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Published byFrederica Rodgers Modified over 9 years ago
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LLFOM: A Nonlinear Hemodynamic Response Model Bing Bai NEC Labs America Oct 2014
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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
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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
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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.
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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
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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
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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
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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.
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fMRI Retrieval Based on GLM Condition 1 Condition 2
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Results: GLM-based Features
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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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