Macroscale Traveling Waves Evoked by Single-Pulse Stimulation of the Human Brain

Abstract

Understanding the spatiotemporal dynamics of neural signal propagation is fundamental to unraveling the complexities of brain function. Emerging evidence suggests that corticocortical-evoked potentials (CCEPs) resulting from single-pulse electrical stimulation (SPES) may be used to characterize the patterns of information flow between and within brain networks. At present, the basic spatiotemporal dynamics of CCEP propagation cortically and subcortically are incompletely understood. We hypothesized that SPES evokes neural traveling waves detectable in the three-dimensional space sampled by intracranial stereoelectroencephalography. Across a cohort of 21 adult males and females with intractable epilepsy, we delivered 17,631 stimulation pulses and recorded CCEP responses in 1,019 electrode contacts. The distance between each pair of electrode contacts was approximated using three different metrics (Euclidean distance, path length, and geodesic distance), representing direct, tractographic, and transcortical propagation, respectively. For each robust CCEP, we extracted amplitude-, spectral-, and phase-based features to identify traveling waves emanating from the site of stimulation. Many evoked responses to stimulation appear to propagate as traveling waves (∼14–28%, ∼5–19% with false discovery rate correction), despite sparse sampling throughout the brain. These stimulation-evoked traveling waves exhibited biologically plausible propagation velocities (range, 0.1–9.6 m/s). Our results reveal that direct electrical stimulation elicits neural activity with variable spatiotemporal dynamics that can be modeled as a traveling wave.

Significance Statement

Using single-pulse stimulation, we identify a subset of intracranial-evoked potentials that propagate as neural traveling waves. Our results were robust across a range of distinct but complementary analysis methods. The identification of stimulation-evoked traveling waves may help to better characterize the pathways traversed by spontaneous, pathological, or task-evoked traveling waves and distinguish biologically plausible propagation from volume-conducted signals.

Introduction

With the advent of multisensor brain imaging, brain signals have been revealed to propagate in space and time (Prechtl et al., 1997). These so-called neural traveling waves—spatiotemporally organized patterns of neural activity with a wave-like motif of propagation—have gained increasing interest over the past decade (Muller et al., 2018; Foster and Scheinost, 2024). In recent years, the concept of neural traveling waves has extended beyond that of cortical oscillations and now encompasses other forms of evoked signals (Aggarwal et al., 2022; Smith et al., 2022; Yearley et al., 2024) and coordinated functional activity (i.e., brain states; Foster and Scheinost, 2024).

Neural traveling waves are ubiquitous, showing important roles during development (Schoch et al., 2018), sleep (Muller et al., 2016), epileptic activity (Alarcon et al., 1997; Smith et al., 2016, 2022; Martinet et al., 2017; Yearley et al., 2024), cognitive states (Zhang et al., 2018; Mohan et al., 2024), and evoked sensory activity (Muller et al., 2014; Zhaoyang et al., 2020; Aggarwal et al., 2022). Mesoscopic waves typically propagate at speeds from 0.1 to 0.8 m/s, reflecting axonal conduction delays (Girard et al., 2001). While traveling waves have generally been characterized in oscillations across a two-dimensional grid of sensors, they have also been observed in three-dimensional space (Yearley et al., 2024).

Corticocortical-evoked potentials (CCEPs) provide causal insight into the effective connectivity of the brain (Keller et al., 2014b). These responses to single pulses of electrical current applied directly to the human brain have been used for many different applications—for example, localizing epileptogenic tissue and seizure spread (Valentín et al., 2002; Lega et al., 2015; Matsumoto et al., 2017), mapping distinct types of connectivity (Entz et al., 2014; Keller et al., 2014a; Crocker et al., 2021a), quantifying signal complexity across levels of consciousness (Comolatti et al., 2019; Arena et al., 2021, 2022; Mofakham et al., 2021), and tracking the effects of stimulation on neural plasticity (Keller et al., 2018; Huang et al., 2019). Researchers have begun to investigate the temporal properties of CCEPs, characterizing the relationship between the amplitude and latency of the early N1 component (10–50 ms) and axonal conduction delays resulting from the underlying white matter architecture (Trebaul et al., 2018; Silverstein et al., 2020; Lemaréchal et al., 2021). For example, a recent study that combined CCEPs with tractography reported considerable age-related changes in the transmission speed of corticocortical signals (Blooijs et al., 2023). Emerging evidence suggests that the temporal dynamics of CCEPs may also provide novel insights into the patterns of information flow between and within brain networks (Veit et al., 2021; Seguin et al., 2023).

In this study, we employed contemporary methods to test the hypothesis that single-pulse stimulation of the human brain evokes neural traveling waves. We found that, indeed, a large proportion of CCEPs met the definition of traveling waves and characterized their patterns of propagation across the brain surface and through white matter tracts. Our findings were robust across distinct but corroborative analysis methods that capture different characteristics of the evoked response (i.e., amplitude, spectral power, phase). Taken together, these results highlight a previously uncharacterized response to direct electrical stimulation. Showing that CCEPs behave as traveling waves open the possibility of using these evoked potentials to characterize the pathways trod by spontaneous, pathological, or task-related traveling waves. Furthermore, biologically plausible propagation may be used as a method of discriminating authentic, local CCEPs from artifactual or volume-conducted CCEPs, improving the spatial and temporal localization of these electrophysiological markers.

Materials and Methods

Participants

Twenty-one adult patients with medically intractable epilepsy (n = 7 female) underwent intracranial monitoring with stereoelectroencephalography (SEEG) to localize their seizure foci (Table 1). We performed stimulation mapping while patients were off their antiseizure medications during their inpatient hospital stay. Results from some of these stimulation sessions were reported in prior studies of evoked potential recordings (Kundu et al., 2020; Davis et al., 2021a). All patients provided informed consent prior to participation, and our team took care to implement the recommended principles and practices for ethical intracranial neuroscientific research (Feinsinger et al., 2022). The study was approved by the University of Utah Institutional Review Board.

Table 1.

Demographics and clinical characteristics of the patient cohort

Patient ID	Age (yrs.)	Sex	Electrode (no.)	Stimulated (no. %)	SPES (no.)	SOZ
P1	25.5	M	56	56 (100%)	448	Bilateral mesial temporal lobe
P2	25.9	M	97	94 (96.9%)	940	None identified
P3	35.3	F	81	81 (100%)	648	Right hippocampus
P4	44.3	M	69	69 (100%)	966	Right hippocampus
P5	42.4	F	48	48 (100%)	480	Right OFC
P6	42.2	F	54	54 (100%)	540	None identified
P7	35.6	F	28	24 (85.7%)	240	Right MFG
P8	45.0	M	52	52 (100%)	520	None identified
P9	41.7	F	30	23 (76.7%)	1150	Bilateral mesial temporal lobe
P10	29.1	F	39	28 (71.8%)	1400	Bilateral mesial temporal lobe
P11	33.2	M	40	36 (90.0%)	1800	Left temporal
P12	27.5	M	46	38 (82.6%)	1634	Right OFC
P13	22.7	M	48	44 (91.7%)	880	Right mesial temporal
P14	54.0	M	20	20 (100%)	600	Right PVNH
P15	30.3	M	40	32 (80.0%)	960	Left mesial temporal
P16	29.8	M	49	43 (87.8%)	1,161	Left frontal operculum
P17	59.6	M	36	31 (86.1%)	930	Left temporal
P18	43.2	M	34	34 (100%)	374	Bilateral hippocampi
P19	45.1	F	42	39 (92.9%)	780	Left hippocampus
P20	26.5	M	55	38 (69.1%)	760	Bitemporal
P21	37.7	M	51	30 (58.8%)	330	Bilateral hippocampi

SPES, single-pulse electrical stimulation; SOZ, seizure onset zone; OFC, orbitofrontal cortex; MFG, middle frontal gyrus; PVNH, periventricular nodular heterotopia.

Electrode localization and registration

To localize electrodes, we coregistered each patient's preoperative magnetization-prepared rapid gradient echo, fluid-attenuated inversion recovery, or T1 MRI to their postoperative CT using the custom MATLAB software and the Statistical Parametric Mapping Toolbox (SPM 12; https://www.fil.ion.ucl.ac.uk/spm/software/spm12/). Automated image processing, electrode detection, and anatomical localization of intracranial electrodes were performed using the open-source Locate electrodes Graphical User Interface (LeGUI; https://github.com/Rolston-Lab/LeGUI) software (Davis et al., 2021a) and the Brainnetome Atlas (Fan et al., 2016). Electrode contact locations are visualized in MNI space using the Visbrain software package (Combrisson et al., 2019; Fig. 1A).

Figure 1.

Electrode contact locations, distance metrics, and stimulation summary. A, Brain models depicting SEEG electrode contact locations in MNI space with midsagittal and coronal views (n = 21 patients). B, Schematic comparison of distance measurements between two hypothetical electrode locations. EUC (dark purple) represents the shortest straight-line distance between two points. PL (blue) represents the shortest distance between two points along each patient's individualized MRI tractography map. GEO (green) represents the shortest distance between two points along a path restricted within the cortex. C, A chord diagram illustrating the regions where stimulation was applied and where corresponding CCEP responses were recorded. Lines are colored by the number of unique stim–response contact pairs with robust CCEPs (lines with <50 contact pairs are not shown). Hipp, hippocampus; WM, white matter; MTG, middle temporal gyrus; OrG, orbitofrontal gyrus; Amyg, amygdala; MFG, middle frontal gyrus; CG, cingulate gyrus; INS, insula; Str, striatum; STG, superior temporal gyrus; IFG, inferior frontal gyrus; ITG, inferior temporal gyrus; PrG, precentral gyrus; FuG, fusiform gyrus; SFG, superior frontal gyrus; IPL, inferior parietal lobule; PoG, postcentral gyrus; PhG, parahippocampal gyrus; Pcun, precuneus; Tha, thalamus.

Electrophysiological recordings and stimulation

Neurophysiological data were recorded from intracranial SEEG electrodes with variable contact spacing (Ad-Tech Medical Instrument; DIXI Medical) using a 128-channel neural signal processor (NeuroPort, Blackrock Microsystems) and sampled at 1 kHz. Following recommended practices, we chose an intracranial electrode in the white matter with minimal artifact and epileptiform activity as the online reference (Mercier et al., 2022). Stimulation was delivered using a 96-channel neurostimulator (CereStim, Blackrock Microsystems).

CCEP mapping consisted of monopolar single-pulse electrical stimulation (SPES; biphasic, 5.0–7.5 mA, 500 µs pulse width per phase) administered to a subset of electrodes in a randomly selected order every 2.5–3.5 s over an ∼45 min session (Kundu et al., 2020). Each electrode contact received between 4 and 50 discrete trials of SPES; variability in trial count across contacts stemmed from time constraints and clinical considerations (i.e., emphasis on hypothesized seizure foci).

Signal processing

Intracranial recordings were first divided into prestimulation and poststimulation epochs (−1,000 to −5 ms and 5–1,000 ms, respectively), with stimulation onset set at time zero. Peristimulation data (−5 to 5 ms) were removed to mitigate stimulation artifacts. Next, data were bandpass filtered at 0.3–250 Hz and re-referenced off-line to the common median across channels to minimize noise (Rolston et al., 2009). We subsequently measured the broadband, high-gamma power (70–150 Hz) envelope from local field potentials recorded during the poststimulation epochs to characterize the spectrotemporal response to single pulses of electrical stimulation. Specifically, we bandpass filtered the poststimulation data using a 70–150 Hz fourth-order Butterworth filter, applied the Hilbert transform, and multiplied the result by its complex conjugate. For the amplitude and high-gamma analyses, causal filters were applied to the poststimulation data (5–1,000 ms), beginning at the end of the epoch (t = 1,000 ms) and moving toward the stimulation onset; this approach mitigated the introduction of filter edge effects near the beginning of the evoked response. In contrast, a zero-phase filter was used for phase-based analyses so as not to introduce distortions in the phase of the underlying signal.

Distance metrics

We used three distinct measures of distance to capture subcortical and cortical traveling waves in three-dimensional (3D) SEEG space: Euclidean distance (EUC), path length (PL), and geodesic distance (GEO; Fig. 1B). These metrics were chosen to compare biologically plausible metrics (i.e., PL, GEO) against naive approaches which do not account for the brain's unique geometry (i.e., EUC).

EUC

The EUC between each electrode pair is defined by the length of the shortest line segment connecting the two electrode locations in 3D space. Accordingly, we calculated the pairwise 3D EUC between all possible contacts using the following:

$$d=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2},$$

where x_n, y_n, and z_n correspond to the 3D anatomical coordinates of the electrode contact within the patient's brain.

PL

The PL is the average distance between two electrodes derived from patient-specific tractography. Diffusion-weighted imaging (DWI) was acquired for all patients as part of standard clinical care. The diffusion MRI data and tractography pipeline in this study were conducted using the same rigorous approach outlined in prior papers from our group (Johnson et al., 2020; Charlebois et al., 2022; Yearley et al., 2024). The scans exhibited a range in quality, with the minimum-quality data consisting of 10 directions at a b value of 1,000 s/mm², while higher-quality multishell datasets included 64 directions each at b values of 1,000 s/mm² and 2,000 s/mm². Using the FMRIB Software Library, DWI images were eddy corrected, and a network connectivity matrix was generated using a network mode in the probtractx2 function (Behrens et al., 2007; Charlebois et al., 2022). A volume with a 0.5 cm radius at each electrode centroid was used as the seed region, and segmentation was computed in FreeSurfer (Fischl, 2011; Anderson et al., 2021). We used default tracking parameters: 5,000 streamlines per voxel, 0.5 mm step size, 2,000 step max PL, 0.2 curvature limit, and volume threshold of 0.01. Additionally, any streamlines that looped back on themselves or passed through the ventricles were discarded. We conducted additional quality checks by assessing the correlation of tractography matrices with EUC, demonstrating a high level of agreement. Finally, the output N × N network matrix, which corresponds to average tractographic distances between each combination of N number of contacts, was made symmetric by averaging the N × N network matrix with its transpose. Electrodes were excluded from analyses of PL if the pairwise tractographic PL could not be calculated or if the probability of connection between contacts was 0% (11.4% of stim–response contact pairs exhibiting robust CCEPs).

GEO

The GEO is the shortest distance along the cortical surface between two electrodes, following gyri and sulci. Cortical surface segmentations for each hemisphere were generated within FreeSurfer using each patient's structural MRI (Fischl, 2011). Using these surfaces, the GEO was calculated with the SurfDist Python package (v 0.15.5; https://pypi.org/project/surfdist/) between each electrode pair on the same hemisphere. Electrodes were excluded from this distance calculation if that electrode's centroid was >1 cm from the nearest cortical surface (33.7% of stim–response contact pairs).

CCEP detection

Fundamental considerations in the detection and analysis of CCEPs have been reviewed previously (Prime et al., 2018). Numerous methods for CCEP detection have been employed in prior studies, including amplitude thresholding (Crocker et al., 2021b), machine-learning frameworks analyzing evoked response shapes (Miller et al., 2021, 2023), stimulation-induced gamma–based network identification (Crowther et al., 2019), and others (Prime et al., 2020b).

In this study, evoked responses were considered CCEPs if (1) the trial median of the early response period (5–100 ms poststimulation) contained ≥15 ms of continuous values more than threefold greater than the median (across time and trial) of the immediate prestimulation epoch (−100 to −5 ms) and (2) the median (across time and trial) of the early response period (5–100 ms poststimulation) was >30 µV, as previously described (Kundu et al., 2020). Responses measured from contacts located within the white matter were excluded. Evoked responses that did not meet these criteria were excluded from subsequent analyses. Our analyses were repeated using an alternative, well-established method for CCEP detection, in which poststimulation-evoked responses >6 z-scores of the prestimulation baseline are included (Keller et al., 2011).

CCEP feature extraction

To characterize patterns of macroscale CCEP propagation, we adapted methods used to analyze evoked traveling waves emanating from interictal epileptiform discharges [maximal descent (MD); Smith et al., 2022] and to characterize the phase of broadband oscillations in local field potentials [generalized phase (GP); Davis et al., 2020].

MD

For each CCEP identified, we determined the time at which the evoked response was most rapidly decreasing (i.e., MD), using the following:

$$\mathrm{MD}=\mathrm{argmi}{\mathrm{n}}_t\left({\displaystyle \frac{\mathrm{\Delta }L(t)}{\mathrm{\Delta }\mathrm{t}}}\right),$$

where L represents the CCEP local field potential amplitude or high-gamma power (Fig. 2A,B). MD was chosen, among other possible CCEP features (e.g., N1/N2 peak latency), because prior research has validated the feature as a computationally efficient and robust predictor for traveling wave analyses (Liou et al., 2017) and because CCEP morphology can be highly variable, often without canonical N1/N2 components (Miller et al., 2021, 2023).

Figure 2.

Traveling wave identification using MD features. A, Example CCEP evoked by SPES. B, Subset of CCEPs with amplitude MD marked. Stimulation at this location evoked robust CCEPs in several other electrodes, some of which are highlighted to show variability in MD time (indicated with a circle and dashed line). C, Example of significant traveling wave. The distance (EUC shown) between electrodes was linearly regressed onto AMP to identify traveling waves. Dots represent electrodes with robust CCEPs, colored by time to MD (purple→green, early→late). The shaded area represents 95% CI. Kernel density estimate plots along the axes represent the distributions of distance and MD time. D, Example 1,000-fold permutation test comparing linear model t values against a null distribution of shuffled distances. See Movie 1 for an example of traveling wave propagation versus volume conduction.

GP

The GP is a recently developed method that analyzes the phase of nonstationary broadband neural signals while overcoming the limitations of narrow-band filtering (Davis et al., 2020). Briefly, the evoked response is filtered in a wide 5–40 Hz bandpass (zero-phase fourth–order Butterworth filter), the Hilbert Transform is applied to the broadband signal, phase is computed using the four-quadrant arctangent function, and negative frequencies are corrected via cubic interpolation. The result captures the phase of the largest fluctuation on the recorded electrode. Finally, we extracted the average GP from the evoked response in a time window containing the empirical median CCEP amplitude MD time (35–45 ms poststimulation; Fig. 3A,B).

Figure 3.

Traveling wave identification using GP. A, Example CCEPs evoked by electrical stimulation. The trial-averaged response from a single contact is highlighted; the line color represents the GP value at each point in time. Red lines highlight the time window used to extract the average GP for regression (10–20 ms). B, Corresponding phase values for each of the recorded CCEPs, spanning −π to +π. C, Linear regression of EUC onto GP reveals a traveling wave (p < 0.001). The circular histogram (panel inset, top right) shows the distribution of GP values from CCEPs included in the model.

Traveling wave identification and characterization

For each contact stimulated, we regressed the distance (EUC, PL, or GEO) between each stimulation contact and the contacts where robust CCEPs were recorded onto their respective analysis metric (amplitude MD time, AMP; high-gamma MD time, HG; GP). A stimulation contact was determined to evoke a traveling wave if a significant linear relationship between distance and analysis metric was observed across response contacts; to control for false positives and identify robust model fits, we performed 1,000-fold permutation testing against a null distribution of shuffled distances (Figs. 2C,D, 3C). Only the linear models with a test statistic at the p < 0.05 level compared with the permuted distribution were considered traveling waves. The propagation velocity of traveling waves identified from amplitude or HG was obtained from the slope of the linear model and converted to meters per second to facilitate comparison with what has been reported previously. To estimate propagation velocity in the phase-based models, we calculated the average instantaneous frequency during the 35–45 ms poststimulation period, took the median instantaneous frequency across response contacts, multiplied the result by 2π, and divided by the slope of the regression model. We also tested whether traveling wave propagation velocity was associated with the maximum distance traversed by the wave and whether propagation velocity differed between contacts located in the gray versus white matter.

Experimental design and statistical analyses

We used a linear mixed-effect model to analyze the effect of stimulated region, distance (EUC; PL; GEO), and analysis metric (AMP; HG; GP) on the proportion of stimulated contacts which evoked traveling waves; patient ID was included as a random effect due to the variability in traveling waves elicited across patients (Extended Data Fig. 4-2). The model equation is provided below:

$$Y_{ij}={\beta }_0+{\beta }_1(\mathrm{Distance}\mathrm{Metric})+{\beta }_2(\mathrm{Analysis}\mathrm{Metric})+{\beta }_3(\mathrm{Region})+u_{ij}+{\epsilon }_{ij},$$

where Y represents the proportion of stimulated contacts identified as traveling waves, u represents the random effect associated with patient ID, and ɛ represents the residual error. Pairwise post hoc testing of distance and analysis metrics was performed using Tukey's or Dunn's tests. Given the large number of regions stimulated, we chose to further characterize the proportions of traveling waves expected by stimulating inside versus outside each region using a series of χ² tests for independence followed by false discovery rate correction.

To characterize differences in model fit and traveling wave velocity, we first performed Anderson–Darling tests for normality (Anderson and Darling, 1952), which determined that nonparametric statistical tests were most appropriate. Accordingly, we used a two-way ANOVA on ranks to compare median model R² values (distance metric and analysis metric as factors) and pairwise Kolmogorov–Smirnov tests to compare the distributions of traveling wave velocities across distance metrics. Statistical analyses were performed using the scipy (Virtanen et al., 2020) and statsmodels (Seabold and Perktold, 2010) libraries. Data were visualized using matplotlib (Hunter, 2007), seaborn (Waskom, 2021), and MNE (Gramfort et al., 2014).

Results

Across all patients, we recorded from 1,019 intracranial electrode contacts (48.5 ± 17.5 per patient, mean ±  SD; Fig. 1A). We administered a total of 17,631 trials of SPES (839.6 ± 421.7 per patient) to 917 intracranial electrode contacts (43.7 ± 19.0 per patient; Fig. 1C). The demographics and clinical characteristics of the patient cohort are shown in Table 1.

We observed traveling waves across all analysis metrics (AMP; HG, GP) and distance metrics (EUC; PL; GEO) (Fig. 4A; example shown in Movie 1). Similar patterns were observed even when analyses were replicated using an alternative method for thresholding CCEPs (Extended Data Fig 4-1). The linear mixed-effect model revealed significant differences in the proportion of traveling waves evoked across region stimulated and distance metrics while accounting for individual differences (p < 0.05). There were no significant differences in the proportion of traveling waves identified across analysis metrics. Pairwise post hoc testing revealed that the mean proportion of traveling waves measured with EUC was greater than PL (mean difference, 6.4%; 95% CI [2.8, 9.9%]; p = 0.001), PL was more common than GEO (mean difference, 5.0%; 95% CI [1.5, 8.5%]; p = 0.003), and EUC was more common than GEO (mean difference, 11.3%; 95% CI [7.8, 14.9%]; p < 0.001).

Figure 4.

Proportion of traveling waves evoked by stimulating different regions. A, Bars represent the proportion of stimulated contacts which evoked a traveling wave (%), separated by region (n = 20), distance metric, and analysis metric. B, The number of unique contacts stimulated in each region (ordered high→low). EUC, Euclidean (purple); PL, path length (blue); GEO, geodesic (green). See Extended Data Figure 4-1 for a contrast of two alternative methods for CCEP detection and Extended Data Figure 4-2 for a comparison of the proportion of traveling waves evoked across patients.

Figure 4-1

Contrast of methods used for CCEP detection. A. The number of CCEPs that met the criteria for inclusion using the median contrast approach defined in the manuscript (red) and an alternative threshold in which the max amplitude of the evoked response must exceed 6 z-scores of the pre-stimulation baseline (blue). B. Venn diagrams contrasting the number of CCEPs detected with each method. C. Proportion of traveling waves evoked by stimulation across distance and analysis metrics. EUC = Euclidean, PL = path length, GEO = geodesic, AMP = amplitude MD time, HG = high-gamma MD time, GP = generalized phase. Download Figure 4-1, TIF file ^{(3MB, tif)} .

Figure 4-2

Proportion of traveling waves evoked by stimulation in each patient, collapsed across regions. EUC = Euclidean, PL = path length, GEO = geodesic. Download Figure 4-2, TIF file ^{(2.9MB, tif)} .

Movie 1.

Download video file ^{(2.8MB, mp4)}

DOI: 10.1523/JNEUROSCI.1504-24.2025.video1

Illustrative example of a stimulation-evoked traveling wave versus null response to single-pulse stimulation in a single patient. Patient-specific 3D brain models are shown with superimposed electrode contact locations. Stimulation of Contact 5 (caudate) evoked a traveling wave (left), whereas stimulation of Contact 16 (middle temporal gyrus) resulted in a null response indicative of volume conduction (right); stimulated contacts are shown in red. The MD time of each robust CCEP is highlighted at the moment it occurs (yellow). Bottom panels show robust CCEPs resulting from stimulation. [View online]

Since stimulation was applied to areas distributed throughout the brain, we next sought to characterize regional differences in the proportion of CCEPs that appeared as evoked traveling waves. The electrode localization and registration pipeline identified stimulated electrodes located in 20 distinct regions (Fig. 4B). A series of χ² tests, with subsequent multiple-comparison correction, revealed many regions with an observed frequency of traveling waves that deviated from what would be expected by chance (Table 2).

Table 2.

Traveling waves observed across brain regions and distance metrics

Brain region	Distance metric	χ2 statistic	p value*	Observed freq.
Hipp	EUC	46.0	p < 0.001	More
	PL	43.8	p < 0.001	More
	GEO	23.5	p < 0.001	More
WM	EUC	6.6	p = 0.044	More
	PL	7.8	p = 0.029	More
Amyg	PL	6.4	p = 0.044	More
	GEO	7.8	p = 0.029	More
STG	EUC	8.0	p = 0.029	More
MFG	EUC	17.0	p = 0.001	Less
	PL	6.4	p = 0.044	Less
	GEO	6.6	p = 0.044	Less
Str	EUC	10.9	p = 0.010	Less
	GEO	8.0	p = 0.029	Less
IFG	EUC	7.1	p = 0.039	Less
CG	PL	13.2	p = 0.003	Less
MTG	PL	6.1	p = 0.044	Less

A χ² test was performed to determine if the observed frequency was significantly more/less than would be expected by chance; only the significant results are shown (n  =  20 unique regions total). Hipp, hippocampus; WM, white matter; Amyg, amygdala; STG, superior temporal gyrus; MFG, middle frontal gyrus; Str, striatum; IFG, inferior frontal gyrus; CG, cingulate gyrus; MTG, middle temporal gyrus; EUC, Euclidean; PL, path length; GEO, geodesic. *p values were adjusted for multiple comparisons by applying the Benjamini–Hochberg procedure for controlling the false discovery rate.

By measuring the slope of the regression, we were able to estimate the propagation velocity of each traveling wave identified; to minimize the effect of velocities that were biologically implausible, we excluded values that were negative or were outside the range defined by three times the median absolute deviation (Leys et al., 2013). A series of pairwise Kolmogorov–Smirnov tests comparing the velocity distributions observed across distance metrics revealed that EUC < GEO < PL for each analysis metric (Table 3). The median (Q1–Q3) propagation velocities of traveling waves identified with AMP were 1.0 (0.8−1.3), 2.0 (1.3–2.6), and 3.1 (2.4–4.0) m/s for EUC, GEO, and PL, respectively; we observed similar, albeit slightly slower, velocities with HG [EUC, 0.8 (0.5–1.1) m/s; GEO, 1.5 (1.1–2.1) m/s; PL, 2.2 (1.5–3.2) m/s]. In contrast, propagation velocities estimated from GP models were faster than those calculated for AMP and HG across all distance metrics [EUC, 1.5 (1.0–2.1) m/s; GEO, 2.4 (1.8–3.3) m/s; PL, 4.5 (2.7–5.9) m/s; Fig. 5]. We did not observe significant differences in the propagation velocity of traveling waves from stimulation of contacts located within the gray versus white matter for any combination of distance and analysis metrics (Extended Data Fig. 5-1). However, we did observe strong, positive linear associations between propagation velocity and max distance traversed by the wave across all metrics (Extended Data Fig. 5-2).

Table 3.

Pairwise Kolmogorov–Smirnov tests comparing velocity distributions across distance metrics

Analysis metric	Contrast	D statistic	p value
AMP	EUC versus GEO	D = 0.56	p < 0.001
	EUC versus PL	D = 0.84	p < 0.001
	GEO versus PL	D = 0.46	p < 0.001
HG	EUC versus GEO	D = 0.58	p < 0.001
	EUC versus PL	D = 0.76	p < 0.001
	GEO versus PL	D = 0.34	p < 0.001
GP	EUC versus GEO	D = 0.40	p < 0.001
	EUC versus PL	D = 0.74	p < 0.001
	GEO versus PL	D = 0.47	p < 0.001

AMP, amplitude MD time; HG, high-gamma MD time; GP, generalized phase; EUC, Euclidean; PL, path length; GEO, geodesic.

Figure 5.

Gaussian kernel density estimate of the traveling wave velocities observed using the analysis metrics (amplitude MD, high-gamma MD, GP); colors represent distance metrics. EUC, Euclidean (purple); PL, path length (blue); GEO, geodesic (green). The inset on the bottom panel shows the distribution of instantaneous frequencies observed across all responses during the 35–45 ms GP analysis window. See Extended Data Figure 5-1 for a contrast of traveling wave velocities observed with gray versus white matter stimulation and Extended Data Figure 5-2 for further characterization of the relationship between maximum distance traversed by waves and propagation velocity.

Figure 5-1

Gaussian kernel-density estimate of the traveling wave velocities observed across distance and analysis metrics, separated by whether contact stimulated was in gray matter vs. white matter; gray matter stimulation traveling wave speed distributions are colored by distance metric, whereas distributions are light gray for white matter stimulation. EUC = Euclidean, PL = path length, GEO = geodesic, GM = gray matter, WM = white matter. Download Figure 5-1, TIF file ^{(2.4MB, tif)} .

Figure 5-2

Characterization of the max distance traversed by traveling waves and association with propagation velocity. A. Histograms of max distance traversed by traveling waves, separated by distance and analysis metrics; max distance is defined as the distance to the furthest contact with a robust evoked response following stimulation. Red lines indicate the median value of the distribution. B. Linear regressions of traveling wave velocity and max distance traversed, separated by distance and analysis metrics. The associated model R² and p-value are shown in the top left of each panel. Download Figure 5-2, TIF file ^{(6MB, tif)} .

The median time to MD in the CCEPs was 38.0 ms (±34.6) and 25.0 ms (±44.1) for evoked amplitude and high-gamma power, respectively. MD timings across the two measures of amplitude and high-gamma power were positively correlated [r_(13583) = 0.26 (p < 0.001); Fig. 6A]. To further characterize model performance, we compared the proportion of variance explained (R²) using a two-way ANOVA on ranks, with distance and analysis metrics as factors. We observed a significant main effect of distance metric (F_(2,1574) = 25.6; p < 0.001), but not for analysis metric (F_(2,1574) = 2.9; p = 0.054). A post hoc Dunn's test revealed that models using GEO had a median R² value greater than that of EUC (p < 0.001) and PL (p = 0.002) and that EUC > PL (p = 0.001; Fig. 6B; Extended Data Fig. 6-1). Exploratory analyses comparing the proportion of stimulation contacts mutually identified across analysis metrics suggests that AMP, HG, and GP are largely capturing distinct features of the evoked response (Fig. 6C).

Figure 6.

Comparison of different metrics used for traveling wave identification. A, A scatterplot of evoked amplitude and high-gamma (70–150 Hz) MD times with overlaid Gaussian kernel density estimate. The shaded area represents the probability of values at each location (green→dark purple, low→high; probabilities of <20% are not shown). Histograms along axes show the distributions of MD times. B, Heatmaps of the proportion of traveling waves detected (left) and model R² values across distance and analysis metrics. C, Venn diagrams showing the proportion of traveling waves mutually identified across different distance and analysis metrics. EUC, Euclidean; PL, path length; GEO, geodesic; AMP, amplitude MD time; HG, high-gamma MD time; GP, generalized phase. See Extended Data Figure 6-1 for distributions of linear model R² values across distance and analysis metrics.

Figure 6-1

Gaussian kernel-density estimate of the linear model R² values across distance and analysis metrics. EUC = Euclidean, PL = path length, GEO = geodesic. Download Figure 6-1, TIF file ^{(2.6MB, tif)} .

Discussion

We applied SPES to intracranial SEEG electrodes in a cohort of patients with intractable epilepsy to test the hypothesis that direct electrical stimulation evokes neural traveling waves. In doing so, we observed a subset of CCEPs that propagate as neuronal traveling waves and exhibit similar characteristics to traveling waves observed in spontaneous and task-evoked activity.

The range of propagation velocities we observed (0.1–9.6 m/s) was comparable to those reported previously for mesoscopic (0.1–0.8 m/s) and macroscopic traveling waves (1–10 m/s)—consistent with the axonal conduction velocities of unmyelinated and myelinated white matter fibers within the cortex, respectively (Muller et al., 2018). Large-scale network models suggest that neural traveling waves emerge spontaneously from these axonal conduction delays (Davis et al., 2021b). Similar traveling wave velocities have also been reported in the human brain from microelectrode array recordings of IEDs (Smith et al., 2022) and spontaneous neocortical alpha and theta oscillations (Zhang et al., 2018). Additionally, a recent study that leveraged biologically informed modeling of CCEPs and tractography from patients in the F-TRACT database (f-tract.eu) reported a median corticocortical axonal conduction velocity of 3.9 m/s (Lemaréchal et al., 2021), a value very close to what we observed in our analogous AMP-PL models of traveling wave propagation along white matter tracts: 3.1 m/s.

Numerous models of traveling wave propagation have been proposed; for example, a traveling wave may result from delayed excitation from a single source or via a propagating impulse within an excitable network (Sato et al., 2012). Alternatively, ephaptic transmission may also result in nonsynaptic propagation of neural activity (Anastassiou et al., 2011; Subramanian et al., 2022). Importantly, these putative mechanisms may be dissociated via differences in propagation speed—waves have been proposed to travel within a cortical area based on the conduction velocity of unmyelinated horizontal fibers (Davis et al., 2021b), but spiral waves associated with sleep spindles travel at faster speeds consistent with faster thalamocortical fibers (Muller et al., 2016). Moreover, the transmission speed of evoked neural responses varies with age as the brain develops and matures (Blooijs et al., 2023). Thus, characterization of the temporal dynamics of signal propagation may provide insight into the underlying structure and properties of the traversed networks, as well as the likely mode of transmission.

We recorded traveling waves in ∼14–28% of the channels stimulated (∼5–19% with false discovery rate correction), depending on the detection metrics used. There are several reasons why stimulation-evoked traveling waves may not have been observed more ubiquitously. For one, we utilized SEEG recordings, which inherently provide a sparse representation of 3D volumes and the cortical surface, since contacts along the same lead are arranged linearly (Anderson et al., 2021). Moreover, SEEG contact orientation relative to the nearest neural source may add an additional source of variance, compared with consistently oriented surface electrodes. Subsequent investigation of stimulation-evoked traveling wave dynamics in high-density electrocorticographic recordings would offer superior spatial resolution for estimating wave speed and shape. Additionally, since the shape of CCEP responses can be highly variable, metrics like MD may fail to generalize to less stereotypical response shapes, necessitating the use of phase-based metrics like GP.

Methodological constraints aside, the observation that only a subset of CCEPs exhibit traveling wave characteristics raises an interesting question: Are spatiotemporal delays in CCEP propagation a possible means of separating biologically plausible evoked responses from spurious signals? Volume conduction, for example, is a commonly observed artifact in evoked responses to stimulation that confounds the interpretation of CCEPs (Prime et al., 2020a). With our approach, volume-conducted signals could be distinguished from genuine traveling waves because they lack a robust, linear relationship between the CCEP-derived feature and the distance between electrodes. This is particularly true with respect to our analysis of GP—responses attributable to volume conduction, which represents the near-instantaneous passive spread of electrical activity, would exhibit zero-phase lag even if the underlying signal strength is attenuated with distance. Because we measure significant phase offsets that are consistent with a velocity on the order of 0.1–10 m/s, we can discount volume conduction as a major contributor to our observations.

Robust CCEPs were most often observed near the stimulation site, adjacent to the stimulating electrode, or along the same lead. These closely spaced electrodes may be best characterized by EUC, which could explain why this metric led to a higher proportion of traveling waves identified relative to PL or GEO, metrics which are more biologically plausible paths for subcortical and cortical traveling wave propagation. That notwithstanding, models using GEO appear to explain a greater proportion of variance than those using EUC or tractographic PL. This suggests that stimulation-evoked traveling waves are best modeled via propagation along the cortical surface.

Our comparison of the regional differences in the response to stimulation suggests that stimulation-evoked traveling waves are more common from particular brain regions, like the hippocampus and amygdala; previous studies have reported that single-pulse stimulation of these areas tends to elicit robust, broadly distributed CCEPs (Enatsu et al., 2015; Mégevand et al., 2017; Guo et al., 2021). Prior studies have observed traveling waves in areas throughout the human neocortex (Zhang et al., 2018). Given that medial temporal lobe structures tend to be oversampled relative to other brain regions, the increased electrode density may have some relationship to the regional differences in stimulation-evoked traveling waves that we observed.

The study has a few noteworthy limitations. First, electrode locations are determined solely by clinical considerations, leading to heterogeneity between patients and a denser sampling of regions known to be highly epileptogenic (e.g., mesial temporal lobe). Our prior work on traveling waves was performed using Utah electrode arrays, which have the advantage of a grid-like orientation, allowing a more straightforward characterization of the spatiotemporal dynamics of traveling wave propagation. In contrast, SEEG recordings provide a broader sampling of brain regions, albeit with less uniform coverage. Additionally, while the evoked responses appear to propagate as traveling waves, many mechanistic questions remain incompletely understood—which specific routes do the signals traverse (e.g., through the cortical surface vs via subcortical white matter tracts), how are they transmitted (e.g., synaptic vs nonsynaptic), and what are their physiological implications? While our methodological approach was intended to explore some of these questions, for instance, by evaluating several distinct measures of distance and contrasting their model fits, our results simply suggest that certain interpretations better fit the pattern of specific responses observed.

Although MD is a validated measure for traveling wave analyses (Liou et al., 2017), it reduces the entirety of the CCEP to a single, discrete measurement with respect to time. Other statistical approaches that leverage the high sampling rate of continuous time-series recordings (e.g., phase-based analyses) have been used in prior studies of endogenous traveling waves (Halgren et al., 2019; Davis et al., 2020). For this reason, we additionally characterized the GP of the evoked response. With both approaches, we observed statistically significant stimulation-evoked traveling waves. These results suggest that this approach to traveling wave detection is robust and that our observations are not simply an artifact of data processing. It is important to note that although these measures may overlap in the responses they identify as traveling waves, these different measures capture distinct features of different evoked responses. That is, amplitude-, spectral-, and phase-based measures capture separable components of the evoked response, which may suggest a sensitivity to different types of waves.

Finally, we restricted the CCEP feature extraction window to 5–150 ms poststimulation for our analyses. This window was chosen to include the first downward deflection typically observed in our population of CCEPs. In other studies, this has been referred to as N1 (10–50 ms) or the early negative deflection of the slower N2 (50–200 ms) component. When these separate components are observable, recent evidence suggests they may represent intra- and internetwork communication, respectively (Veit et al., 2021). Other analyses have shown that morphological characteristics of evoked waveforms, outside the traditional N1/N2 paradigm, may offer more powerful insights into the anatomy underlying the observed CCEPs (Miller et al., 2021). Subsequent studies of stimulation-evoked traveling waves may benefit from analyzing the evoked responses from these two components separately or leveraging the full response profile of the evoked signal.

Conclusions

Our analyses of CCEPs revealed that many evoked responses to SPES propagate as traveling waves. The stimulation-evoked traveling waves we observed were robust across multiple distinct methods of identification and exhibited characteristics in line with what has been reported previously for spontaneous traveling waves. Traveling waves were observed across distributed brain areas but were most frequently evoked when stimulating highly connected hub regions (e.g., hippocampus). These results highlight previously uncharacterized spatiotemporal dynamics of signal propagation in response to stimulation.