Characterizing phase-only fMRI data with an angular regression model
Introduction
Functional magnetic resonance imaging (fMRI) is an invaluable tool used to investigate biological phenomena in both animals and humans. However, the results derived from fMRI depend on the model used to analyze the data. Although voxel time courses are complex-valued (Haacke et al., 1999), traditionally the real–imaginary voxel measurements are converted to magnitude-phase measurements and only the magnitude portion of the data is analyzed for experimental or task related changes (Bandettini et al., 1993, Rowe and Logan, 2005). This discards potentially important information. Recently, models that determine task related magnitude changes within the complex-valued data have shown improvements over those that examine magnitude-only data (Rowe and Logan, 2004, Rowe and Nencka, 2006).
In addition, there is evidence that the phase portion of the data also contains biological information not wholy contained in the magnitude portion, namely, data indicative of vascularization (Menon, 2002, Nencka and Rowe, 2005, Nencka and Rowe, 2006) or of possible direct detection of neuronal firing (Borduka et al., 1999). Thus it is also important to analyze the phase portion of the fMRI data.
Historically, when phase-only data has even been analyzed, an ordinary least squares (OLS) regression model is used. But this method neglects the problem of the phase angle wrapping back over itself after it has crossed the ±π value. Fisher and Lee (1992) developed an angular regression model which has never been applied to fMRI data. We aim to improve the modeling of the generally discarded phase portion of the data by using the Fisher and Lee model compared to OLS without unwrapping and an intermediate approach of OLS which attempts to (artificially) unwrap the data.
Section snippets
Background
As previously mentioned, the model for brain function and distributional specifications are essential for fMRI analysis results. It is well established that the real and imaginary parts of the complex-valued voxel observations are normally distributed (Gudbjartsson and Patz, 1995, Haacke et al., 1999) provided the dominant noise is scanner related. When viewed from the magnitude and phase angle, ρ and θ, point of view, the phase lies in a plane taking on values only between and including −π to +
Models for phase data analysis
As previously noted, phase-only time series data is not generally analyzed in fMRI, because it is sensitive to physiologic noise. It has been argued that respiration causes movement of internal organs which in turn alters the B-field and thus the phase (Pfeuffer et al., 2002). Pfeuffer et al. (2002) used the common phase data across a whole slice to correct for this respiration caused movement.
When fMRI phase time series data is analyzed, the OLS model is utilized (Borduka et al., 1999). Before
Results with simulated fMRI phase-only data
In order to compare the three phase-only models: (1) OLS without unwrapping, (2) OLS with manual unwrapping and (3) the FL model with automatic unwrapping via angular regression, we use data simulated data from two separate cases.
Case one is where the baseline magnitude is large relative to the standard deviation (high SNR = β0/σ) and the mean phase is not near the ±π boundary. For this case the three models should agree. Case two has a small baseline magnitude relative to the standard deviation
Experimental data
We now will compare the two models using actual experimental data. A bilateral sequential finger tapping experiment was performed in a block design with 16 s off followed by eight epochs of 16 s on and 16 s off. Scanning was performed using a 1.5 T GE Signa in which five axial slices of size 96 × 96 were acquired with a full k-space single shot gradient echo pulse sequence having a FA = 90° and a TE = 47 ms. In image reconstruction, the acquired data was zero filled to 128 × 128. After Fourier image
Conclusion
Modeling fMRI phase time series with OLS regression may result in some troublesome phenomena, which may include poor fit, incorrect parameter estimation, and potentially inaccurate test statistics, even after being unwrappped. Most of these problem arise from the issue of phase-wrap in the time series. We discussed using the linear-circular regression model proposed by Fisher and Lee (1992) to solve these problems. It allowed us to define a design matrix which could account for several
Acknowledgments
This work is supported in part by NIH RR00058, AG020279 and EB00215.
References (25)
- et al.
An evaluation of thresholding techniques in fMRI analysis
NeuroImage
(2004) Parameter estimation in the magnitude-only and complex-valued fMRI data models
NeuroImage
(2005)- et al.
A complex way to compute fMRI activation
NeuroImage
(2004) - et al.
Complex fMRI analysis with unrestricted phase is equivalent to a magnitude-only model
NeuroImage
(2005) - et al.
Investigation of low frequency drift in fMRI signal
NeuroImage
(1999) - et al.
Processing strategies for time-course data sets in functional MRI of the human brain
Magn Reson Med
(1993) - et al.
Current-induced magnetic resonance phase imaging
J Magn Reson
(1999) - et al.
An analysis of transformations
J Roy Stat Soc
(1964) - et al.
Regression models for an angular response
Biometrics
(1992) - et al.
Digital image processing
(1992)
A regression technique for angular variates
Biometrics
The Rician distribution of noisy data
Magn Reson Med
Cited by (17)
A fully Bayesian approach for comprehensive mapping of magnitude and phase brain activation in complex-valued fMRI data
2024, Magnetic Resonance ImagingModel order effects on ICA of resting-state complex-valued fMRI data: Application to schizophrenia
2018, Journal of Neuroscience MethodsCitation Excerpt :To date, most studies on model order effects on ICA have considered magnitude-only fMRI data. fMRI data initially are acquired as a bivariate complex-valued form containing magnitude and phase image pairs (Rowe, 2005; Rowe et al., 2007; Adalı and Calhoun, 2007; Calhoun and Adalı, 2012; Hagberg and Tuzzi, 2014). Although phase data tend to be noisy, phase fMRI data may contribute unique biological information.
Functional quantitative susceptibility mapping (fQSM)
2014, NeuroImageCitation Excerpt :Conventionally, BOLD-contrast is measured from the magnitude image time-series, where the non-local intensity changes related to susceptibility changes are less pronounced than in phase time-series. Only a few studies have investigated BOLD contrast by also using the phase information in time-series (Arja et al., 2010; Bianciardi et al., 2014; Chen et al., 2013; Hagberg et al., 2008, 2012; Hahn et al., 2009; Menon, 2002; Petridou et al., 2009; Rowe, 2005; Rowe and Logan, 2004; Rowe et al., 2007; Tomasi and Caparelli, 2007). At the spatial resolution allowed by conventional magnetic fields (e.g. 1.5 T and 3 T), the BOLD phase effect, despite being stronger than the magnitude effect at microscopic level, is averaged out due to the orientation dependence of microscopic field perturbation effects, hence substantial phase contrast can only be found near a few large veins of diameter comparable to the voxel dimensions.
Susceptibility-based functional brain mapping by 3D deconvolution of an MR-phase activation map
2013, Journal of Neuroscience MethodsCitation Excerpt :Conventionally, only magnitude data are used for functional brain mapping. Recent research has begun to evaluate the benefits of utilising the available phase information (Arja et al., 2009; Feng et al., 2009; Rowe and Logan, 2004; Rowe et al., 2007). However, the phase maps are not perfect representations of the underlying brain activity; in particular, they can be highly nonlocal in nature due to the 3D convolution mentioned above.
Physiologic noise regression, motion regression, and TOAST dynamic field correction in complex-valued fMRI time series
2012, NeuroImageCitation Excerpt :Once this processing has been carried out, the field maps were applied using the one-dimensional (phase-encoding direction) Simulated Phase Rewinding (SPHERE) (Kadah and Hu, 1997) correction method to remove their effects from the original images. As a final processing step, the angular mean (Rowe et al., 2007) of each voxel time series following the dynamic field correction was subtracted to prevent phase wrapping within the imaged object. No voxels inside the object drifted more than 2π radians over the length of the experiment, especially after being corrected for the field dynamics, and zeroing the mean was sufficient in all cases to prevent wraparound in voxels within the head.
Functional magnetic resonance imaging brain activation directly from k-space
2009, Magnetic Resonance ImagingCitation Excerpt :This idea of computing fMRI activation from complex-valued data has recently been expanded upon [4,5,8,9]. Work has also been performed on computing fMRI activation from phase-only time series [10]. However, the processes of image reconstruction and statistical activation have been treated separately.