Report

Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December 2011 1 Outline 1. Introduction and Objectives 2. Methods: Problem Formulation, Simulations and Real Data 3. Results and Discussion 4. Conclusions 2 Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. Conclusions 3 Introduction Arterial Spin Labeling (ASL): Se [1] e [2] são refs, deviam aparecer antes com nome e ano -Non invasive technique for generating perfusion images of the brain [1] -Cerebral Blood Flow (CBF): Volume of blood flowing per unit time[2] -Perfusion: CBF per unit volume of tissues 4 Introduction ASL: Labeled acquisiton Este slide e o seguinte deviam ser 1 só 2. Image acquisition 1. Labeling of inflowing arterial blood 5 Introduction ASL Control acquisiton 4. Image acquisition 3. No labeling 6 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. n length vector Ci – ith control image [C1, L1, C2, L2,…, Cn/2, Ln/2] Li – ith labeled image P- perfusion 7 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)] Sinc-interpolated subtraction: 2 2 [P1, P2,…, Pn/2]=[C1- L1/2, C2- L3/2,…, Cn/2-Ln/2-1/2] 8 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) 9 Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. Conclusions 10 Problem Formulation Mathematical model Y(t)=F+D(t)+v(t)ΔM+Γ(t) Y (NxMxL) (1) – 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) 11 Problem Formulation Mathematical model Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1) 12 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) (2) v(L x 1) Δm(NM x 1) Γ(NM x 1) 13 Problem Formulation Algorithm implementation 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 (3) Ill-posed problem 14 Problem Formulation Algorithm implementation θ=arg min Ey(Y,v,θ) θ (3) Using the Maximum a posteriori (MAP) criterion, regularization is introduced by the prior distribution of the parameters θ=arg min E (Y,v,θ) θ (4) E (Y,v,θ)=Ey (Y,v, θ) + Eθ(θ) Data – fidelity term (5) Prior term 15 Problem Formulation Algorithm implementation Figure from [11] 16 Problem Formulation Algorithm implementation E (Y,v,θ)=Ey (Y,v, θ) + Eθ(θ) (5) E (Y,v,θ)= ½ Trace [(Y-fuT-D-ΔmvT) T (Y-fuT-D-ΔmvT)] +αTrace[(φhD)T(φhD)+(φvD)T(φvD)+(φtD)T(φtD)] +β(φhf)T(φhf)+(φvf)T(φvf) (6) +γ(φhΔm)T(φhΔm)+(φvΔm)T(φvΔm) 17 Problem Formulation Algorithm implementation -In equation (6), the matrices φh,v,t are used to compute the horizontal, Vertical and temporal first order differences, respectively Φ= 1 0 0 . -1 -1 1 0 . 0 0 -1 1 . . . . . . . . . . . . . . 0 0 0 . -1 1 0 -α, β and γ are the priors. 18 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 19 Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. Conclusions 20 Experimental Results and Discussion Synthetic data -Brain mask (64x64) -Axial slice -White matter (WM) and Gray matter (GM) - SNR= Asignal 2 Anoise - Mean error(%)= ; ISNR=SNRf-SNRi 100 NxM ∑ N,M ^ |xi,j-xi,j| xi,j i=1,j=1 21 Experimental Results and Discussion Synthetic data Parameters: σ=1 Δm(GM)=1 Δm(WM)=0.5 D=[-1,1] F=10000 α=0 β=0 γ=0 Control acquisition Labeled acquisition 22 Experimental Results and Discussion Synthetic data Parameters: σ=1 Δm(GM)=1 Δm(WM)=0.5 D=[-1,1] F=10000 α=0 β=0 γ=0 Proposed algorithm Pair-wise subtraction Surround Subtraction 23 Experimental Results and Discussion 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 24 Experimental Results and Discussion Synthetic data Prior optimization 25 Experimental Results and Discussion Synthetic data Prior optimization Incresasing prior value 26 Experimental Results and Discussion Synthetic data Prior optimization 27 Experimental Results and Discussion Synthetic data Prior optimization β=1 γ=5 28 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 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 30 Experimental Results and Discussion Synthetic data Method ISNR(dB) Mean Error (%) Proposed algorithm 16.990 17.807 Pair-wise subtraction 14.026 24.492 Surround Subtraction 14.103 24.269 31 Experimental Results and Discussion Synthetic data Method ISNR(dB) Mean Error (%) Proposed algorithm 16.990 17.807 Pair-wise subtraction 14.026 24.492 Surround Subtraction 14.103 24.269 3dB 23% 7% -30% 32 Experimental Results and Discussion Synthetic data Monte Carlo Simulation for different noise levels 33 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 -spatial resolution: 3.5x3.5x7.0 mm3 -201 repetitions -Matrix size: 64x64x9 34 Experimental Results and Discussion Real data Control image Labeled image 35 Experimental Results and Discussion Real data Proposed algorithm Pair-wise subtraction Surround Subtraction 36 Experimental Results and Discussion Real data -Influence of the number of iterations 37 Experimental Results and Discussion Real data Proposed algorithm Pair-wise subtraction Surround Subtraction 38 Experimental Results and Discussion Real data 39 Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. Conclusions 40 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 41 Bibliography [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. [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. [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. [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. [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. 42 Questions 43