Pulsation artifact removal from intra-operatively recorded local field potentials using sparse signal processing and data-specific dictionary

Abstract

Neural recordings frequently get contaminated by ECG or pulsation artifacts. These large amplitude components can mask the neural patterns of interest and make the visual inspection process difficult. The current study describes a sparse signal representation strategy that targets to denoise pulsation artifacts in local field potentials (LFPs) recorded intraoperatively. To estimate the morphology of the artifact, we first detect the QRS-peaks from the simultaneously recorded ECG trace as an anchor point. After the LFP data has been epoched with respect to each beat, a pool of raw data segments of a specific length is generated. Using the K-singular value decomposition (K-SVD) algorithm, we constructed a data-specific dictionary to represent each contaminated LFP epoch in a sparse fashion. Since LFP is aligned to each QRS complex and the background neural activity is uncorrelated to the anchor points, we assumed that constructed dictionary will be formed to mainly represent the pulsation artifact. In this scheme, we performed an orthogonal matching pursuit to represent each LFP epoch as a linear combination of the dictionary atoms. The denoised LFP data is thus obtained by calculating the residual between the raw LFP and its approximation. We discuss and demonstrate the improvements in denoised data and compare the results with respect to principal component analysis (PCA). We noted that there is a comparable change in the signal for visual inspection to observe various oscillating patterns in the alpha and beta bands. We also see a noticeable compression of signal strength in the lower frequency band (<13 Hz), which was masked by the pulsation artifact, and a strong increase in the signal-to-noise ratio (SNR) in the denoised data.

I. Introduction

Local field potentials (LFPs) are electrical potentials generated in the extracellular space around a group of neurons and can be assessed in deep brain structures with implanted electrodes such as deep brain stimulation (DBS) leads. In order to properly deploy electrodes at the desired targets and select electrode contacts for DBS, these recordings are essential for estimating and predicting various key parameters [1], [2]. LFPs recorded from DBS leads can serve as a neuro biomarker in movement disorders such as Parkinson’s disease (PD), and essential tremor (ET) [1], [3]. Its functional utility in psychiatric disorders such as obsessive-compulsive disorder (OCD), and depression is now under investigation as well [4].

A number of groups have been working on various types of artifacts that corrupt the LFP recordings, such as movement artifacts, spiking activity, and electrocardiogram (EKG) artifacts [5]. A few articles show the recovery and reconstruction of LFP data, which is masked by the stimulation artifact of known frequencies and amplitudes [6]. In the last couple of decades, others have addressed the pulse artifact in the EEG recorded inside an MR scanner for EEG/fMRI studies. Most of them have used the period-based average artefact subtraction (AAS) method where the shape of each pulse is represented by the average of a few pulses before and after the current segment [7], [8]. Due to variability in shape at every beat, an average signal subtraction might not eliminate the artifact efficiently.

In this study, we highlight and discuss pulsation artifacts which are slow rhythms variable over multiple cardiac cycles that obscure the LFP. While pulsation artifacts occur with a rate of heartbeats, the resulting signal might have fast instantaneous fluctuations due to the rapid dynamics of the systolic cycle. Our observations indicate that such rapid local variations can have spectral leaks up to 10–13 Hz masking alpha-beta rhythms. Interestingly, we also see that the morphology of the pulsation artifact is different across channels in the same subject. We propose a method that generates a data-specific dictionary using K-singular value decomposition (K-SVD) that can be used to approximate each pulse in a sparse fashion where the residual represents the neural activity of interest. Figure 1 illustrates the schematic of the proposed method, each step involved in the algorithm is explained in later sections.

Fig. 1.

Schematic diagram of the proposed method. Initially, the raw data is extracted into epochs based on the QRS peaks. The K-SVD algorithm is used to learn a dictionary of atoms which are then used to represent the raw data epoch using OMP. The approximation is then subtracted from the raw LFP data, and the residual (denoised signal) was visualized.

II. Materials and Methods

A. Recording Cohort

Our study utilizes LFP data collected from four patients, of which two have PD and two have OCD. Data were recorded intraoperatively using the Summit amplifier (Ripple Neuromed, UT, USA) with Medtronic Sensight^™ directional deep brain stimulating leads (Model B33005). The data were collected under studies that were approved by the Institutional Review Boards (IRBs) at the University of Houston and Baylor College of Medicine. Informed consent was taken from the subjects before surgery, stating that the data would be used for research purposes.

B. Data acquisition and preprocessing

Neural data were collected from bilaterally implanted segmented DBS leads intraoperatively during awake brain surgery, and a lead-II EKG was recorded simultaneously. Raw LFP and EKG data were recorded at a sampling rate of 2 kHz. The recorded data were filtered using a 2^nd order IIR bandpass filter between 1 to 500 Hz and a notch filter at 60 Hz. The data was then down-sampled to 1 kHz before denoising. For the analysis, the raw LFP data were converted into a bipolar montage, and only those channels with pulsation noise were selected. The visualization, preprocessing, and analysis of the data were performed using MATLAB R2020a (MathWorks, Inc., MA, USA). The QRS-peaks from the recorded EKG were identified using a first derivative-based approach [9]. Then, the raw LFP data were epoched into 700ms segments aligned to the QRS-peaks from EKG as anchor points. To account for the temporal variation in the inter-beat intervals, we created two sets of epochs with different alignments. The first alignment was considered 100ms to the left and 600ms to the right of QRS peaks, and the second alignment was vice versa, as shown in Fig. 2(A). An example of epoched data for two different alignments is shown in Fig. 2(B–C).

Fig. 2.

Raw LFP Data and its average. (A) Epoch extraction using EKG R-peaks as the anchor shown on a raw data segment (B) Image representation for 590 epochs of a LFP channel, each row representing one epoch. (C) Overlap plot of all the extracted epochs and (D) Average of the extracted epochs.

C. PCA Denoising

Principal component analysis (PCA) is a linear transformation that is commonly used to reduce the dimensionality of a dataset, denoising electrophysiological data and medical images [10]. Here we use PCA to pick the eigenvectors with the highest variance, which served as a template for denoising. LFP data is epoched into segments of 700ms, and a 2D matrix $\mathit{X}\in {\mathrm{R}}^{\mathrm{B}\times \mathrm{M}}$ is formed where B is the number of beats and $\mathrm{M}$ is the number of samples. The eigenvectors of the covariance matrix

$$C=X^{T}X$$ (1)

were computed to determine the principal axes. The eigenvectors corresponding to the largest eigenvalues were selected as bases to be used for denoising. Initially, we used the first eigenvector with the highest variance as the template to denoise the data, as a simple template subtraction method. Next, we selected the top three eigenvectors as their corresponding eigenvalues appear before the elbow and used them as a dictionary to denoise the data. In order to match the raw LFP data for both segments, we constructed a train of approximated templates with respect to the anchor points and calculated their mean. Lastly, we calculate the residual by subtracting the template from the raw LFP data.

D. K-SVD Denoising

K-SVD is a generalized k-means clustering algorithm for sparse representation using a dictionary learned via singular value decomposition. These dictionary elements are referred to as signal atoms that can be used to describe the signal by sparse linear combinations of these atoms [11]. If $\mathit{X}$ is the pool of signals and $\mathit{D}$ is the learned dictionary elements, the K-SVD algorithm can be represented as,

$$\underset{D,\theta }{\mathrm{m}\mathrm{i}\mathrm{n}}\{\parallel \mathit{X}-\mathit{D}\mathit{\theta }{\parallel }_F^2\}subjectto{\forall }_i,{∥{\mathbf{\theta }}_i∥}_0\le T_0$$ (2)

The K-SVD algorithm iterates between sparse coding of the current dictionary through each column ${\mathit{\theta }}_i$ and a process to update the current dictionary to fit the data better. A random vector was used to initiate the learning process, and input data epochs were Z-score normalized. The algorithm is set to learn four dictionary atoms (based on the elbow curve) with two linear combinations for 20 iterations. We learned four atoms to shape the dictionary $\mathit{D}$ for every channel individually. Using each learned atom, we calculated the amount of energy that they account for in approximation and rejected those atoms that account for less than 15% of energy. The selected atoms are then smoothed with a Savitzky-Golay filter of 4^th order and then L2-normalized [12]. In order to represent each pulsation event with respect to the selected atoms, we use the greedy orthogonal matching pursuit (OMP) method [13]. The sparse representation of an event y using a linear combination of atoms in dictionary $\mathit{D}$

$$\underset{\alpha }{\mathrm{m}\mathrm{i}\mathrm{n}}\parallel \alpha {\parallel }_{0}subjecttoy=D\alpha .$$ (3)

In the OMP method, the maximum number of atoms to represent each epoch was set to two or three, and the residual was computed from each epoch as the denoised signal. The entire process was repeated for the second alignment. Then we averaged these reconstructed signals and smoothed the signal using a 4^th order sgolay filter.

E. Validation

We validated the method by comparing the signal-to-noise ratio (SNR) of the epoched data segments of raw and denoised LFP signals with respect to their averages. We take the ratio of the variance of the extracted epochs and their respective average for all the channels,

$$SN{R}_{dB}=10{log}_{10}\left(\frac{Var\left(epochs\right)}{Var(Avg(epochs\left)\right)}\right).$$ (4)

As an LFP signal tends to oscillate randomly, for a sufficiently large number of epochs, the average should represent a straight line at zero amplitude. Implying a good denoising method would have higher SNR. We also computed the power spectral density (PSD) of raw, denoised LFP and the reconstructed signal to show the frequency content of the pulsation artifact and the changes in the power spectrum in the signal after the denoising step.

III. Results

This study used raw LFP data from four subjects (two PD and two OCD). Each subject had at least 12 bipolar LFP channels that were corrupted due to pulsation artifacts. An example of the learned PCA-based signal templates for each alignment based on a single and three eigenvectors is shown in Fig. 3(A) & 3(B), respectively. These eigenvectors were further used to reconstruct the signal that mimics the pulsation pattern in both cases, as shown in Fig. 3(C) & 3(D). A sample LFP trace was denoised using the PCA denoising approaches, as shown in Fig 4. There is a clear reduction in pulsation morphology, although it still exists when a single eigenvector was used. If we observe the third signal shown in Fig. 3(C), the reconstructed template (black) does not appear to trace over the pulsation morphology in the LFP data (red). Due to the varying pulse duration of each beat, an entire signal cannot be approximated with a single eigenvector as we see in Fig. 5(A–C). On the counterpart, we get better results when three eigenvectors are used as shown in Fig. 5(D–F). We see a drastic improvement when three eigenvectors are used as shown in Fig. 5(F). The variability in the beat duration over a given time period was well represented.

Fig. 3.

Artifact Template. (A-B) Selected eigenvectors using PCA approach. (C-D) Approximated signal templates with PCA approach using one template and three eigenvectors respectively.

Fig. 4.

Denoised LFP data using the PCA approach. (A) Denoised data using one template. (B) Denoised data using three templates.

Fig. 5.

Denoised LFP Data and its average using the PCA approach with one (A-C) and three eigenvectors (D-F). (A,D) Image representation for 590 epochs of a denoised LFP channel. (B,E) Overlap plot of all the denoised epochs and (C,F) are the respective average of the denoised epochs.

An example of the learned dictionary atoms using the K-SVD algorithm is shown in Fig. 6(A). The learned atoms are used to approximate the raw signal epoch with the OMP method and thus reconstructing the signal, as shown in Fig. 6(B). Fig. 7 illustrates the results of denoising the data using a K-SVD algorithm. We see a noticeable reduction in noise attenuation. As shown in Fig. 6, the constructed template using the dictionary atoms appears well synchronized with the pulsation morphology of background raw LFP. Fig. 8 shows the extracted epochs and their average for the denoised data using the K-SVD approach. The results of the K-SVD approach and the three eigenvector PCA approaches are visually similar. Figure. 9 shows the PSD of the raw data, denoised data, and the templates developed to denoise. When compared to PCA, the K-SVD template decays faster and is much smoother. We show the signal-to-noise ratio in Table I for the four subjects we used in this study. We see that SNR for three eigenvectors PCA was higher compared to one eigenvector, and K-SVD approach was the highest.

Fig. 6.

Artifact Template. (A) Selected dictionary atoms using K-SVD approach. (B) Approximated signal template with K-SVD approach.

Fig. 7.

Denoised LFP data using the K-SVD approach.

Fig. 8.

Denoised LFP Data and its average using the K-SVD approach. (A) is the image representation for 590 epochs of an LFP channel from two different subjects. (B) is the overlap plot of all the denoised epochs and (C) is the respective average of the denoised epochs.

Fig. 9.

Power spectral density (PSD) plots. (A) PSD of raw and denoised data. (B) PSD of raw data and the templates used to denoise.

TABLE I.

Signal-to-noise ratio (dB) of different methods.

Subject	Raw Data	Denoising Method
		PCA - 1	PCA - 3	K-SVD
PI	3.09	12.81	20.15	20.87
P2	1.96	19.33	14.90	17.54
P3	1.19	19.05	22.03	22.57
P4	1.31	14.27	17.42	21.72

IV. Discussions

LFP data is a key biomarker to identify the type and severity of the underlining diseases in movement disorders and psychiatric indications. In our understanding, pulsation corrupting the LFPs is produced as the blood gets pumped into the brain where the resulting pressure changes might create micro-movements and/or induce capacitive effects due to changes in the volume surrounding the electrode surface that we refer to as the pulsation artifact.

As shown in the PSD plots of the denoised signals, we see a dominating lower band activity (<13 Hz) denoting the pulsation artifact, which is suppressed after denoising. We see that the templates constructed by the PCA approach have higher background activity and larger activity at 10–30 Hz frequency when compared to K-SVD (See Fig 9). This suggests that the PCA approach might also eliminate some of the actual LFP oscillations in the alpha-beta band range.

This study aimed to remove the pulsation artifact from the intra-op. LFP recording using PCA and K-SVD approaches. We showed the denoising results for both approaches and discussed our observations. We have also validated our algorithm using synthetic data that was not included in this paper.

Clinical Relevance—

Pulsation artifact can mask relevant neural activity patterns and make their visual inspection difficult. Using sparse signal representation, we established a new approach to reconstruct the quasiperiodic pulsation template and computed the residue signal to achieve noise-free neural activity.