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Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December

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2 Outline 1. Introduction and Objectives 2. Methods: Problem Formulation, Simulations and Real Data 3.Results and Discussion 4. Conclusions

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Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. Conclusions 3

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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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5 Introduction Labeled acquisiton 1.Labeling of inflowing arterial blood 2. Image acquisition ASL: Este slide e o seguinte deviam ser 1 só

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6 Introduction ASL Control acquisiton 3. No labeling 4. Image acquisition

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7 Introduction ASL Control imageLabeled 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. [C 1, L 1, C 2, L 2,…, C n/2, L n/2 ] n length vector C i – i th control image L i – i th labeled image P- perfusion

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8 Introduction ASL signal processing methods Pair-wise subtraction: [P 1, P 2,…, P n/2 ]=[C 1 - L 1, C 2 - L 2,…, C n/2 -L n/2 ] Surround subtraction: [P 1, P 2,…, P n/2 ]=[C 1 - L 1, C 2 - (L 1 +L 2 ),…, C n/2 -(L (n/2)-1 -L n/2 )] 22 Sinc-interpolated subtraction: [P 1, P 2,…, P n/2 ]=[C 1 - L 1/2, C 2 - L 3/2,…, C n/2 -L n/2-1/2 ]

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9 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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10 Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. Conclusions

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11 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,σ y 2 ) (1)

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12 Problem Formulation Mathematical model Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1)

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13 Problem Formulation Algorithm implementation Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1) Vectorization Y=fu T +D+Δmv T +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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14 Problem Formulation Algorithm implementation Since noise is AWGN, p(Y)~ N (μ, σ y 2 ), whereμ=fu T +D+Δmv T Maximum likelihood (ML) estimation of unknown images, θ={f,D, Δm} θ=arg min E y (Y,v,θ) θ Ill-posed problem (3)

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15 Problem Formulation Algorithm implementation Using the Maximum a posteriori (MAP) criterion, regularization is introduced by the prior distribution of the parameters θ=arg min E y (Y,v,θ) θ (3) θ=arg min E (Y,v,θ) θ (4) E (Y,v,θ)=E y (Y,v, θ) + E θ (θ) (5) Data – fidelity termPrior term

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16 Problem Formulation Algorithm implementation Figure from [11]

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17 Problem Formulation Algorithm implementation E (Y,v,θ)=E y (Y,v, θ) + E θ (θ) (5) ½ Trace [(Y-fu T -D-Δmv T ) T (Y-fu T -D-Δmv T )] E (Y,v,θ)= +αTrace[(φ h D) T (φ h D)+(φ v D) T (φ v D)+(φ t D) T (φ t D)] +β(φ h f) T (φ h f)+(φ v f) T (φ v f) +γ(φ h Δm) T (φ h Δm)+(φ v Δm) T (φ v Δm) (6)

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18 Problem Formulation Algorithm implementation -In equation (6), the matrices φ h,v,t are used to compute the horizontal, Vertical and temporal first order differences, respectively Φ=Φ= -α, β and γ are the priors.

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19 Problem Formulation Algorithm implementation -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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20 Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. Conclusions

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21 Experimental Results and Discussion Synthetic data -Brain mask (64x64) -Axial slice -White matter (WM) and Gray matter (GM) ISNR=SNR f -SNR i ∑ 100 NxM N,M i=1,j=1 |x i,j -x i,j | x i,j ^ Mean error(%)= SNR= A signal A noise 2 - ; -

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22 Experimental Results and Discussion Synthetic data Control acquisitionLabeled acquisition Parameters: σ=1 Δm(GM)=1 Δm(WM)=0.5 D=[-1,1] F=10000 α=0 β=0 γ=0

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23 Experimental Results and Discussion Synthetic data Proposed algorithm Pair-wise subtraction Surround Subtraction Parameters: σ=1 Δm(GM)=1 Δm(WM)=0.5 D=[-1,1] F=10000 α=0 β=0 γ=0

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24 Experimental Results and Discussion Synthetic data MethodISNR(dB)Mean Error (%) Proposed algorithm Pair-wise subtraction Surround Subtraction

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25 Experimental Results and Discussion Synthetic data Prior optimization

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26 Experimental Results and Discussion Synthetic data Prior optimization Incresasing prior value

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27 Experimental Results and Discussion Synthetic data Prior optimization

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28 Experimental Results and Discussion Synthetic data Prior optimization β=1 γ=5

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29 Experimental Results and Discussion Synthetic data Parameters: σ=1 Δm(GM)=1 Δm(WM)=0.5 D=[-1,1] F=10000 α=1 β=1 γ=5 Proposed algorithm Pair-wise subtraction Surround Subtraction

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30 Experimental Results and Discussion Synthetic data Parameters: σ=1 Δm(GM)=1 Δm(WM)=0.5 D=[-1,1] F=10000 α=1 β=1 γ=5

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31 Experimental Results and Discussion Synthetic data MethodISNR(dB)Mean Error (%) Proposed algorithm Pair-wise subtraction Surround Subtraction

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32 Experimental Results and Discussion Synthetic data MethodISNR(dB)Mean Error (%) Proposed algorithm Pair-wise subtraction Surround Subtraction dB 7% 23% -30%

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33 Experimental Results and Discussion Synthetic data Monte Carlo Simulation for different noise levels

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34 Experimental Results and Discussion 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 mm 3 -Matrix size: 64x64x9

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35 Control imageLabeled image Experimental Results and Discussion Real data

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36 Experimental Results and Discussion Real data Proposed algorithm Pair-wise subtraction Surround Subtraction

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37 Experimental Results and Discussion Real data -Influence of the number of iterations

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38 Proposed algorithm Pair-wise subtraction Surround Subtraction Experimental Results and Discussion Real data

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39 Experimental Results and Discussion Real data

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40 Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. Conclusions

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41 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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42 [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): , [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, [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, [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: , 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, [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, [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, [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, [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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43 Questions

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