Developing pCT

Proton Computed TomographyThe Positive Medical Imaging TechniqueKeith Evan SchubertProfessor of Computer Science and EngineeringCalifornia State University, San Bernardino

Why Protons?Dose %100PhotonProtonDepth in TissueElectronpCT Scanner

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Problem Flow4Discretized Area

Using the discretized area described earlier and here by the dashed-dotted square between the detectorsWith 21.21cm x 21.21cm and a voxel size of 0.25mm x 0.25mm gives 5A Proton Path

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Problem Size~107 voxels~ 108 proton paths (min)~ 400 voxels/paths

Thus:

Size(A)~ 107108 = 1 PB (dense)

Computation SVD~ 107107108 = 1010 Tflops/Cycle

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Problem Size~107 voxels~ 108 proton paths (min)~ 400 voxels/paths

Thus:

Size(A)~ 108 103 =100 GB

Computation ART~ 103103108 = 102 Tflops/Cycle9

Problem Flow10Convex Hull

11Convex Hull

12Convex Hull

13Convex Hull

14Convex Hull

15Convex Hull

16Simulation

No NoiseNoiseSpace CarvingFiltered Back ProjectionActual Scans

PediatricHeadPhantomRat HeadSpace CarvingFiltered Back ProjectionConvex hull approximation provides 18Calculating Entry and Exit Points

We have the information for the entry and exit positions provided by the detectors.Using that information, we calculate the entry and exit anglesWe then project forward and backward the respective positions until one of the voxels marked as being in the image is hitThese voxels will be used as the entry and exit points when calculating the most likely path through the object19Problem Flow

20The Most Likely Path (1)

21The Most Likely Path (2)79 flops / stepRedundant calculations (Sigma/R)1600 possible (20.0 cm depth x 0.125 mm step)108 -109 historiesPrecalculate all Sigma/R terms

7 flops/step

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Proton Histories vs. Depth23ReconstructionSparse Sequential algorithmARTSparse Parallel algorithmFully simultaneous algorithmsCimmino, CAVBlock iterativeBIP, BICAV, DROP, OS-SARTString averagedSAP, CARP24ARTx0x0x1x2x3x4x5x625Cimminox0x0x126Block Iterative Projectionsx0x0x127Block Iterative Projectionsx0x0x1x228String Averaged Projectionsx0x0x129BIP

xkXk+1ai3030Fermi

31Iteration-b - A x = RCalculate ResidualSync BlocksUpdate xx += c AT RSumming In Inner Product0123456789101112131415810121416182022242832365664120

SAP Number of HistoriesProtons=voxelsProtons=10 voxelsProtons=5 voxelsProtons=20 voxels

SAP Relaxation Parameter0.010.10.20.5

ConclusionsA simple convex hull calculation is fast and preciseGPGPU acceleration yields a three order of magnitude increase in speedPre-calculating and binning yields a two order of magnitude increase in speedSAP gives good convergence and image quality2D (single machine) 12 hours to a few seconds3D (cluster) day to under 30 minutesMore to do36