Spatiotemporal Reconstruction of PET Data

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Spatiotemporal Reconstruction of PET Data

• Andrew McLennan

Professor Sir Mike Brady FRS FREng Professor Nick
Trefethen FRS David Schottlander, Siemens
Molecular Imaging
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What is PET?

• Positron Emission Tomography (PET) enables
  doctors to look and study non-invasively inside
  the body
• Detects areas of heightened metabolic activity

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Positron Emission Tomography

• Positron emitting tracer compound injected into
  patient
• Radionuclide decays emitting a high energy
  positron
• Positron is annihilated by an electron, producing
  two 511 keV photons travelling in opposite
  directions
• Signal noise caused by
• Compton scattering
• Random observations

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PET Image Reconstruction

• The 3 main Static PET algorithms
• Filtered Back Projection (FBP)
• Maximum a Posteriori (MAP)
• Ordered Subset Expectation Maximisation (OSEM)
• Current Dynamic PET ideas arebased around Static
  PET

Wait 45-60mins
20 mins acquisition
Start acquisition immediately
Combine acquisitions
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Dynamic List-Mode PET

• We would like to combine the spatial resolution
  of Static PET and temporal resolution of Dynamic
  PET
• List-mode data records both the detector pair and
  the time of acquisition, avoidingthe need to use
  Sinograms

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Dynamic List-Mode Reconstruction

• We assume that both the observed detection data,
  and each voxels emission rate, can be modelled
  using inhomogeneous Poisson process (i.e. Rate
  functions dependent on time)
• The rate functions of the observed data are then
  linear combinations of the dynamic voxel tracer
  densities
• Rate functions are parameterise by Cubic B-Spline
  Basis

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Calculation of each w i j

• Account for Randoms and Scatter
• Likelihood function of an inhomogeneous Poisson
  process is
• Taking Logs and using Bayes Theorem, we penalize
  our objective function so that it includes 3
  smoothing terms
• Temporal roughness
• Spatial roughness
• Penalizes negativity of the rate function

Bayesian Prior A Spatiotemporal Regularise
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Implementation

• We choose the B-Spline knotlocations to be
  equally spreadalong the head curve, to
  accountfor the early high concentrations
• The objective function is strictly concave with a
  global maximum, hence can befound using a
  preconditionedPolak-Ribiere ConjugateGradient
  search method

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Project Aims

• Implement the model in a modular fashion
• Run the program on provided List-Mode data
• Determine the Phantoms list-mode geometry
• Analyse the variance and bias for Phantom PET
  data
• Improving the implementation There is always a
  trade off between accuracy/stability biological
  meaning of the model
• Implement different basis functions
• Use more accurate spatial temporal regularizes
• Compare different optimisation methods