Autoregressive model based algorithm for correcting motion and serially correlated errors in fNIRS

Abstract

Systemic physiology and motion-induced artifacts represent two major sources of confounding noise in functional near infrared spectroscopy (fNIRS) imaging that can reduce the performance of analyses and inflate false positive rates (i.e., type I errors) of detecting evoked hemodynamic responses. In this work, we demonstrated a general algorithm for solving the general linear model (GLM) for both deconvolution (finite impulse response) and canonical regression models based on designing optimal pre-whitening filters using autoregressive models and employing iteratively reweighted least squares. We evaluated the performance of the new method by performing receiver operating characteristic (ROC) analyses using synthetic data, in which serial correlations, motion artifacts, and evoked responses were controlled via simulations, as well as using experimental data from children (3-5 years old) as a source baseline physiological noise and motion artifacts. The new method outperformed ordinary least squares (OLS) with no motion correction, wavelet based motion correction, or spline interpolation based motion correction in the presence of physiological and motion related noise. In the experimental data, false positive rates were as high as 37% when the estimated p-value was 0.05 for the OLS methods. The false positive rate was reduced to 5-9% with the proposed method. Overall, the method improves control of type I errors and increases performance when motion artifacts are present.

Keywords: (100.2960) Image analysis; (170.2655) Functional monitoring and imaging; (170.5380) Physiology; (300.0300) Spectroscopy.

Fig. 1

A simulated fNIRS signal generated from an AR(5) process with simulated motion artifacts is shown in (a). After generating an optimal pre-whitening filter via fitting an AR(2) model, the whitened signal (b) has significantly reduced autocorrelations (c). An experimental fNIRS signal is shown in (d). After generating an optimal pre-whitening filter via fitting an AR(2) model, the whitened signal (e) has significantly reduced autocorrelations (d).

Fig. 2

Examples of recovered hemodynamic response functions for simulated block design (a–c) and event-related (d–f) design using the experimental data as baseline physiology/noise.

Fig. 3

Partial AUC (AUC_0.05) for detection of evoked responses with a deconvolution/FIR model for simulated block (a) and event (b) tasks using an AR model as baseline signal with no artifacts (AR/None), spike artifacts (AR/Spike), or shift artifacts (AR/Shift) or with experimental data as a baseline signal containing motion artifacts. Error bars indicate 99% confidence interval.

Fig. 4

False positive rate of detection as a function of estimated p-value (i.e., estimated false positive rate) with the deconvolution/FIR model for simulated block (top row) and event (bottom row) tasks using a simulated AR model as baseline signal with no artifacts (AR/None), spike artifacts (AR/Spike), or shift artifacts (AR/Shift) or with experimental data as a baseline signal containing motion artifacts.

Fig. 5

Partial AUC for detection of evoked responses with the canonical regression model for simulated block (a) and event (b) tasks using a simulated AR model as baseline signal with no artifacts (AR/None), spike artifacts (AR/spike), or shift artifacts (AR/shift) or with experimental data as a baseline signal containing motion artifacts. Error bars indicate 99% confidence interval.

Fig. 6

False positive rate of detection as a function of estimated p-value (i.e., estimated false positive rate) with the canonical regression model for simulated block (top row) and event (bottom row) tasks using a simulated AR model as baseline signal with no artifacts (AR/None), spike artifacts (AR/spike), or shift artifacts (AR/shift) or with experimental data as a baseline signal containing motion artifacts.