Fundamental Limits of Positron Emission Tomography

1. Outline: Spatial Resolution Efficiency Noise Other Modalities Fundamental Limits ofPositron Emission Tomography William W. Moses Lawrence Berkeley National Laboratory Department of Functional Imaging September 5, 2002 (Best Viewed in “Slide Show” Mode)

2. Positron Emission Tomography (PET) Ring of Photon Detectors • Patient injected with positron (+ ) emitting radiopharmaceutical. • + annihilates with e– from tissue, forming back-to-back 511 keV photon pair. • 511 keV photon pairs detected via time coincidence. • Positron lies on line defined by detector pair (i.e., chord). • Reconstruct 2-D Image using Computed Tomography • Multiple Detector Rings  3-D Volumetric Image

3. Fundamental Limits of Spatial Resolution • Dominant Factor is Crystal Width • Limit for 80 cm Ring w/ Block Detectors is 3.6 mm • Ultimate Limit is 0.6 mm (Positron Range)

4. Tangential Projection Radial Projection Radial Elongation • Penetration of 511 keV photons into crystal ring blurs measured position. • Blurring worsens as detector’s attenuation length increases. • Effect variously known as Radial Elongation, Parallax Error, or Radial Astigmatism. • Can be removed (in theory) by measuring depth of interaction.

5. 1 cm Spatial Resolution Away From Center Point Source Images in 60 cm Ring Diameter Camera Near Tomograph Center 14 cm from Tomograph Center Resolution Degrades Significantly...

6. Theoretical Spatial Resolution(all units in mm) Resolution = d = Crystal Width R = Detector Ring Radius r = Distance from Center of Tomograph

7. Caveat: Spatial Resolution is DefinedAssuming Infinite Statistics Resolution Does Not Include Effects from Noise,but Image Quality Does...

8. Effect of Noise On Image Quality 55M Events 3 mm fwhm 1M Events 3 mm fwhm 1M Events 6 mm fwhm • All Three Images Have Same Camera Resolution • Statistical Noise  Reduced Image Resolution

9. Low Image Noise  High Sensitivity Sensitivity Definition: • Place 20 cm diameter phantom in camera. • Measure True Event Rate. • Sensitivity = True Event Rate / µCi / cc. Sensitivity Measures Efficiency for Detecting Signal

10. Increase Sensitivity by Removing Septa Inter-Plane Septa No Septa 2-D (w/ Septa) Septa Reduce Scatter Smaller Solid Angle for Trues 3-D (w/o Septa) No Scatter Suppression Larger Solid Angle for Trues

11. Sensitivity Includes Noise from Background T = Trues S = Scatter R = Randoms Even when you subtract the background, statistical noise from the background remains. Image Noise Not Determined by Sensitivity Alone!

12. Noise Equivalent Count Rate (NECR) NECR Properties: • Like a Signal / Noise Ratio(Sensitivity only Includes Signal) • Includes Noise from Backgrounds Maximize NECR to Minimize Image Noise

13. Obeys Counting Statistics Equals Signal x Contrast Phantom Geometry Must Be Defined Usually 20 cm diameter, 20 cm tall cylinder NEC Properties T

14. NEC Behavior: Ideal Camera(No Dead Time, No Coincidence Processor Limit) T  R 2 NEC Plateaus as Activity () Increases!

15. NEC Behavior(With Dead Time, No Coincidence Processor Limit) Tdead  e–(t) Rdead  2e–(t) • Dead Time (t) reduces T and R by same factor. • As  increases, NEC eventually decreases (paralyzing dead time).

16. RCP = Max. Rate TCP = Max. Rate Tdead  e–(t) Rdead  2e–(t) Tdead Rdead NEC Behavior(With Dead Time and Coincidence Processor Limit) • Total throughput becomes constant (T+2R = Max. Rate). • True / Randoms ratio not affected by rate limit. • R constant, T  1/.

17. More Solid Angle Is Not Always Better... 20 cm Phantom • 3-D has Higher NECR at Low Activity • Peak NECR in 2-D > Peak NECR in 3-D (Less Scatter)

18. Noise From Reconstruction Algorithm • Basic measurement of chord(crystal-crystal coincidence) represents the integral of the activity along that line. • Measurements from other chords needed to constrain activity to its source voxel. • Activity in other voxels complicates the image reconstruction. • Signals from Different Voxels are Coupled • Statistical Noise from One Voxel Affects All Voxels

19. Object Dependence “Uniform” Object 1,000,000 Events “Point-Like” Object 100,000 Events Point-Like Objects Reconstruct with Less Noise

20. Spatial Resolution Dominated by Crystal Size Other effects can be important at high resolution No Intrinsic Resolution / Efficiency Tradeoff,but Effective Tradeoffs Because of Noise Noise from Counting Statistics: Depends on Camera Efficiency / Geometry Higher Efficiency Doesn’t Always Imply Lower Noise! Noise from Reconstruction Algorithm: Depends on Object Geometry PET Take-Home Messages Think About Signal/Noise, Not Just Signal!!!

21. How Does PET Compare to Other Modalities? • Parallel Hole Collimator • Pinhole Collimator • Coded Aperture • Compton Camera

22. Parallel Hole Collimator Properties Gamma Detector • Typical Values: • w= 2 mm • L= 30 mm • t= 0.25 mm Collimator Collimator Geometry Defines Acceptance Angle 

23. Spatial Resolution • Typical Values: • R= 6 mm (@ 5 cm) • R= 12 mm (@ 10 cm) • Resolution Proportional to  • Resolution Proportional to Distance from Source

24. Efficiency • Typical Values: • Efficiency = 0.02% • Efficiency Proportional to 2 • Efficiency Independent of Distance from Source

25. Pinhole Camera • Compared to Parallel Hole Collimator, Pinhole  • Different Resolution / Efficiency Tradeoff • Higher Resolution, but Smaller Field of View

26. Coded Aperture Camera • Compared to Pinhole Camera, Many (n) Pinholes  • Similar Resolution w/ Higher Efficiency

27. Image Overlap with Coded Apertures “Uniform” Object “Point-Like” Object • Removing the Overlap Increases the Noise • Noise Increase Depends on Object

28. Intrinsic Resolution / Efficiency Dependency • Dependence on: • w d L • Par. Hole • Resol. w d L-1 • Effic. w2 – L-2 • Area – – – • Pinhole/CA • Resol. w – – • Effic. w2 d-2 – • Area – d L-1 Gamma Detector Generic Collimating Structure • Very Different Geometrical Dependencies • Pinhole / Aperture Best for Small Area, High Resol.

29. How They Work: • Measure first interaction with good Energy resolution. • Measure first and second interaction with moderate Position resolution. • Compton kinematics determines scatter angle. • Source constrained to lie on the surface of a cone. Compton Cameras No Collimator, but Reconstruction Difficult

30. Compton Camera Tradeoffs Advantages: • No Intrinsic Resolution / Efficiency Tradeoff • (Resolution Limited by Energy Resolution) • No Collimator  Much Higher Efficiency • Large Imaging Volume Disadvantages: • “Value” of Each Gamma is Lower • Difference in “Value” Depends on Object • (“Point-Like” Objects are Better) • Random Coincidence Background / NEC

31. CodedAperture Thin Cones PET Thin Line Collimator Thin Cone Pinhole Thin Cone Compton Cone Surface Detected Events Can Have Different Values Value Inversely Proportional to Volume of Objectthat the Gamma Could Have Come From?

32. Different Modalities Have Different Imaging Tradeoffs Resolution, Efficiency, Noise, Imaging Volume Consider Noise As Well As Signal Counting Statistics Background Events Reconstruction Algorithms Complex Sources Some Gammas Are Worth More Than Others Volume that Detected Gamma Could Have Come From Value Can Be Estimated Using Simulation Use Reasonable Source Geometry & Number of Events Include All Background Sources Conclusions

33. U.S. Department of Energy Office of Environmental and Biological Research Laboratory Technology Research Division National Institutes of Health National Cancer Institute University of California Office of the President Breast Cancer Research Program U.S. Army Breast Cancer Directive Commercial Partners Capintec, Inc. Digrad, Inc. Acknowledgements

34. 1-Dimensional Horizontal Projection 1-Dimensional Vertical Projection Principle of Computed Tomography 2-Dimensional Object By measuring all 1-dimensional projections of a 2-dimensional object, you can reconstruct the object

35. Computed Tomography Planar X-Ray Computed Tomography Separates Objects on Different Planes Images courtesy of Robert McGee, Ford Motor Company