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Advancements in Nonlinear Hemodynamic Response Models in fMRI Studies

This work presents the Lagged, Limited First Order Model (LLFOM), a nonlinear hemodynamic response model applied in fMRI studies. Developed under the mentorship of Paul, it bridges machine learning and neuroimaging, focusing on the dynamic correlation of voxel intensity changes with stimuli. LLFOM is notable for its physiological explanations and suitability for large-scale processing. This research highlights overlooked contributions to the field, aiming to refine methods for detecting activated voxels and enhancing understanding of brain responses to various stimuli.

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Advancements in Nonlinear Hemodynamic Response Models in fMRI Studies

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  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, …)

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