GENERATION OF PARAMETRIC IMAGES

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GENERATION OF PARAMETRIC IMAGES

• PROSPECTS
• PROBLEMS

Vesa Oikonen Turku PET Centre 2004-03-25
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Multiple-Time Graphical Analysis

• Gjedde-Patlak plot for irreversible uptake
• Logan plot for reversible uptake
• Independent on model structure
• Plasma and reference tissue input
• Fast computation
• Available everywhere

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Multiple-Time Graphical Analysis

1. Regional analysis to determine the time when plot
   becomes linear
2. For Logan analysis with reference tissue input
   compartment model fit to determine population
   average of reference tissue k2

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Multiple-Time Graphical Analysis

• Examples of DV and DVR images

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Multiple-Time Graphical Analysis

• Different regions have different kinetics
• Usually linear phase is reached later in regions
  of high uptake
• Solution select fit range separately for each
  pixel

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Multiple-Time Graphical Analysis
Nr of frames used in line fit(darkermore frames
DVR image where fit range was determined separatel
y for each pixel
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Compartmental model fit

• Also time before equilibrium is used in the fit
• Parametersare solvedfrommultilinearequations

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Compartmental model fit

• Fast computation from multilinear equations with
  standard techniques
• Multilinear equations can be transformed to solve
  macroparameters (DV or Ki) without division

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Compartmental model fit
DV
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Compartmental model fit

• Pixel-by-pixel selection between 2CM and 3CM
  based on Akaike Information Criteria (AIC), or
• Akaike weighted average of DV from 2CM and 3CM
  fits (Turkheimer et al 2003)

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Compartmental model fit
Relative weights of2CM (white) and 3CM
(black)based on AIC
Akaike weighted average ofDV from 2CM and 3CM
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Compartmental model fit

• Alternative to Akaike weightingLawson-Hanson
  non-negative least-squares (NNLS) produces
  good-quality DV and DVR images from multilinear
  3CM

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Simplified Reference Tissue Method (SRTM)
Binding Potential (BP) solved using

• Basis Function Method (BFM)
• Multilinear equations

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SRTM-BFM

• Parameter bounds must be determined based on
  regional analysis
• Tight bounds cause poor fit and bias in some
  regions
• Wide bounds may lead to long-tailed BP
  distribution and positive bias

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SRTM-NNLS

• Multilinear equation can be transformed to solve
  BP1 without division
• Provides good-quality BP images when NNLS is used

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SRTM-NNLS
BP image calculatedusing SRTM-NNLS
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Parametric sinogram

• Faster ( iterative ) reconstruction
• Intrinsic heterogeneity
• All linear models applicable

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Parametric sinogram
DVR sinogram
DVR imageFBP reconstruction
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Calculation on sinogram level

1. Correct for physical decay
2. Correct for frame lengths
3. Model calculation as usual
4. Reconstruction
5. Divide pixel values by volume (if not done in
   reconstruction or calibration)
6. Calibration (only with plasma input, and not even
   then for all parameters)
7. Calculations with parameters after reconstruction

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Parametric sinogram problems

• Multiple-Time Graphical Analysis when linear
  phase starts?
• Multilinear equations which model?
• Reference input TAC pre-reconstruction needed

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Parametric sinogrammore problems

• Dynamic sinogram must be filtered before
  calculation avoid another filtering in
  reconstruction!
• Requires full knowledge on raw data collection
  and processing steps

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Parametric sinogram

• In futureIterative reconstruction and model
  calculation combined

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PROBLEMS

• Noise induses bias in all linear methods for
  reversible uptake
• Logan plot no satisfactory method for removing
  bias
• Multilinear methods GLLS can not be applied to
  reference tissue models

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More problems

• SRTM can not be used for all tracers
• Weights for fitting are not known
• Partial volume error (PVE)may lead to
  artefactual second tissue compartment in
  reference region

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More problems

• Movement during scanning

DVR image without movement and after moving 3
frames 4 mm (2 pxls) upward
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Movement during scanning

• Complicated models are more sensitive to movement

Same simulation, but Logan plot computed with
variable line fit start time
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Image filtering

• Only working method to reduce bias in linear
  models
• Resolution need not to be preserved if next
  analysis step is SPM or other brain averaging
  method
• Biases may be cancelled out in calculation of
  occupancy maps

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Cluster analysis

• Resolution preserving smoothing for dynamic
  images
• Automatic extraction of reference tissue curve
• Extraction of curves with different kinetics
  Validation that selected model can fit them all

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CONCLUSION

• Problems image noise, patient movement and
  inconsistent input data
• Until solved, use only simple models causing
  biases but less artefacts
• Validation in animal models and in vitro is
  essential