Minimum-Phase Property of the Hemodynamic Response Function, and Implications for Granger Causality in fMRI

Area of Science:

• Neuroimaging
• Computational Neuroscience
• Biophysics

Background:

• Granger causality (GC) estimates directed statistical dependence in brain activity time series.
• Functional MRI (fMRI) uses the blood-oxygen-level-dependent (BOLD) signal, indirectly measuring neural activity.
• Variations in the haemodynamic response function (HRF) across brain regions may distort GC estimates.

Purpose of the Study:

• To investigate the impact of HRF variations on Granger causality (GC) validity in fMRI.
• To determine if realistic biophysical models of the HRF satisfy the minimum-phase condition required for valid GC analysis.
• To identify conditions under which GC inferences in fMRI may be distorted.

Main Methods:

• Analysis of transfer functions for three realistic biophysical models of the HRF.
• Assessment of the minimum-phase condition across a range of physiologically plausible parameter values.
• Evaluation of the impact of BOLD signal sampling rates on GC inference.

Main Results:

• The minimum-phase condition for the HRF is met for a wide range of physiologically plausible parameters.
• Violation of the minimum-phase condition occurs with HRFs exhibiting an initial dip.
• Slow BOLD signal sampling (seconds) relative to neural timescales (milliseconds) can introduce spurious GC inferences.

Conclusions:

• Granger causality analysis is generally viable in fMRI even with HRF variability, provided the HRF is minimum-phase.
• Initial dips in the HRF and slow BOLD sampling are critical limitations to consider for accurate GC inference.
• Closed-form HRF transfer functions offer a balance of mathematical tractability and biological plausibility for fMRI time series modeling.