MRI, FBP and phase MRI, FBP and phase encodingencoding

SpinsSpins

PrecessionPrecession

RF pulseRF pulse

T1 and T2T1 and T2

Bloch EquationsBloch Equations

ReceiverReceiver

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

Slice selectionSlice selection

FBPFBP

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’(,).

Phase EncodingPhase Encoding

Gradient

Slice Plane Slice Phase Frequency

XY Z X or Y Y or X

XZ Y X or Z Z or X

YZ X Y or Z Z or Y

Phase encodingPhase encoding

K spaceK space

K SpaceK Space

Partial K Partial K space space

reconstrucreconstructiontion

Partial K space Partial K space reconstructionreconstruction

Partial K space Partial K space reconstructionreconstruction