Expert-augmented machine learning.

Machine learning is proving invaluable across disciplines. However, its success is often limited by the quality and quantity of available data, while its adoption is limited by the level of trust afforded by given models. Human vs. machine performance is commonly compared empirically to decide whether a certain task should be performed by a computer or an expert. In reality, the optimal learning strategy may involve combining the complementary strengths of humans and machines. Here, we present expert-augmented machine learning (EAML), an automated method that guides the extraction of expert knowledge and its integration into machine-learned models. We used a large dataset of intensive-care patient data to derive 126 decision rules that predict hospital mortality. Using an online platform, we asked 15 clinicians to assess the relative risk of the subpopulation defined by each rule compared to the total sample. We compared the clinician-assessed risk to the empirical risk and found that, while clinicians agreed with the data in most cases, there were notable exceptions where they overestimated or underestimated the true risk. Studying the rules with greatest disagreement, we identified problems with the training data, including one miscoded variable and one hidden confounder. Filtering the rules based on the extent of disagreement between clinician-assessed risk and empirical risk, we improved performance on out-of-sample data and were able to train with less data. EAML provides a platform for automated creation of problem-specific priors, which help build robust and dependable machine-learning models in critical applications.

Building more accurate decision trees with the additive tree.

The expansion of machine learning to high-stakes application domains such as medicine, finance, and criminal justice, where making informed decisions requires clear understanding of the model, has increased the interest in interpretable machine learning. The widely used Classification and Regression Trees (CART) have played a major role in health sciences, due to their simple and intuitive explanation of predictions. Ensemble methods like gradient boosting can improve the accuracy of decision trees, but at the expense of the interpretability of the generated model. Additive models, such as those produced by gradient boosting, and full interaction models, such as CART, have been investigated largely in isolation. We show that these models exist along a spectrum, revealing previously unseen connections between these approaches. This paper introduces a rigorous formalization for the additive tree, an empirically validated learning technique for creating a single decision tree, and shows that this method can produce models equivalent to CART or gradient boosted stumps at the extremes by varying a single parameter. Although the additive tree is designed primarily to provide both the model interpretability and predictive performance needed for high-stakes applications like medicine, it also can produce decision trees represented by hybrid models between CART and boosted stumps that can outperform either of these approaches.

Dentate gyrus neurogenesis ablation via cranial irradiation enhances morphine self-administration and locomotor sensitization.

Adult dentate gyrus (DG) neurogenesis is important for hippocampal-dependent learning and memory, but the role of new neurons in addiction-relevant learning and memory is unclear. To test the hypothesis that neurogenesis is involved in the vulnerability to morphine addiction, we ablated adult DG neurogenesis and examined morphine self-administration (MSA) and locomotor sensitization. Male Sprague-Dawley rats underwent hippocampal-focused, image-guided X-ray irradiation (IRR) to eliminate new DG neurons or sham treatment (Sham). Six weeks later, rats underwent either MSA (Sham = 16, IRR = 15) or locomotor sensitization (Sham = 12, IRR = 12). Over 21 days of MSA, IRR rats self-administered ~70 percent more morphine than Sham rats. After 28 days of withdrawal, IRR rats pressed the active lever 40 percent more than Sham during extinction. This was not a general enhancement of learning or locomotion, as IRR and Sham groups had similar operant learning and inactive lever presses. For locomotor sensitization, both IRR and Sham rats sensitized, but IRR rats sensitized faster and to a greater extent. Furthermore, dose-response revealed that IRR rats were more sensitive at a lower dose. Importantly, these increases in locomotor activity were not apparent after acute morphine administration and were not a byproduct of irradiation or post-irradiation recovery time. Therefore, these data, along with other previously published data, indicate that reduced hippocampal neurogenesis confers vulnerability for multiple classes of drugs. Thus, therapeutics to specifically increase or stabilize hippocampal neurogenesis could aid in preventing initial addiction as well as future relapse.

Validation and clinical implementation of an accurate Monte Carlo code for pencil beam scanning proton therapy.

Monte Carlo (MC)-based dose calculations are generally superior to analytical dose calculations (ADC) in modeling the dose distribution for proton pencil beam scanning (PBS) treatments. The purpose of this paper is to present a methodology for commissioning and validating an accurate MC code for PBS utilizing a parameterized source model, including an implementation of a range shifter, that can independently check the ADC in commercial treatment planning system (TPS) and fast Monte Carlo dose calculation in opensource platform (MCsquare). The source model parameters (including beam size, angular divergence and energy spread) and protons per MU were extracted and tuned at the nozzle exit by comparing Tool for Particle Simulation (TOPAS) simulations with a series of commissioning measurements using scintillation screen/CCD camera detector and ionization chambers. The range shifter was simulated as an independent object with geometric and material information. The MC calculation platform was validated through comprehensive measurements of single spots, field size factors (FSF) and three-dimensional dose distributions of spread-out Bragg peaks (SOBPs), both without and with the range shifter. Differences in field size factors and absolute output at various depths of SOBPs between measurement and simulation were within 2.2%, with and without a range shifter, indicating an accurate source model. TOPAS was also validated against anthropomorphic lung phantom measurements. Comparison of dose distributions and DVHs for representative liver and lung cases between independent MC and analytical dose calculations from a commercial TPS further highlights the limitations of the ADC in situations of highly heterogeneous geometries. The fast MC platform has been implemented within our clinical practice to provide additional independent dose validation/QA of the commercial ADC for patient plans. Using the independent MC, we can more efficiently commission ADC by reducing the amount of measured data required for low dose "halo" modeling, especially when a range shifter is employed.

Exploratory analysis using machine learning to predict for chest wall pain in patients with stage I non-small-cell lung cancer treated with stereotactic body radiation therapy.

BACKGROUND AND PURPOSE: Chest wall toxicity is observed after stereotactic body radiation therapy (SBRT) for peripherally located lung tumors. We utilize machine learning algorithms to identify toxicity predictors to develop dose-volume constraints. MATERIALS AND METHODS: Twenty-five patient, tumor, and dosimetric features were recorded for 197 consecutive patients with Stage I NSCLC treated with SBRT, 11 of whom (5.6%) developed CTCAEv4 grade ≥2 chest wall pain. Decision tree modeling was used to determine chest wall syndrome (CWS) thresholds for individual features. Significant features were determined using independent multivariate methods. These methods incorporate out-of-bag estimation using Random forests (RF) and bootstrapping (100 iterations) using decision trees. RESULTS: Univariate analysis identified rib dose to 1 cc < 4000 cGy (P = 0.01), chest wall dose to 30 cc < 1900 cGy (P = 0.035), rib Dmax < 5100 cGy (P = 0.05) and lung dose to 1000 cc < 70 cGy (P = 0.039) to be statistically significant thresholds for avoiding CWS. Subsequent multivariate analysis confirmed the importance of rib dose to 1 cc, chest wall dose to 30 cc, and rib Dmax. Using learning-curve experiments, the dataset proved to be self-consistent and provides a realistic model for CWS analysis. CONCLUSIONS: Using machine learning algorithms in this first of its kind study, we identify robust features and cutoffs predictive for the rare clinical event of CWS. Additional data in planned subsequent multicenter studies will help increase the accuracy of multivariate analysis.

A study of the beam-specific interplay effect in proton pencil beam scanning delivery in lung cancer.

BACKGROUND: For lung tumors with large motion amplitudes, the use of proton pencil beam scanning (PBS) can produce large dose errors. In this study, we assess under what circumstances PBS can be used to treat lung cancer patients who exhibit large tumor motion, based on the quantification of tumor motion and the dose interplay. MATERIAL AND METHODS: PBS plans were optimized on average 4DCT datasets using a beam-specific PTV method for 10 consecutive patients with locally advanced non-small-cell-lung-cancer (NSCLC) treated with proton therapy to 6660/180 cGy. End inhalation (CT0) and end exhalation (CT50) were selected as the two extreme scenarios to acquire the relative stopping power ratio difference (Δrsp) for a respiration cycle. The water equivalent difference (ΔWET) per radiological path was calculated from the surface of patient to the iCTV by integrating the Δrsp of each voxel. The magnitude of motion of voxels within the target follows a quasi-Gaussian distribution. A motion index (MI (>5mm WET)), defined as the percentage of target voxels with an absolute integral ΔWET larger than 5 mm, was adopted as a metric to characterize interplay. To simulate the treatment process, 4D dose was calculated by accumulating the spot dose on the corresponding respiration phase to the reference phase CT50 by deformable image registration based on spot timing and patient breathing phase. RESULTS: The study indicated that the magnitude of target underdose in a single fraction plan is proportional to the MI (p < .001), with larger motion equating to greater dose degradation and standard deviations. The target homogeneity, minimum, maximum and mean dose in the 4D dose accumulations of 37 fractions varied as a function of MI. CONCLUSIONS: This study demonstrated that MI can predict the level of dose degradation, which potentially serves as a clinical decision tool to assess whether lung cancer patients are potentially suitable to receive PBS treatment.

IMRT QA using machine learning: A multi-institutional validation.

PURPOSE: To validate a machine learning approach to Virtual intensity-modulated radiation therapy (IMRT) quality assurance (QA) for accurately predicting gamma passing rates using different measurement approaches at different institutions. METHODS: A Virtual IMRT QA framework was previously developed using a machine learning algorithm based on 498 IMRT plans, in which QA measurements were performed using diode-array detectors and a 3%local/3 mm with 10% threshold at Institution 1. An independent set of 139 IMRT measurements from a different institution, Institution 2, with QA data based on portal dosimetry using the same gamma index, was used to test the mathematical framework. Only pixels with ≥10% of the maximum calibrated units (CU) or dose were included in the comparison. Plans were characterized by 90 different complexity metrics. A weighted poison regression with Lasso regularization was trained to predict passing rates using the complexity metrics as input. RESULTS: The methodology predicted passing rates within 3% accuracy for all composite plans measured using diode-array detectors at Institution 1, and within 3.5% for 120 of 139 plans using portal dosimetry measurements performed on a per-beam basis at Institution 2. The remaining measurements (19) had large areas of low CU, where portal dosimetry has a larger disagreement with the calculated dose and as such, the failure was expected. These beams need further modeling in the treatment planning system to correct the under-response in low-dose regions. Important features selected by Lasso to predict gamma passing rates were as follows: complete irradiated area outline (CIAO), jaw position, fraction of MLC leafs with gaps smaller than 20 or 5 mm, fraction of area receiving less than 50% of the total CU, fraction of the area receiving dose from penumbra, weighted average irregularity factor, and duty cycle. CONCLUSIONS: We have demonstrated that Virtual IMRT QA can predict passing rates using different measurement techniques and across multiple institutions. Prediction of QA passing rates can have profound implications on the current IMRT process.

A benchmarking method to evaluate the accuracy of a commercial proton monte carlo pencil beam scanning treatment planning system.

AcurosPT is a Monte Carlo algorithm in the Eclipse 13.7 treatment planning system, which is designed to provide rapid and accurate dose calculations for proton therapy. Computational run-time in minimized by simplifying or eliminating less significant physics processes. In this article, the accuracy of AcurosPT was benchmarked against both measurement and an independent MC calculation, TOPAS. Such a method can be applied to any new MC calculation for the detection of potential inaccuracies. To validate multiple Coulomb scattering (MCS) which affects primary beam broadening, single spot profiles in a Solidwater® phantom were compared for beams of five selected proton energies between AcurosPT, measurement and TOPAS. The spot Gaussian sigma in AcurosPT was found to increase faster with depth than both measurement and TOPAS, suggesting that the MCS algorithm in AcurosPT overestimates the scattering effect. To validate AcurosPT modeling of the halo component beyond primary beam broadening, field size factors (FSF) were compared for multi-spot profiles measured in a water phantom. The FSF for small field sizes were found to disagree with measurement, with the disagreement increasing with depth. Conversely, TOPAS simulations of the same FSF consistently agreed with measurement to within 1.5%. The disagreement in absolute dose between AcurosPT and measurement was smaller than 2% at the mid-range depth of multi-energy beams. While AcurosPT calculates acceptable dose distributions for typical clinical beams, users are cautioned of potentially larger errors at distal depths due to overestimated MCS and halo implementation.

Quantitative assessment of anatomical change using a virtual proton depth radiograph for adaptive head and neck proton therapy.

The aim of this work is to demonstrate the feasibility of using water-equivalent thickness (WET) and virtual proton depth radiographs (PDRs) of intensity corrected cone-beam computed tomography (CBCT) to detect anatomical change and patient setup error to trigger adaptive head and neck proton therapy. The planning CT (pCT) and linear accelerator (linac) equipped CBCTs acquired weekly during treatment of a head and neck patient were used in this study. Deformable image registration (DIR) was used to register each CBCT with the pCT and map Hounsfield units (HUs) from the planning CT (pCT) onto the daily CBCT. The deformed pCT is referred as the corrected CBCT (cCBCT). Two dimensional virtual lateral PDRs were generated using a ray-tracing technique to project the cumulative WET from a virtual source through the cCBCT and the pCT onto a virtual plane. The PDRs were used to identify anatomic regions with large variations in the proton range between the cCBCT and pCT using a threshold of 3 mm relative difference of WET and 3 mm search radius criteria. The relationship between PDR differences and dose distribution is established. Due to weight change and tumor response during treatment, large variations in WETs were observed in the relative PDRs which corresponded spatially with an increase in the number of failing points within the GTV, especially in the pharynx area. Failing points were also evident near the posterior neck due to setup variations. Differences in PDRs correlated spatially to differences in the distal dose distribution in the beam's eye view. Virtual PDRs generated from volumetric data, such as pCTs or CBCTs, are potentially a useful quantitative tool in proton therapy. PDRs and WET analysis may be used to detect anatomical change from baseline during treatment and trigger further analysis in adaptive proton therapy.

Incident learning in pursuit of high reliability: implementing a comprehensive, low-threshold reporting program in a large, multisite radiation oncology department.

BACKGROUND: Incident learning programs have been recognized as cornerstones of safety and quality assurance in so-called high reliability organizations in industries such as aviation and nuclear power. High reliability organizations are distinguished by their drive to continuously identify and proactively address a broad spectrum of latent safety issues. Many radiation oncology institutions have reported on their experience in tracking and analyzing adverse events and near misses but few have incorporated the principles of high reliability into their programs. Most programs have focused on the reporting and retrospective analysis of a relatively small number of significant adverse events and near misses. To advance a large, multisite radiation oncology department toward high reliability, a comprehensive, cost-effective, electronic condition reporting program was launched to enable the identification of a broad spectrum of latent system failures, which would then be addressed through a continuous quality improvement process. METHODS: A comprehensive program, including policies, work flows, and information system, was designed and implemented, with use of a low reporting threshold to focus on precursors to adverse events. RESULTS: In a 46-month period from March 2011 through December 2014, a total of 8,504 conditions (average, 185 per month, 1 per patient treated, 3.9 per 100 fractions [individual treatments]) were reported. Some 77.9% of clinical staff members reported at least 1 condition. Ninety-eight percent of conditions were classified in the lowest two of four severity levels, providing the opportunity to address conditions before they contribute to adverse events. CONCLUSIONS: Results after approximately four years show excellent employee engagement, a sustained rate of reporting, and a focus on low-level issues leading to proactive quality improvement interventions.

Comparing proton treatment plans of pediatric brain tumors in two pencil beam scanning nozzles with different spot sizes.

Target coverage and organ-at-risk sparing were compared for 22 pediatric patients with primary brain tumors treated using two distinct nozzles in pencil beam scanning (PBS) proton therapy. Consecutive patients treated at our institution using a PBS-dedicated nozzle (DN) were replanned using a universal nozzle (UN) beam model and the original DN plan objectives. Various cranial sites were treated among the patients to prescription doses ranging from 45 to 54 Gy. Organs at risk (OARs) evaluated were patient-dependent; 15 unique OARs were analyzed, all of which were assessed in at least 10 patients. Clinical target volume (CTV) coverage and organ sparing were compared for the two nozzles using dose-volume histogram data. Statistical analysis using a confidence-interval approach demonstrates that CTV coverage is equivalent for UN and DN plans within ± 5% equivalence bounds. In contrast, average mean and maximum doses are significantly higher for nearly all 15 OARs in the UN plans. The average median increase over all OARs and patients is approximately 1.7 Gy, with an increase in the 25%-75% of 1.0-2.3 Gy; the median increase to the pituitary gland, temporal lobes, eyes and cochleas are 1.8, 1.7, 0.7, and 2.7 Gy, respectively. The CTV dose distributions fall off slower for UN than for the DN plans; hence, normal tissue structures in close proximity to CTVs receive higher doses in UN plans than in DN plans. The higher OAR doses in the UN plans are likely due to the larger spot profile in plans created with UN beams. In light of the high rates of toxicities in pediatric patients receiving cranial irradiation and in light of selected brain tumor types having high cure rates, this study suggests the smaller DN beam profile is preferable for the advantage of reducing dose to OARs.

Breaking bad IMRT QA practice.

Agreement between planned and delivered dose distributions for patient-specific quality assurance in routine clinical practice is predominantly assessed utilizing the gamma index method. Several reports, however, fundamentally question current IMRT QA practice due to poor sensitivity and specificity of the standard gamma index implementation. An alternative is to employ dose volume histogram (DVH)-based metrics. An analysis based on the AAPM TG 53 and ESTRO booklet No.7 recommendations for QA of treatment planning systems reveals deficiencies in the current "state of the art" IMRT QA, no matter which metric is selected. The set of IMRT benchmark plans were planned, delivered, and analyzed by following guidance of the AAPM TG 119 report. The recommended point dose and planar dose measurements were obtained using a PinPoint ionization chamber, EDR2 radiographic film, and a 2D ionization chamber array. Gamma index criteria {3% (global), 3 mm} and {3% (local), 3 mm} were used to assess the agreement between calculated and delivered planar dose distributions. Next, the AAPM TG 53 and ESTRO booklet No.7 recommendations were followed by dividing dose distributions into four distinct regions: the high-dose (HD) or umbra region, the high-gradient (HG) or penumbra region, the medium-dose (MD) region, and the low-dose (LD) region. A different gamma passing criteria was defined for each region, i.e., a "divide and conquer" (D&C) gamma method was utilized. The D&C gamma analysis was subsequently tested on 50 datasets of previously treated patients. Measured point dose and planar dose distributions compared favorably with TG 119 benchmark data. For all complex tests, the percentage of points passing the conventional {3% (global), 3 mm} gamma criteria was 97.2% ± 3.2% and 95.7% ± 1.2% for film and 2D ionization chamber array, respectively. By dividing 2D ionization chamber array dose measurements into regions and applying 3mm isodose point distance and variable local point dose difference criteria of 7%, 15%, 25%, and 40% for HD, HG, MD, and LD regions, respectively, a 93.4% ± 2.3% gamma passing rate was obtained. Identical criteria applied using the D&C gamma technique on 50 clinical treatment plans resulted in a 97.9% ± 2.3% gamma passing score. Based on the TG 119 standard, meeting or exceeding the benchmark results would indicate an exemplary IMRT QA program. In contrast to TG 119 analysis, a different scrutiny on the same set of data, which follows the AAPM TG 53 and ESTRO booklet No.7 guidelines, reveals a much poorer agreement between calculated and measured dose distributions with large local point dose differences within different dose regions. This observation may challenge the conventional wisdom that an IMRT QA program is producing acceptable results.

Use of a novel two-dimensional ionization chamber array for pencil beam scanning proton therapy beam quality assurance.

The need to accurately and efficiently verify both output and dose profiles creates significant challenges in quality assurance of pencil beam scanning (PBS) proton delivery. A system for PBS QA has been developed that combines a new two-dimensional ionization chamber array in a waterproof housing that is scanned in a water phantom. The MatriXX PT has the same detector array arrangement as the standard MatriXX(Evolution) but utilizes a smaller 2 mm plate spacing instead of 5mm. Because the bias voltage of the MatriXX PT and Evolution cannot be changed, PPC40 and FC65-G ionization chambers were used to assess recombination effects. The PPC40 is a parallel plate chamber with an electrode spacing of 2mm, while the FC65-G is a Farmer chamber FC65-G with an electrode spacing of 2.8 mm. Three bias voltages (500, 200, and 100 V) were used for both detectors to determine which radiation type (continuous, pulse or pulse-scanned beam) could closely estimate Pion from the ratios of charges collected. In comparison with the MatriXX(Evolution), a significant improvement in measurement of absolute dose with the MatriXX PT was observed. While dose uncertainty of the MatriXX(Evolution) can be up to 4%, it is < 1% for the MatriXX PT. Therefore the MatriXX(Evolution) should not be used for QA of PBS for conditions in which ion recombination is not negligible. Farmer chambers should be used with caution for measuring the absolute dose of PBS beams, as the uncertainty of Pion can be > 1%; chambers with an electrode spacing of 2 mm or smaller are recommended.

Beam-specific planning target volumes incorporating 4D CT for pencil beam scanning proton therapy of thoracic tumors.

The purpose of this study is to determine whether organ sparing and target coverage can be simultaneously maintained for pencil beam scanning (PBS) proton therapy treatment of thoracic tumors in the presence of motion, stopping power uncertainties, and patient setup variations. Ten consecutive patients that were previously treated with proton therapy to 66.6/1.8 Gy (RBE) using double scattering (DS) were replanned with PBS. Minimum and maximum intensity images from 4D CT were used to introduce flexible smearing in the determination of the beam specific PTV (BSPTV). Datasets from eight 4D CT phases, using ± 3% uncertainty in stopping power and ± 3 mm uncertainty in patient setup in each direction, were used to create 8 × 12 × 10 = 960 PBS plans for the evaluation of 10 patients. Plans were normalized to provide identical coverage between DS and PBS. The average lung V20, V5, and mean doses were reduced from 29.0%, 35.0%, and 16.4 Gy with DS to 24.6%, 30.6%, and 14.1 Gy with PBS, respectively. The average heart V30 and V45 were reduced from 10.4% and 7.5% in DS to 8.1% and 5.4% for PBS, respectively. Furthermore, the maximum spinal cord, esophagus, and heart doses were decreased from 37.1 Gy, 71.7 Gy, and 69.2 Gy with DS to 31.3 Gy, 67.9 Gy, and 64.6 Gy with PBS. The conformity index (CI), homogeneity index (HI), and global maximal dose were improved from 3.2, 0.08, 77.4 Gy with DS to 2.8, 0.04, and 72.1 Gy with PBS. All differences are statistically significant, with p-values <0.05, with the exception of the heart V45 (p = 0.146). PBS with BSPTV achieves better organ sparing and improves target coverage using a repainting method for the treatment of thoracic tumors. Incorporating motion-related uncertainties is essential.

Commissioning and verification of the collapsed cone convolution superposition algorithm for SBRT delivery using flattening filter-free beams.

Linacs equipped with flattening filter-free (FFF) megavoltage photon beams are now commercially available. However, the commissioning of FFF beams poses challenges that are not shared with traditional flattened megavoltage X-ray beams. The planning system must model a beam that is peaked in the center and has an energy spectrum that is softer than the flattened beam. Removing the flattening filter also increases the maximum possible dose rates from 600 MU/min up to 2400 MU/min in some cases; this increase in dose rate affects the recombination correction factor, P(ion), used during absolute dose calibration with ionization chambers. We present the first reported experience of commissioning, verification, and clinical use of the collapsed cone convolution superposition (CCCS) dose calculation algorithm for commercially available flattening filter-free beams. Our commissioning data are compared to previously reported measurements and Monte Carlo studies of FFF beams. Commissioning was verified by making point-dose measurement of test plans, irradiating the RPC lung phantom, and performing patient-specific QA. The average point-dose difference between calculations and measurements of all test plans and all patient specific QA measurements is 0.80%, and the RPC phantom absolute dose differences for the two thermoluminescent dosimeters (TLDs) in the phantom planning target volume (PTV) were 1% and 2%, respectively. One hundred percent (100%) of points in the RPC phantom films passed the RPC gamma criteria of 5% and 5 mm. Our results show that the CCCS algorithm can accurately model FFF beams and calculate SBRT dose distributions using those beams.

Implementation of an improved dose-per-MU model for double-scattered proton beams to address interbeamline modulation width variability.

Because treatment planning systems (TPSs) generally do not provide monitor units (MUs) for double-scattered proton plans, models to predict MUs as a function of the range and the nominal modulation width requested of the beam delivery system, such as the one developed by the MGH group, have been proposed. For a given nominal modulation width, however, the measured modulation width depends on the accuracy of the vendor's calibration process and may differ from this nominal value, and also from one beamline to the next. Although such a difference can be replicated in our TPS, the output dependence on range and modulation width for each beam option or suboption has to be modeled separately for each beamline in order to achieve maximal 3% inaccuracy. As a consequence, the MGH output model may not be directly transferable. This work, therefore, serves to extend the model to more general clinic situations. In this paper, a parameterized linear-quadratic transformation is introduced to convert the nominal modulation width to the measured modulation width for each beam option or suboption on a per-beamline basis. Fit parameters are derived for each beamline from measurements of 60 reference beams spanning the minimum and maximum ranges, and modulation widths from 2 cm to full range per option or suboption. Using the modeled modulation width, we extract the MGH parameters for the output dependence on range and modulation width. Our method has been tested with 1784 patient-specific fields delivered across three different beamlines at our facility. For these fields, all measured outputs fall within 3%, and 64.4% fall within 1%, of our model. Using a parameterized linear-quadratic modulation width, MU calculation models can be established on a per-beamline basis for each double scattering beam option or suboption.