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A Bayesion perfusion estimation using spatio-temporal priors in ASL-MRI

A Bayesion perfusion estimation using spatio-temporal priors in ASL-MRI. Miguel Lourenço Rodrigues. Master’s thesis in Biomedical Engineering December 2011. Outline. Introduction and Objectives Methods : Problem Formulation , Simulations and Real Data Results and Discussion

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A Bayesion perfusion estimation using spatio-temporal priors in ASL-MRI

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  1. A Bayesionperfusionestimationusingspatio-temporalpriorsin ASL-MRI Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December 2011

  2. Outline • Introductionand Objectives • Methods: ProblemFormulation, Simulationsand Real Data • ResultsandDiscussion • Conclusions

  3. Outline • Introduction • LiteratureReview • ProblemFormulation • Experimental ResultsandDiscussion • Conclusions

  4. Introduction Arterial SpinLabeling (ASL): Se [1] e [2] são refs, deviamaparecer antes com nomeeano -Noninvasivetechnique for generatingperfusionimagesofthebrain[1] -Cerebral BloodFlow (CBF): Volume ofbloodflowingperunit time[2] -Perfusion: CBF perunit volume oftissues

  5. Introduction ASL: Este slide eoseguintedeviam ser 1 só Labeledacquisiton 2. Imageacquisition Labelingofinflowing arterial blood

  6. Introduction ASL Controlacquisiton 4. Imageacquisition 3. No labeling

  7. Introduction ASL CBF Controlimage Labeledimage 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 lengthvector Ci – ithcontrolimage Li – ithlabeledimage P- perfusion [C1, L1, C2, L2,…, Cn/2, Ln/2]

  8. Introduction ASL signalprocessingmethods Pair-wisesubtraction: [P1, P2,…, Pn/2]=[C1- L1, C2- L2,…, Cn/2-Ln/2] Surroundsubtraction: [P1, P2,…, Pn/2]=[C1- L1, C2- (L1+L2),…, Cn/2-(L(n/2)-1-Ln/2)] 2 2 Sinc-interpolatedsubtraction: [P1, P2,…, Pn/2]=[C1- L1/2, C2- L3/2,…, Cn/2-Ln/2-1/2]

  9. Objectives Objectives -IncreaseimageSignal to Noise Ratio (SNR) -Reduceacquisitiontime Approach - Newsignalprocessingmodel No drasticsignalvariatons - Bayesianapproach (exceptinorganboundaries) - spatio-temporalpriors

  10. Outline • Introduction • LiteratureReview • ProblemFormulation • Experimental ResultsandDiscussion • Conclusions

  11. ProblemFormulation Mathematicalmodel Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1) Y (NxMxL) – SequenceofL PASL images F (NxM) – Staticmagnetizationofthetissues D(NxM x L) – Slowvariantimage (baselinefluctuationsofthesignal – Drift) v(L x 1) - Binarysignalindicatinglabelingsequences ΔM(NxM ) - Magnetizationdifferencecausedbytheinversion Γ(NxMxL)– AdditiveWhiteGaussianNoise ~N (0,σy2)

  12. ProblemFormulation Mathematicalmodel Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1)

  13. ProblemFormulation Algorithmimplementation Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1) Vectorization Y=fuT+D+ΔmvT+Γ (2) 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)

  14. ProblemFormulation Algorithmimplementation Sincenoiseis AWGN, p(Y)~N (μ, σy2), where μ=fuT+D+ΔmvT Maximumlikelihood(ML) estimationofunknownimages, θ={f,D,Δm} (3) θ=argminEy(Y,v,θ) θ Ill-posedproblem

  15. ProblemFormulation Algorithmimplementation (3) θ=argminEy(Y,v,θ) θ UsingtheMaximum a posteriori (MAP) criterion, regularizationis introducedbythe prior distributionoftheparameters (4) θ=argmin E(Y,v,θ) θ (5) E(Y,v,θ)=Ey (Y,v, θ) + Eθ(θ) Data – fidelityterm Prior term

  16. ProblemFormulation Algorithmimplementation Figure from[11]

  17. ProblemFormulation Algorithmimplementation (5) E(Y,v,θ)=Ey (Y,v, θ) + Eθ(θ) 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)] (6) +β(φhf)T(φhf)+(φvf)T(φvf) +γ(φhΔm)T(φhΔm)+(φvΔm)T(φvΔm)

  18. ProblemFormulation Algorithmimplementation -Inequation (6), thematricesφh,v,t are used to compute the horizontal, Vertical and temporal firstorderdifferences, respectively Φ= -α, βandγ are thepriors.

  19. ProblemFormulation Algorithmimplementation -MAP solution as a global mininum -StationarypointsoftheEnergyFunction – equation (6) - EquationsimplementedinMatlabandcalculatediteratively

  20. Outline • Introduction • LiteratureReview • ProblemFormulation • Experimental ResultsandDiscussion • Conclusions

  21. Experimental ResultsandDiscussion Synthetic data -Brainmask (64x64) -Axial slice -Whitematter (WM) andGraymatter (GM) 2 Asignal ; ISNR=SNRf-SNRi - SNR= Anoise N,M - ^ ∑ 100 |xi,j-xi,j| Meanerror(%)= NxM xi,j i=1,j=1

  22. Experimental ResultsandDiscussion Synthetic data Parameters: σ=1 Δm(GM)=1 Δm(WM)=0.5 D=[-1,1] F=10000 α=0 β=0 γ=0 Controlacquisition Labeledacquisition

  23. Experimental ResultsandDiscussion 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

  24. Experimental ResultsandDiscussion Synthetic data

  25. Experimental ResultsandDiscussion Synthetic data Prior optimization

  26. Experimental ResultsandDiscussion Synthetic data Prior optimization Incresasing prior value

  27. Experimental ResultsandDiscussion Synthetic data Prior optimization

  28. Experimental ResultsandDiscussion Synthetic data Prior optimization β=1 γ=5

  29. Experimental ResultsandDiscussion 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

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

  31. Experimental ResultsandDiscussion Synthetic data

  32. Experimental ResultsandDiscussion Synthetic data 3dB 23% 7% -30%

  33. Experimental ResultsandDiscussion Synthetic data Monte CarloSimulation for differentnoiselevels

  34. Experimental ResultsandDiscussion Real data -Onehealthysubject -3T Siemens MRI system (Hospital da Luz, Lisboa) -PICORE-Q2TIPS PASL sequence -TI1/TI1s/TI2=750ms/900ms/1700ms -GE-EPI -TR/TE=2500ms/19ms -spatialresolution: 3.5x3.5x7.0 mm3 -201 repetitions -Matrixsize: 64x64x9

  35. Experimental ResultsandDiscussion Real data Controlimage Labeledimage

  36. Experimental ResultsandDiscussion Real data Proposed algorithm Pair-wise subtraction Surround Subtraction

  37. Experimental ResultsandDiscussion Real data -Influenceofthe numberofiterations

  38. Experimental ResultsandDiscussion Real data Proposed algorithm Pair-wise subtraction Surround Subtraction

  39. Experimental ResultsandDiscussion Real data

  40. Outline • Introduction • LiteratureReview • ProblemFormulation • Experimental ResultsandDiscussion • Conclusions

  41. Conclusion -Theproposedbayesianalgorithmshowedimprovementof SNR and ME -SNR increasedby 3db (23%) -ME decreasedby 7% (30%) -Applied to real data Futurework: -Automatic prior calculation -Reducingthenumberofcontrolacquisitions -Validationtestsonempirical data

  42. 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-continuousowdrivenadiabaticinversion for arterial spinlabeling. InProcIntSocMagnResonMed, 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 spinlabeling. MagneticResonanceinMedicine, 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. ImplementationofQuantitativePerfusionImagingTechniques 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-Lyapunovequation. IEEE transactionsonimageprocessing, 17(9), 2008.

  43. Questions

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