Variational solution to hemodynamic and perfusion response - PowerPoint PPT Presentation

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

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 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 1 / 18

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 BOLD direct quantitative measure indirect measure cerebral blood flow mix of parameters low SNR higher SNR (» ASL) 2 / 18

Arterial Spin Labeling data acquisition Ref: http://fmri.research.umich.edu/research/main_topics/asl.php 3 / 18

Statistical analysis of ASL fMRI data ASL data contain both hemodynamic & perfusion components CBF + blood volume CBF + oxygen consumption 4 / 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 5 / 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 6 / 18

ASL signal model 7 / 18

Physiological prior 8 / 18

Variational Expectation Maximization § Expectation Maximization. p p r q “ arg max p , θ p r q q E-step: ˜ F p ˜ ˜ p M-step: θ p r ` 1 q “ arg max p p r q , θ q F p ˜ θ being “ ‰ “ ‰ F p ˜ p , θ q “ E ˜ log p p y , a , h , c , g , q ; θ q ´ E ˜ log ˜ p p a , h , c , g , q q p p loooooooooooooomoooooooooooooon entropy of ˜ p § Variational EM: class of probability distributions restricted to the set of distributions that satisfy ˜ p p a , h , c , g , q q “ ˜ p a p a q ˜ p h p h q ˜ p c p c q ˜ p g p g q ˜ p q p q q 9 / 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: 10 / 18

VEM steps (2) The E-step become: E-H-step: ˜ p h “ arg max F p ˜ p a ˜ p h ˜ p c ˜ p g ˜ p q ; θ q ˜ p h P D H E-G-step: ˜ p g “ arg max F p ˜ p a ˜ p h ˜ p c ˜ p g ˜ p q ; θ q p g P D G ˜ and similar for the rest of the variables. The M-step can also be divided into separate steps: „ log p p y | a , ˜ g ; α , ℓ , σ 2 q “ ‰ θ “ arg max E ˜ h , c , ˜ p a ˜ p c θ P Θ ` log p p ˜ “ ‰ ` E ˜ log p p a | q ; µ a , σ a q h ; v h q p a ˜ p q “ ‰ ` E ˜ log p p c | q ; µ c , σ c q ` log p p ˜ g ; v g q p c ˜ p q ‰ “ ` E ˜ log p p q ; β q p q 11 / 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 “ ˜ ˜ h ˜ g ˜ p a δ ˜ p c δ ˜ p q so that, for example for H, the E-H step ˜ p h “ arg max F p ˜ p a ˜ p h ˜ p c ˜ p g ˜ p q ; θ q p h P D H ˜ ˜ becomes h “ arg max F p ˜ p a δ ˜ h ˜ p c δ ˜ g ˜ p q ; θ q ˜ h This facilitates the inclusion of constraints on h and g like } h } 2 2 “ 1 and } g } 2 2 “ 1. 12 / 18

Simulation results Artificial data generation ‚ Fast event-related paradigm: ‚ Repetition time: TR “ 3 s mean ISI “ 5 s. ‚ Number of scans: N “ 288 ‚ 1 experimental condition 20 ˆ 20 binary activation label maps: ‚ White noise b j „ N p 0 , 2 q hemodyn. maps „ N p 2 . 2 , 0 . 3 q ‚ Response functions simulated with physiological model [Friston et al, 00] perfusion maps „ N p 1 . 6 , 0 . 3 q 13 / 18

Simulation results: Low SNR scenario, TR “ 3s ‚ Response function ‚ Response levels hemodyn. perfusion activation maps maps states ∆ signal SNR ground 2 . 4 dB truth SNR time (s) 2 . 4 dB SNR ∆ signal SNR 0 . 5 dB 0 . 5 dB time (s) 14 / 18

Simulation results: Low SNR scenario, TR “ 3s Comparison to MCMC solution of joint detection estimation (JDE): SNR (dB) SNR (dB) 15 / 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) 16 / 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 17 / 18

Thanks for your attention 18 / 18