Algorithmic localization of high-density EEG electrode positions using motion capture

Abstract

Background:

Accurate source localization from electroencephalography (EEG) requires electrode co-registration to brain anatomy, a process that depends on precise measurement of 3D scalp locations. Stylus digitizers and camera-based scanners for such measurements require the subject to remain still and therefore are not ideal for young children or those with movement disorders.

New method:

Motion capture accurately measures electrode position in one frame but marker placement adds significant setup time, particularly in high-density EEG. We developed an algorithm, named MoLo and implemented as an open-source MATLAB toolbox, to compute 3D electrode coordinates from a subset of positions measured in motion capture using spline interpolation. Algorithm accuracy was evaluated across 5 different-sized head models.

Results:

MoLo interpolation reduced setup time by approximately 10 min for 64-channel EEG. Mean electrode interpolation error was 2.95 ± 1.3 mm (range: 0.38–7.98 mm). Source localization errors with interpolated compared to true electrode locations were below 1 mm and 0.1 mm in 75 % and 35 % of dipoles, respectively.

Comparison with existing methods:

MoLo location accuracy is comparable to stylus digitizers and camera-scanners, common in clinical research. The MoLo algorithm could be deployed with other tools beyond motion capture, e. g., a stylus, to extract high-density EEG electrode locations from a subset of measured positions. The algorithm is particularly useful for research involving young children and others who cannot remain still for extended time periods.

Conclusions:

Electrode position and source localization errors with MoLo are similar to other modalities supporting its use to measure high-density EEG electrode positions in research and clinical settings.

1. Introduction

Electroencephalography (EEG) is a noninvasive technique that records electrical brain activity with high temporal resolution. Information collected by electrodes on the scalp can be used to estimate the underlying cortical sources, assuming sufficient scalp coverage, as described by the inverse problem of EEG (Grech et al., 2008). This spatial analysis of brain activation has important implications for diagnoses (e.g. assessing locations of seizures in epileptic patients), research (e.g. understanding brain activation patterns in developing children), and brain machine interfaces (e.g. designing mind-controlled communication tools or robotic prostheses). Accurate recording of scalp electrode locations and co-registration of the electrical potentials recorded from them to the brain anatomy are necessary to obtain meaningful source localization results (Dalal et al., 2014; Khosla et al., 1999; Van Hoey et al., 2000).

Several different technologies are currently available to measure EEG electrode locations, including stylus digitizers, camera-based 3D scanners, and 3D motion capture. Digitizers typically make use of electromagnetic fields or ultrasound to detect the location of a stylus, which is manually placed at each electrode to record the 3D coordinates of one location at a time. This method is subject to operator error and can also consume substantial time while the subject is wearing the EEG cap, typically at least 15 min (Taberna et al., 2019). Manufacturers of stylus digitizers report sub-millimeter errors; however, studies evaluating their use have reported mean errors ranging from 3.4 mm to 8.7 mm (Clausner et al., 2017; Dalal et al., 2014; Ettl et al., 2013; Whalen et al., 2008).

Photogrammetric tools, or camera-based 3D scanners, record the locations of electrodes by taking pictures of the head from different angles, minimizing acquisition time compared to the manual location collection of stylus digitizers. Acquisition times of 3D scanners are reported to be around 2 min (Koessler et al., 2011; Taberna et al., 2019). Although many photogrammetric techniques require additional post-processing steps to identify the electrode locations in the recorded images, the total time required for electrode localization may still be reduced compared to stylus digitization techniques (Homölle and Oostenveld, 2019; Taberna et al., 2019). Several studies have also found that these systems can result in lower electrode localization errors than the stylus digitizing devices, generally less than 2 mm (Clausner et al., 2017; Dalal et al., 2014; Taberna et al., 2019). In addition, there have been recent advances in which 3D scanners can be employed through pre-existing tools, such as the camera on an iPad, which can help to drastically reduce the cost compared to other specialized structured-light cameras (Homölle and Oostenveld, 2019; Shirazi and Huang, 2019). However, photogrammetry methods are variable and largely non-standardized, which makes it challenging to validate custom algorithms developed in individual labs. The accuracy of these tools is also highly dependent on the quality, quantity, and positioning of the cameras, as well as the electrode detection algorithm used (e.g. manual detection vs. highly automated processes) (Clausner et al., 2017; Homölle and Oostenveld, 2019; Shirazi and Huang, 2019).

While there are multiple methods to locate EEG electrode positions, some may be better suited for young or impaired populations than others. For example, when collecting EEG from infants and toddlers, fast electrode localization is important for the comfort and temperament of the subject, as well as for maximizing data collection time. Other nuances in infant populations such as varying infant head shapes and developmental changes in head anatomy (e.g. skull thickness and conductivity) make accurate electrode localization even more important for subsequent source reconstruction in the infant population (Noreika et al., 2020).

Motion capture offers the least disruption to participants since the locations of reflective markers placed on top of electrodes can be recorded in a single frame after the EEG cap is in place (Reis and Lochmann, 2015). Motion capture demonstrated the best reliability and smallest variability (submillimeter differences between trials) in a study that compared it to stylus digitization by ultrasound and 3D scans (Shirazi and Huang, 2019). However, similar to the digital stylus technique, placing these reflective markers on each electrode is typically done after all electrodes have been inserted in the proper-sized cap and this can add significant setup time, particularly in high-density EEG (more than 32 channels). From our own experience, placing markers on 64 electrodes can take around 10–15 min, which may impinge on data collection time especially for less compliant or more involved participants. To address this issue, we developed a novel algorithm which uses spline interpolation in tandem with the previously established 10–10 international system EEG electrode systems (“American Electroencephalographic Society guidelines for standard electrode position nomenclature,” 1991) to extract high-density channel locations from the smallest possible subset of electrode positions measured with motion capture. The goal of the algorithm, named MoLo (short for More Locations), is to generate reliable estimates of unmarked electrode locations. This paper describes the development, implementation and evaluation of the accuracy of the MoLo interpolation algorithm compared to 64 electrodes each with a reflective marker across a broad range of EEG cap sizes. The ultimate goal was to reduce EEG setup effort and time to maximize data collection time, while maintaining accuracy of electrode locations for determination of cortical sources of activation.

2. Materials and methods

2.1. Electrode localization

2.1.1. MoLo electrode interpolation

To accomplish the first aim of developing a custom algorithm with a reduced set of motion capture markers in a 64 channel EEG system, we first investigated the accuracy of different interpolation patterns along natural cubic spline lines (MATLAB, Mathworks, Natick, MA) defined by the 10–10 international system. Initial trials along individual splines (e. g. from the nasion to the inion as shown in step C of Fig. 1) showed that the interpolation of more than one missing electrode along the curve between two adjacent locations resulted in drastically higher error than the interpolation of only one missing electrode. With this knowledge and the decision to interpolate in steps, building on previously-interpolated locations, the smallest subset was determined for the placement of motion capture markers. For an algorithm based on interpolating only one missing electrode between two adjacent locations in a 64-channel montage, the minimum number of electrode locations in the initial subset is 26. The nasion and left and right preauricular points were also included in the subset for interpolation to align electrodes with subject anatomy, resulting in 29 marked locations as indicated by yellow circles in Fig. 1.

Fig. 1.

Locations recorded by motion capture (top panel, left) are used by MoLo to compute the full set of electrodes (top panel, right) in 6 iterative steps (bottom panel, a-g). Newly interpolated electrodes (solid light blue circle) are those computed in the current iteration. Previously interpolated locations (yellow circle with blue outline) are used in the computation of neighboring electrodes in iteration steps c, e, f, and g.

With this reduced subset of electrode and anatomical positions, we iteratively used the spline algorithm to calculate 3D curves along the 10–10 system and interpolate missing electrodes along the curves. In each step of the algorithm, a spline is computed from the relevant initial subset locations (Fig. 1). The first step (Fig. 1b) utilizes only measured locations (shown as yellow circles in Fig. 1) for spline computation; missing electrodes are then interpolated along the spline (shown as blue circles). Interpolation then proceeds in a stepwise manner using measured or previously interpolated locations (shown as yellow circles with a blue outer ring) to compute successive splines in the following order (Fig. 1a–g): outer ring, inner ring, column four, columns two and six, row three, rows two and four, rows one and five. All electrodes were referenced to the origin, defined as the midpoint of the left and right preauricular points in the MoLo algorithm. The interpolation algorithm demonstrated in Fig. 1 has also been implemented in a graphical user interface (GUI) available for download (see Appendix A).

We then evaluated our custom interpolation algorithm for accuracy. For this, we used motion capture to record the locations of reflective markers placed on top of each electrode on five 3D head models across a wide range of sizes (42 cm–58 cm circumferences) and calculated the Euclidean distance between the true locations, collected via motion capture, and their corresponding interpolated locations.

2.1.2. Head models

Five different sizes of physical 3D head models (Table 1) were used in this study to determine the accuracy of MoLo’s interpolation scheme. The 42 cm and 46 cm circumference heads were 3D printed from an infant model (CGTrader, New York, NY). The 50 cm (Alexnld.com, Tiberias, Israel), 56 cm (JF Corps, Santa Fe, CA), and 58 cm circumference heads (RoxyDisplay, East Brunswick, NJ), were commercially available mannequin heads constructed from foam (50 cm) and plastic (56 cm, 58 cm). These size increments were chosen to assess MoLo across a range of head sizes spanning from infancy through adulthood. The EEG cap size used in each collection matched the size of the corresponding head phantom (i.e. 42 cm circumference cap with 42 cm circumference head). Each head model with the EEG cap in place can be seen in Fig. 2.

Table 1.

3D head model specifications used to assess MoLo interpolation accuracy in full range of ages.

Head Circumference	Typical Age (50th Percentile Circumference)		3D Head Model
	Male	Female
42 cm	4 monthsa	5.5 monthsa	3D printed
46 cm	11 monthsa	15.5 monthsa	3D printed
50 cm	3 years, 8 monthsb	5 yearsb	Foam mannequin
56 cm	Teen to Adultc	Adultc	Plastic mannequin
58 cm	Adultc		Plastic mannequin

^a(CDC).

^b(WHO).

^c(Bushby et al., 1992).

Fig. 2.

Head models (42 cm, 46 cm, 50 cm, 56 cm, 58 cm circumference from left to right) were prepped with an active, 64-channel EEG system with all electrodes marked for position measurement in motion capture. The enlarged picture on the left shows the location of the reflective motion capture marker on top of a single electrode.

We also evaluated the MoLo interpolation algorithm using previously-established electrode templates in order to better assess interpolation accuracy without potential motion capture error. We extracted the initial subset of locations for interpolation from two different templates: one realistic, based on a canonical MRI (Oostenveld and Praamstra, 2001) and one ideal, from a spherical model (Brain Products, Morrisville, NC).

2.1.3. EEG

A 64-channel actiCap EEG system was used with each head model for the collection of electrode locations (Brain Products, Morrisville, NC). As can be seen in Fig. 2, the caps used on the two largest head models (56 and 58 cm) allow for collection of 128-channels. However, only the 64-channel set corresponding to the 10–10 international system was used with each head model. To ensure consistent cap placement, the total distance from the nasion to inion was measured and the ground electrode on the cap was placed 10 % of this distance from the nasion.

2.1.4. Motion capture

We collected all electrode locations in motion capture to use as the gold standard to assess the accuracy of the interpolated locations. Motion capture (Vicon Motion Systems, Denver, CO) was used to record a total of 69 locations on each head model: 66 electrode locations (10–10 international system of 64 plus a ground and reference), as well as 3 anatomical positions (nasion and left and right preauricular points) in order to co-register the electrode locations with each head model. Each location was marked with a 4 mm diameter solid hemisphere covered with reflective tape attached to a 6 mm diameter plastic base. Markers were attached to the top surface of the EEG electrodes using double-sided tape and were positioned so that the edge of the base was tangent with the outer rim of the gel channel (Fig. 2). The Cartesian coordinates of the markers were recorded with a Vicon Vantage system with V16 cameras at 100 Hz. Twelve cameras were arranged around the perimeter of the collection room and calibrated according to the manufacturer’s instructions. The system detects the center point of the hemisphere markers and records the corresponding 3D coordinates. After the 3D locations were recorded, the markers were manually identified and labeled in Nexus software (Vicon Motion Systems, Denver, CO). The Cartesian (x,y,z) coordinates obtained from the motion capture collection were used to assess the accuracy of interpolated locations from MoLo.

2.2. Source localization errors

2.2.1. Data

To assess the effect of electrode position errors on dipole source localization, the Talairach coordinates of the equivalent dipoles fit using measured and interpolated electrode locations were compared using a pediatric EEG dataset collected previously in our laboratory.

Data from 15 healthy volunteers (mean age = 13.8 years, age range =8–18 years, 6 females, 9 males) who had participated in a study on upper limb motor performance in participants with and without bilateral cerebral palsy were utilized in the source localization analysis. The study protocol (#13-CC-0110) was approved by the institutional review board of the National Institutes of Health and data from the upper limb motor performance tasks are being analyzed separately and will be published elsewhere. Written consent was obtained from all participants or legal guardian if under 18, in which case assent was also obtained. The data were from an upper limb task in which participants were instructed to press an LED button upon its illumination. Participants completed two sets of 25 trials for each arm (100 total trials) in the button-press task while EEG data were collected at 1000 Hz. All datasets included 64 EEG electrodes each with reflective markers locations determined from 3D motion capture.

2.2.2. EEG processing and dipole fitting

Recorded EEG data were processed in MATLAB using EEGLABv14 functions (Delorme and Makeig, 2004). As the signal processing steps are not the focus of this paper, they will be summarized in brief but generally followed a previously established pre-processing approach (Bulea et al., 2015). EEG data were labeled with the button-pressing events gathered from the kinematic data, high pass filtered at 1 Hz, resampled to 250 Hz, concatenated within each participant to create a single data file, and re-referenced to a common average. Adaptive mixture independent component analysis (Palmer et al., 2008) was applied to the datasets to identify event-related cortical components. Lastly, the EEGLAB DIPFIT toolbox, which deployed a boundary element model and the Montreal Neurological Institute (MNI) template MRI (Montreal Neurological Institute, Quebec, Canada), was used to fit equivalent dipoles to each independent component (Oostenveld and Oostendorp, 2002).

For each participant, 66 electrode channel locations (64 channels plus ground and reference) were extracted from a standard 10–5 international system location file (Brain Products, Morrisville, NC), an extension of the previously described 10–10 system but containing the same base set of 66, and warped to an MNI template. To assess the effect of MoLo electrode position interpolation error on source localization, dipole fitting was run twice on each participant: once with the original 66 channel locations as defined above, and again using interpolated channel locations obtained using MoLo. Source localization error for each dipole was defined as the Euclidean distance between the 3D coordinates of the dipole computed from the true and interpolated electrode locations in MNI space.

The residual variance of each dipole, computed as the amount of scalp-projected variance of each independent component that cannot be accounted for by the projection of a single equivalent dipole, was also examined between the interpolated and true electrode positions. To assess the localization error distribution after excluding non-physiological dipoles, a second analysis of dipoles with less than 20 % residual variance (Bulea et al., 2015; Gwin et al., 2011) and with a topographical sparseness measure greater than 5 (Melnik et al., 2017), was conducted. We also examined the relationship between source localization error magnitude and dipole location by computing the three-dimensional Euclidean distance between each dipole location and the center of the MNI coordinate system, which is defined as the location of the anterior commissure.

3. Results

3.1. Electrode localization

A representative 3D plot produced by the MoLo graphical user interface shows a top view of the interpolation results (Fig. 3). The yellow circles are the initial subset and the blue circles are the interpolated electrode positions. The black lines correspond to the natural cubic spline functions that were calculated using the initial subset of electrodes in accordance to the 10–10 international system.

Fig. 3.

MoLo graphical user interface with 3D plot of interpolated electrodes from the 42 cm head model. The black curves are the natural cubic spline lines calculated from the locations of the initial subset. Yellow circles represent the initial subset of recorded locations. Blue circles represent those electrodes that have been interpolated. User follows steps 1–4 to obtain the full set of locations. Step 3 allows users to subtract the electrode offset from the 3D locations.

Interpolation by MoLo reduced setup time by up to 10 min compared to placing markers on every electrode in the 64 channel setup. The mean electrode position error across the five head models ranged from 2.67 to 3.40 mm. The smallest and largest individual electrode error recorded across all head models were 0.38 mm and 7.98 mm, respectively (Table 2). Errors from each head model were normally distributed, confirmed by the Shapiro-Wilk test of normality (alpha = 0.05). A one-way ANOVA test showed no statistical difference (alpha = 0.05) between mean errors across head sizes. We also report localization errors calculated from two electrode templates, one from a realistic MRI in MNI coordinates and another based on a spherical head model (Table 2).

Table 2.

Electrode localization errors across all interpolated electrodes within each head model.

	3D Head Models					Electrode Templates
	42 cm	46 cm	50 cm	56 cm	58 cm	Realistic	Ideal
Mean (mm)	2.67	2.86	2.81	3.40	3.00	2.37	1.47
Std (mm)	1.12	1.02	1.09	1.60	1.41	1.18	1.16
Min (mm)	0.44	1.05	0.91	0.76	0.38	0.34	0.05
Max (mm)	4.76	5.21	5.03	7.98	6.07	4.81	3.64

Electrode errors resulted in a grand mean of 2.95 ± 1.3 mm, calculated from errors from the five physical head models. The cumulative distribution of all interpolated electrode errors across all head models was not normally distributed (Fig. 4), as tested with the Shapiro-Wilk test of normality (alpha = 0.05), but was skewed to the right (skewness factor of 0.61). This indicates that the errors are not symmetric around the mean, and tend more towards the lower-error region (0–4 mm) than the higher-error region (4–8 mm). Topographically, electrodes that exhibited the highest error across all head models were toward the front of the head (i.e., FPz and AFz locations) as indicated with a bracket in Fig. 5.

Fig. 4.

Histogram showing electrode localization errors (mm) across all five head models. The bulk of the error lies within 2–3 mm range, with a grand mean of 2.95 mm. The dashed lines represent the 50, 68, and 95 percentiles.

Fig. 5.

Scalp topography showing mean errors (mm) and standard deviation bars for each interpolated electrode position across all five head models. The highest error locations were the bracketed FPz and AFz channels.

3.2. Source localization

Source localization with the interpolated electrode locations compared to localization with true electrode locations resulted in 90 % of the dipoles exhibiting error (calculated as the Euclidean distance in Talairach coordinates) less than 1 cm, 75 % of the dipoles with error less than 1 mm, and 35 % with error less than 0.1 mm. The median error from source localization was 0.22 mm, while the mean error was 2.88 mm (Fig. 6).

Fig. 6.

Dipole localization errors that resulted from interpolated electrode errors in the millimeter range. The top histogram (A) includes the full range of dipole error, including several outliers, with the largest being 78 mm. The bottom histogram (B) omits these outliers to visualize errors below 3 mm.

We aimed to assess whether high-error dipoles exhibited increased residual variance values, calculated as the variance projected at the scalp that cannot be accounted for by the projection of a single dipole. Because dipoles with large residual variance (greater than 20 %) are typically considered non-cortical and omitted from further analysis (Bulea et al., 2015; Gwin et al., 2011), we sought to determine if the high-error dipoles in our results would fall into the same category and to what effect varying thresholds of “high” errors impacted results. To do so, we assessed the residual variance distributions of “high” versus “low” error dipoles at increasing thresholds (0.1 mm, 1 mm, and 10 mm). We calculated the means and skewness values for each of the high-error distributions shown in Fig. 7 to better assess the relationship between dipole location error and residual variance. We found that the high-error residual variance data were not normally distributed (Shapiro-Wilk test; alpha = 0.05), and a non-parametric Kruskal-Wallis test showed that there were differences between each of the medians (alpha = 0.05). This means that there was a significant shift in the distributions depending on the error cutoff used, and that choice of this threshold matters when analyzing the data.

Fig. 7.

All dipole residual variance distributions shown above are skewed to the right. High and low error distributions in plot A were assessed at a threshold of 0.1 mm, plot B at 1 mm, and plot C at 10 mm. Residual variance of dipoles with greater than 0.1 mm error (plot A) are most shifted towards the y-axis, whereas residual variance of dipoles with greater than 10 mm error (plot C) are least shifted towards the y-axis, indicating higher residual variance values in this distribution.

Skewness values for the orange high-error distributions in plots A, B, and C of Fig. 7 were 1.35, 1.31, and 0.95, respectively. Based on these values, dipoles with greater than 10 mm error (orange distribution in Fig. 7, plot C) exhibited the smallest skew towards the low residual variance range than did the other distributions (plots A and B).

In addition to our reporting on all computed sources, we subsequently removed non-physiological dipoles based on both residual variance and topographical sparseness measures for further analysis. The mean number of physiological dipoles remaining across all subjects was 19 +/− 6 dipoles, with a range of 11–31 dipoles. The mean localization error of only the physiological dipoles was 2.45 mm, which was not significantly different from the mean error computed before non-physiological dipoles were omitted (2.88 mm), as confirmed with a paired t-test (p = 0.45). The largest recorded error in this reduced set, 52 mm, was less than that of the full dipole set, which was 78 mm.

Fig. 8 shows error circles at the physiological dipole locations for all subjects from three different views of the MNI brain. Centrally-located dipoles exhibited smaller error than those located towards the exterior of the brain volume (Fig. 8). Yet, many of the dipoles located greater than 60 mm from the center (plotted in shades of red) still exhibited localization errors below 10 mm (plotted with small circles).

Fig. 8.

Coronal (A), sagittal (B), and top (C) views of the MNI brain to show the magnitude of localization error as a function of location at each physiological dipole position across all 15 subjects. The color range of the error circles represents the distance of each dipole from the center of the volume, defined as the anterior commissure, with black/reds indicating the furthest distances and white/yellows the closest. The size of the circle represents the error magnitude at the plotted location, with larger circles representing larger localization error.

We also explored the relationship between dipole distance from the origin and magnitude of localization error. Although no significant linear correlation was found between these two measures, all dipoles with greater than 5 mm error were found to be a minimum of 55 mm from the origin (Fig. 9).

Fig. 9.

Physiological dipole localization error versus distance from the center of the brain volume. The majority of dipoles exhibit errors well below 5 mm regardless of distance from origin. High-error dipoles (greater than 10 mm) are at least 55 mm away from the origin.

4. Discussion

4.1. Electrode localization

The accuracy of the MoLo electrode localization method using motion capture and spline interpolation (mean error 2.95 ±1.3 mm) is better than or comparable to other, pre-existing methods such as stylus digitizers (reported mean errors range from 3.4–8.7 mm; (Clausner et al., 2017; Dalal et al., 2014; Ettl et al., 2013; Whalen et al., 2008) and 3D scanners (reported mean errors under 2 mm; (Clausner et al., 2017; Dalal et al., 2014; Taberna et al., 2019), which are considered acceptable for clinical applications. In fact, the largest observed electrode error of 7.98 mm from MoLo is still less than other cases of reported mean errors when using stylus digitizers (Whalen et al., 2008). It is important to note that the reported errors here are calculated from the motion capture locations, taken as the gold standard, and therefore do not include error stemming from the motion capture collection itself or any potential marker displacement.

However, we predicted minimal contribution to the absolute error, given that motion capture has been shown to provide the most accurate electrode localization results, compared to both digitizers and 3D scanners (Shirazi and Huang, 2019). The manufacturer of the motion capture system we used has also reported submillimeter errors in its accuracy and precision tests, with the results posted on the Vicon website (Vicon, 2020).

We assessed electrode error with template locations to bypass the use of motion capture and therefore isolate the error stemming from MoLo interpolation alone. We tested two templates, one from a realistic MRI in MNI coordinates and another based on a spherical head model, obtaining mean errors of 2.37 ± 1.18 mm and 1.47 ± 1.16 mm, respectively. Comparing our own 3D head model mean error to that from the realistic model (2.95 vs. 2.37 mm), it appears as though contribution to the absolute error due to the motion capture collection is minimal and that our reported errors from the five 3D head models provide a reasonable estimate of MoLo interpolation uncertainty. It was also not surprising that lower interpolation errors were found using the spherical model, because interpolation on a uniform shape is more consistent than on a realistic head model.

Motion capture requires collection of only one image to measure electrode marker position and thus acquisition time is substantially shorter compared to the average acquisition time of both stylus digitizers (15 min) (Taberna et al., 2019) and 3D scanners (2 min) (Koessler et al., 2011; Taberna et al., 2019). For this reason, use of motion capture is particularly beneficial in young children who may not be able to sit completely still for more than a few seconds. However, motion analysis setup requires that the markers be placed over the electrodes. In our experience, implementation of MoLo interpolation has reduced our setup time by up to 10 min compared to placing markers on all 64 electrodes. In cases where the cap size is already known (e.g. in longitudinal studies), both the electrodes and markers can be placed in the cap in advance; in that case, this algorithm would still be beneficial in reducing experimental preparation time and effort.

No significant differences in mean errors of the interpolated electrode locations were seen across the five 3D head models. This demonstrates that the accuracy of MoLo interpolation is not sensitive to head size and suggests that the algorithm is suitable for use across a broad age range. Future work will focus on algorithm validation in human participants from infancy to adulthood. However, there were error differences at specific electrode locations. The largest mean electrode localization errors were found to occur at the FPz and AFz electrode locations (indicated with the bracket in Fig. 5). We postulate that this is because of the proximity to the nasion, which is used to calculate the spline curve from the nasion to the inion locations. The nasion position was manually marked on the head model, and is not a position built into the EEG cap. It is therefore possible that the variability of the nasion marker placement relative to the EEG cap contributed to this observed higher error in the calculation of the FPz and AFz electrode locations along the nasion-inion spline.

Initial trials showed that the interpolation of more than one missing electrode along the curve between two adjacent locations resulted in drastically higher error than the interpolation of only one missing electrode. We performed interpolation of this kind along the calculated splines in accordance with the 10–10 international system (64 electrodes) and found that the error was more than doubled in many cases. With this knowledge, the interpolation scheme was constructed to calculate the location of every-other electrode for a single iteration of the algorithm. Overall, 14 interpolated locations were used in downstream calculations of other electrode coordinates. We saw no difference in localization error of neighboring electrodes computed from previously interpolated locations, indicating that this approach in the interpolation algorithm does not sacrifice localization accuracy. This finding may have important implications for the extension of the MoLo algorithm to compute locations in even higher-density EEG setups, e.g., 128 or 256 channels. Because these higher-density setups have extra splines in addition to those in the 10–10 international system, it would be necessary to incorporate these calculations into the algorithm. It should be possible to build upon the results of MoLo using the initial subset of 29 positions to compute these new positions in higher-density setups, helping to reduce setup time relative to the total number of electrodes by marking the same number of starting positions.

Further, there are several ways we believe the setup time could be reduced while the subject wears the cap. Although in our presented method markers for detection in motion capture were placed on the electrodes after the cap had been fitted on the subject, this step could potentially happen prior to cap placement. However, extra caution would be required to ensure none of the markers fall off during the cap adjustment and gelling steps. This change could be especially beneficial for longitudinal or multi-visit studies where the head size is known ahead of time, so that the cap and electrodes could be fully prepped before the subject arrives, therefore eliminating the setup time while the subject is wearing the cap. Another avenue to minimize the setup time for the localization of 64 EEG channels involves reducing the required number of electrodes in the initial subset that must be marked. This change to the MoLo algorithm could be implemented with further customization of the code and necessary validation. It is expected that this could affect the accuracy of the electrode localization results, however this would help to further reduce setup time and may be beneficial in cases of EEG systems with fewer than 64 electrode channels.

4.2. Source localization

After quantifying and characterizing electrode localization errors on part of the MoLo algorithm, we sought to assess the effects on dipole source localization. Previous studies have also considered source localization accuracy by comparing different electrode localization tools, generally finding that the tools with the least reliable electrode localization results produced greater source estimation uncertainties (Homölle and Oostenveld, 2019; Shirazi and Huang, 2019). The first study found that the most accurate electrode localization method tested (mean error: 9.4 mm) resulted in the lowest source errors (mean: 7 mm) (Homölle and Oostenveld, 2019), while the second study found the best electrode position reliability with reported source uncertainty (mean error: 1.5 mm) to also produce the lowest source errors (mean: 3.44 mm) (Shirazi and Huang, 2019). Our results point to the same conclusion, as our electrode errors (mean: 2.95 mm), which are less than many of those reported in the aforementioned studies, also resulted in lower source uncertainties (mean: 2.88 mm, median: 0.22 mm). Additionally, the mean dipole source location error was slightly but not significantly lower (mean: 2.45 mm) when non-physiological dipoles were removed.

Our decision to use a boundary element model based on the MNI template brain was informed by findings (Akalin Acar and Makeig, 2013) showing that the BEM MNI template resulted in the smallest source localization errors compared to other various template head models. Using this model, the smallest median source localization errors were reported in the 4.1–6.2 mm range. The median source localization error obtained here was 0.22 mm, meaning that there is greater inherent error during use of the BEM MNI method itself for source localization than due to error from MoLo interpolated electrodes. The source localization errors obtained with MoLo interpolated electrodes are therefore well-within published errors when using a BEM MNI template, indicating that interpolation did not negatively affect the accuracy of dipole localization and should therefore allow accurate spatial analysis of brain activity.

Characterization of various high-error dipoles and their respective residual variance values showed that these distributions were sensitive to the high-error threshold we chose to analyze. We found that dipoles with greater than 10 mm error were the least skewed towards the low residual variance range compared to the other distributions (greater than 1 mm, and 0.1 mm), pointing to a positive relationship between the magnitude of the dipole error and the corresponding residual variance which could help inform decisions about omitting dipoles for further analysis. Spatial analysis of only physiological dipoles, as determined by residual variance and topographical sparseness thresholds, demonstrated that although there was no significant correlation between the dipole distance from the center of the brain volume and localization error, all dipoles with greater than 5 mm error were at least 55 mm from the origin (Fig. 9). To aid interpretation of the dipole locations, we estimated the Euclidean distances from the origin (defined as the anterior commissure) to the closest and farthest points of the cortical surface in the BEM MNI template used in our dipole fitting method. These distances, roughly 22 mm and 106 mm respectively, align with the results in Fig. 9, demonstrating most dipoles are localized within the cortex. Of course, these distances only approximate the cortical extremes, because the brain is non-spherical. Therefore, it is possible that a few dipoles within the 22 mm–106 mm range could still fall outside of the cortex, e.g. a dipole which is 105 mm from the origin in the frontal lobe may be positioned beyond the cortical surface whereas one at a 105 mm radius in the parietal lobe may be within it.

In addition to errors associated with the interpolated electrode misplacements and inherent errors associated with the use of the BEM MNI template, there are other forward model errors that may result in source localization inconsistencies, e.g. those due to electrode co-registration to the brain volume (Akalin Acar and Makeig, 2013), limited electrode positions in low-density montages (Laarne et al., 2000), and errors caused by noisy channels (Wang and Gotman, 2001). These forward model errors should also be considered during the analysis of EEG information and source localization results, and are acknowledged here to further highlight the importance of obtaining accurate electrode locations for consequent source reconstruction.

4.3. Implications

While used with motion capture in this study, the MoLo algorithm could be deployed with other tools, e.g., a stylus digitizer or 3D scanner, to extract high-density electrode locations from a subset of measured EEG electrode positions. However, the accuracy of MoLo with these other modalities should be validated prior to implementation. We also suggest first assessing the accuracy of the pre-existing electrode localization tool alone prior to quantifying accuracy of the MoLo interpolation.

Although the algorithm is currently designed to work with 64-channels, we believe it could be extended to higher-density setups (e.g. 128, or 256) through the introduction of additional spline curves. The accuracy of such extensions remain to be tested, however, we expect that the interpolation accuracy with increased electrodes will remain clinically acceptable since we have also shown that the computation of neighboring electrodes using previously interpolated positions does not reduce accuracy.

In summary, the accuracy of the interpolation results is comparable to that of other electrode localization tools which are considered acceptable in clinical and research settings. In addition, the consequent dipole localization results are well within published errors of use of the boundary element model based on the MNI template head. MoLo interpolation algorithm reduced setup time by as much as 10 min, and was shown to be particularly beneficial for infant and toddler populations due to the minimal collection time during which the subject must remain still. In labs imaging younger or impaired subjects, or simply wishing to reduce the time required for the electrode localization process, MoLo is a viable tool, and can be extended to include the incorporation of other pre-existing electrode localization tools.