Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December 2011 1.

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A Bayesion perfusion estimation using spatio-temporal priors in

ASL-MRIMiguel Lourenço Rodrigues

Master’s thesis in Biomedical EngineeringDecember 2011

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Outline

1. Introduction and Objectives

2. Methods: Problem Formulation, Simulations and Real Data

3. Results and Discussion

4. Conclusions

Outline

1. Introduction

2. Literature Review

3. Problem Formulation

4. Experimental Results and Discussion

5. Conclusions

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4

Introduction

-Cerebral Blood Flow (CBF):

Volume of blood flowing per unit time[2]

-Perfusion:

CBF per unit volume of tissues

Arterial Spin Labeling (ASL):

-Non invasive technique for generating perfusion images of the brain [1]

Se [1] e [2] são refs, deviam aparecer antes com nome e ano

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Introduction

Labeled acquisiton

1. Labeling of inflowingarterial blood

2. Image acquisition

ASL: Este slide e o seguinte deviam ser 1 só

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Introduction

ASL

Control acquisiton

3. No labeling

4. Image acquisition

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Introduction

ASL

Control image Labeled image CBF

A number of control-label repetitions is required in order to achieve sufficient SNR to detect the magnetization difference signal, hence increasing scan duration.

[C1, L1, C2, L2,…, Cn/2, Ln/2] n length vectorCi – ith control imageLi – ith labeled imageP- perfusion

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Introduction

ASL signal processing methods

Pair-wise subtraction:

[P1, P2,…, Pn/2]=[C1- L1, C2- L2,…, Cn/2-Ln/2]

Surround subtraction:

[P1, P2,…, Pn/2]=[C1- L1, C2- (L1+L2),…, Cn/2-(L(n/2)-1-Ln/2)] 2 2

Sinc-interpolated subtraction:

[P1, P2,…, Pn/2]=[C1- L1/2, C2- L3/2,…, Cn/2-Ln/2-1/2]

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Objectives

Objectives

-Increase image Signal to Noise Ratio (SNR)

-Reduce acquisition time

Approach

- New signal processing model

- Bayesian approach

- spatio-temporal priors

No drastic signal variatons

(except in organ boundaries)

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Outline

1. Introduction




5. Conclusions

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Problem Formulation

Mathematical model

Y(t)=F+D(t)+v(t)ΔM+Γ(t)

Y (NxMxL) – Sequence of L PASL images

F (NxM) – Static magnetization of the tissues

D(NxM x L) – Slow variant image (baseline fluctuations of the signal – Drift)

v(L x 1) - Binary signal indicating labeling sequences ΔM(NxM ) - Magnetization difference caused by the inversion

Γ(NxM xL) – Additive White Gaussian Noise ~N (0,σy2)

(1)

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Problem Formulation

Mathematical model

Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1)

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Problem Formulation

Algorithm implementation

Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1)

Vectorization

Y=fuT+D+ΔmvT+Γ

Y(NM x L)

f(NM x1)

u(L x 1)

D(NM x L)

v(L x 1)

Δm(NM x 1)

Γ(NM x 1)

(2)

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Problem Formulation


Since noise is AWGN,

p(Y)~N (μ, σy2), where μ=fuT+D+ΔmvT

Maximum likelihood (ML) estimation of unknown images, θ={f,D, Δm}

θ=arg min Ey(Y,v,θ)θ

Ill-posed problem

(3)

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Problem Formulation


Using the Maximum a posteriori (MAP) criterion, regularization isintroduced by the prior distribution of the parameters

θ=arg min Ey(Y,v,θ)θ

(3)

θ=arg min E (Y,v,θ)θ

(4)

E (Y,v,θ)=Ey (Y,v, θ) + Eθ(θ) (5)

Data – fidelity term Prior term

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Problem Formulation


Figure from [11]

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Problem Formulation


E (Y,v,θ)=Ey (Y,v, θ) + Eθ(θ) (5)

½ Trace [(Y-fuT-D-ΔmvT) T (Y-fuT-D-ΔmvT)] E (Y,v,θ)=

+αTrace[(φhD)T(φhD)+(φvD)T(φvD)+(φtD)T(φtD)]

+β(φhf)T(φhf)+(φvf)T(φvf)

+γ(φhΔm)T(φhΔm)+(φvΔm)T(φvΔm)

(6)

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Problem Formulation


-In equation (6), the matrices φh,v,t are used to compute the horizontal, Vertical and temporal first order differences, respectively

1 0 0 . -1

-1 1 0 . 0

0 -1 1 0

. . . . .

. . . . .

. . . . 0

0 0 . -1 1

Φ=

-α, β and γ are the priors.

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Problem Formulation


-MAP solution as a global mininum

-Stationary points of the Energy Function – equation (6)

- Equations implemented in Matlab and calculated iteratively

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Outline

1. Introduction




5. Conclusions

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Experimental Results and Discussion

Synthetic data

-Brain mask (64x64)

-Axial slice

-White matter (WM) and Gray matter (GM)

ISNR=SNRf-SNRi

∑100

NxM

N,M

i=1,j=1

|xi,j-xi,j|

xi,j

^

Mean error(%)=

SNR=Asignal

Anoise

2

- ;

-

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Synthetic data

Control acquisition Labeled acquisition

Parameters:

σ=1Δm(GM)=1Δm(WM)=0.5D=[-1,1]F=10000α=0β=0γ=0

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Synthetic data

Proposed algorithm

Pair-wisesubtraction

SurroundSubtraction

Parameters:

σ=1Δm(GM)=1Δm(WM)=0.5D=[-1,1]F=10000α=0β=0γ=0

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Synthetic data

Method ISNR(dB)

Mean Error (%)

Proposed algorithm 13.906 24.658

Pair-wise subtraction 13.906 24.658

Surround Subtraction 13.999 24.393

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Synthetic data

Prior optimization

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Synthetic data

Prior optimization

Incresasing prior value

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Synthetic data

Prior optimization

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Synthetic data

Prior optimization

β=1γ=5

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Synthetic data

Parameters:

σ=1Δm(GM)=1Δm(WM)=0.5D=[-1,1]F=10000α=1β=1γ=5

Proposed algorithm


SurroundSubtraction

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Synthetic data

Parameters:

σ=1Δm(GM)=1Δm(WM)=0.5D=[-1,1]F=10000α=1β=1γ=5

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Synthetic data

Method ISNR(dB)

Mean Error (%)




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Synthetic data

Method ISNR(dB)

Mean Error (%)




3dB

7%

23%

-30%

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Synthetic data

Monte Carlo Simulation for different noise levels

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Real data

-One healthy subject

-3T Siemens MRI system (Hospital da Luz, Lisboa)

-PICORE-Q2TIPS PASL sequence

-TI1/TI1s/TI2=750ms/900ms/1700ms

-GE-EPI

-TR/TE=2500ms/19ms

-201 repetitions

-spatial resolution: 3.5x3.5x7.0 mm3

-Matrix size: 64x64x9

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Control image Labeled image


Real data

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Real data

Proposed algorithm


SurroundSubtraction

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Real data

-Influence of thenumber of iterations

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Proposed algorithm


SurroundSubtraction


Real data

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Real data

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Outline

1. Introduction




5. Conclusions

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Conclusion

-The proposed bayesian algorithm showed improvement of SNR and ME

-SNR increased by 3db (23%)

-ME decreased by 7% (30%)

-Applied to real data

Future work:

-Automatic prior calculation

-Reducing the number of control acquisitions

-Validation tests on empirical data

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[1] T.T. Liu and G.G. Brown. Measurement of cerebral perfusion with arterial spin labeling: Part 1. Methods. Journal of the International neuropsychological Society, 13(03):517-525, 2007.

[2]A.C. Guyton and J.E. Hall. Textbook of medical physiology. WB Saunders (Philadelphia),1995.

[4]ET Petersen, I. Zimine, Y.C.L. Ho, and X. Golay. Non-invasive measurement of perfusion: a critical review of arterial spin labeling techniques. British journal of radiology, 79(944):688, 2006.

[3]D.S. Williams, J.A. Detre, J.S. Leigh, and A.P. Koretsky. Magnetic resonance imaging of perfusion using spin inversion of arterial water. Proceedings of the National Academy of Sciences, 89(1):212, 1992.

[5]R.R. Edelman, D.G. Darby, and S. Warach. Qualitative mapping of cerebral blood flow and functional localization with echo-planar mr imaging and signal targeting with alternating radio frequency. Radiology, 192:513-520, 1994.

Bibliography

[6]DM Garcia, C. De Bazelaire, and D. Alsop. Pseudo-continuous ow driven adiabatic inversion for arterial spin labeling. In Proc Int Soc Magn Reson Med, volume 13, page 37, 2005.

[7]E.C. Wong, M. Cronin, W.C. Wu, B. Inglis, L.R. Frank, and T.T. Liu. Velocity-selective arterial spin labeling. Magnetic Resonance in Medicine, 55:1334{1341, 2006.

[8]W.C. Wu and E.C. Wong. Feasibility of velocity selective arterial spin labeling in functional mri. Journal of Cerebral Blood Flow & Metabolism, 27(4):831{838, 2006

[9]GK Aguirre, JA Detre, E. Zarahn, and DC Alsop. Experimental Design and the Relative Sensitivity of BOLD and Perfusion fMRI. NeuroImage, 15:488{500, 2002.

[10]E.C. Wong, R.B. Buxton, and L.R. Frank. Implementation of Quantitative Perfusion Imaging Techniques for Functional Brain Mapping using Pulsed Arterial Spin Labeling. NMR in Biomedicine, 10:237{249, 1997.

[11] J.M. Sanches, J.C. Nascimento, and J.S. Marques. Medical image noise reduction using the Sylvester-Lyapunov equation. IEEE transactions on image processing, 17(9), 2008.

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Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December 2011 1.

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Transcript of Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December 2011 1.