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LLFOM: A Nonlinear Hemodynamic Response Model

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LLFOM: A Nonlinear Hemodynamic Response Model

Bing Bai

NEC Labs America

Oct 2014

- 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

- 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

- 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.

- 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.

- Hypothesis:
- Canonical HRF
- An ad-hoc 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

- Balloon model (Buxton et al. 1998)
- LLFOM model
- With physiological explanation
- Simple enough for large-scale processing

- 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

- 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.

Condition 1

Condition 2

- 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, …)