A novel analytical method to measure intra-individual variability of steady-state evoked potentials; new insights into attention deficit

https://doi.org/10.1016/j.bspc.2021.103109Get rights and content

Highlights

  • Variation in amplitude and phase of frequency component taken from SSEP is measured.

  • We fitted the Fourier estimates using an ellipse instead of a circle.

  • Covariance to eigenvectors conversion yields the ellipse parameters.

  • The ellipse Length-Width difference reveals meaningful fluctuations in brain response.

  • The Angle of the ellipse estimates the correlation between the amplitude and phase.

Abstract

Background

The intra-individual variability of steady-state evoked potential (SS-EP) recordings reveals unique individual behavioral capabilities in neuroscience experiments and individual attention deficit in clinical studies. In this paper, we show how to measure the intra-individual variability in both amplitude and phase of frequency component.

Methods

To estimate the variability, multiple Fourier measurements at a frequency component using a non-overlapping moving time window are extracted from SS-EP data and represented in the two-dimensional complex plane. In contrast to the common approach to fit the Fourier estimates with a circle based on the assumption that the brain response is stable over time, our approach based on the reasonable assumption of fluctuating attention is to fit the samples using an ellipse with three new parameters: Length, Width, and Angle of the ellipse. We believe that attention fluctuations can produce a significant Length-Width difference (LW-Diff).

Results

We applied our method to simulations to demonstrate validity. If the LW-Diff is significant using standard error of standard deviation, the cluster of Fourier estimates is non-circular in the complex plane. In such cases, we assume the maximum variation corresponds to a meaningful fluctuation in brain response presumably as a function of attention.

Conclusion

Our method enables us, for the first time, to estimate individual attention fluctuation using the Length-to-Width Ratio and to test whether Fourier measurements distribute circularly in the complex plane. The method is useful for distinguishing individuals with different behavioral capabilities, differentiating cases with inconsistent control of attention from healthy subjects, and monitoring therapeutic interventions.

Introduction

The dynamics of our brain activity provide a challenge for neuroscientists and clinicians. There is intra-individual variability of brain activity within or across runs for any experimental condition [1]. The intra-individual variation is a unique individual character and may reveal the subject’s behavioral capabilities [1]. Furthermore, the intra-individual variability has been correlated with the subject’s attention level [2]. The subject’s ability to sustain attention to a stimulus plays an important role in determining how significantly the subject’s neural response to the stimulus varies over time. The poor ability to maintain attention leads to a high variation of brain response. Therefore, an analytical method to measure the variation would enable us to objectively estimate the subject’s ability to control attention, to differentiate cases with attention deficit typically those with attention deficit hyperactive disorder (ADHD) from normal healthy subjects, and to monitor their response to therapeutic interventions. In addition to the within-individual variability, the between-individual variability of brain activity measured at the scalp would reveal inter-individual variations of characteristics like skull conductivity [3]. Our method described in this paper will enable us to measure the intra-individual variability of brain response as well as the inter-individual variability in the group analysis.

An efficient technique to monitor brain neural activity with a good signal-to-noise ratio is steady-state evoked potential (SS-EP) [4], [5], [6]. SS-EP, whether visual, auditory, or somatosensory, includes stereotypic changes of electrical activity evoked by rapid repetitive stimuli [7]. SS-EP response is thus confined to a specific set of frequencies. The temporal variation in frequency components is in both amplitude and phase, and there may be a correlation between amplitude and phase. Given that the variation in either amplitude or phase corresponds to different underlying brain processes, we need an analytical method to measure the variation of frequency component using both amplitude and phase information together. That would enable us to measure the correlation between amplitude and phase both in the same microvolts (μV) unit. Given that the variation of frequency component is correlated with attention [8], an assessment of the variation in both amplitude and phase of frequency component would help explore neural correlates of attention as well as investigating the patho-neurophysiology of attention deficit.

Current statistics like T2circ statistics explore the variation of the real and imaginary components of Fourier measurements [9], but T2circ statistics assume that the real and imaginary parts are of equal variances and independent. It thus corresponds to the notion that the cluster of Fourier estimates is circularly symmetric in the complex plane. Our SS-EP-based analytical method described in this paper will measure the variation of frequency component and will enable us to test whether the cluster of Fourier measurements is circular in the complex plane. If one rejects the null hypothesis that Fourier estimates distribute circularly, one would be able to obtain two significantly different variations of Fourier measurements in the complex plane as the maximum and minimum variations. In such cases, we assume that the maximum variation correlates with an important fluctuation in brain function presumably as a function of attention. Our method will, therefore, reveal how significantly the subject’s attention varies over time. The present paper will focus on the information available to a single electroencephalography (EEG) electrode. We will present a simple case as a demo in Fig. 1.

In Fig. 1a, there are four red dots at (1, 0) on the complex plane where we arbitrarily shifted them slightly apart to make them visible. The red dots simulate Fourier measurements at a frequency of interest in the absence of noise. If we add symmetric 2-dimensional noise from 0.14 μV standard deviation to the red dots, they could be moved to the blue dots. The blue dots are located circularly around the mean. In Fig. 1b, we presented the same four red dots but two of the dots arbitrarily deviated from the two central dots. Now, the red dots simulate a fluctuation of the Fourier measurements presumably as a function of attention in the absence of noise from any other sources. If we add the same amount of noise to the red dots, they would be shifted to the blue dots. Thus, the variation of the blue dots in the vertical direction derives from unrelated neural activity or so-called noise, whereas the horizontal variation derives from two sources: fluctuating attention and noise. In this methodology paper, we will show how to characterize the cluster of Fourier estimates using eigenvectors, and how to test whether the cluster of Fourier estimates is circular around the mean estimate in the complex plane. We will explain our method in detail in the Methods section using Fig. 1b-d.

Section snippets

Step 1; getting amplitude and phase of the mean estimate

At the first step, the frequency component of interest is measured using the Fourier transform:Xf=V(t).e-i2πftwhere V(t) is the EEG data at a single electrode, and Xf is a single Fourier measurement transformed at frequency f in hertz (cycles/second) over time T in seconds where t is [1fs,2fs,3fs, …, T] and fs is the sampling rate of EEG recording system (samples/second). At any frequency of interest, the Fourier estimate Xf is a complex number. Written as Xf = r∙e, the amplitude r in μV is

Results

In this section, we will apply our method to simulated random data to demonstrate validity. We will test the difference between the Length and the Width, and we will present how the difference is influenced by the number of samples. Moreover, we will obtain the LWR as an estimate of circularity for the cluster of Fourier measurements and show that the LWR, unlike covariance, is independent of the Phase of the mean estimate.

Discussion

Dynamic brain activity during neuroscience experiments and clinical trials produces variations in the neural response independent of the stimuli used in the studies [1]. Since SS-EP enables us to monitor the brain response to stimuli with a good signal-to-noise ratio, it is of particular interest to record the variability of the neural response. Variations in amplitude and phase of frequency component over time may correspond to fluctuations in the subject’s attention level [8]. Our method

Conclusion

In this methodology paper, we showed how to measure the variation of frequency component and how to test whether Fourier measurements at a frequency component distribute circularly in the complex plane using the difference between the maximum and minimum SDs of the Fourier estimates. A significant difference would reveal a meaningful fluctuation in brain activity. If the fluctuation is confirmed to be correlated with the subject’s attention, our method will help investigate the neural

Funding sources

This work was supported by Cognitive Sciences & Technologies Council [Grant No. 2096].

CRediT authorship contribution statement

Amir Norouzpour: Software, Validation, Formal analysis, Investigation, Resources, Writing – original draft, Visualization, Funding acquisition. Stanley A. Klein: Conceptualization, Methodology, Validation, Formal analysis, Resources, Writing – review & editing, Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (10)

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  • A complementary note for the analytical method to estimate individual attention fluctuation using steady-state evoked potentials

    2023, Biomedical Signal Processing and Control
    Citation Excerpt :

    As shown in Fig. 1, the blue dots represent T-second Fourier estimates at the frequency of interest where T is the duration of the time window used for the discrete Fourier transform. The details have been previously published [7]. Next, the Fourier estimates are fit using a mean-centered ellipse where the major and minor axes of the ellipse represent the maximum and minimum variations of the Fourier estimates on the complex plane respectively as shown by the dash-dotted lines in Fig. 1 [7].

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