Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Iterative methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 505 records · Page 28

Cerebral perfusion computed tomography deconvolution via structure tensor total variation regularization

Purpose: Cerebral perfusion computed tomography (PCT) imaging as an accurate and fast acute ischemic stroke examination has been widely used in clinic. Meanwhile, a major drawback of PCT imaging is the high radiation dose due to its dynamic scan protocol. The purpose of this work is to develop a robust perfusion deconvolution approach via structure tensor total variation (STV) regularization (PD-STV) for estimating an accurate residue function in PCT imaging with the low-milliampere-seconds (low-mAs) data acquisition. Methods: Besides modeling the spatio-temporal structure information of PCT data, the STV regularization of the present PD-STV approach can utilize the higher order derivatives of the residue function to enhance denoising performance. To minimize the objective function, the authors propose an effective iterative algorithm with a shrinkage/thresholding scheme. A simulation study on a digital brain perfusion phantom and a clinical study on an old infarction patient were conducted to validate and evaluate the performance of the present PD-STV approach. Results: In the digital phantom study, visual inspection and quantitative metrics (i.e., the normalized mean square error, the peak signal-to-noise ratio, and the universal quality index) assessments demonstrated that the PD-STV approach outperformed other existing approaches in terms of the performance of noise-induced artifacts reduction and accurate perfusion hemodynamic maps (PHM) estimation. In the patient data study, the present PD-STV approach could yield accurate PHM estimation with several noticeable gains over other existing approaches in terms of visual inspection and correlation analysis. Conclusions: This study demonstrated the feasibility and efficacy of the present PD-STV approach in utilizing STV regularization to improve the accuracy of residue function estimation of cerebral PCT imaging in the case of low-mAs.

60 APPLIED LIFE SCIENCES↗

TH-AB-BRA-02: Automated Triplet Beam Orientation Optimization for MRI-Guided Co-60 Radiotherapy

Purpose: MRI guided Co-60 provides daily and intrafractional MRI soft tissue imaging for improved target tracking and adaptive radiotherapy. To remedy the low output limitation, the system uses three Co-60 sources at 120° apart, but using all three sources in planning is considerably unintuitive. We automate the beam orientation optimization using column generation, and then solve a novel fluence map optimization (FMO) problem while regularizing the number of MLC segments. Methods: Three patients—1 prostate (PRT), 1 lung (LNG), and 1 head-and-neck boost plan (H&NBoost)—were evaluated. The beamlet dose for 180 equally spaced coplanar beams under 0.35 T magnetic field was calculated using Monte Carlo. The 60 triplets were selected utilizing the column generation algorithm. The FMO problem was formulated using an L2-norm minimization with anisotropic total variation (TV) regularization term, which allows for control over the number of MLC segments. Our Fluence Regularized and Optimized Selection of Triplets (FROST) plans were compared against the clinical treatment plans (CLN) produced by an experienced dosimetrist. Results: The mean PTV D95, D98, and D99 differ by −0.02%, +0.12%, and +0.44% of the prescription dose between planning methods, showing same PTV dose coverage. The mean PTV homogeneity (D95/D5) was at 0.9360 (FROST) and 0.9356 (CLN). R50 decreased by 0.07 with FROST. On average, FROST reduced Dmax and Dmean of OARs by 6.56% and 5.86% of the prescription dose. The manual CLN planning required iterative trial and error runs which is very time consuming, while FROST required minimal human intervention. Conclusions: MRI guided Co-60 therapy needs the output of all sources yet suffers from unintuitive and laborious manual beam selection processes. Automated triplet orientation optimization is shown essential to overcome the difficulty and improves the dosimetry. A novel FMO with regularization provides additional controls over the number of MLC segments and treatment time. Varian Medical Systems; NIH grant R01CA188300; NIH grant R43CA183390.

60 APPLIED LIFE SCIENCES↗

TomoTherapy MLC verification using exit detector data

Purpose: Treatment delivery verification (DV) is important in the field of intensity modulated radiation therapy (IMRT). While IMRT and image guided radiation therapy (IGRT), allow us to create more conformal plans and enables the use of tighter margins, an erroneously executed plan can have detrimental effects on the treatment outcome. The purpose of this study is to develop a DV technique to verify TomoTherapy's multileaf collimator (MLC) using the onboard mega-voltage CT detectors. Methods: The proposed DV method uses temporal changes in the MVCT detector signal to predict actual leaf open times delivered on the treatment machine. Penumbra and scattered radiation effects may produce confounding results when determining leaf open times from the raw detector data. To reduce the impact of the effects, an iterative, Richardson-Lucy (R-L) deconvolution algorithm is applied. Optical sensors installed on each MLC leaf are used to verify the accuracy of the DV technique. The robustness of the DV technique is examined by introducing different attenuation materials in the beam. Additionally, the DV technique has been used to investigate several clinical plans which failed to pass delivery quality assurance (DQA) and was successful in identifying MLC timing discrepancies as the root cause. Results: The leaf open time extracted from the exit detector showed good agreement with the optical sensors under a variety of conditions. Detector-measured leaf open times agreed with optical sensor data to within 0.2 ms, and 99% of the results agreed within 8.5 ms. These results changed little when attenuation was added in the beam. For the clinical plans failing DQA, the dose calculated from reconstructed leaf open times played an instrumental role in discovering the root-cause of the problem. Throughout the retrospective study, it is found that the reconstructed dose always agrees with measured doses to within 1%. Conclusions: The exit detectors in the TomoTherapy treatment systems can provide valuable information about MLC behavior during delivery. A technique to estimate the TomoTherapy binary MLC leaf open time from exit detector signals is described. This technique is shown to be both robust and accurate for delivery verification.

60 APPLIED LIFE SCIENCES↗

SU-G-JeP1-10: Feasibility of CyberKnife Tracking Using the Previously-Implanted Permanent Brachytherapy Seed Cloud

Purpose: Robotic radiosurgery is a salvage treatment option for patients with recurrent prostate cancer. We explored the feasibility of tracking the bolus of permanent prostate implants (PPI) using image recognition software optimized to track spinal anatomy. Methods: Forty-five inert iodine seeds were implanted into a gelatin-based prostate phantom. Four superficial gold seeds were inserted to provide ground-truth alignment. A CT scan of the phantom (120 kVp, 1 mm slice thickness) was acquired and a single-energy iterative metal artifact reduction (MAR) algorithm was used to enhance the quality of the DRR used for tracking. CyberKnife treatment plans were generated from the MAR CT and regular CT (no-MAR) using spine tracking. The spine-tracking grid was centered on the bolus of seeds and resized to encompass the full seed cloud. A third plan was created from the regular CT scan, using fiducial tracking based on the 4 superficial gold seeds with identical align-center coordinates. The phantom was initially aligned using the fiducial-tracking plan. Then the MAR and no-MAR spine-tracking plans were loaded without moving the phantom. Differences in couch correction parameters were recorded in the case of perfect alignment and after the application of known rotations and translations (roll/pitch of 2 degrees; translations XYZ of 2 cm). Results: The spine tracking software was able to lock on to the bolus of seeds and provide couch corrections both in the MAR and no-MAR plans. In all cases, differences in the couch correction parameters from fiducial alignment were <0.5 mm in translations and <1 degree in rotations. Conclusion: We were able to successfully track the bolus of seeds with the spine-tracking grid in phantom experiments. For clinical applications, further investigation and developments to adapt the spine-tracking algorithm to optimize for PPI seed cloud tracking is needed to provide reliable tracking in patients. One of the authors (MD) has received research support and speaker honoraria from Accuray.

60 APPLIED LIFE SCIENCES↗

Efficient thermo-mechanical simulation approaches for arc-and-wire based additive manufacturing

This study aims at the thermo-mechanical features inherent with the arc and wire metal deposition process to advance the structural simulation of additive manufacturing. Simulation approaches including iterative substructure method (ISM), dynamic mesh refining method (DMRM), and graphics processing unit (GPU) based explicit FEM code (GPU code) were developed for accelerating stress analysis and compared in terms of efficiency and accuracy. ISM and DMRM both take advantage of the strong nonlinearity phenomenon near the moving heat source, by reducing the global iterations and refining the local mesh respectively. The explicit FEM code was accelerated by a mass scaling technique based on the inherent strain concept. Two large parts by wire and arc additive manufacturing were analyzed, and the numerical results agreed very well with each other. The predicted distortion and residual stresses in the deposited layers were validated by experimental measurement. Compared with commercial software ABAQUS, the novel approaches reduced the computation cost substantially without compromising on accuracy. GPU code shows the highest computation efficiency (x30~70), while DMRM and ISM has an acceleration factor of x9 and x3 respectively. Owing to the minimum model simplification, such advanced simulation approaches will be very useful for structural analysis of additive manufacturing with complex deposition paths and product geometry.

Huang, Hui↗

A parallel in energy Krylov solution algorithm for the variational nodal method

To reduce the computational expense caused by the large number of energy groups in thermal and fast reactor calculations, we researched using parallelization in energy (i.e. group) of the multi-group response matrix equations derived from the Variational Nodal Method. This study focuses on solving steady-state eigenvalue problems in diffusion theory that are typically needed for depletion and reactivity coefficient calculations. To examine serial and parallel performance, GMRES, a Krylov algorithm, is applied to the multi-group system of equations at each fission source iteration. We also study the impact of using Wielandt acceleration on the eigenvalue/eigenvector problem. Numerical results based on a 72 group thermal and a 216 group fast reactor core problems are obtained for both serial and parallel calculations. The results show reduced CPU times when using GMRES and Wielandt acceleration in both serial and parallel calculations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Low level coupling scheme between neutronics and thermal-hydraulics based on Anderson acceleration

The simulation of nuclear reactors is a multiphysics problem mixing, amongst other fields, neutron transport and thermal-hydraulics. The simplest and most used approach in multiphysics simulation is based on the coupling of single-physics codes in a black-box fashion. However, in order to reduce the computational time needed for such simulations, case-dependent optimizations are often required. In this paper, we aim at reducing the computational time required to solve a coupled neutronic/thermal-hydraulic steady-state problem on a simplified Pressurized Water Reactor (PWR) core. The idea is to deal simultaneously with the coupling of the energy groups of the deterministic neutronic description of the core and its thermal-hydraulic description with the Anderson acceleration. By doing so, the fission source terms are directly accelerated instead of the power map as done in most cases. The power method used to solve the k-eigenvalue problem inside the neutronic solver is thus accelerated with the Anderson acceleration. The numerical experimentations conducted in this work are performed using APOLLO3 and THEDI, and indicate that such coupling strategy improves the convergence rates in terms of number of iterations required and the total computational time. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

An analytical method as a preconditioning modeling for systems of linear equations

In this paper, we propose a simple and practical preconditioner based on the homotopy analysis method. Furthermore, using this modeling, we design an efficient algorithm to solve linear systems. Within the computational framework, convection–diffusion equation candidates are investigated and evaluated. Finally, computational comparisons of the standard methods against preconditioned methods based on experiments are presented which illustrate the merits of the simplicity, power, and effectiveness of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

SU-F-T-347: An Absolute Dose-Volume Constraint Based Deterministic Optimization Framework for Multi-Co60 Source Focused Radiotherapy

Purpose: Treatment plan optimization in multi-Co60 source focused radiotherapy with multiple isocenters is challenging, because dose distribution is normalized to maximum dose during optimization and evaluation. The objective functions are traditionally defined based on relative dosimetric distribution. This study presents an alternative absolute dose-volume constraint (ADC) based deterministic optimization framework (ADC-DOF). Methods: The initial isocenters are placed on the eroded target surface. Collimator size is chosen based on the area of 2D contour on corresponding axial slice. The isocenter spacing is determined by adjacent collimator sizes. The weights are optimized by minimizing the deviation from ADCs using the steepest descent technique. An iterative procedure is developed to reduce the number of isocenters, where the isocenter with lowest weight is removed without affecting plan quality. The ADC-DOF is compared with the genetic algorithm (GA) using the same arbitrary shaped target (254cc), with a 15mm margin ring structure representing normal tissues. Results: For ADC-DOF, the ADCs imposed on target and ring are (D100>10Gy, D50,10, 0<12Gy, 15Gy and 20Gy) and (D40<10Gy). The resulting D100, 50, 10, 0 and D40 are (9.9Gy, 12.0Gy, 14.1Gy and 16.2Gy) and (10.2Gy). The objectives of GA are to maximize 50% isodose target coverage (TC) while minimize the dose delivered to the ring structure, which results in 97% TC and 47.2% average dose in ring structure. For ADC-DOF (GA) techniques, 20 out of 38 (10 out of 12) initial isocenters are used in the final plan, and the computation time is 8.7s (412.2s) on an i5 computer. Conclusion: We have developed a new optimization technique using ADC and deterministic optimization. Compared with GA, ADC-DOF uses more isocenters but is faster and more robust, and achieves a better conformity. For future work, we will focus on developing a more effective mechanism for initial isocenter determination.

60 APPLIED LIFE SCIENCES↗

Using a derivative-free optimization method for multiple solutions of inverse transport problems

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.

42 ENGINEERING↗

2D/1D approximations to the 3D neutron transport equation. I: Theory

A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)

97 MATHEMATICS AND COMPUTING↗

Analysis of cell-based diffusion acceleration for the slice balance approach

In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)

42 ENGINEERING↗

SU-D-9A-04: Brain PET/CT Imaging On a Scanner with a Large Axial Field-Of-View

Purpose: Large axial field-of-view (FOV) PET/CT scanners are valued for high sensitivity. Brain PET image quality may depend on the head position within the FOV. We investigated the precision of activity estimation for brain PET imaging when the brain was positioned at the end (END) and in the middle (CEN) of the FOV. The additional CT dose for the CEN position was recorded. Methods: An image quality (Jaszczak) phantom and a striatal phantom were filled with F-18 and positioned in END and CEN locations. For each phantom and each location, we acquired a ∼1-hr listmode PET, rebinned the data into 10 frames with equal number of coincidence events, and reconstructed each frame using an iterative algorithm. For the striatal phantom, END and CEN were compared by drawing on each image three regions of interest (ROI) in axially separated uniform areas. The standard deviation of the activity estimation within each ROI was averaged over the 10 images. The coefficient of variation (CV) for activity estimation was calculated at each position. Image quality was assessed by inspecting the resolution bar pattern in the Jaszczak phantom at two different head positions. Results: The CV was the lowest for ROIs near the center of the FOV. For slices near the end, not only was the CV highest, but also the resolution pattern was degraded. CTDIvol summarized in the dose report indicated that the CT dose was ∼ 10% higher for CEN as compared to END position. Conclusion: Positioning the brain in the middle of the FOV in a large FOV PET/CT scanner allows more precise measurement of tracer uptake and better image quality at the cost of increased CT dose. For the end location longer scan times may minimize image quality degradation without any additional CT dose.

60 APPLIED LIFE SCIENCES↗

SU-E-J-184: Stereo Time-Of-Flight System for Patient Positioning in Radiotherapy

Purpose: The objective of this work is to test the advantage of using the surface acquired by two stereo Time-of-Flight (ToF) cameras in comparison of the use of one camera only for patient positioning in radiotherapy. Methods: A first step consisted on validating the use of a stereo ToFcamera system for positioning management of a phantom mounted on a linear actuator producing very accurate and repeatable displacements. The displacements between two positions were computed from the surface point cloud acquired by either one or two cameras thanks to an iterative closest point algorithm. A second step consisted on determining the displacements on patient datasets, with two cameras fixed on the ceiling of the radiotherapy room. Measurements were done first on voluntary subject with fixed translations, then on patients during the normal clinical radiotherapy routine. Results: The phantom tests showed a major improvement in lateral and depth axis for motions above 10 mm when using the stereo-system instead of a unique camera (Fig1). Patient measurements validate these results with a mean real and measured displacement differences in the depth direction of 1.5 mm when using one camera and 0.9 mm when using two cameras (Fig2). In the lateral direction, a mean difference of 1 mm was obtained by the stereo-system instead of 3.2 mm. Along the longitudinal axis mean differences of 5.4 and 3.4 mm with one and two cameras respectively were noticed but these measurements were still inaccurate and globally underestimated in this direction as in the literature. Similar results were also found for patient subjects with a mean difference reduction of 35%, 7%, and 25% for the lateral, depth, and longitudinal displacement with the stereo-system. Conclusion: The addition of a second ToF-camera to determine patient displacement strongly improved patient repositioning results and therefore insures better radiation delivery.

60 APPLIED LIFE SCIENCES↗

SU-E-T-258: Parallel Optimization of Beam Configurations for CyberKnife Treatments

Purpose: The CyberKnife delivers a large number of beams originating at different non-planar positions and with different orientation. We study how much the quality of treatment plans depends on the beams considered during plan optimization. Particularly, we evaluate a new approach to search for optimal treatment plans in parallel by running optimization steps concurrently. Methods: So far, no deterministic, complete and efficient method to select the optimal beam configuration for robotic SRS/SBRT is known. Considering a large candidate beam set increases the likelihood to achieve a good plan, but the optimization problem becomes large and impractical to solve. We have implemented an approach that parallelizes the search by solving multiple linear programming problems concurrently while iteratively resampling zero weighted beams. Each optimization problem contains the same set of constraints but different variables representing candidate beams. The search is synchronized by sharing the resulting basis variables among the parallel optimizations. We demonstrate the utility of the approach based on an actual spinal case with the objective to improve the coverage. Results: The objective function is falling and reaches a value of 5000 after 49, 31, 25 and 15 iterations for 1, 2, 4, and 8 parallel processes. This corresponds to approximately 97% coverage in 77%, 59%, and 36% of the mean number of iterations with one process for 2, 4, and 8 parallel processes, respectively. Overall, coverage increases from approximately 91.5% to approximately 98.5%. Conclusion: While on our current computer with uniform memory access the reduced number of iterations does not translate into a similar speedup, the approach illustrates how to effectively parallelize the search for the optimal beam configuration. The experimental results also indicate that for complex geometries the beam selection is critical for further plan optimization.

07 ISOTOPE AND RADIATION SOURCES↗

SU-F-J-214: Dose Reduction by Spatially Optimized Image Quality Via Fluence Modulated Proton CT (FMpCT)

Purpose: Proton CT (pCT) is a promising imaging modality for reducing range uncertainty in image-guided proton therapy. Range uncertainties partially originate from X-ray CT number conversion to stopping power ratio (SPR) and are limiting the exploitation of the full potential of proton therapy. In this study we explore the concept of spatially dependent fluence modulated proton CT (FMpCT), for achieving optimal image quality in a clinical region of interest (ROI), while reducing significantly the imaging dose to the patient. Methods: The study was based on simulated ideal pCT using pencil beam (PB) scanning. A set of 250 MeV protons PBs was used to create 360 projections of a cylindrical water phantom and a head and neck cancer patient. The tomographic images were reconstructed using a filtered backprojection (FBP) as well as an iterative algorithm (ITR). Different fluence modulation levels were investigated and their impact on the image was quantified in terms of SPR accuracy as well as noise within and outside selected ROIs, as a function of imaging dose. The unmodulated image served as reference. Results: Both FBP reconstruction and ITR without total variation (TV) yielded image quality in the ROIs similar to the reference images, for modulation down to 0.1 of the full proton fluence. The average dose was reduced by 75% for the water phantom and by 40% for the patient. FMpCT does not improve the noise for ITR with TV and modulation 0.1. Conclusion: This is the first work proposing and investigating FMpCT for producing optimal image quality for treatment planning and image guidance, while simultaneously reducing imaging dose. Future work will address spatial resolution effects and the impact of FMpCT on the quality of proton treatment plans for a prototype pCT scanner capable of list mode data acquisition. Acknowledgement: DFG-MAP DFG - Munich-Centre for Advanced Photonics (MAP)

60 APPLIED LIFE SCIENCES↗

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Pilot Point Optimization of Mining Boundaries for Lateritic Metal Deposits: Finding the Trade-off Between Dilution and Ore Loss

Geological contacts in lateritic metal deposits (footwall topographies) often delineate the orebody boundaries. Spatial variations seen in such contacts are frequently higher than those for the metal grades of the deposit. Therefore, borehole spacing chosen based on the grade variations cannot adequately capture the geological contact variability. Consequently, models created using such boreholes cause high volumetric uncertainties in the actual and targeted ore extraction volumes, which, in turn, lead to high unplanned dilution and ore losses. In this paper, a method to design optimum ore/mining boundaries for lateritic metal deposits is presented. The proposed approach minimizes the dilution/ore losses and comprises two main steps. First, the uncertainty on the orebody boundary is represented using a set of stochastic realizations generated with a multiple-point statistics algorithm. Then, the optimal orebody boundary is determined using an optimization technique inspired by a model calibration method called Pilot Points. The pilot points represent synthetic elevation values, and they are used to construct smooth mining boundaries using the multilevel B-spline technique. The performance of a generated surface is evaluated using the expected sum of losses in each of the stochastic realizations. The simulated annealing algorithm is used to iteratively determine the pilot point values which minimize the expected losses. The results show a significant reduction in the dilution volume as compared to those obtained from the actual mining operation.

58 GEOSCIENCES↗