Dynamic retrospective filtering of physiological noise in BOLD fMRI: DRIFTER

doi:10.1016/j.neuroimage.2012.01.067

NeuroImage

Volume 60, Issue 2, 2 April 2012, Pages 1517-1527

https://doi.org/10.1016/j.neuroimage.2012.01.067 Get rights and content

Abstract

In this article we introduce the DRIFTER algorithm, which is a new model based Bayesian method for retrospective elimination of physiological noise from functional magnetic resonance imaging (fMRI) data. In the method, we first estimate the frequency trajectories of the physiological signals with the interacting multiple models (IMM) filter algorithm. The frequency trajectories can be estimated from external reference signals, or if the temporal resolution is high enough, from the fMRI data. The estimated frequency trajectories are then used in a state space model in combination of a Kalman filter (KF) and Rauch–Tung–Striebel (RTS) smoother, which separates the signal into an activation related cleaned signal, physiological noise, and white measurement noise components. Using experimental data, we show that the method outperforms the RETROICOR algorithm if the shape and amplitude of the physiological signals change over time.

Highlights

► New Bayesian method for removing physiological noise from fMRI data. ► Cardiac and respiration frequencies from reference signals with the IMM algorithm. ► Possible to estimate the frequencies from fMRI data if time-resolution allows. ► Separation of fMRI into activation and noise with Kalman filtering and RTS smoothing. ► Outperforms the RETROICOR method when physiological signals change much over time.

Introduction

The methodology of functional Magnetic Resonance Imaging (fMRI, Ogawa et al., 1990, Belliveau et al., 1991, Kwong et al., 1992) is rapidly evolving and as the spatial resolution, sampling frequency and signal-to-noise-ratio (SNR) of fMRI increases, the accurate treatment of various noise sources in measurements becomes more and more important. In addition to thermal and other random noises, which can be modeled as white noise, there exists several non-white noise sources as well (Lund et al., 2006). One of the most significant non-white factors is physiological noise, which mainly consists of vascular fluctuations and quasi-periodic oscillations caused by cardiac and respiratory activity (Krüger and Glover, 2001). At 3 T, in gray matter, the cardiac and respiratory noise account for a bit over 30% of the total standard deviation. At higher fields the physiological noise is likely to be more dominant (Krüger and Glover, 2001).

There exist several approaches to suppress cardiac, respiration and related physiological noise from fMRI measurements. If the temporal resolution of the fMRI time series is high enough, it is possible to design notch filters, which remove the frequency bands corresponding to cardiac pulsation, respiration and their harmonics (Biswal et al., 1996). However, this approach cannot cope with spectral aliasing, and it assumes stationarity of the signal, which is not a valid assumption if the frequency of the cardiac activity or respiration changes.

One widely used approach to physiological noise elimination is RETROICOR (Glover et al., 2000), which is based on fitting a low-order Fourier basis to the data and eliminating the components corresponding to the cardiac activity and respiration together with their harmonics. The phases of the cardiac and respiratory cycles are estimated from reference signals by peak-detection and histogram based methods, respectively (Glover et al., 2000). Unlike the notch filtering approach, RETROICOR is able to cope well with spectral aliasing and time-varying frequencies.

Other image-based physiological noise reduction approaches include adaptive filtering (Deckers et al., 2006), Principal Component Analysis (PCA) and Independent Component Analysis (ICA, Thomas et al., 2002), and IMPACT (Chuang and Chen, 2001). It is also possible to do retrospective noise reduction in k-space (Hu et al., 1995, Le and Hu, 1996, Frank et al., 2001) or to utilize the phase information (Cheng and Li, 2010).

Due to the typical 2–4 s time resolution of echo planar imaging (EPI) based fMRI, the physiological signals are heavily aliased in the data and thus the methods have to be able to cope with the aliasing. In image-based retrospective methods this usually means using reference signals or taking the timings of individual slices into account (Frank et al., 2001). In recent fast acquisition methods such as Inverse Imaging (InI, Lin et al., 2006, Lin et al., 2008) the sampling rates can reach 10 Hz (0.1 s), which enables possibility to eliminate physiological noises even without reference signals (Lin et al., in press).

In this article, we introduce the DRIFTER algorithm, which is a Bayesian method for physiological noise modeling and removal allowing accurate dynamical tracking of the variations in the cardiac and respiratory frequencies by using Interacting Multiple Models (IMM), Kalman Filter (KF) and Rauch–Tung–Striebel (RTS) smoother algorithms (Bar-Shalom et al., 2001, Grewal and Andrews, 2001). Due to the model based approach DRIFTER is not limited by the Nyquist frequency, and can remove physiological noises also from long TR fMRI data, provided that the frequency trajectories are estimated from a more densely sampled signal. The frequency trajectories can be either estimated from reference signals, or if the time resolution allows, directly from the fMRI signal. The estimated frequency trajectory is used for accurate model based separation of the spatio-temporal fMRI signal into activation, physiological noise and white noise components using Kalman filter and RTS smoother algorithms. We test the performance of the method with simulated data and fMRI data, and compare it to the RETROICOR method.

Section snippets

Kalman filtering, RTS smoothing and IMM

The Kalman filter and Rauch–Tung–Striebel smoother (Grewal and Andrews, 2001) are algorithms, which can be used for computing the exact Bayesian posterior distributions of the state in discrete-time linear Gaussian state space models of the form: $\begin{array}{l} \vec{x} (t_{k + 1}) = A_{k} \vec{x} (t_{k}) + \vec{q} (t_{k}) \\ \vec{y} (t_{k}) = H_{k} \vec{x} (t_{k}) + \vec{ε} (t_{k}), \end{array}$ where $\vec{x} (t_{k}) \in R^{n}$ is the state at time t_k, where k = 0, 1, 2, …, $\vec{y} (t_{k}) \in R^{d}$ is the measurement at time t_k, $\vec{q} (t_{k}) \sim N (0, Q_{k})$ is the Gaussian process noise, and $\vec{ε} (t_{k}) \sim N (0, Σ_{k})$ is the Gaussian measurement noise. Matrix A

Simulated data

For testing the overall behavior of the method we generated a simple artificial data. Because all methods work quite well with constant amplitude periodic signals, we concentrated on the less ideal cases. The simulated data involves frequency changes, amplitude changes, and stimulus-related drifting of the signal.

To further test the performance of the method in known conditions, we generated fMRI-like artificial data. The goal was to include all the main effects in the real data to the

Results with simulated data

Fig. 2 shows the performance of the RETROICOR method and the proposed DRIFTER method in tracking simulated signals with changing frequency, changing amplitude, and DC-level shift. Both methods can cope with time-varying frequency quite well. Because such effects seem to have a stronger presence in respiration signals than in cardiac signals, we used the respiration reference signal processing algorithm of RETROICOR (Eq. (3) in Glover et al., 2000). Normally, the RETROICOR algorithm only

Interpretation of experimental results

The simulated and experimental fMRI results clearly point out the main difference between the RETROICOR and DRIFTER methods: the dynamic nature of DRIFTER makes it able to adapt to changes in both shape and amplitude in periodic noise signals, without requiring these effects to be present in the reference signal. The proposed method was also shown to be able to track varying frequency and ignore level changes in reference signals, whereas RETROICOR has often problems with keeping track of

Conclusion

In this paper we have introduced the DRIFTER algorithm, which is a new image-based Bayesian method for retrospective elimination of physiological noise from fMRI measurements. The method uses a stochastic state space model and the interacting multiple models (IMM) algorithm for estimating the frequency trajectories of cardiac and respiration from reference signals, or if the time resolution allows, from the fMRI signal itself. The estimated frequency trajectories are then used as known

Acknowledgments

This work was supported by grants from the United States National Institutes of Health (NIH) (R01HD040712, R01NS037462, R01NS048279, P41RR014075, R01MH083744, R21DC010060, R21EB007298, National Center for Research Resources), National Science Council, Taiwan (NSC 98-2320-B-002-004-MY3, NSC 100-2325-B-002-046), National Health Research Institute, Taiwan (NHRI-EX100-9715EC), and Academy of Finland (124698, 125349, 127624, 129670, 218054, 218248, and the FiDiPro program). We thank Marita Kattelus

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Dynamic retrospective filtering of physiological noise in BOLD fMRI: DRIFTER

Abstract

Highlights

Introduction

Section snippets

Kalman filtering, RTS smoothing and IMM

Simulated data

Results with simulated data

Interpretation of experimental results

Conclusion

Acknowledgments

NeuroImage

Magn. Reson. Imaging

NeuroImage

NeuroImage

NeuroImage

NeuroImage

NeuroImage

NeuroImage

NeuroImage

NeuroImage

NeuroImage

NeuroImage

Cubature Kalman filters

IEEE Trans. Autom. Control.

Estimation with Applications to Tracking and Navigation

Functional mapping of the human visual cortex by magnetic resonance imaging

Science

Reduction of physiological fluctuations in fMRI using digital filters

Magn. Reson. Med.

Dynamics of blood flow and oxygenation changes during brain activation: the balloon model

Magn. Reson. Med.

An introduction to compressive sampling

IEEE Signal Process. Mag.

IMPACT: image-based physiological artifacts estimation and correction technique for functional MRI

Magn. Reson. Med.

Space-time Kalman filter