Variational solution to hemodynamic and perfusion response estimation from ASL fmri data

Transcription

1 Variational solution to hemodynamic and perfusion response estimation from ASL fmri data Aina Frau-Pascual, Florence Forbes, Philippe Ciuciu June, 2015

2 1 / 18 BOLD: Qualitative functional MRI Blood Oxygen Level Dependent [Ogawa et al, PNAS 1990] What does BOLD contrast really measure? BOLD measures the ratio of oxy- to deoxy-hemoglobin in the blood

3 1 / 18 BOLD: Qualitative functional MRI Blood Oxygen Level Dependent [Ogawa et al, PNAS 1990] What does BOLD contrast really measure? BOLD measures the ratio of oxy- to deoxy-hemoglobin in the blood

4 ASL: Quantitatively imaging cerebral perfusion Arterial Spin Labeling [Williams et al, PNAS 1992] WHAT? Cerebral perfusion: Delivery of nutritive blood to the brain tissue capillary bed WHY? Quantification is important: eg. perfusion altered in various diseases (stroke, tumors) ASL direct quantitative measure cerebral blood flow low SNR BOLD indirect measure mix of parameters higher SNR (» ASL) 2 / 18

5 Arterial Spin Labeling data acquisition Ref: 3 / 18

6 4 / 18 Statistical analysis of ASL fmri data ASL data contain both hemodynamic & perfusion components CBF CBF + blood volume + oxygen consumption

7 5 / 18 Statistical analysis of ASL fmri data GLM Unique fixed canonical hemodynamic response function (HRF) [Hernandez-Garcia et al, 10, Mumford et al, 06] Inaccurate PRF shapes Joint Detection-Estimation (JDE) Separate estimation of 2 response functions (HRF & PRF) Use of MCMC methods [Vincent et al, 13, Frau-Pascual et al, 14] Computationally very expensive

8 6 / 18 GOAL Providing an efficient solution to hemodynamic and perfusion response estimation from ASL fmri data Based on: Variational Expectation-Maximization [Chaari et al, 12] Acceptable computational times Physiological prior information

9 ASL signal model 7 / 18

10 Physiological prior 8 / 18

11 Variational Expectation Maximization Expectation Maximization. E-step: p prq arg max p Fp p, θ prq q M-step: θ pr`1q arg max θ Fp p prq, θq being Fp p, θq E p log ppy, a, h, c, g, q ; θq E p log ppa, h, c, g, qq loooooooooooooomoooooooooooooon entropy of p Variational EM: class of probability distributions restricted to the set of distributions that satisfy ppa, h, c, g, qq p a paq p h phq p c pcq p g pgq p q pqq 9 / 18

12 10 / 18 VEM steps (1) The E-step becomes an approximate E-step that can be further decomposed into five stages updating the different variables: The M-step can also be divided into separate steps:

13 VEM steps (2) The E-step become: E-H-step: p h arg max Fp p a p h p c p g p q ; θq p h PD H E-G-step: p g arg max Fp p a p h p c p g p q ; θq p gpd G and similar for the rest of the variables. The M-step can also be divided into separate steps: θ arg max E pa p c log ppy a, h, c, g; α, l, σ 2 q θpθ ` E pa p q log ppa q; µa, σ a q ` log pp h; v h q ` E pc p q log ppc q; µc, σ c q ` log pp g; v g q ` E pq log ppq; βq j 11 / 18

14 12 / 18 Constraints on h and g We can constraint the search to pointwise estimates h and g by replacing the probabilities on h and g by Dirac functions: p p a δ h p c δ g p q so that, for example for H, the E-H step becomes p h arg max Fp p a p h p c p g p q ; θq p h PD H h arg max Fp p a δ h p c δ g p q ; θq h This facilitates the inclusion of constraints on h and g like }h} and }g}2 2 1.

15 13 / 18 Simulation results Artificial data generation Repetition time: TR 3 s Number of scans: N 288 White noise b j N p0, 2q Response functions simulated with physiological model [Friston et al, 00] Fast event-related paradigm: mean ISI 5 s. 1 experimental condition 20 ˆ 20 binary activation label maps: hemodyn. maps N p2.2, 0.3q perfusion maps N p1.6, 0.3q

16 14 / 18 Simulation results: Low SNR scenario, TR 3s Response function Response levels hemodyn. perfusion activation maps maps states SNR 2.4 db signal ground truth time (s) SNR 2.4 db SNR 0.5 db signal SNR 0.5 db time (s)

17 15 / 18 Simulation results: Low SNR scenario, TR 3s Comparison to MCMC solution of joint detection estimation (JDE): SNR (db) SNR (db)

18 16 / 18 Real data Paradigm: fast event-related design (mean ISI 5.1s.), with 60 auditory and visual stimuli Auditory cortex hemodyn. maps perfusion maps responses region signal time (sec) Visual cortex hemodyn. maps perfusion maps responses region signal time (sec)

19 17 / 18 Conclusions Jointly detecting activity and estimating hemodynamic and perfusion responses from functional ASL data It facilitates the inclusion of additional information Future directions Performance optimization Investigation of other constraints

20 Thanks for your attention 18 / 18