1 - Nuclear Science and Engineering Lab (NSEL) - Virginia Tech

Advanced Hybrid Transport Methodologies forMedical Image Reconstruction in Real‐TimeProf. Alireza HaghighatDirector of VT 3 G & NSELNuclear Engineering ProgramMechanical Engineering DepartmentVirginia Tech Research Center (VTRC)Arlington, VAhaghighat@vt.eduPresented at the ANS‐ASME meeting, Lynchburg, VA, Dec 13, 2012Nuclear EngineeringProgram1

Virginia Tech Nuclear Engineering Program , VT‐NEP(regional, multidisciplinary)NSEL @ VTRC, ArlingtonNuclear Science and Engineering Lab (NSEL) – Institute ofCritical Technology and Applied Science (ICTAS)NEP @ VT, BlacksburgNuclear Engineering Program (NEP),Mechanical Engineering Department• Government agencies• industry• Medical centers• Universities engaged in nuclearpolicyCollege of EngineeringCollege of ScienceCollege of Veterinary‐MedicineCollege of Arts and Human SciencesCAER @ LynchburgCenter for Advanced Engineering Research (CAER) –A partnershipof State of VA, industry and UniversitiesNuclear EngineeringProgramAREVAB&WUVA, VT, VCU2

Status of VT‐NEP• 5 Core faculty• Haghighat (Particle transport methods and their application in power, medicineand security, design of non‐destructive detection and imaging systems, reactordigital I&C, severe reactor accidents )• Hin (Nuclear and Thermoelectric Materials Modeling)• Liu (Reactor Thermal Hydraulics and Safety)• Pierson (Nuclear fuel cycle, Reactor operations and instrumentation, nuclearsecurity and non‐proliferation, radiation detection)• Winfrey (Plasma physics, materials fabrication and evaluation, and fusion)• 8 Affiliate faculty [Battaglia (ME ‐ CFD), Brown (ME‐CFD/MD), Farkas (MSE‐Materials), Hendricks (MSE‐Materials), Kulkarni (ESM‐Nuclear nonproliferationand policy), Mahajan (ME‐Materials), Tafti (ME‐CFD) & Schmid(STS‐Nuclear policy)]• 1 Adjunct faculty [Turso (Northrop Grumman – Reactor Control]• NEP faculty has initiated/established multi‐disciplinary activities in differentapplications of Nuclear Science and Engineering including:power, safeguards and non‐proliferation, medicine, & policyNuclear EngineeringProgram3

Nuclear Theory, experiment, and Computation: (Haghighat, Liu, Pierson and Winfrey,Battaglia, Tafti, and Brown, plus 1-2 hires)Hybrid particle transport methods and their application to nuclear systems, High performancecomputing, multi-scale and multi-physics methodologies, and virtual visualization, High energydensity plasma modeling, Thermal hydraulics modeling, Computational methods in reactorphysics and shielding, perturbation methodsNuclear Safety, Security, Non-proliferation, and Safeguards: (Haghighat,Kulkarni & Pierson, Schmid plus 1-2 new hires)Nonproliferation, Radiation protection and shielding, Nuclear fuel cycle management, Nuclearwaste disposal, Science-based analysis and support of nuclear policy formationNuclear Materials Research: (Farkas, Hendricks, Clark, and Hin, plus 1-2 new hires)Novel nuclear materials design, Thermoelectric materials, Materials modeling and simulation,Hard coatings, plasma-material interactionsNuclear Fuel Cycle: (Pierson, Clark, Hin, Haghighat, plus 1-2 new hire)Fuel design and modeling, used nuclear fuel processing, waste forms, waste disposition, MaterialProtection Accounting and Control Technologies (MPACT)Nuclear Power Operations: (Pierson & Haghighat, plus 1-2 new hires)Design of digital instrumentation and control, Alternative reactor technology, Reactor operationsand safetyEmerging Nuclear Technologies: (Haghighat, Mahajan & Winfrey, plus1-2 new hire)Design of nondestructive detection systems, New methods of medical imaging, Fusion reactorfueling Nano-nuclear scienceNuclear EngineeringProgram4

• Leadership: Haghighat, Kulkarni & Farkas• Activities:• Teaching (within the regional triangle)• NSEG 5124 (Nuclear Reactor Analysis); NSEG 5134 (Monte Carlo Method); & NSEG 6124(Advanced Nuclear Reactor Analysis); ESM 6984 (S&T and Policy –Their Interplay);Nuclear Security: Nonproliferation and Safeguards," NSEG (or ME)/STS 5984; InCollaboration with UT, developing a course on Digital I&C (funded by NRC)• Research – Virginia Tech Transport Theory Group, VT 3 G• Nuclear power• Nuclear non‐proliferation and safeguards• Medicine• Seeking collaborations• Other VT faculty members, and NCR universities, government agencies andprivate organizations• Initiating new activities• Contribution to formulation of Nuclear policy, Public engagement, Emergencyresponse to nuclear events• Organizing seminars/workshops/symposia/forums• Nov 7‐11, 2011, 13 th international workshop on particle transport methodologies(www.cpe.vt.edu/lpcf)• June 2013, 14 th international workshop on particle transport methodologies• March 12, 2012 ‐ A Symposium on Low Power Critical Facilities, sponsored by SUNRISE(Southeast Universities Nuclear Reactors Institute for Science and Education)(www.ictas.vt.edu/nuclear)• Nov. 5, 2012 ‐ A Forum on Nuclear Regimes: Future OutlookNSEL at ArlingtonNuclear EngineeringProgram5

VT‐NEPFuture• Finalize MS and PhD degrees in Nuclear Engineering ‐under review by SCHEV• Increase the size of Core faculty to 8‐12• Establish a School Nuclear Engineering & Science(SNES) and/or Nuclear Engineering DepartmentNuclear EngineeringProgram6

What is Particle Transport Theory?Determination of the expected number (average) ofparticles in a phase space (dVdEd) at time t:n ( r , E,ˆ, t)dvdEdzdvdΩΩdEryxTo determine particle flux, current, and reaction rates.Nuclear EngineeringProgram 7

Simulation Approaches• Deterministic Methods• Solve the linear Boltzmann equation to obtain the expected flux in aphase space• Statistical Monte Carlo Methods• Perform particle transport experiments in a random manner on acomputer to estimate average behavior of a particle in phase spaceNuclear EngineeringProgram8

Deterministic – Linear Boltzmann Equationˆ ˆ .(r,E,)( r,E)(r,E,ˆ) streamingdE'0 4(E)4d' ( r,E'dE's0 4scatteringfissiond'fcollisionˆ ˆ E,' )(r,E',ˆ) Indp. source ˆ ( r,E)(r,E',) S(r,E,ˆ)Nuclear EngineeringProgram 9

Integro-differential – Discretized formulation• Discretized angular variable – DiscreteOrdinates (Sn) method: considering aconservation criteria,ˆmA set of { ˆ , w m } obtained, and.m ˆ . ( , , ) ( , ) ( , , ˆ r E r E r E ) q(r,E,ˆmmm), m=1, M0.20.4V20.60.8110.80.6V10.40.2X10000• Discretized spatial variable:Integrated over fine meshes using Finite Volume or FEmethodsm,g,AVdVijkg ( r ) m,gVijk( r )• Discretized energy variable:Multigroup approach: Energyrange, e.g., [0, 20 MeV], ispartitioned into G groups,g=5g=4g=3g=2g=1Where,Nuclear EngineeringProgram 10

Monte Carlo Methods• Perform an experiment on a computer; “exact”simulation of a physical processPathlengthr lntType ofcollision stScattering angle(isotropicscattering)0 21SampleS (r, E, Ω)absorbedabsorbedabsorbedTally (count)Variance Reduction techniques are need for real‐world shielding problems!Nuclear EngineeringProgram11

Deterministic vs. Monte CarloItem Deterministic MCGeometry Discrete/ Exact ExactEnergy treatment – DiscreteExactcross sectionDirection Discrete/ Truncated series ExactInput preparation Difficult simpleComputer memory Large SmallComputer time Small LargeNumerical issues Convergence Statistical uncertaintyAmount of LargeLimitedinformationParallel computing Complex TrivialNuclear EngineeringProgram12

Therefore, hybrid methods are needed.What is “hybrid”?It is a combination ofDifferent forms of the LBEDeterministic and/or Monte Carlo approachesDifferent numerical techniques,Forward & Adjoint/Importance LBETime‐dependent & Time‐independentNuclear EngineeringProgram13

Virginia Tech Transport Theory Group ‐ VT 3 GVisionTo be able to perform detailed 3‐D, timedependent,neutral‐ and charged‐particletransport calculation efficiently (computertime & engineer’s time) and accurately forapplication to power, safeguards andnonproliferation, and medicineNuclear EngineeringProgram14

VT3G ‐Advanced Computer codes/Formulations/AlgorithmsOver the last 26 years, VT3G has developed numerousadvanced formulations and computer codes, and applied thesecodes to real-world problems.Advanced numerical formulations:Differencing schemes (DTW, EDW, ADS), Cross-section generation (CPXSD),angular quadrature (Pn-Tn, Ordinate Splitting, fictitious), acceleration scheme(EP-SSn), response function for subcritical multiplication, & hybrid techniquesTransport codes• PENTRAN (Parallel Environment Neutral-particle TRANSport) – A 3-D parallelparticle transport code, Sjoden and Haghighat, 1997.• A 3 MCNP – Automated Adjoint Accelerated MCNP for Monte Carlo neutral particletransport with automated variance reduction, Wagner and Haghighat, 1997.• TITAN –A 3-D Hybrid parallel transport code, Yi and Haghighat, 2007.• ADIES - Angular-dependent Adjoint Driven Electron-photon Importance Samplingfor Monte Carlo electron transport with automated variance reduction, Dionne andHaghighat, 2007.Cross-section generation code• CPXSD – Contributon Point-wise cross-section Driven for generation of arbitrarymultigroup cross-section librariesSpecialized Hybrid methods/algorithms/codes• TITAN-SPECT algorithm• INSPCT-S (inspection of spent fuel pool)• AIMS (Active Interrogation for Monitoring of Special-nuclear-materials) PENTRANstTITANADIES0 2 1AIMS ln r 5453 0.580498 0.561644 0.491674 0.420538 0.353999 0.28285 0.27647 0.897903 0.880437 0.770597 0.653747 0.543993 0.427576 0.38686 1.271323 1.252983 1.094413 0.922518 0.761393 0.591298 0.49337 1.696988 INSPCT‐S1.669344 1.453015 1.219392 1.002015 0.772365 0.59258 1.978009 1.923356 1.665877 1.394836 1.14574 0.880125 0.67336 1.093457 1.058167 0.914234 0.765146 0.628852 0.482792 0.3tNuclear EngineeringProgram

Graduate studentsKatherine Royston, PhD candidateNathan Roskoff, MS candidateWilliam Walters, PhD candidate&CollaborationsProfs. Petrovic, Rahnema & Sjoden, and Dr. Yi, Georgia TechProf. Upadhyaya, University of TennesseePlus a new contract led by Georgia Tech with collaborators from Univ. ofMichigan, Westinghouse, Univ. of Cambridge, Politecnico di Milano, INL,Univ of Idaho, Southern Nuclear, Morehouse CollegeRecruitmentSeeking graduate students and postdoctoral fellowsNuclear EngineeringProgram 16

Nuclear Power• Development of advanced multigroup algorithms forSimulation of Advanced Reactors (Funded by DOE–Jointwith Georgia Tech);• VT task: Developing an algorithm for TITAN• In collaboration with Prof. Upadhyaya from University ofTennessee is developing a course on digital I&C (fundedby NRC)• Neutronics Simulation in Support of mPower ReactorModeling (Funded by B&W mPower Generation);• Reactor core and ex‐core detector modeling and simulationin support of their licensing activities, and development ofeffective core monitoring.• Design of an Integral Inherently Safe LWR (I 2 S‐LWR)system (Recently funded by DOE – led by GT, include 9organizations, a budget of $6 M for three years);• VT task: Design an inherently safe spent fuel pool with onlinemonitoring systemNuclear EngineeringProgram

Nuclear non‐proliferation• Advanced hybrid algorithms fordevelopment of tools forinspection of shipping containers(Funded by NNSA ‐Joint withGeorgia Tech): VT task: Developedhybrid response functionmethodologiesNuclear Safeguards• Developed the INSPCT tool formonitoring of spent fuel pool(funded by LLNL)Monitoring of Spent Fuel PoolInspection of Containers for SNM† ( r , E , ˆ) SEstimated current alongcontainer depth0 10 20 30 40 50INPUTOUTPUTsrc file C:\Users\ali\Documents\haghD\ufttg\LLNL\INSPCT-s\se.dsrcINSPCT‐SCOLUMNS 8 fm file C:\Users\ali\Documents\haghD\ufttg\LLNL\INSPCT-s\seResponse Tolerance Detector NormalizationROWS 6 imp file C:\Users\ali\Documents\haghD\ufttg\LLNL\INSPCT-s\se 15.00% 5.28E-10runBurnupIndependent Source(x,y) 1 2 3 4 5 6 7 8 (x,y) 1 2 3 4 5 6 7 81 9000 9000 9000 9000 9000 9000 9000 9000 1 4.60E+07 3.39E+07 2.84E+07 2.48E+07 2.21E+07 1.94E+07 1.56E+07 130369482 10000 10000 10000 10000 10000 10000 10000 10000 2 6.89E+07 5.30E+07 4.49E+07 3.86E+07 3.39E+07 2.91E+07 2.26E+07 181016923 11000 11000 11000 11000 11000 11000 11000 11000 3 1.00E+08 8.04E+07 6.86E+07 5.84E+07 5.06E+07 4.29E+07 3.23E+07 250472564 12000 12000 12000 12000 12000 12000 12000 12000 4 1.42E+08 1.17E+08 1.01E+08 8.51E+07 7.33E+07 6.15E+07 4.53E+07 342048425 13000 13000 13000 13000 13000 13000 13000 13000 5 1.98E+08 1.67E+08 1.45E+08 1.22E+08 1.04E+08 8.67E+07 6.28E+07 464929946 14000 14000 14000 14000 14000 14000 14000 14000 6 2.68E+08 2.32E+08 2.01E+08 1.69E+08 1.44E+08 1.19E+08 8.52E+07 62072007Cooling timeFission Source(x,y) 1 2 3 4 5 6 7 8 (x,y) 1 2 3 4 5 6 7 81 1 2 5 10 15 20 30 40 1 4.03E+07 4.68E+07 4.25E+07 3.66E+07 3.11E+07 2.57E+07 1.98E+07 125211882 1 2 5 10 15 20 30 40 2 6.88E+07 8.12E+07 7.41E+07 6.34E+07 5.32E+07 4.33E+07 3.26E+07 201996393 1 2 5 10 15 20 30 40 3 9.82E+07 1.17E+08 1.07E+08 9.08E+07 7.54E+07 6.05E+07 4.47E+07 271698784 1 2 5 10 15 20 30 40 4 1.32E+08 1.58E+08 1.44E+08 1.21E+08 9.98E+07 7.93E+07 5.78E+07 347511345 1 2 5 10 15 20 30 40 5 1.62E+08 1.92E+08 1.73E+08 1.45E+08 1.19E+08 9.42E+07 6.80E+07 408239416 1 2 5 10 15 20 30 40 6 1.49E+08 1.74E+08 1.56E+08 1.30E+08 1.06E+08 8.38E+07 6.03E+07 36229288Response (experimental)Response(Calculated)(x,y) 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 (x,y) 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.50.5 0.5 0.123198 0.230998 0.221266 0.193583 0.166627 0.141523 0.114534 0.083892 0.0366111.5 0.6 0.3 1.5 0.305453 0.580498 0.561644 0.491674 0.420538 0.353999 0.28285 0.203871 0.0875992.5 0.8 2.5 0.467647 0.897903 0.880437 0.770597 0.653747 0.543993 0.427576 0.301569 0.1278193.5 3.5 0.658686 1.271323 1.252983 1.094413 0.922518 0.761393 0.591298 0.410909 0.1725544.5 1.4 4.5 0.879337 1.696988 1.669344 1.453015 1.219392 1.002015 0.772365 0.532245 0.2226165.5 1.2 5.5 1.029258 1.978009 1.923356 1.665877 1.394836 1.14574 0.880125 0.605581 0.2531926.5 6.5 0.57336 1.093457 1.058167 0.914234 0.765146 0.628852 0.482792 0.332139 0.139652dgnSlide10Nuclear non‐proliferation & safeguardsNuclear EngineeringProgramResponse Difference0.5 1.5 (x,y) 2.5 3.5 4.5 5.5 6.5 7.5 8.50.51.5 3.36% -15.25%2.5 3.82%3.54.5 -3.65%5.5 4.74%6.5

Slide11Medicine• Development of an image reconstruction algorithmfor SPECT (Single Phone Emission ComputedTomography); developed hybrid algorithms, to bediscussed in this presentation.Nuclear EngineeringProgram

TITAN Algorithm allows for the use of different algorithms,even Monte Carlo, in different coarse meshes.Sn Solver –coarse mesh( n)gijk2n 2n 2nxin y in z inQx y z2n 2n 2nijk x y z( n)gijkCM solver‐coarse meshoutginkginkin gisQink gingisinkginke (1 e )giinoutQgingink gink s gi ink gi A P BA B P B AB AANuclear EngineeringProgram 20B

TITAN Code SystemTITAN is a 3‐D, parallel code system with a hybridSn and Characteristics algorithm1. Written from scratch in Fortran 90 with somefeatures in Fortran 2003 standard, such asdynamic memory allocation and object orientedprogramming. (uses similar approach as PENTRAN)2. Compiled by Intel Fortran Compiler (ifc 8.0+) orPGI f90 compiler (pgf90 6.1), still underdevelopment, over 22,000 lines nowNuclear EngineeringProgram 21

Introduction to SPECT (Single Photon Emission Computed Tomography )Imaging Device• Functional imaging modalityInject aradioactivematerialExampleD~1.5 mmL=23 mmAspectratio=~15A projectionangleNotes• Limited image quality and spatial resolution• Traditionally simulated using Monte Carlo methodsNuclear EngineeringProgram

Goal•Simulation of the SPECT (Single PhotonEmission Computed Tomography) using accurateand fast hybrid deterministic formulation•Use simulation results for imageconstruction:• Improving the image quality• Reducing radioactive uptakeNuclear EngineeringProgram

Reference Model• A SPECT myocardial perfusion study withTechnecium‐99m (Tc‐99m) was simulated.• Tc‐99m is absorbed by the heart wall where it emits140.5 keV gamma rays.• The NURBS‐based cardiac‐torso (NCAT) code wasused to create a 64 x 64 x 64 voxel phantom with a Tc‐99m source in the heart wall.Nuclear EngineeringProgram

Nuclear EngineeringProgramNCAT voxel phantom

Multigroup cross sections for TITAN‣Energy group structureSince source energy is 140.5 keVEnergyGroupUpper Bound(keV)Lower Bound(keV)1 154.55 126.452 126.45 98.353 98.35 10‣Used CEPXS multigroup photon cross sections(Sandia National Laboratories)Nuclear EngineeringProgram26

Discrete ordinatesXHow to model thecollimators?100000.20.20.40.4V20.60.80.80.6V111Nuclear EngineeringProgram27

TITAN Hybrid formulation for SPECT simulationStep 4 – Ray‐tracingfor transport throughthe collimatorStep 3 – Snwithfictitious quadratureStep 2 – Selectfictitious directionsStep 1 – SnCalculationNuclear EngineeringProgram28

Step 2 – Selection of fictitious directionsParticles blocked byCollimatorPhantomDetectorAcceptance angle‣Solve for angular fluxalong directions withinacceptance angleProjectionangleCircular SplittingNuclear EngineeringProgram29

Step 3 –Snwith fictitious direction• To calculate angular fluxes along directions ofinterest, TITAN Sn algorithm is modified for treatinga fictitious quadrature set• Fictitious quadrature represents all the projection anglesand directions created through circular splittingNuclear EngineeringProgram30

Step 3 ‐ Sn with Fictitious Quadrature• To calculate the angular flux for the fictitiousquadrature set on the surface of the phantom, wedeveloped the following algorithm:• Obtain flux moments from step 1• Calculate Scattering Source for Extra Sweep along fictitiousquadrature set• Perform an extra sweep to obtain angular flux along thefictitious quadrature set.Nuclear EngineeringProgram31

Step 4 –Ray tracing along collimators• Since the spatial meshing of the phantom is much coarser than thecollimator opening• The characteristic rays are drawn from each pixel of the projection imagebackward to the phantom surface along the projection angle and thesplit directions circularly surrounding it• Using a bi‐linear interpolation procedure, angular fluxes along theprojection angle and its split directions are determine• Using a ray‐tracing formulation through vacuum ‐ particles leavingthe phantom surface are transported through a set of collimatorsnormal to the SPECT camera.• The intensity of each pixel in the projection images is evaluated bythe integration of the angular flux at that pixel over the smallcollimator acceptance angle.Nuclear EngineeringProgram

Collimator CasesCaseAcceptanceAngleAspect Ratio1 2.97° 9.52 1.42° 20.13 0.98° 29.3Nuclear EngineeringProgram33

Collimator Case 3 (0.97º)Anterior Projection Images(Based on 1 st energy group)TITANMCNP5Nuclear EngineeringProgram34

Maximum difference of TITAN results relative to MCNP5results * in the heart for each collimator caseCaseNumberAcceptance Angle(degrees)Maximum RelativeDifference (%)1 2.97 21.32 1.42 11.93 0.98 8.3*All MCNP5 data had 1‐ uncertainty 3% in the heartNuclear EngineeringProgram35

Profiles through column 44 ofprojection imagesNuclear EngineeringProgram

Profiles through row 33 ofprojection imagesNuclear EngineeringProgram

TimingCaseNumberAcceptanceAngle(degrees)MCNP5(min)*CodeTITAN(min) †SpeedupFactor(MCNP5/TITAN)1 2.97 313.8 0.82 3822 1.42 1071.8 0.82 13043 0.98 2289.7 0.82 2787*Time to achieve 1‐ uncertainty of 3.0% in the heart†180 projection anglesNuclear EngineeringProgram

Nuclear EngineeringProgram 39

Improvement of accuracy for collimators withrelatively low aspect ratioTo improve the accuracy, i.e., allowing for more ray penetration through thecollimators, in the Circular Ordinate Splitting (COS), we consideredincrease number of circles and increase number of directions per circle.This measure increased the accuracy, but was limitedNuclear EngineeringProgram40

Further Improvement of COS1. Split directions areweighted by the detectorsurface area projected alongthat direction to the frontof the collimator.2. The number of directionsper concentric circle isscaled to the circle area,except for the innermost,which is user specified.Phantom SurfaceNuclear EngineeringProgram41

Simple modelParameter Case 1 Case 2CollimatorDetectorAcceptance Angle 2.1° 7.7°Aspect Ratio 13.5:1 3.7:1Detector Pixel Size 0.17x0.17 cm 2 0.625x0.625 cm 2Number of DetectorPixels15 7Nuclear EngineeringProgram42

Collimator2.1Normalized Gamma Flux7.7Nuclear EngineeringProgram43

Average difference relative to MCNP5 for7.7° collimator acceptance angleNuclear EngineeringProgram 44

Comparison of serial computation times*There is no appreciable difference in computation timebetween the two COS methods for this modelNuclear EngineeringProgram 45

Future Work• Future work will focus on the development of an iterativereconstruction algorithm for SPECT.• This algorithm will incorporate the TITAN code for forwardprojection.• Our goal is to demonstrate that the TITAN code’sinclusion will result in a fast and accurate reconstructionalgorithm.• Also, this new collimator algorithm is applicable in otherareas, such as modeling streaming radiation throughducts in a reactor.Nuclear EngineeringProgram46

To solve 3‐D, real‐world particle transport problemsaccurately and efficiently,HYBRID methods which combine the benefits ofdifferent techniques/methodologies are neededNuclear EngineeringProgram47

Questions?Nuclear EngineeringProgram 48