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

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

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43. Questions