A Stochastic Linear Model for fMRI Activation Analyses

Purpose:

The debate regarding how best to model variability of the hemodynamic response function in fMRI data has focussed on the linear vs. nonlinear nature of the optimal signal model, with few studies exploring the deterministic vs. stochastic nature of the dynamics. We propose a stochastic linear model (SLM) of the hemodynamic signal and noise dynamics to more robustly infer fMRI activation estimates.

Methods:

The SLM models the hemodynamic signal by an exogenous input autoregressive model driven by Gaussian state noise. Activation weights are inferred by a joint state-parameter iterative coordinate descent algorithm based on the Kalman smoother.

Results:

The SLM produced more accurate parameter estimates than the GLM for event-design simulated data. In application to block-design experimental visuo-motor task fMRI data, the SLM resulted in more punctate and well-defined motor cortex activation maps than the GLM, and was able to track variations in the hemodynamics, as expected from a stochastic model.

Conclusions:

We demonstrate in application to both simulated and experimental fMRI data that in comparison to the GLM, the SLM produces more flexible, consistent and enhanced fMRI activation estimates.