Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December

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

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

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

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

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

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

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 ]

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)

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

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)

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

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)

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)

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

16 Problem Formulation Algorithm implementation Figure from [11]

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)

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.

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

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

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 - ; -

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

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

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

25 Experimental Results and Discussion Synthetic data Prior optimization

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

27 Experimental Results and Discussion Synthetic data Prior optimization

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

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

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

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

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

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

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

35 Control imageLabeled image Experimental Results and Discussion Real data

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

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

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

39 Experimental Results and Discussion Real data

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

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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43 Questions