Generalized least-squares method applied to fMRI time series with empirically determined correlation matrix

Area of Science:

• Neuroimaging
• Statistical modeling
• Signal processing

Background:

• Functional magnetic resonance imaging (fMRI) time series analysis commonly uses linear models.
• Linear models require assumptions about error distribution and correlation, which are often violated in fMRI data.
• Generalized least squares can be used when assumptions are violated, but requires knowledge of the error covariance matrix.

Purpose of the Study:

• To propose a flexible time domain noise model for fMRI time series analysis.
• To improve statistical inferences about regional cerebral blood flow (rCBF) changes during cognitive tasks.
• To provide an interpretable noise model that does not require predefining correlations between coefficients.

Main Methods:

• Developed a method based on empirically determined autocorrelation functions to build a Toeplitz correlation matrix.
• Tested the method on simulated fMRI time series data with and without an effect of interest.
• The method requires stationarity of the autocorrelation function but is more flexible than autoregressive models.

Main Results:

• The proposed method accurately determined F values corresponding to the correct false positive level for time series without an effect.
• For time series with an effect of interest, the method generated an F value density function enabling null hypothesis rejection.
• The method demonstrated flexibility and interpretability as a time domain noise model.

Conclusions:

• The developed noise model offers a flexible and interpretable approach for fMRI time series analysis.
• This method enhances the reliability of statistical inferences in neuroimaging studies, particularly for event-related designs.
• The approach effectively addresses limitations of traditional linear models in handling complex error structures in fMRI data.