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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 Bayesionperfusionestimationusingspatio-temporalpriorsin ASL-MRI Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December 2011
Outline • Introductionand Objectives • Methods: ProblemFormulation, Simulationsand Real Data • ResultsandDiscussion • Conclusions
Outline • Introduction • LiteratureReview • ProblemFormulation • Experimental ResultsandDiscussion • Conclusions
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
Introduction ASL: Este slide eoseguintedeviam ser 1 só Labeledacquisiton 2. Imageacquisition Labelingofinflowing arterial blood
Introduction ASL Controlacquisiton 4. Imageacquisition 3. No labeling
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]
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]
Objectives Objectives -IncreaseimageSignal to Noise Ratio (SNR) -Reduceacquisitiontime Approach - Newsignalprocessingmodel No drasticsignalvariatons - Bayesianapproach (exceptinorganboundaries) - spatio-temporalpriors
Outline • Introduction • LiteratureReview • ProblemFormulation • Experimental ResultsandDiscussion • Conclusions
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)
ProblemFormulation Mathematicalmodel Y(t)=F+D(t)+v(t)ΔM+Γ(t) (1)
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)
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
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
ProblemFormulation Algorithmimplementation Figure from[11]
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)
ProblemFormulation Algorithmimplementation -Inequation (6), thematricesφh,v,t are used to compute the horizontal, Vertical and temporal firstorderdifferences, respectively Φ= -α, βandγ are thepriors.
ProblemFormulation Algorithmimplementation -MAP solution as a global mininum -StationarypointsoftheEnergyFunction – equation (6) - EquationsimplementedinMatlabandcalculatediteratively
Outline • Introduction • LiteratureReview • ProblemFormulation • Experimental ResultsandDiscussion • Conclusions
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
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
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
Experimental ResultsandDiscussion Synthetic data
Experimental ResultsandDiscussion Synthetic data Prior optimization
Experimental ResultsandDiscussion Synthetic data Prior optimization Incresasing prior value
Experimental ResultsandDiscussion Synthetic data Prior optimization
Experimental ResultsandDiscussion Synthetic data Prior optimization β=1 γ=5
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
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
Experimental ResultsandDiscussion Synthetic data
Experimental ResultsandDiscussion Synthetic data 3dB 23% 7% -30%
Experimental ResultsandDiscussion Synthetic data Monte CarloSimulation for differentnoiselevels
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
Experimental ResultsandDiscussion Real data Controlimage Labeledimage
Experimental ResultsandDiscussion Real data Proposed algorithm Pair-wise subtraction Surround Subtraction
Experimental ResultsandDiscussion Real data -Influenceofthe numberofiterations
Experimental ResultsandDiscussion Real data Proposed algorithm Pair-wise subtraction Surround Subtraction
Experimental ResultsandDiscussion Real data
Outline • Introduction • LiteratureReview • ProblemFormulation • Experimental ResultsandDiscussion • Conclusions
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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