med. Phys. 26, 715-720 (1990)] but also used by others for treatment planning in the lung [Int. J. Radiat. Oncol., Biol., Phys. 53, 822-834 (2002); Med. Phys. 30, 1086-1095 (2003)]. We have implemented fluence and dose convolution methods within a Monte Carlo based dose calculation system with the intent of comparing these approaches for planning in the lung. All treatment plans in this study have been calculated with Monte Carlo using the breath-hold exhale CT data sets. An analysis of treatment plans for 3 patients showed substantial differences (hot and cold spots consistently greater than +/- 15%) between the motion convolved and static treatment plans. As fluence convolution accounts for the spatial variance of the dose distribution in the presence of tissue inhomogeneities, the doses were approximately 5% greater than those calculated with dose convolution in the vicinity of the lung. DVH differences between the static, fluence and dose convolved distributions for the CTV were relatively small, however, larger differences were observed for the PTV. An investigation of the effect of the breathing PDF asymmetry on the motion convolved dose distributions showed that reducing the asymmetry resulted in increased hot and cold spots in the motion convolved distributions relative to the static cases. In particular, changing from an asymmetric breathing function to one that is symmetric results in an increase in the hot/cold spots of +/- 15% relative to the static plan. This increase is not unexpected considering that the target spends relatively more time at inhale as the asymmetry decreases (note that the treatment plans were generated using the exhale CT scans).

Purpose: To assess the clinical significance of differences between treatment planning calculations based on static computed tomography (CT) and more realistic predictions of the actual delivered dose to intrahepatic lesions by a geometric convolution approach that accounts for random setup variations and breathing-induced organ motion., Materials and Methods: We recalculated target and normal liver doses for 40 patients previously treated on a conformal therapy dose escalation protocol to include the effect of setup uncertainties and liver motion due to patient breathing. Initial three-dimensional (3D) dose calculations based on pretreatment CT scans taken with voluntary breath-hold at normal exhalation were convolved with 3D anisotropic probability distribution functions reflecting population measurements of position setup variation. The convolution also included a distribution function (one-dimensional, inferior-superior direction only) representing the asymmetric temporal pattern (biased toward exhalation, based on population measurements) of a typical breathing cycle, scaled in amplitude for each patient., Results: After convolution, the minimum clinical target volume (CTV) dose met or exceeded the minimum planning target volume (PTV) dose from the static plan in all but one case, indicating adequate PTV design. However, clinically relevant and statistically significant increases (decreases) in liver normal tissue complication probability (NTCP) from values computed for the static cases occurred for tumors located toward the bottom (top) of the liver, as predicted for these patients scanned at exhalation. The change in liver NTCP (from a nominal 20%) ranged from +12.0% to -11.7% (average magnitude change 3.9% [sigma = 3.3%]). Changes in prescription dose required to restore the original 20% NTCP ranged from -3.7 Gy to +7.9 Gy (average magnitude change 1.9 Gy [sigma = 1.9 Gy])., Conclusions: Although the PTV concept can ensure adequate CTV coverage, the doses to normal liver are incorrectly modeled without including patient-related geometric uncertainties.

Purpose: To develop an intensity modulated radiotherapy (IMRT) technique for postmastectomy RT that improves target coverage while sparing all appropriate normal tissues., Materials and Methods: IMRT plans were generated using an in-house optimization system. Priority was given to matching the heart doses achieved with partially wide tangent fields (PWTFs) while maintaining 50 Gy +/- 5% to the chest wall, internal mammary nodes, and supraclavicular nodes. Other normal tissue doses were then minimized. Metrics for plan comparisons included minimal, maximal, and mean doses and normal tissue complication probability., Results: IMRT resulted in more uniform chest wall coverage than did PWTFs. The average chest wall minimal dose was 43.7 +/- 1.1 Gy for IMRT and 31.2 +/- 16.5 Gy for PWTFs (p = 0.04). The average internal mammary node minimal dose was 42.8 +/- 2.1 Gy for IMRT and 21.8 +/- 13.2 Gy for PWTFs (p = 0.001). IMRT matched the <1% heart normal tissue complication probability achieved using PWTFs. The average contralateral breast mean dose was 2.8 +/- 1.7 Gy for IMRT, but a greater breast volume was exposed compared with PWTFs. The mean ipsilateral lung normal tissue complication probability was lower for IMRT (0.0) than for PWTFs (0.07 +/- 0.07; p = 0.02). The mean contralateral lung dose was greater for IMRT (5.8 +/- 1.8 Gy) than for PWTFs (1.6 +/- 0.1 Gy; p = <0.0001)., Conclusion: A new IMRT technique achieves full target coverage while maintaining similar doses to heart and ipsilateral lung as conventional techniques. However, contralateral lung and breast volumes exposed to low doses were increased with IMRT and will need to be reduced in future studies.

We describe the implementation of a fluence convolution method to account for the influence of superior-inferior (SI) respiratory induced motion on a Monte Carlo-based dose calculation of a tumor located in the liver. This method involves convolving the static fluence map with a function describing the SI motion of the liver-the motion function has been previously derived from measurements of diaphragm movement observed under fluoroscopy. Significant differences are noted between fluence-convolved and static dose distributions in an example clinical treatment plan; hot and cold spots (on the order of 25%) are observed in the fluence-convolved plan at the superior and inferior borders of the liver, respectively. This study illustrates that the fluence convolution method can be incorporated into Monte Carlo dose calculation algorithms to account for some of the effects of patient breathing during radiotherapy treatment planning, thus leading to more accurate dose calculations.

Validation experiments have been conducted using 6 and 15 MV photons in inhomogeneous (water/lung/water) media to benchmark the accuracy of the DPM Monte Carlo code for photon beam dose calculations. Small field sizes (down to 2 x 2 cm2) and low-density media were chosen for this investigation because the intent was to test the DPM code under conditions where lateral electronic disequilibrium effects are emphasized. The treatment head components of a Varian 21EX linear accelerator, including the jaws (defining field sizes of 2 x 2, 3 x 3 and 10 x 10 cm2), were simulated using the BEAMnrc code. The phase space files were integrated within the DPM code system, and central axis depth dose and profile calculations were compared against diode measurements in a homogeneous water phantom in order to validate the phase space. Results of the homogeneous phantom study indicated that the relative differences between DPM calculations and measurements were within +/- 1% (based on the rms deviation) for the depth dose curves; relative profile dose differences were on average within +/- 1%/1 mm. Depth dose and profile measurements were carried out using an ion-chamber and film, within an inhomogeneous phantom consisting of a 6 cm slab of lung-equivalent material embedded within solid water. For the inhomogeneous phantom experiment, DPM depth dose calculations were within +/- 1% (based on the rms deviation) of measurements; relative profile differences at depths within and beyond the lung were, on average, within +/- 2% in the inner and outer beam regions, and within 1-2 mm distance-to-agreement within the penumbral region. Relative point differences on the order of 2-3% were within the estimated experimental uncertainties. This work demonstrates that the DPM Monte Carlo code is capable of accurate photon beam dose calculations in situations where lateral electron disequilibrium effects are pronounced.

A previously described system for modeling organ deformation using finite element analysis has been extended to permit dose calculation. Using this tool, the calculated dose to the liver during radiotherapy can be compared using a traditional static model (STATIC), a model including rigid body motion (RB), and finally a model that incorporates rigid body motion and deformation (RBD). A model of the liver, consisting of approximately 6000 tetrahedral finite elements distributed throughout the contoured volume, is created from the CT data obtained at exhale. A deformation map is then created to relate the liver in the exhale CT data to the liver in the inhale CT data. Six intermediate phase positions of each element are then calculated from their trajectories. The coordinates of the centroid of each element at each phase are used to determine the dose received. These intermediate dose values are then time weighted according to a population-modeled breathing pattern to determine the total dose to each element during treatment. This method has been tested on four patient datasets. The change in prescribed dose for each patient's actual tumor as well as a simulated tumor of the same size, located in the superior, intermediate, and inferior regions of the liver, was determined using a normal tissue complication model, maintaining a predicted probability of complications of 15%. The average change in prescribed dose from RBD to STATIC for simulated tumors in the superior, intermediate, and inferior regions are 4.0 (range 2.1 to 5.3), -3.6 (range -5.0 to -2.2), and -14.5 (range -27.0 to -10.0) Gy, respectively. The average change in prescribed dose for the patient's actual tumor was -0.4 Gy (range -4.1 to 1.7 Gy). The average change in prescribed dose from RBD to RB for simulated tumors in the superior, intermediate, and inferior regions are -0.04 (range -2.4 to 2.2), 0.2 (range -1.5 to 1.9), and 3.9 (range 0.8 to 7.3) Gy, respectively. The average change in the prescribed dose for the patient's actual tumor was 0.7 Gy (range 0.2 to 1.1 Gy). This patient sampling indicates the potential importance of including deformation in dose calculations.

A comprehensive set of measurements and calculations has been conducted to investigate the accuracy of the Dose Planning Method (DPM) Monte Carlo code for electron beam dose calculations in heterogeneous media. Measurements were made using 10 MeV and 50 MeV minimally scattered, uncollimated electron beams from a racetrack microtron. Source distributions for the Monte Carlo calculations were reconstructed from in-air ion chamber scans and then benchmarked against measurements in a homogeneous water phantom. The in-air spatial distributions were found to have FWHM of 4.7 cm and 1.3 cm, at 100 cm from the source, for the 10 MeV and 50 MeV beams respectively. Energy spectra for the electron beams were determined by simulating the components of the microtron treatment head using the code MCNP4B. Profile measurements were made using an ion chamber in a water phantom with slabs of lung or bone-equivalent materials submerged at various depths. DPM calculations are, on average, within 2% agreement with measurement for all geometries except for the 50 MeV incident on a 6 cm lung-equivalent slab. Measurements using approximately monoenergetic, 50 MeV, 'pencil-beam'-type electrons in heterogeneous media provide conditions for maximum electronic disequilibrium and hence present a stringent test of the code's electron transport physics; the agreement noted between calculation and measurement illustrates that the DPM code is capable of accurate dose calculation even under such conditions.

A comprehensive set of measurements and calculations has been conducted to investigate the accuracy of the Dose Planning Method (DPM) Monte Carlo code for dose calculations from 10 and 50 MeV scanned electron beams produced from a racetrack microtron. Central axis depth dose measurements and a series of profile scans at various depths were acquired in a water phantom using a Scanditronix type RK ion chamber. Source spatial distributions for the Monte Carlo calculations were reconstructed from in-air ion chamber measurements carried out across the two-dimensional beam profile at 100 cm downstream from the source. The in-air spatial distributions were found to have full width at half maximum of 4.7 and 1.3 cm, at 100 cm from the source, for the 10 and 50 MeV beams, respectively. Energy spectra for the 10 and 50 MeV beams were determined by simulating the components of the microtron treatment head using the code MCNP4B. DPM calculations are on average within +/- 2% agreement with measurement for all depth dose and profile comparisons conducted in this study. The accuracy of the DPM code illustrated in this work suggests that DPM may be used as a valuable tool for electron beam dose calculations.

A study was performed to determine the relative advantage of computer-controlled couch movement versus manual repositioning to correct patient setup error measured using an electronic portal imaging device (EPID). Twenty-eight on-line setup adjustment trials of anterior-posterior (AP) pelvic projections were evaluated, with 13 setups corrected by automated couch movement determined by direct feedback from the EPID image alignment tool and 15 setups manually corrected based on the transformation displayed from the same tool. The speed of setup adjustment and accuracy of corrected setup were determined. Computer controlled setup adjustment was determined to be faster (25.4 s versus 101.9 s) and slightly more accurate (1.8 mm versus 2.5 mm error in adjusted setup) than manual correction.

Purpose: To study the impact of incorporation of lung perfusion information in the optimization of radical radiotherapy (RT) treatment plans for patients with medically inoperable non-small cell lung cancer (NSCLC)., Materials and Methods: The treatment plans for a virtual phantom and for five NSCLC patients with typical defects of pre-RT lung perfusion were optimized to minimize geometrically determined parameters as the mean lung dose (MLD), the lung volume receiving more than 20 Gy (V20), and the functional equivalent of the MLD, using perfusion-weighted dose-volume histograms. For the patients the (perfusion-weighted) optimized plans were compared to the clinically applied treatment plans., Results: The feasibility of perfusion-weighted optimization was demonstrated in the phantom. Using perfusion information resulted in an increase of the weights of those beams that were directed through the hypo-perfused lung regions both for the phantom and for the studied patients. The automatically optimized dose distributions were improved with respect to lung toxicity compared with the clinical treatment plans. For patients with one hypo-perfused hemi-thorax, the estimated gain in post-RT lung perfusion was 6% of the prescribed dose compared to the geometrically optimized plan. For patients with smaller perfusion defects, perfusion-weighted optimization resulted in the same plan as the geometrically optimized plan., Conclusion: Perfusion-weighted optimization resulted in clinically well applicable treatment plans, which cause less radiation damage to functioning lung for patients with large perfusion defects.

Purpose: Various published reports involving intensity-modulated radiotherapy (IMRT) plans developed using automated optimization (inverse planning) have demonstrated highly conformal plans. These reported conformal IMRT plans involve significant target dose inhomogeneity, including both overdosage and underdosage within the target volume. In this study, we demonstrate the development of optimized beamlet IMRT plans that satisfy rigorous dose homogeneity requirements for all target volumes (e.g., +/-5%), while also sparing the parotids and other normal structures., Methods and Materials: The treatment plans of 15 patients with oropharyngeal cancer who were previously treated with forward-planned multisegmental IMRT were planned again using an automated optimization system developed in-house. The optimization system allows for variable sized beamlets computed using a three-dimensional convolution/superposition dose calculation and flexible cost functions derived from combinations of clinically relevant factors (costlets) that can include dose, dose-volume, and biologic model-based costlets. The current study compared optimized IMRT plans designed to treat the various planning target volumes to doses of 66, 60, and 54 Gy with varying target dose homogeneity while using a flexible optimization cost function to minimize the dose to the parotids, spinal cord, oral cavity, brainstem, submandibular nodes, and other structures., Results: In all cases, target dose uniformity was achieved through steeply varying dose-based costs. Differences in clinical plan evaluation metrics were evaluated for individual cases (eight different target homogeneity costlets), and for the entire cohort of plans. Highly conformal plans were achieved, with significant sparing of both the contralateral and ipsilateral parotid glands. As the homogeneity of the target dose distributions was allowed to decrease, increased sparing of the parotids (and other normal tissues) may be achieved. However, it was shown that relatively few patients would benefit from the use of increased target inhomogeneity, because the range of improvement in the parotid dose is relatively limited. Hot spots in the target volumes are shown to be unnecessary and do not assist in normal tissue sparing., Conclusion: Sparing of both parotids in patients receiving bilateral neck radiation can be achieved without compromising strict target dose homogeneity criteria. The geometry of the normal tissue and target anatomy are shown to be the major factor necessary to predict the parotid sparing that will be possible for any particular case.

Purpose: A system has been implemented for daily localization of the prostate through radiographic localization of implanted markers. This report summarizes an initial trial to establish the accuracy of patient setup via this system., Methods and Materials: Before radiotherapy, three radiopaque markers are implanted in the prostate periphery. Reference positions are established from CT data. Before treatment, orthogonal radiographs are acquired. Projected marker positions are extracted semiautomatically from the radiographs and aligned to the reference positions. Computer-controlled couch adjustment is performed, followed by acquisition of a second pair of radiographs to verify prostate position. Ten patients (6 prone, 4 supine) participated in a trial of daily positioning., Results: Three hundred seventy-four fractions were treated using this system. Treatment times were on the order of 30 minutes. Initial prostate position errors (sigma) ranged from 3.1 to 5.8 mm left-right, 4.0 to 10.1 mm anterior-posterior, and 2.6 to 9.0 mm inferior-superior in prone patients. Initial position was more reproducible in supine patients, with errors of 2.8 to 5.0 mm left-right, 1.9 to 3.0 mm anterior-posterior, and 2.6 to 5.3 mm inferior-superior. After prostate localization and adjustment, the position errors were reduced to 1.3 to 3.5 mm left-right, 1.7 to 4.2 mm anterior-posterior, and 1.6 to 4.0 mm inferior-superior in prone patients, and 1.2 to 1.8 mm left-right, 0.9 to 1.8 mm anterior-posterior, and 0.8 to 1.5 mm inferior-superior in supine patients., Conclusions: Daily targeting of the prostate has been shown to be technically feasible. The implemented system provides the ability to significantly reduce treatment margins for most patients with cancer confined to the prostate. The differences in final position accuracy between prone and supine patients suggest variations in intratreatment prostate movement related to mechanisms of patient positioning.

Purpose: To reduce the dose in the rectal wall from prostate irradiation at high dose levels., Methods and Materials: Treatment plans in which the boost fields were integrated into the large fields (simultaneous integrated boost [SIB]) were compared with plans in which the large fields and boost fields were planned individually and applied in a sequential manner (sequential boost). Two target volumes were delineated: PTV1, the target volume of the large fields that is irradiated to 68 Gy, and PTV2, the target volume of the boost fields that is irradiated to 10 Gy. The sequential boost and the SIB were normalized to the mean dose in PTV2, being 78 Gy. We used a five-field intensity-modulated radiotherapy (IMRT) technique, applied in a step and shoot mode, and included beam weight optimization. A set of 5 patients with varying degree of overlap between PTV1 and the rectal wall was used for analysis., Results: The SIB resulted in a reduction of the dose in the rectal wall. Rectal normal tissue complication probability (NTCP) decreased for the SIB, on average, by a factor of almost 2, compared with the sequential boost., Conclusion: The SIB reduced the dose in the rectal wall, compared with the sequential boost technique.

Introduction: A system has been developed for daily targeting of intrahepatic tumors using a combination of ventilatory immobilization, in-room diagnostic imaging, and on-line setup adjustment. By reducing geometric position uncertainty, as well as organ movement, this system permits reduction of margins and thus potentially higher treatment doses. This paper reports our initial experience treating 8 patients with focal liver tumors using this system., Methods and Materials: The system includes diagnostic X-ray tubes mounted on the wall and ceiling of a treatment room, an active matrix flat panel imager, in-room control for image acquisition and setup adjustment, and a ventilatory immobilization system via active breathing control (ABC). Eight patients participated in the study, two using an early prototype ABC unit, and the remaining six with a commercial ABC system and improved setup measurement tools. Treatment margins were reduced, and dose consequently increased because of increased confidence in target position under this protocol. After daily setup via skin marks, orthogonal radiographs were acquired at suspended ventilation. The images were aligned to the CT model using the diaphragm for inferior-superior (IS) alignment, and the skeleton for left-right (LR) and anterior-posterior (AP) alignment. Adjustments were made for positioning errors greater than a threshold (3 or 5 mm). After treatment, retrospective analysis determined the final setup accuracy, as well as the error in initial setup measurement performed before setup adjustment., Results: Two hundred sixty-two treatment fractions were delivered on eight patients, with 171 treatments requiring repositioning. Typical treatment times were 25-30 min. Patients were able to tolerate ABC throughout the course of treatment. Breath holds up to 35 s long were used for treatment. The use of on-line imaging and setup adjustment reduced setup errors (sigma) from 4.0 mm (LR), 6.7 mm (IS), and 3.8 mm (AP) to 2.1 mm (LR), 3.5 mm (IS), and 2.3 mm (AP). Prescribed doses were increased using this system by an average of 5 Gy., Conclusions: Daily targeting of intrahepatic targets has been demonstrated to be feasible. The potential for reduction in treatment margin and consequential safe dose escalation has been demonstrated, while maintaining reasonable treatment delivery times.

Multileaf collimator (MLC) systems are available on most commercial linear accelerators, and many of these MLC systems utilize a design with rounded leaf ends and linear motion of the leaves. In this kind of system, the agreement between the digital MLC position readouts and the light field or radiation field edges must be achieved with software, since the leaves do not move in a focused motion like that used for most collimator jaw systems. In this work we address a number of the calibration and quality assurance issues associated with the acceptance, commissioning, and routine clinical use of this type of MLC system. These issues are particularly important for MLCs used for various types of intensity modulated radiation therapy (IMRT) and small, conformal fields. For rounded leaf end MLCs, it is generally not possible to make both the light and radiation field edges agree with the digital readout, so differences between the two kinds of calibrations are illustrated in this work using one vendor's MLC system. It is increasingly critical that the MLC leaf calibration be very consistent with the radiation field edges, so in this work a methodology for performing accurate radiation field size calibration is discussed. A system external to the vendor's MLC control system is used to correct or handle limitations in the MLC control system. When such a system of corrections is utilized, it is found that the MLC radiation field size can be defined with an accuracy of approximately 0.3 mm, much more accurate than most vendor's specifications for MLC accuracy. Quality assurance testing for such a calibration correction system is also demonstrated.

Monte Carlo studies have recently renewed interest in the use of the effect of strong transverse and longitudinal magnetic fields to manipulate the dose characteristics of clinical photon and electron beams. A 3.5 T superconducting solenoidal magnet was used to evaluate the effect of a longitudinal field on both photon and electron beams. This note describes the apparatus and demonstrates some of the effects on the beam trajectory and dose distributions for measurements in a homogeneous phantom. The effects were studied using film in air and in phantoms which fit in the magnet bore. The magnetic field focused and collimated the electron beams. The converging, non-uniform field confined the beam and caused it to converge with increasing depth in the phantom. Due to the field's collecting and focusing effect, the beam flux density increased, leading to increased dose deposition near the magnetic axis, especially near the surface of the phantom. This study illustrates some benefits and challenges associated with the use of non-uniform longitudinal magnetic fields in conjunction with clinical electron and photon beams.

Purpose: To develop and verify a multisegment technique for prostate irradiation that results in better sparing of the rectal wall compared to a conventional three-field technique, for patients with a concave-shaped planning target volume (PTV) overlapping the rectal wall., Methods and Materials: Five patients have been selected with various degrees of overlap between PTV and rectal wall. The planned dose to the ICRU reference point is 78 Gy. The new technique consists of five beams, each having an open segment covering the entire PTV and several smaller segments in which the rectum is shielded. Segment weights are computer-optimized using an algorithm based on simulated annealing. The score function to be minimized consists of dose-volume constraints for PTV, rectal wall, and femoral heads. The resulting dose distribution is verified for each patient by using point measurements and line scans made with an ionization chamber in a water tank and by using film in a cylindrical polystyrene phantom., Results: The final number of segments in the five-field technique ranges from 7 to 9 after optimization. Compared to the standard three-field technique, the maximum dose to the rectal wall decreases by approximately 3 Gy for patients with a large overlap and 1 Gy for patients with no overlap, resulting in a reduction of the normal tissue complication probability (NTCP) by a factor of 1.3 and 1.2, respectively. The mean dose to the PTV is the same for the two techniques, but the dose distribution is slightly less homogeneous with the five-field technique (Average standard deviation of five patients is 1.1 Gy and 1.7 Gy for the three-field and five-field technique, respectively). Ionization chamber measurements show that in the PTV, the calculated dose is in general within 1% of the measured dose. Outside the PTV, systematic dose deviations of up to 3% exist. Film measurements show that for the complete treatment, the position of the isodose lines in sagittal and coronal planes is calculated fairly accurately, the maximum distance between measured and calculated isodoses being 4 mm., Conclusions: We developed a relatively simple multisegment "step-and-shoot" technique that can be delivered within an acceptable time frame at the treatment machine (Extra time needed is approximately 3 minutes). The technique results in better sparing of the rectal wall compared to the conventional three-field technique. The technique can be planned and optimized relatively easily using automated procedures and a predefined score function. Dose calculation is accurate and can be verified for each patient individually.

Intensity-modulated radiation therapy (IMRT) may be performed with many different treatment delivery techniques. This article summarizes the clinical use and optimization of multisegment IMRT plans that have been used to treat more than 350 patients with IMRT over the last 4.5 years. More than 475 separate clinical IMRT plans are reviewed, including treatments of brain, head and neck, thorax, breast and chest wall, abdomen, pelvis, prostate, and other sites. Clinical planning, plan optimization, and treatment delivery are summarized, including efforts to minimize the number of additional intensity-modulated segments needed for particular planning protocols. Interactive and automated optimization of segmental and full IMRT approaches are illustrated, and automation of the segmental IMRT planning process is discussed.

Purpose: To analyze treatment delivery errors for three-dimensional (3D) conformal therapy performed at various levels of treatment delivery automation and complexity, ranging from manual field setup to virtually complete computer-controlled treatment delivery using a computer-controlled conformal radiotherapy system (CCRS)., Methods and Materials: All treatment delivery errors which occurred in our department during a 15-month period were analyzed. Approximately 34,000 treatment sessions (114,000 individual treatment segments [ports]) on four treatment machines were studied. All treatment delivery errors logged by treatment therapists or quality assurance reviews (152 in all) were analyzed. Machines "M1" and "M2" were operated in a standard manual setup mode, with no record and verify system (R/V). MLC machines "M3" and "M4" treated patients under the control of the CCRS system, which (1) downloads the treatment delivery plan from the planning system; (2) performs some (or all) of the machine set up and treatment delivery for each field; (3) monitors treatment delivery; (4) records all treatment parameters; and (5) notes exceptions to the electronically-prescribed plan. Complete external computer control is not available on M3; therefore, it uses as many CCRS features as possible, while M4 operates completely under CCRS control and performs semi-automated and automated multi-segment intensity modulated treatments. Analysis of treatment complexity was based on numbers of fields, individual segments, nonaxial and noncoplanar plans, multisegment intensity modulation, and pseudoisocentric treatments studied for a 6-month period (505 patients) concurrent with the period in which the delivery errors were obtained. Treatment delivery time was obtained from the computerized scheduling system (for manual treatments) or from CCRS system logs. Treatment therapists rotate among the machines; therefore, this analysis does not depend on fixed therapist staff on particular machines., Results: The overall reported error rate (all treatments, machines) was 0.13% per segment, or 0.44% per treatment session. The rate (per machine) depended on automation and plan complexity. The error rates per segment for machines M1 through M4 were 0.16%, 0.27%, 0.12%, 0.05%, respectively, while plan complexity increased from M1 up to machine M4. Machine M4 (the most complex plans and automation) had the lowest error rate. The error rate decreased with increasing automation in spite of increasing plan complexity, while for the manual machines, the error rate increased with complexity. Note that the real error rates on the two manual machines are likely to be higher than shown here (due to unnoticed and/or unreported errors), while (particularly on M4) virtually all random treatment delivery errors were noted by the CCRS system and related QA checks (including routine checks of machine and table readouts for each treatment). Treatment delivery times averaged from 14 min to 23 min per plan, and depended on the number of segments/plan, although this analysis is complicated by other factors., Conclusion: Use of a sophisticated computer-controlled delivery system for routine patient treatments with complex 3D conformal plans has led to a decrease in treatment delivery errors, while at the same time allowing delivery of increasingly complex and sophisticated conformal plans with little increase in treatment time. With renewed vigilance for the possibility of systematic problems, it is clear that use of complete and integrated computer-controlled delivery systems can provide improvements in treatment delivery, since more complex plans can be delivered with fewer errors, and without increasing treatment time.

The performance of ultrasound (US) and fluoroscopic-guided permanent 125I source implant of the prostate using CT identification of the source positions has been evaluated. Marker seeds were implanted during the planning study to assist in the alignment of the US and CT prostate volumes for treatment planning and to guide the placement of needles. The relative positions of the needles and marker seeds were checked by fluoroscopy. A postimplant CT study was used to input the radioactive source positions and to register the sources relative to the preimplant CT and US prostate volumes and the planned source distribution. Source placement errors observed were categorized as: (1) source-to-source spacing differences; (2) needle placement error, both depth and position; and (3) seed splaying, particularly near the prostate periphery. Errors due to source splaying and spacing were in part attributed to prostate motion. Later refinements included fixed-spaced string sources, for which placement errors were smaller than for unattached sources. However, source placement errors due to needle placement error and prostate motion remained unchanged.

Advances in computer technology have led to the availability of sophisticated three-dimensional treatment planning systems for use in many radiotherapy centers. However, additional complexity in both the planning and delivery of treatments has accompanied their use. Thus, even more computer-aided tools are beginning to appear to address these needs. Aspects of recent enhancements to 3-D treatment planning at the University of Michigan are presented.

Purpose: The design and implementation of a system for electronically tracking relevant plan, prescription, and treatment data for computer-controlled conformal radiation therapy is described., Methods and Materials: The electronic charting system is implemented on a computer cluster coupled by high-speed networks to computer-controlled therapy machines. A methodical approach to the specification and design of an integrated solution has been used in developing the system. The electronic chart system is designed to allow identification and access of patient-specific data including treatment-planning data, treatment prescription information, and charting of doses. An in-house developed database system is used to provide an integrated approach to the database requirements of the design. A hierarchy of databases is used for both centralization and distribution of the treatment data for specific treatment machines., Results: The basic electronic database system has been implemented and has been in use since July 1993. The system has been used to download and manage treatment data on all patients treated on our first fully computer-controlled treatment machine. To date, electronic dose charting functions have not been fully implemented clinically, requiring the continued use of paper charting for dose tracking., Conclusions: The routine clinical application of complex computer-controlled conformal treatment procedures requires the management of large quantities of information for describing and tracking treatments. An integrated and comprehensive approach to this problem has led to a full electronic chart for conformal radiation therapy treatments.

Purpose: Safe and efficient delivery of radiotherapy using computer-controlled machines requires new procedures to design and verify the actual delivery of these treatments. Graphical simulation and monitoring techniques for treatment delivery have been developed for this purpose., Methods and Materials: A graphics-based simulator of the treatment machine and a set of procedures for creating and manipulating treatment delivery scripts are used to simulate machine motions, detect collisions, and monitor machine positions during treatment. The treatment delivery simulator is composed of four components: a three-dimensional dynamic model of the treatment machine; a motion simulation and collision detection algorithm, user-interface widgets that mimic the treatment machine's control and readout devices; and an icon-based interface for creating and manipulating treatment delivery scripts. These components are used in a stand-alone fashion for interactive treatment delivery planning and integrated with a machine control system for treatment implementation and monitoring., Results: A graphics-based treatment delivery simulator and a set of procedures for planning and monitoring computer-controlled treatment delivery have been developed and implemented as part of a comprehensive computer-controlled conformal radiotherapy system. To date, these techniques have been used to design and help monitor computer-controlled treatments on a radiotherapy machine for more than 200 patients. Examples using these techniques for treatment delivery planning and on-line monitoring of machine motions during therapy are described., Conclusion: A system that provides interactive graphics-based tools for defining the sequence of machine motions, simulating treatment delivery including collision detection, and presenting the therapists with continual visual feedback from the treatment machine has been successfully implemented for routine clinical use as part of an overall system for computer-controlled conformal radiotherapy treatment, and is considered a necessary part of the routine treatment methodology.

Purpose: To aid in design of conformal radiation therapy treatment plans involving many conformally shaped fields, this work investigates the use of two methodologies to enhance the ease of interactive treatment planning: high-level beam constructs and beam's-eye view volumetric mapping., Methods and Materials: High-performance computer graphics running on various workstations using a graphical visualization system (AVS) have been used in this work. Software specific to this application has been written in standard FORTRAN and C languages. A new methodology is introduced by defining radiation therapy "fields" to be composed of multiple beam "segments." Fields can then be defined as higher-level entities such as arcs, cones, and other shapes. A "segmental cone" field, for example, is defined by a symmetry axis and a cone angle, and can be used to rapidly place a series of beam segments that converge at the target volume, while reducing the degree of overlap elsewhere. A new beam's-eye view (BEV) volumetric mapping technique is presented to aid in selecting the placement of conformal radiation fields. With this technique, the relative average dose within an organ of interest is calculated for a sampling of isocentric, conformally shaped beams and displayed either as a "globe," which can be combined with the display of anatomical surfaces, or as a two-dimensionally mapped projection. The dose maps from multiple organs can be generated, stacked, or composited with relative weightings to aid in the placement of fields that minimize overlap with critical structures., Results: The use of these new methodologies is demonstrated for prostate and lung treatment sites and compared to conventional planning techniques., Discussion: The use of many beams for conformal treatment delivery is difficult with current interactive planning. The use of high-level beam constructs provides a means to quickly specify, place, and configure multiple beam arrangements. The BEV volumetrics aids in the placing of fields, which minimize involvement with critical normal tissues., Conclusions: Early experience with the new methodologies suggest that the new methods help to enhance (or at least speed up) the ability of a treatment planner to create optimal radiation treatment field arrangements.

Purpose: A sequence processor (SP) is described as part of a larger computer-controlled conformal radiotherapy system (CCRS). The SP provides the means to accept and then translate highly sophisticated radiation therapy treatment plans into vendor specific instructions to control treatment delivery on a computer-controlled treatment machine., Methods and Materials: The sequence processor (SP) is a small workstation computer that interfaces to the control computer of computer-controlled treatment machines, and to other parts of the larger CCRS system. The system reported here has been interfaced to a computer-controlled racetrack microtron with two treatment gantries, and also to other linear accelerator treatment machines equipped with multileaf collimators. An extensive design process has been used in defining the role of the SP within the context of the larger CCRS project. Flexibility and integration with various components of the project, including databases, treatment planning system, graphical simulator, were key factors in the development. In conjunction with the planned set of treatment fields, a procedural scripting language is used to define the sequence of treatment events that are performed, including operator interactions, communications to other systems such as dosimetry and portal imaging devices, and database management., Results: A flexible system has been developed to allow investigation into procedural steps required for simulating and delivering complex radiation treatments. The system has been used to automate portions of the acceptance testing for the control system of the microtron, and is used for routine daily quality assurance testing. The sequence processor system described here has been used to deliver all clinical treatments performed on the microtron system in 2 years of clinical treatment (more than 200 patients treated to a variety of treatment sites)., Conclusions: The sequence processor system has enabled the delivery of complex treatment using computer-controlled treatment machines. The flexibility of the system allows integration with secondary devices and modification of procedural steps, making it possible to develop effective techniques for insuring safe and efficient computer-controlled conformal radiation therapy treatments.

Purpose: Equipment developed for use with computer-controlled conformal radiotherapy (CCRT) treatment techniques, including multileaf collimators and/or computer-control systems for treatment machines, are now available. The purpose of this work is to develop a system that will allow the safe, efficient, and accurate delivery of CCRT treatments as routine clinical treatments, and permit modifications of the system so that the delivery process can be optimized., Methods and Materials: The needs and requirements for a system that can fully support modern computer-controlled treatment machines equipped with multileaf collimators and segmental or dynamic conformal therapy capabilities have been analyzed and evaluated. This analysis has been used to design and then implement a complete approach to the delivery of CCRT treatments., Results: The computer-controlled conformal radiotherapy system (CCRS) described here consists of a process for the delivery of CCRT treatments, and a complex software system that implements the treatment process. The CCRS system described here includes systems for plan transfer, treatment delivery planning, sequencing of the actual treatment delivery process, graphical simulation and verification tools, as well as an electronic chart that is an integral part of the system. The CCRS system has been implemented for use with a number of different treatment machines. The system has been used clinically for more than 2 years to perform CCRT treatments for more than 200 patients., Conclusions: A comprehensive system for the implementation and delivery of computer-controlled conformal radiation therapy (CCRT) plans has been designed and implemented for routine clinical use with multisegment, computer-controlled, multileaf-collimated conformal therapy. The CCRS system has been successfully implemented to perform these complex treatments, and is considered quite important to the clinical use of modern computer-controlled treatment techniques.

Modern computer controlled radiotherapy treatment equipment offers the possibility of delivering complex, multiple field treatments with minimal operator intervention, thus making multiple field conformal therapy practical. Conventional quality control programs are inadequate for this new technology, so new quality control procedures are needed. A reasonably fast, sensitive, and complete daily quality control program has been developed in our clinic that includes nearly automated mechanical as well as dosimetric tests. Automated delivery of these quality control fields is performed by the control system of the MM50 racetrack microtron, directed by the CCRS sequence processor [D. L. McShan and B. A. Fraass, Proceedings of the XIth International Conference on the use of computers in Radiation Therapy, 20-24 March 1994, Manchester, U.K. (North Western Medical Physics Department, Manchester, U.K., 1994), pp. 210-211], which controls the treatment process. The mechanical tests involve multiple irradiations of a single film to check the accuracy and reproducibility of the computer controlled setup of gantry and collimator angles, table orientation, collimator jaws, and multileaf collimator shape. The dosimetric tests, which involve multiple irradiations of an array of ionization chambers in a commercial dose detector (Keithly model 90100 Tracker System) rigidly attached to the head of the treatment gantry, check the output and symmetry of the treatment unit as a function of gantry and collimator angle and other parameters. For each of the dosimetric tests, readings from the five ionization chambers are automatically read out, stored, and analyzed by the computer, along with the geometric parameters of the treatment unit for that beam.(ABSTRACT TRUNCATED AT 250 WORDS)