Imaging PET Course Layout Class + ContentDateClass Physical Principles of PET23.2.2005I Physical...

ImagingImaging

PETPET

Course LayoutCourse LayoutClassDateClass + Content

I23.2.2005Physical Principles of PET

II2.3.2005Physical principles of MRI

III9.3.2005Imaging applications

IV16.3.2005Image Reconstruction PET and MRI

V23.3.2005Automatic Image Alignment

VI30.3.2005PCA

VII6.4.2005No Class

VIII13.4.2005GLM

IX4.5.2005GLM relation to classical tests (Anova, T-test..)

X18.5.2005Covariates

XI25.5.2005Gaussian fields Theory

XII1.6.2005Specific experiment design and analysis

XIII8.6.2005Specific experiment design and analysis

XIV15.6.2005Correction for multiple measurements

Talk LayoutTalk Layout

Repetition of PET princinplesRepetition of PET princinples PET image reconstruction -FBPPET image reconstruction -FBP Physics of NMRPhysics of NMR Application to imaging of NMR -MRIApplication to imaging of NMR -MRI

PETPET

Positron emissionPositron emission

PETPET

Coincidence EventsCoincidence Events

1

1. Detected True Coincidence Event

2

2. True Event Lost to Sensitivity or Deadtime

3

3. True Event Lost to Photon Attenuation

4

4. Scattered Coincidence Event

5a 5b

5a,b. Random Coincidence Event

Attenuation CorrectionAttenuation Correction

0 0

( ') ' ( ') ' ( ') '

1 2

x R R

x

x dx x dx x dx

p p p e e e

Filtered Back ProjectionFiltered Back Projection

FilteredFiltered B Baack Projectionck Projection

Filtered Back Projection

Filtered backprojection• Filter the measured projection data at different projection angles with a special function.• Backproject the filtered projection data to form the reconstructed image.

Filtering can be implemented in 2 ways, in the spatial domain, the filter operation is equivalent to to convolving the measured projection data using a special convolving function h(t)

p t p t h t, ( , ) ( , ) ( )

More efficient multiplication will be in the spatial frequency domain.• FFT the measured projection data into the frequency domain:p(,)=FT {p(t, )• Multiply the the fourier transform projections with the special function.•Inverse Fourier transform the product p’(,).

2D Vs. 3D2D Vs. 3D

RandomsRandoms

ScattersScatters

Principles of MRIPrinciples of MRI

Felix BlochFelix Bloch

AtomsAtoms

SpinsSpins

PrecessionPrecession

RF pulseRF pulse

T1 and T2T1 and T2

T1 and T2T1 and T2

T1 and T2T1 and T2

Effect of tissueEffect of tissueT1 and T2 CONSTANTS

T1 Constants at 1.5 T Controlled by TR

T2 Constants at 1.5 T Controlled by TE

Fat85

Muscle86045

White matter78090

Gray matter920100

CSF30001400

Slice selectionSlice selection

K spaceK space

K SpaceK Space

NMRNMR