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DOE OSTI2016

A Benders based rolling horizon algorithm for a dynamic facility location problem

This study presents a well-known capacitated dynamic facility location problem (DFLP) that satisfies the customer demand at a minimum cost by determining the time period for opening, closing, or retaining an existing facility in a given location. To solve this challenging NP-hard problem, this paper develops a unique hybrid solution algorithm that combines a rolling horizon algorithm with an accelerated Benders decomposition algorithm. Extensive computational experiments are performed on benchmark test instances to evaluate the hybrid algorithm’s efficiency and robustness in solving the DFLP problem. Computational results indicate that the hybrid Benders based rolling horizon algorithm consistently offers high quality feasible solutions in a much shorter computational time period than the standalone rolling horizon and accelerated Benders decomposition algorithms in the experimental range.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

A performance evaluation framework for building fault detection and diagnosis algorithms

Fault detection and diagnosis (FDD) algorithms for building systems and equipment represent one of the most active areas of research and commercial product development in the buildings industry. However, far more effort has gone into developing these algorithms than into assessing their performance. As a result, considerable uncertainties remain regarding the accuracy and effectiveness of both research-grade FDD algorithms and commercial products - a state of affairs that has hindered the broad adoption of FDD tools. This article presents a general, systematic framework for evaluating the performance of FDD algorithms. The article focuses on understanding the possible answers to two key questions: in the context of FDD algorithm evaluation, what defines a fault and what defines an evaluation input sample? The answers to these questions, together with appropriate performance metrics, may be used to fully specify evaluation procedures for FDD algorithms.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2014

Hybrid nested sampling algorithm for Bayesian model selection applied to inverse subsurface flow problems

A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Statistical behaviour of adaptive multilevel splitting algorithms in simple models

Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to direct transitions from one metastable state to another. The algorithm is based on successive selection–mutation steps performed on the system in a controlled way. It has two intrinsic parameters, the number of particles/trajectories and the reaction coordinate used for discriminating good or bad trajectories. We investigate first the convergence in law of the algorithm as a function of the timestep for several simple stochastic models. Second, we consider the average duration of reactive trajectories for which no theoretical predictions exist. The most important aspect of this work concerns some systems with two degrees of freedom. They are studied in detail as a function of the reaction coordinate in the asymptotic regime where the number of trajectories goes to infinity. We show that during phase transitions, the statistics of the algorithm deviate significatively from known theoretical results when using non-optimal reaction coordinates. In this case, the variance of the algorithm is peaking at the transition and the convergence of the algorithm can be much slower than the usual expected central limit behaviour. The duration of trajectories is affected as well. Moreover, reactive trajectories do not correspond to the most probable ones. Such behaviour disappears when using the optimal reaction coordinate called committor as predicted by the theory. We finally investigate a three-state Markov chain which reproduces this phenomenon and show logarithmic convergence of the trajectory durations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Rendezvous algorithms for large-scale modeling and simulation

Rendezvous algorithms encode a communication pattern that is useful when processors sending data do not know who the receiving processors should be, or vice versa. The idea is to define an intermediate decomposition where datums from different sending processors can ”rendezvous” to perform a computation, in a manner that both the senders and eventual receivers of the results can identify the appropriate rendezvous processor. Though they were originally designed for interpolating between overlaid grids with independent parallel decompositions (Plimpton et al., 2004), we have recently found rendezvous algorithms useful for a variety of operations in particle- or grid-based simulation codes when running large problems on large numbers of processors. In particular, we show they can perform well when a load-balanced intermediate decomposition is randomized and not spatial, requiring all-to-all communication to move data between processors. In this case rendezvous algorithms leverage the large bisection communication bandwidths which parallel machines provide. We describe how rendezvous algorithms work in a scientific computing context and give specific examples for molecular dynamics and Direct Simulation Monte Carlo codes which result in dramatic performance improvements versus simpler algorithms which do not scale as well. We explain how a generic rendezvous algorithm can be implemented, and also point out similarities with the MapReduce paradigm popularized by Google and Hadoop.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Effect of Acuros XB algorithm on monitor units for stereotactic body radiotherapy planning of lung cancer

Stereotactic body radiotherapy (SBRT) is a curative regimen that uses hypofractionated radiation-absorbed dose to achieve a high degree of local control in early stage non–small cell lung cancer (NSCLC). In the presence of heterogeneities, the dose calculation for the lungs becomes challenging. We have evaluated the dosimetric effect of the recently introduced advanced dose-calculation algorithm, Acuros XB (AXB), for SBRT of NSCLC. A total of 97 patients with early-stage lung cancer who underwent SBRT at our cancer center during last 4 years were included. Initial clinical plans were created in Aria Eclipse version 8.9 or prior, using 6 to 10 fields with 6-MV beams, and dose was calculated using the anisotropic analytic algorithm (AAA) as implemented in Eclipse treatment planning system. The clinical plans were recalculated in Aria Eclipse 11.0.21 using both AAA and AXB algorithms. Both sets of plans were normalized to the same prescription point at the center of mass of the target. A secondary monitor unit (MU) calculation was performed using commercial program RadCalc for all of the fields. For the planning target volumes ranging from 19 to 375 cm{sup 3}, a comparison of MUs was performed for both set of algorithms on field and plan basis. In total, variation of MUs for 677 treatment fields was investigated in terms of equivalent depth and the equivalent square of the field. Overall, MUs required by AXB to deliver the prescribed dose are on an average 2% higher than AAA. Using a 2-tailed paired t-test, the MUs from the 2 algorithms were found to be significantly different (p < 0.001). The secondary independent MU calculator RadCalc underestimates the required MUs (on an average by 4% to 5%) in the lung relative to either of the 2 dose algorithms.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2016

Dosimetric comparison of lung stereotactic body radiotherapy treatment plans using averaged computed tomography and end-exhalation computed tomography images: Evaluation of the effect of different dose-calculation algorithms and prescription methods

The purpose of this article is to quantitatively evaluate differences in dose distributions calculated using various computed tomography (CT) datasets, dose-calculation algorithms, and prescription methods in stereotactic body radiotherapy (SBRT) for patients with early-stage lung cancer. Data on 29 patients with early-stage lung cancer treated with SBRT were retrospectively analyzed. Averaged CT (Ave-CT) and expiratory CT (Ex-CT) images were reconstructed for each patient using 4-dimensional CT data. Dose distributions were initially calculated using the Ave-CT images and recalculated (in the same monitor units [MUs]) by employing Ex-CT images with the same beam arrangements. The dose-volume parameters, including D{sub 95}, D{sub 90}, D{sub 50}, and D{sub 2} of the planning target volume (PTV), were compared between the 2 image sets. To explore the influence of dose-calculation algorithms and prescription methods on the differences in dose distributions evident between Ave-CT and Ex-CT images, we calculated dose distributions using the following 3 different algorithms: x-ray Voxel Monte Carlo (XVMC), Acuros XB (AXB), and the anisotropic analytical algorithm (AAA). We also used 2 different dose-prescription methods; the isocenter prescription and the PTV periphery prescription methods. All differences in PTV dose-volume parameters calculated using Ave-CT and Ex-CT data were within 3 percentage points (%pts) employing the isocenter prescription method, and within 1.5%pts using the PTV periphery prescription method, irrespective of which of the 3 algorithms (XVMC, AXB, and AAA) was employed. The frequencies of dose-volume parameters differing by >1%pt when the XVMC and AXB were used were greater than those associated with the use of the AAA, regardless of the dose-prescription method employed. All differences in PTV dose-volume parameters calculated using Ave-CT and Ex-CT data on patients who underwent lung SBRT were within 3%pts, regardless of the dose-calculation algorithm or the dose-prescription method employed.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2018

AAA and AXB algorithms for the treatment of nasopharyngeal carcinoma using IMRT and RapidArc techniques

The aim of this study is to evaluate the impact of anisotropic analytical algorithm (AAA) and 2 reporting systems (AXB-D{sub m} and AXB-D{sub w}) of Acuros XB algorithm (AXB) on clinical plans of nasopharyngeal patients using intensity-modulated radiotherapy (IMRT) and RapidArc (RA) techniques. Six plans of different algorithm-technique combinations are performed for 10 patients to calculate dose-volume histogram (DVH) physical parameters for planning target volumes (PTVs) and organs at risk (OARs). The number of monitor units (MUs) and calculation time are also determined. Good coverage is reported for all algorithm-technique combination plans without exceeding the tolerance for OARs. Regardless of the algorithm, RA plans persistently reported higher D{sub 2%} values for PTV-70. All IMRT plans reported higher number of MUs (especially with AXB) than did RA plans. AAA-IMRT produced the minimum calculation time of all plans. Major differences between the investigated algorithm-technique combinations are reported only for the number of MUs and calculation time parameters. In terms of these 2 parameters, it is recommended to employ AXB in calculating RA plans and AAA in calculating IMRT plans to achieve minimum calculation times at reduced number of MUs.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2018

Data fusion for a vision-aided radiological detection system: Calibration algorithm performance

In order to improve the ability to detect, locate, track and identify nuclear/radiological threats, the University of Florida nuclear detection community has teamed up with the 3D vision community to collaborate on a low cost data fusion system. The key is to develop an algorithm to fuse the data from multiple radiological and 3D vision sensors as one system. The system under development at the University of Florida is being assessed with various types of radiological detectors and widely available visual sensors. A series of experiments were devised utilizing two EJ-309 liquid organic scintillation detectors (one primary and one secondary), a Microsoft Kinect for Windows v2 sensor and a Velodyne HDL-32E High Definition LiDAR Sensor which is a highly sensitive vision sensor primarily used to generate data for self-driving cars. Each experiment consisted of 27 static measurements of a source arranged in a cube with three different distances in each dimension. The source used was Cf-252. The calibration algorithm developed is utilized to calibrate the relative 3D-location of the two different types of sensors without need to measure it by hand; thus, preventing operator manipulation and human errors. The algorithm can also account for the facility dependent deviation from ideal data fusion correlation. Use of the vision sensor to determine the location of a sensor would also limit the possible locations and it does not allow for room dependence (facility dependent deviation) to generate a detector pseudo-location to be used for data analysis later. Using manually measured source location data, our algorithm-predicted the offset detector location within an average of 20 cm calibration-difference to its actual location. Calibration-difference is the Euclidean distance from the algorithm predicted detector location to the measured detector location. The Kinect vision sensor data produced an average calibration-difference of 35 cm and the HDL-32E produced an average calibration-difference of 22 cm. Using NaI and He-3 detectors in place of the EJ-309, the calibration-difference was 52 cm for NaI and 75 cm for He-3. In conclusion, the algorithm is not detector dependent; however, from these results it was determined that detector dependent adjustments are required.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

The Primary Interaction Compton Couple algorithm for sorting GRETINA/GRETA interaction points

The Primary Interaction Compton Couple (PICC) algorithm is presented in this work. The algorithm is used to determine the first-interaction-point position for $γ$-ray events in GRETINA. The first-interaction-point position is crucial for in-beam $γ$-ray spectroscopy experiments with fast beams due to the effect of Doppler broadening on the in-beam energy resolution. The development of the algorithm and its performance compared to a tracking algorithm and the Main Interaction assumption is presented. The PICC algorithm is demonstrated with real data to outperform the $γ$-ray energy tracking algorithm used for comparison here and the Main Interaction assumption in first-interaction-point determinations.

GRETINA↗

DOE OSTI2015

An adaptive multi-level simulation algorithm for stochastic biological systems

Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multi-level method [Anderson and Higham, “Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics,” SIAM Multiscale Model. Simul. 10(1), 146–179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders the multi-level method very efficient as only a relatively small number of paired paths are required to calculate each correction term. In the original multi-level method, each sample path is simulated using the tau-leap algorithm with a fixed value of τ. This approach can result in poor performance when the reaction activity of a system changes substantially over the timescale of interest. By introducing a novel adaptive time-stepping approach where τ is chosen according to the stochastic behaviour of each sample path, we extend the applicability of the multi-level method to such cases. We demonstrate the efficiency of our method using a number of examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Quantum-classical hybrid algorithm for the simulation of all-electron correlation

While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. Furthermore, we obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Evaluating algorithmic bias on biomarker classification of breast cancer pathology reports

Objectives: This work evaluated algorithmic bias in biomarkers classification using electronic pathology reports from female breast cancer cases. Bias was assessed across 5 subgroups: cancer registry, race, Hispanic ethnicity, age at diagnosis, and socioeconomic status. Materials and Methods: We utilized 594 875 electronic pathology reports from 178 121 tumors diagnosed in Kentucky, Louisiana, New Jersey, New Mexico, Seattle, and Utah to train 2 deep-learning algorithms to classify breast cancer patients using their biomarkers test results. We used balanced error rate (BER), demographic parity (DP), equalized odds (EOD), and equal opportunity (EOP) to assess bias. Results: We found differences in predictive accuracy between registries, with the highest accuracy in the registry that contributed the most data (Seattle Registry, BER ratios for all registries >1.25). BER showed no significant algorithmic bias in extracting biomarkers (estrogen receptor, progesterone receptor, human epidermal growth factor receptor 2) for race, Hispanic ethnicity, age at diagnosis, or socioeconomic subgroups (BER ratio <1.25). DP, EOD, and EOP all showed insignificant results. Discussion: We observed significant differences in BER by registry, but no significant bias using the DP, EOD, and EOP metrics for socio-demographic or racial categories. This highlights the importance of employing a diverse set of metrics for a comprehensive evaluation of model fairness. Conclusion: A thorough evaluation of algorithmic biases that may affect equality in clinical care is a critical step before deploying algorithms in the real world. We found little evidence of algorithmic bias in our biomarker classification tool. Artificial intelligence tools to expedite information extraction from clinical records could accelerate clinical trial matching and improve care.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Quantum Krylov subspace algorithms for ground- and excited-state energy estimation

Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground- and excited-state energies of a quantum many-body system. While QKSD algorithms typically rely on using the Hadamard test for estimating Krylov subspace matrix elements of the form $\langle \phi_i|e^{-\widehat{H}τ}|\phi_j\rangle$, the associated quantum circuits require an ancilla qubit with controlled multiqubit gates that can be quite costly for near-term quantum hardware. In this paper, we show that a wide class of Hamiltonians relevant to condensed-matter physics and quantum chemistry contain symmetries that can be exploited to avoid the use of the Hadamard test. We propose a multifidelity estimation protocol that can be used to compute such quantities, showing that our approach, when combined with efficient single-fidelity estimation protocols, provides a substantial reduction in circuit depth. In addition, here we develop a unified theory of quantum Krylov subspace algorithms and present three quantum-classical algorithms for the ground- and excited-state energy estimation problems, where each algorithm provides various advantages and disadvantages in terms of total number of calls to the quantum computer, gate depth, classical complexity, and stability of the generalized eigenvalue problem within the Krylov subspace.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Automatic Code Generation for High-Performance Graph Algorithms

Graph problems are common across fields of scientific computing and social sciences. However, despite their importance, implementing graph algorithms effectively on modern computing systems is a challenging task that requires significant programming effort and generally results in customized implementations. Current computing and memory hierarchies are not architected for irregular computations resulting in challenges for graph algorithms to achieve high performance on those architectures. In this paper, we present GraphX, a novel compiler framework and DSL designed to simplify the development of efficient graph algorithms and achieve high performance on modern computing systems. GraphX consists of a DSL for efficient implementation of graph algorithms, various optimizations, such as support for sparse linear algebra and workspace transformations, optimized graph primitives, including semiring and masking, and a high-performance code generation engine. Using GraphX, users can implement graph algorithms using a semantically-rich language with graph-oriented operators. GraphX uses these semantics to automatically generate efficient code for target architectures, increasing performance and portability across architectures. The composable nature of GraphX makes it possible to extend the set of optimizations and architectures without modifying the source code. We demonstrate GraphX outperforms state-of-the-art graph libraries, such as LAGraph, up to $3.7 speedup in semiring operations, $2.19 speedup in an important sparse computational kernel, and $9.05 speedup in graph processing algorithms.

compiler, graph algorithms, semiring, masking, wor↗

DOE OSTI2019

Accelerated Voltage Regulation in Multi-Phase Distribution Networks Based on Hierarchical Distributed Algorithm

Here, we introduce a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm highlights unprecedented scalability to large multi-phase distribution networks by jointly exploring the tree/subtrees structure of a large radial distribution network and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation loads compared to the centrally coordinated implementation of the same primal-dual algorithm without compromising optimality. Numerical findings on a 4,521-node test feeder show that the designed algorithm achieves more than 10-fold acceleration in the speed of convergence compared to the centrally coordinated primal-dual algorithm through reducing and distributing computational loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2014

SU-E-T-313: The Accuracy of the Acuros XB Advanced Dose Calculation Algorithm for IMRT Dose Distributions in Head and Neck

Purpose: To investigate the accuracy of the Acuros XB version 11 (AXB11) advanced dose calculation algorithm by comparing with Monte Caro (MC) calculations. The comparisons were performed with dose distributions for a virtual inhomogeneity phantom and intensity-modulated radiotherapy (IMRT) in head and neck. Methods: Recently, AXB based on Linear Boltzmann Transport Equation has been installed in the Eclipse treatment planning system (Varian Medical Oncology System, USA). The dose calculation accuracy of AXB11 was tested by the EGSnrc-MC calculations. In additions, AXB version 10 (AXB10) and Analytical Anisotropic Algorithm (AAA) were also used. First the accuracy of an inhomogeneity correction for AXB and AAA algorithms was evaluated by comparing with MC-calculated dose distributions for a virtual inhomogeneity phantom that includes water, bone, air, adipose, muscle, and aluminum. Next the IMRT dose distributions for head and neck were compared with the AXB and AAA algorithms and MC by means of dose volume histograms and three dimensional gamma analysis for each structure (CTV, OAR, etc.). Results: For dose distributions with the virtual inhomogeneity phantom, AXB was in good agreement with those of MC, except the dose in air region. The dose in air region decreased in order of MC<AXB11<AXB10. This may be caused by the difference of the electron cut-off energy for algorithms, ie: 0.700 MeV for MC, 0.711 MeV for AXB11, and 1.011 MeV for AXB 10. Since the AAA algorithm is based on the dose kernel of water, the doses in regions for air, bone, and aluminum considerably became higher than those of AXB and MC. The pass rates of the gamma analysis for IMRT dose distributions in head and neck were similar to those of MC in order of AXB11<AXB10<AAA. Conclusion: The dose calculation accuracy of AXB11 was almost equivalent to the MC dose calculation.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

SU-E-T-577: Commissioning of a Deterministic Algorithm for External Photon Beams

Purpose: We report commissioning results for a deterministic algorithm for external photon beam treatment planning. A deterministic algorithm solves the radiation transport equations directly using a finite difference method, thus improve the accuracy of dose calculation, particularly under heterogeneous conditions with results similar to that of Monte Carlo (MC) simulation. Methods: Commissioning data for photon energies 6 – 15 MV includes the percentage depth dose (PDD) measured at SSD = 90 cm and output ratio in water (Spc), both normalized to 10 cm depth, for field sizes between 2 and 40 cm and depths between 0 and 40 cm. Off-axis ratio (OAR) for the same set of field sizes was used at 5 depths (dmax, 5, 10, 20, 30 cm). The final model was compared with the commissioning data as well as additional benchmark data. The benchmark data includes dose per MU determined for 17 points for SSD between 80 and 110 cm, depth between 5 and 20 cm, and lateral offset of up to 16.5 cm. Relative comparisons were made in a heterogeneous phantom made of cork and solid water. Results: Compared to the commissioning beam data, the agreement are generally better than 2% with large errors (up to 13%) observed in the buildup regions of the FDD and penumbra regions of the OAR profiles. The overall mean standard deviation is 0.04% when all data are taken into account. Compared to the benchmark data, the agreements are generally better than 2%. Relative comparison in heterogeneous phantom is in general better than 4%. Conclusion: A commercial deterministic algorithm was commissioned for megavoltage photon beams. In a homogeneous medium, the agreement between the algorithm and measurement at the benchmark points is generally better than 2%. The dose accuracy for a deterministic algorithm is better than a convolution algorithm in heterogeneous medium.

07 ISOTOPE AND RADIATION SOURCES↗