A Signal Processing Model for

Arterial Spin Labeling

Perfusion fMRI

Thomas Liu and Eric Wong

Center for Functional Magnetic Resonance Imaging

University of California, San Diego

Arterial Spin Labeling (ASL)Arterial Spin Labeling (ASL)

Tag by Magnetic Inversion

Wait

Acquire image

Control

Wait

Acquire image

1:

2:

Control - Tag CBF

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are needed to see this picture.

From C. Iadecola 2004

Goal: Accurately measure dynamic CBF response to neural activity

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Example:Perfusion and BOLD in primary and supplementary motor cortex. Measured with PICORE QII with dual-echo spiral readout.

Obata et al. 2004

ASL Data Processing

• CBF = Control - Tag• An estimate of the CBF time series is formed

from a filtered subtraction of Control and Tag images.

• Use of subtraction makes CBF signal more insensitive to low-frequency drifts and 1/f noise.

Pairwise subtraction example

Control Tag

+1 -1 +1

Surround subtraction

Control Tag ControlTag

ControlTagControl

+1/2 -1

Perfusion Time Series

TA = 1 to 4 seconds

+1/2 -1/2 1 -1/2

Generalized Running Subtraction

ytag

+1

1.0

Upsample Low Pass Filter

yperf

ycontrol

Questions

• What is the difference between the various processing schemes?

• How do they effect the estimate of CBF? • What are the noise properties of the estimate?

€

1−α 1+(−1)n( )exp −TI /T1B( )

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q[ n]

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M[ n]€

b[ n]

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e[ n]

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y[ n]

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Perfusion

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1− β exp −TI p /T1( )

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×

€

+

€

×

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×€

+

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Static Tissue€

BOLD Weighting

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Measurements

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Noise

is the inversion efficiency ideal inversion: =1

Tag : n evenControl: n odd

=1 presaturation applied = 0No presat

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(−1)n+1

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g[ n]

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ˆ q [ n]

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y[ n]

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×€

g[ n]

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ˆ b [n]

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Measurements

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Perfusion Estimate

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BOLD Estimate

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g[n] = 1 1[ ]

g[n] = 1 2 1[ ] /2

g[n] = sinc[n /2]

Tag : n evenControl: n odd

Pairwise SubtractionSurround SubtractionSinc Subtraction

€

1−α 1+(−1)n( )exp −TI /T1B( )

€

(−1)n+1

€

q[ n]

€

M[ n]€

b[ n]

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e[ n]€

g[ n]

€

ˆ q [ n]

€

y[ n]

€

Perfusion

€

1− β exp −TI p /T1( )

€

×

€

+

€

×

€

×€

+

€

×€

g[ n]

€

ˆ b [n]

€

Static Tissue€

BOLD Weighting

€

Measurements

€

Perfusion Estimate

€

BOLD Estimate

DemodulateModulate

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ˆ q [n ] = qq[n ]+ qb[n ]+ qe[n ]Perfusion Estimate

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qq[n ] = αb[n ]q[n ]e−TI /T1B( ) ∗g[n ]

Demodulated and filtered perfusion component

Modulated and filtered BOLD component

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qb[n ] = b[n ] sMM[n ]+ sqq[n ]( )[ ] −1( )n +1∗g[n ]

Modulated and filtered noise component

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qe[n ] = (−1)n +1e[n ][ ] ∗g[n ]

Perfusion Component

BOLD Component

Summary

• For block designs with narrow spectrum, use surround subtraction or sinc subtraction

• For randomized designs with broad spectrum, use pair-wise subtraction.

• To minimize noise autocorrelation use pair-wise or surround subtraction.

• General framework can be used to design other optimal filters.