Characterizing phase-only fMRI data with an angular regression model.

FMRI voxel time series are complex-valued with real and imaginary parts that are usually converted to magnitude-phase polar coordinates. Magnitude-only data models that discard the phase portion of the data have dominated fMRI analysis. However, when such analyses are performed, the data that is discarded may contain valuable biologic information that is not in the magnitude data. This biologic information from BOLD fMRI data may be vascular [Menon RS. Postacquisition suppression of large-vessel BOLD signals in high-resolution fMRI. Magn Reson Med 2002;47(1):1-9] or neuronal [Bodurka J, Jesmanowicz A, Hyde JS, Xu H, Estowski L, Li S-J. Current-induced magnetic resonance phase imaging. J Magn Reson 1999;137(1):265-71] in origin. When phase-only time series that discard the magnitude portion of the data have been analyzed, ordinary least squares (OLS) regression has been the technique of choice. However, OLS models may fit poorly when phase-wrap or low signal-to-noise ratio (SNR) is present. We have explored alternatives to the OLS model which will account for the angular response of the phase while also allowing us the flexibility to develop similar hypothesis tests. We adopt an angular regression model by Fisher and Lee [Fisher NI, Lee AJ. Regression models for an angular response. Biometrics 1992;48:665-77] for our analysis and show its improvement over the OLS model at low SNR in terms of both parameter estimation and inferences. We found an improvement in parameter estimation along with modeling for the Fisher and Lee method in simulated data while detailing potential benefits when used with experimentally acquired data. Finally, we look at a map of the statistics testing the association of the observed voxel phase time course and the reference function in our acquired data. This shows the possible detection of biological information in the generally discarded phase.