LLFOM: A Nonlinear Hemodynamic Response Model

1. LLFOM: A Nonlinear Hemodynamic Response Model Bing Bai NEC Labs America Oct 2014

2. About who I am • Paul’s only student that got Ph.D in Computer Science • Thus the least favorite one (orz) • Worked with Paul on: • Question answering • fMRI image retrieval • Currently researcher in NEC Labs America • Machine learning

3. Lagged, Limited First Order Model (LLFOM) • A Nonlinear hemodynamic model used in fMRI study • A example of Paul’s many overlooked great ideas • A nice, novel idea • Published only in my thesis • A example of “Paul is a nice guy” • I could be still doing this right now, if he makes me

4. Active and Inactive voxels • The intensity change of some voxels are correlated with stimulus, they are considered to be “active”. • The unofficial goal of fMRI: detecting voxels activated by visual, audio, conscience, love … and whatever is interesting.

5. Generalized Linear Model (GLM) • How to get Design Matrix X? • Hypothesis: • A voxel is a linear time-invariant (LTI) system • The impulse response function is known as Hemodynamic Response Function (HRF) • If we convolve the HRF with the stimulus we will get a response time series, and we put it in the design matrix as a column. • Canonical HRF • An ad-hoc model

6. Lagged, Limited First Order Model (LLFOM) nonlinear model • Earlier nonlinear hemodynamic models • Balloon model (Buxton et al. 1998) • A model with clear physiological explanations • Complicated • Volterra kernels (Friston et al. 2000). • Black box, no physiological explanations • Complicated • LLFOM model • With physiological explanation • Simple enough for large-scale processing

7. Lagged, Limited First Order Model (LLFOM) nonlinear model • The response is modeled with differential equation of 4 parameters ( ): • The first term is the positive response, proportional to the stimulus with a lag (τ), the the strength of the response, and limited by the capability of blood flow ( ). The second term is an exponential decay. • Can be regrouped as

8. Lagged, Limited First Order Model (LLFOM) nonlinear model • Model fitting: • is the constant component • Nonlinear optimization (BFGS-B) • Initial point in search (A=0.1, B=0.1, C=0.2) • Grid search for • (a) (b) (c) are , and , respectively.

9. fMRI Retrieval Based on GLM Condition 1 Condition 2

10. Results: GLM-based Features

11. Concluding Remarks • Future work (what should have been done) • Smoothing across voxels • Analysis on the good performance on the pure Bayesian approach • I like to thank Paul for his guidance • On research • On many other things (morality, values, life, …)