Image reproduction +fMRI. Filtered Back Projection.

Image reproduction Image reproduction +fMRI+fMRI

Filtered Back ProjectionFiltered Back 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

Zero paddingZero padding

ConjugatConjugate e

symmetrysymmetry

Conjugate symmetryConjugate symmetry

Homodyne Homodyne reconstructionreconstruction

Homodyne Homodyne reconstructionreconstruction

Homodyne Homodyne reconstructionreconstruction

HomodyHomodyne ne

reconstrreconstructionuction

Mechanism of BOLD Mechanism of BOLD Functional MRIFunctional MRI

Brain activity

Oxygen consumption Cerebral blood flow

OxyhemoglobinDeoxyhemoglobin

Magnetic susceptibility

T2*

MRI signal intesity

Magnetic Properties of Magnetic Properties of Oxyhemoglobin and Oxyhemoglobin and DeoxyhemoglobinDeoxyhemoglobin

Deoxyhemoglobin: paramagnetic ( > 0) paramagnetic with respect to the surrounding tissue

Oxyhemoglobin: diamagnetic ( < 0) isomagnetic with respect to the surrounding tissue

22HbOOHb

cdiamagneti ,0 icparamagnet ,0 if

HM

TT22* Effect in fMRI* Effect in fMRI

excitation reception

MR

sig

nal (S

)

actionrest

TE t

Time Series and Activation Time Series and Activation MapsMaps

Off Off Off OffOn On On On

Scan Number

Sig

nal

In

ten

sity

Temporal resolutionTemporal resolution

Impulse-response function

2s

5s

12s

0 20 40 60 80 100 120

4

3

2

1

Com

pone

nt

Frame

Temporal components (sd, % variance explained)

105.7, 77.8%

26.1, 4.8%

15.8, 1.7%

14.8, 1.5%

Slice

Com

pone

nt

Spatial components

0 2 4 6 8 10

1

2

3

4

PCA_IMAGE: PCA of time space:

1: excludefirst frames

2: drift

3: long-range correlationor anatomicaleffect: removeby converting to % of brain

4: signal?