Miguel Lourenço Rodrigues Master’s thesis in Biomedical Engineering December

2 Outline 1. Introduction 2. Literature Review 3. Problem Formulation 4. Experimental Results and Discussion 5. 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 passing through a point in the brain per unit of time [2] -Perfusion: CBF per unit volume of time Arterial Spin Labeling (ASL): -Non invasive technique for generating perfusion images of the brain [1]

5 Introduction Labeled acquisiton 1.Labeling of inflowing arterial blood 2. Image acquisition ASL:

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

7 Introduction ASL Control imageLabeled image CBF

8 Introduction Motivations / Goals -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 Literature review ASL - Continuous ASL (CASL) - Pulsed ASL (PASL) - Pseudo-Continuous ASL (pCASL) - Velocity-Selective ASL (VS-ASL)

11 Literature review CASL [3] -First model to be proposed -Continuous Radio Frequency (RF) pulse (2-4s) -Magnetic field gradient in the direction of the flow -Inversion of the moving arterial spins -Saturation of static tissues

12 Literature review CASL Limitations: - Mean velocity of the blood - Angles of the vessels - RF amplitude - Gradient strenght - Magnetization Transfer (MT)

13 Literature review CASL label acquisition control Figure taken from [4]

14 Literature review PASL [5] -Short RF pulse (5 – 20 ms) -Inversion of a thick portion of spins -Proximal do imaging plane (10-15 cms distance) -Easy to implement -Higher labeling efficiency

15 Literature review PASL Limitations: - The GAP between labeling and acquisitions allows T1 decay - Decreased sensitivity

16 Literature review PASL label acquisition control Image adapted from [4]

17 Literature review pCASL [6] - Created to overcame poor labeling of CASL comparing to PASL -Sequence of RF pulses -Synchronous gradient field -Inversion similar to CASL -Higher labeling efficiency than CASL

18 Literature review pCASL Unbalanced pCASLBalanced pCASL

19 Literature review VS-ASL [7] - Labeling of the blood with velocity superior to a cutoff value (Vc) -Smaller and uniform time delay -Better for slow or collateral flow conditions -Acquisition for V<Vc

20 Literature review VS-ASL Image adapted from [8]

21 Literature review Comparison of the ASL techniques ASL typeAdvantagesDisadvantages CASL Higher SNR Shorter transit delay Low labeling efficiency Specific Absorption Rate (SAR) MT effects Specific hardware required PASL High labeling efficiency Lower SAR Improved transit time Lower SNR Increased transit delay pCASL Higher SNR than PASL Higher labeling efficiency than CASL Higher SAR Limited Clinical Availability VS-ASLAbility to measure low CBFLower SNR

22 Literature review ASL signal processing methods - Pair-wise subtraction [9] - Surround Subtraction [10] - Sinc-interpolated subtraction [9]

23 Literature review ASL signal processing methods [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

24 Literature review 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 ]

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

26 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)

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

28 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)

29 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)

30 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

31 Problem Formulation Algorithm implementation Figure from [11]

32 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)

33 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.

34 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

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

36 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 - ; -

37 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

38 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

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

40 Experimental Results and Discussion Synthetic data Prior optimization

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

42 Experimental Results and Discussion Synthetic data Prior optimization

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

44 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

45 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

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

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

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

49 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

50 Control imageLabeled image Experimental Results and Discussion Real data

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

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

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

54 Experimental Results and Discussion Real data

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

56 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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58 Questions