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19 Event-Related Potentials 253
19.6 Conclusion
This chapter introduced the concept of ERPs, their characteristic waveform, and a
selection of commonly investigated components. ERPs have been studied extensively for more than half a century and have proven to be a powerful tool to explore
sensory and cognitive processing. At the same time, the logic behind the analysis is
easy to grasp: cutting the data into segments around the events, removing offsets,
and averaging over segments. The results can be communicated through a variety of
output measures and compelling figures. Thus, ERPs provide a simple yet elegant
solution to investigate evoked brain responses with high temporal resolution. The
ERP method is still widely popular in EEG research as reflected by the prolific
publication of new studies. Hence, ERPs should be an essential part of the EEG
researcher’s analysis toolkit.
References
Bruin, K. J., & Wijers, A. A. (2002). Inhibition, response mode, and stimulus probability: A
comparative event-related potential study. Clinical Neurophysiology, 113, 1172–1182.
Brunia, C. H. M., Van Boxtel, G. J. M., & Böcker, K. B. E. (2012). Negative slow waves as indices
of
anticipation: The Bereitschaftspotential, the contingent negative variation, and the stimuluspreceding negativity. In E. S. Kappenman & S. J. Luck (Eds.), The Oxford handbook of event-
related potential components. Oxford University Press.
Eimer, M. (2011). The face-sensitive N170 component of the event-related brain potential. In The
Gehring, W. J., Liu, Y., Orr, J. M., & Carp, J. (2012). The error-related negativity (Ern/Ne). In E. S.
Handy, T. C. (2005). Event-related potentials: A methods handbook. MIT Press.
Haxby, J. V., Hoffman, E. A., & Gobbini, M. I. (2000). The distributed human neural system for
Hernandez-Pavon, J. C., Veniero, D., Bergmann, T. O., Belardinelli, P., Bortoletto, M., Casarotto,
Hutzler, F., Braun, M., Võ, M. L. H., Engl, V., Hofmann, M., Dambacher, M., Leder, H., & Jacobs,
Jeffreys, D. A., & Axford, J. G. (1972). Source locations of pattern-specific components of human
Keil, A., Debener, S., Gratton, G., Junghofer, M., Kappenman, E. S., Luck, S. J., Luu, P., Miller,
Kutas, M.,
handbook of face perception (Vol. 28, pp. 329–344). Oxford University Press.
Oxford
Kappenman
Oxford University Press.
face
S.,
Casula, E. P., Farzan, F., Fecchio, M., Julkunen, P., Kallioniemi, E., Lioumis, P., Metsomaa,
J., Miniussi, C., Mutanen, T. P., Rocchi, L., Rogasch, N. C., Shafi, M. M., Siebner, H. R., Thut,
G., Zrenner, C., Ziemann, U., & Ilmoniemi, R. J. (2023). TMS combined with EEG: Recommendations and open issues for data collection and analysis. Brain Stimulation, 16, 567–593.
A.
M. (2007). Welcome to the real world: Validating fixation-related brain potentials for
ecologically valid settings. Brain Research, 1172, 124–129.
visual evoked potentials. I. Component of striate cortical origin. Experimental Brain Research,
16, 1– 21.
A., & Yee, C. M. (2014). Committee report: Publication guidelines and recommendations for
G.
studies using electroencephalography and magnetoencephalography. Psychophysiology, 51,
1–21.
language comprehension. Trends in Cognitive Sciences, 4, 463–470.
& S. J. Luck (Eds.), The Oxford handbook of event-related potential components.
perception. Trends in Cognitive Sciences, 4, 223–233.
& Federmeier, K. D. (2000). Electrophysiology reveals semantic memory use in
254 M. Hoppstädter
Liu, Y., Huang, H., McGinnis-Deweese, M., Keil, A., & Ding, M. (2012). Neural substrate of the
late
positive potential in emotional processing. The Journal of Neuroscience, 32, 14563–14572.
Luck, S. J. (2014). An introduction to
Luck, S. J., & Kappenman, E. S. (2011). The Oxford handbook of event-related potential compo-
nents
. Oxford University Press.
Maris, E., & Oostenveld, R. (2007). Nonparametric statistical testing of EEG- and MEG-data.
Journal of Neuroscience Methods, 164, 177–190.
Näätänen, R., & Kreegipuu, K. (2012). The mismatch negativity (MMN). In E. S. Kappenman &
J. Luck (Eds.), The Oxford handbook of event-related potential components. Oxford Uni-
S.
versity Press.
Nordstrom, H., & Wiens, S. (2012). Emotional event-related potentials are larger to figures than
scenes
Polich, J. (2004). Clinical application of the P300 event-related brain potential. Physical Medicine
Pratt, H. (2012). Sensory ERP components. In E. S. Kappenman & S. J. Luck (Eds.), The Oxford
Rossion, B., & Jacques, C. (2012). The N170: Understanding the time course of face perception in
Sauseng, P., Klimesch, W., Gruber, W. R., Hanslmayr, S., Freunberger, R., & Doppelmayr,
Schandry, R., Sparrer, B., & Weitkunat, R. (1986). From the heart to the brain: A study of heartbeat
Schechter, I., Butler, P. D., Zemon, V. M., Revheim, N., Saperstein, A. M., Jalbrzikowski, M.,
Smulders, F. T. Y., & Miller, J. O. (2012). The lateralized readiness potential. In E. S. Kappenman
Sutton, S., Braren, M., Zubin, J., & John, E. R. (1965). Evoked-potential correlates of stimulus
Tanaka, J. W., & Curran, T. (2001). A neural basis for expert object recognition. Psychological
Walter, W. G., Cooper, R., Aldridge, V., McCallum, W., & Winter, A. (1964). Contingent negative
Wilding, E.
but are similarly reduced by inattention. BMC Neuroscience, 13, 49.
Rehabilitation Clinics of North America, 15, 133–161.
and
handbook of event-related potential components. Oxford University Press.
the
human brain. In E. S. Kappenman & S. J. Luck (Eds.), The Oxford handbook of event-
related potential components. Oxford University Press.
M.
(2007). Are event-related potential components generated by phase resetting of brain
oscillations? A critical discussion. Neuroscience, 146, 1435–1444.
contingent
Pasternak,
transient visual evoked potentials to magno- and parvocellular-selective stimuli in schizophrenia. Clinical Neurophysiology, 116, 2204–2215.
&
University Press.
uncertainty.
Science,
variation:
Nature, 203, 380–384.
processes. In E. S. Kappenman & S. J. Luck (Eds.), The Oxford handbook of event-related
potential components. Oxford University Press.
scalp potentials. The International Journal of Neuroscience, 30, 261–275.
R., Silipo, G., & Javitt, D. C. (2005). Impairments in generation of early-stage
S. J. Luck (Eds.), The Oxford handbook of event-related potential components. Oxford
Science, 150, 1187–1188.
12, 43– 47.
An electric sign of sensori-motor association and expectancy in the human brain.
L., & Ranganath, C. (2012). Electrophysiological correlates of episodic memory
the event-related potential technique. MIT Press.
Chapter 20
EEG Source Analysis
Alejandro Ojeda
Abstract EEG source analysis enables the study of cognitive and physiological
ses closer to their origin within the brain. To that end, it combines anatomical
proces
information, usually derived from participant-specific or template MRI segmentations of the head and inner layers of tissue, with EEG signals using mathematical
methods that transform the latter into a functional brain imaging modality. This
chapter will touch on the fundamentals of EEG source analysis, including its
modeling assumptions, representative source localization algorithms, and sourcelevel statistical inference and connectivity.
Keywords Source imaging · Head model · Forward and inverse problems ·
Regular
space · Multiple comparison correction · Source summarization
ization · Constraints · Statistical analysis and connectivity in the source
20.1 Introduction
As mentioned in Chap. 2, What is EEG?, the EEG is a voltage signal that can be
measured on the scalp surface and originates from the electrical activity of cortical
neurons. The layer of pyramidal neurons in the cortex is thought to be the primary
contributor to the EEG (and MEG) signal because the spatial orientation of these
neurons resembles equivalent current dipoles. When enough localized populations
of these neurons fire synchronously, they can produce extracellular currents large
enough to spread across different layers of conductive tissue (e.g., cerebrospinal
fluid (CSF), bone, and skin) and can be measured with voltage sensors on the scalp.
These conductive layers of tissue form the volume conductor, which has the effect of
mixing currents produced by different neural populations. As a result, an EEG sensor
on the scalp picks up a voltage signal composed of contributions from multiple
A. Ojeda (*)
Brain Vision LLC, Garner, NC, USA
e-mail:
alejandro.ojeda@brainvision.com
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026
T.
Warbrick (ed.), The EEG Handbook,
https://doi.org/10.1007/978-3-032-20450-9_20
255
256 A. Ojeda
neural sources scattered over the cortical surface (and not only those directly
underneath the sensor).
1
Typically, we use electrical models of the head to describe how neural signals
propagate and mix on their way from their source to the EEG sensors. Depending on
the assumptions, these models can furnish different variants of Maxwell’s equations,
which we can solve for simulated, unitary source activities (see Table 20.1). This is
know
n as solving the forward problem of the EEG. The solution of which is the
so-called lead field matrix, which encodes the contribution of a unitary current dipole
normal to the cortical surface at the jth location to the ith scalp sensor. If source
direction is included in the model, the contributions along the x, y, and z axes are also
solved for and included in the lead field.
Terminology
Volume conductor Electrically conductive tissue within the head through which
Volume conductor
effect
Head model Electrical model of the head that describes how neural currents
Sensor space Component of the head model that defines the sensor positions
Source space Component of the head model where neural sources are defined.
Forward problem Given the equations derived from the head model, one finds the
Lead field matrix Matrix that contains the solution to the forward problem for a
neural currents propagate (e.g., brain, cerebrospinal fluid, bone,
and skin).
It is the mixing of extracellular currents produced by distant as
well
as nearby neural populations; therefore, a voltage sensor on
the scalp picks up a signal composed of contributions from
multiple neural sources.
propagate
includes information and assumptions about the geometry and
conductivity of the tissue.
with
digitized and co-registered with a skin segmentation derived from
the participant’s structural MRI.
For
segmentation derived from structural MRI to constrain sources to
the grey matter. Another constraint could be to confine the
sources to the cortical surface only.
voltage
unitary current dipoles placed on the source space.
dense
contribution of every unitary source to the given sensor. For
example, the element k
unitary current dipole onto the ith sensor.
from their sources to the sensors. The model usually
respect to the head. For example, sensor positions could be
example, in realistic head models, one can use grey matter
projection on the sensor space produced by simulated
array of sources. Each row in this matrix represents the
represents the voltage induced by the jth
i, j
1
In addition to cortical sources, there is evidence that subcortical sources contributed to the EEG
signals (Seeber et al., 2019).
20 EEG Source Analysis 257
Inverse problem Estimate the sources that generated a set of scalp voltage
EEG source imaging
(ESI)
Equivalent current
(ECD)
dipole
Constraints Set of mathematical restrictions used to bias the solution of an
Regularization
parameter
Euclidean norm Square root of the sum of squares of a vector’s components. This
Frobenius norm It is an extension of the Euclidean norm to matrices, and it is used
Type I error When statistically testing a hypothesis, this is the error of
Multiple comparisons
problem
Anatomical
connectivity
Functional
connectivity
Effective connectivity Indicates a causal relationship between brain regions.
measurements.
The solution of the inverse problem of the EEG in a dense source
space.
In this case, the output of the inverse algorithm is a map of
estimated current source density values. The resulting map can be
rendered into an image (electrical tomography) or used for subsequent statistical analyses.
A dipole model that summarizes the electrical activity of an
underlying source configuration of unknown spatial extent.
Dipole fitting algorithms utilize this model to determine the
location of a few equivalent sources that best explain a given
scalp topography.
inverse
algorithm toward biologically plausible source
configurations.
A parameter used to obtain a unique inverse solution. It can be
interpreted
weight assigned to the constraints.
norm is typically used to represent the reconstruction error of an
inverse algorithm when solving for a single source vector.
to
solving for multiple source vectors simultaneously.
rejecting
a false positive.
When performing inference on the source space, the larger the
number
therefore, incurring a Type I error.
Indicates connectivity at the structural level (axons and bundles of
axons
Indicates an instantaneous relationship (correlation) between
brain
as a trade-off between the reconstruction error and the
represent the reconstruction error of an inverse algorithm when
the null hypothesis when it is true. This is also known as
of sources, the more likely it is to find erroneous effects,
connecting different brain regions).
regions.
As long as the geometrical and electrical properties of the participant’s brain don’t
change significantly (due to aging, injury, illness, etc.), the lead field matrix can be
calculated once and then used for estimating the neural sources that most likely
generated an observed brain topography for an experimental condition of interest.
This is known as solving the inverse problem of the EEG. The solution to this
problem turns the EEG into a functional brain imaging modality by mapping the
signals measured on the scalp onto anatomically relevant brain structures (see
Fig.
Thereby allowing researchers to study behavioral, physiological, and
20.1).
cognitive responses linked to brain function and anatomy.
258 A. Ojeda
Table 20.1 Common modeling approaches to solve the forward problem of the EEG
Method Summary Pros Cons References
Spherical The sources are dis-
BEM Boundary Element
FEM Finite Element
tributed over a sphere,
typically fitted to the
cortical surface
extracted from participant’s MRI segmentation. The layers
representing the skull
and scalp are modeled
accordingly, increasing the radius parameter and using a ratio
of fixed conductivities
for each layer.
(BEM): MRI
Method
segmentations are
used to extract cortex,
skull, and scalp surfaces and define compartments of
homogeneous isotropic conductivity. The
sources are modeled
as dipoles distributed
over the cortical surface. Potential distributions are solved
numerically on the
boundary of each
compartment.
Method (FEM): MRI
is used to discretize
the entire volume into
small elements. The
anisotropy and inhomogeneity of the tissue can be modeled if
Diffusion Tensor
imaging (DTI) data is
available. The potentials are solved
numerically for each
element.
Has analytical solution.
Serves as
benchmark for more
sophisticated
methods.
Captures the geometry
of the head better
than the spherical
model.
Can accurately
model
any head
shape and manage
heterogeneous and
anisotropic
conductivities.
Inaccurate. Hallez
Does not model
inhomogeneous and
anisotropic conductivities and can be
challenging to apply
on surfaces with
holes.
The method has singularities that need to
be handled by the
numeric solver.
et al.
(
2007)
Stenroos
and Sarvas
(
2012) and
Gramfort
al.
et
(
2010)
Wolters
et al.
(
2007)
Having an EEG source signal representation in a well-defined anatomical space
opens the door to statistical analyses of individuals and groups in the source space.
Furthermore, ERP, frequency-domain, correlation, and causality studies can be
20 EEG Source Analysis 259
EEG voltage
topography
arg min
Fig. 20.1 Schematic representation of EEG forward and inverse problems. The right-to-left arrow
represents the EEG voltage generation model; source dipole currents on the right spread throughout
the tissue, producing a voltage pattern on the left. The left-to-right arrow indicates the inverse
problem: the estimation of the most likely current source pattern that could have generated the
observed EEG voltage scalp pattern
Current source
map
carried out entirely in the source space. In the rest of the chapter, we will delve
further into (1) the fundamentals of EEG source imaging, (2) statistical inference in
the source space, and (3) source connectivity.
20.2 Fundamentals of EEG Source Imaging
In this chapter, we distingu ish between source imaging and source localization. Both
families of algorithms start with a scalp topography typically representing EEG
voltages (or EEG voltage components if a decomposition such as ICA was previously applied (Debener et al.,
ithm’s output is an image (or map) of current source density values that can be
algor
rendered in the source space. By source localization, however, we mean that the
output is a discrete set of points indicating the center of the equivalent current dipoles
that generated the topography. The key difference between the two is that for
imaging, the source model is defined using a dense set of points distributed on a
cortical surface or 3D grid. While for localization, the source model is sparse, and we
identify the location of a handful of equivalent current dipoles that provide a
plausible explanation for the scalp topography. See Fig.
The discrete
source model has been successfully applied to localize auditory and
visual ERPs (Makeig et al., 1997, 2002; Debener et al., 2008). However, despite its
simpli
city, the sparse nature of this source space co mplicates further statistical
analysis because equivalent dipoles may not be found in the same locations across
conditions or subjects. Usually, it requires working on clusters of sources and other
techniques (Bigdely-Shamlo et al.,
beyond
the scope of this chapter, so from now on we will focus on distributed
EEG source Imaging (ESI).
2010)). Then, by source imaging, we mean that the
20.2.
2013). Dealing with this type of analysis is
260 A. Ojeda
Distributed
Forward solver
• Spherical
• BEM
• FEM
• Other
Inverse solver
• LORETA
• Beamformer
• LASSO
• Elastic-Net
• SBL
• Other
Fig. 20.2 Typical EEG source analysis flowchart. The source model determines the subsequent
pipeline. If the model is discrete, we need to go the route of dipole modeling and clustering and
decide how to perform subsequent single-participant and group analyses on dipoles or clusters of
dipoles. If the source model is distributed, we build a participant-speci fic or template head model
and calculate the lead field using a forward solver (see Table
estimate the source maps for selected time points of interest in the EEG (see Table
can perform connectivity analysis on the source time series. Statistical analyses can be performed on
sources or connectivity features at the participant level or in groups. An important caveat for group
analyses is that unless we use the same template head model for all participants, we need to
co-register participant source spaces to ensure that the features on which we perform statistics
correspond to the same anatomical structures
Calculate lead
Estimate sources
Connectivity
estimation
field
Statistical analysis
Source
model
20.1). Next, we use an inverse solver to
Discrete
Dipole fitting
Dipole clustering
Connectivity,
spectral, and
statistical analyses
20.2). Then, we
20.3 Forward Problem
The typical ESI pipeline starts by defining a source space. If participant-specific MRI
segmentations are available, a personalized head model is constructed. Otherwise, a
generic one can be used for all participants based on a population template MRI. We
will revisit the distinction between participant-specific and template-based head
models later when we discuss the statistical analysis in the source space. The head
model is built according to the forward solver of choice. For BEM, we need to
provide the cortex, in-skull, out-skull, and skin surfaces, and we solve for sources
placed on the vertices of the cortical surface. For FEM, grey matter (usually cortex
only), CSF, and head segmentations are needed, and we solve for a 3D grid of
sources placed on the grey matter. A spherical model solver can work on a surface
20 EEG Source Analysis 261
and a 3D grid source space. Next, we need to co-register the MRI-derived head
model with the position of the sensors where voltages were measured. Notwithstanding that every approximation can introduce errors, if participant-specific sensor
positions are missing, we can use a standard montage (that includes our sensors as a
subset) placed on the head surface. Then we proceed to calculate the lead field
matrix.
20.4 Source Estimation
The relationship between scalp voltages and current sources in the brain is referred to
as the measurement model, and can be expressed by a linear equation (Dale &
Sereno,
where v represents a vector of sensor voltages at a given time point, K is the lead field
matrix,
measurement noise usually assum ed normally distributed. The normality of the
sensor noise rests on the assumption that gross artifacts were removed in
pre-processing. So, to estimate the source vector j, we need to invert this equation
(solve the inverse problem of the EEG, see Fig.
probl
assumptions, there are infinite source configurations that can render the same scalp
topography. To tackle this problem, we seek to estimate a source vector
explains the measurements subject to additional constraints,
1993),
v ¼ Kj þ e ð20:1Þ
j is a vector of current density values on the source space, and e is the
20.1). A key aspect of this inverse
em is that there are many more sources than sensors, so without further
j that best
2
þ λP jðÞ
2
ð20:2 Þ
where the first term
j ¼ arg min
( v
kk
2
) is the data fit, taken as the square of the l2-norm
Kj
2
v Kj
kk
j
(Euclidean norm) of the reconstruction error, the second is a penalty function that
biases the solution toward a source configuration that exhibits some desired features,
and λ is a regularization parameter that regulates the weight given to the penalty with
respect to the data fit term. The regularization parameter can be determined by
minimizing the generalized cross-validation curve (Golub et al.,
L-curve
class
method (Hansen, 1992), or by grid search. Equation 20.2 belongs to a
of problems called Regularized Least Squares (RLS), and many popular
1979), the
inverse algorithms can be written in this framework, some of which we summarize
in Table
source
20.2. See Michel and Brunet (2019) for an extended list of popular EEG
analysis tools.
Thanks to
the normality of the measurement noise, even many Bayesian inversion
methods can be represented in the RLS framework and vice versa. In the Bayesian
framework, the error term is derived from a data likelihood function, the penalty
262 A. Ojeda
Table 20.2 Shows a non-exhaustive collection of popular inverse methods from the RLS family
Method Summary Pros Cons References
MNE Minimum norm estimation
is obtained with
(MNE)
P j j
ðÞ¼
kk
2
.
2
wMNE Weighted MNE is
obtained
P jðÞ¼ Wjkk
matrix W acts as a depth
with
2
2
, where the
normalization operator.
LORETA Low-resolution electro-
magnetic
(LORETA) is obtained
with P jðÞ
L is a discrete Laplacian
tomography
2
, where
¼ Lj
kk
2
operator that enforces correlation among nearby
sources.
It has a closedform
solution.
It has a closedform
solution and
can recover
superficial and
deeper sources.
It has a closed-
solution and
form
can recover
superficial and
deeper sources.
Enforces smooth
continuous solutions. It is robust
It is biased toward
superficial sources
and sensitive to
noise.
It is sensitive to
noise.
It is less sensitive
focal sources,
to
and it tends to
overestimate the
spatial extent of
the source
activations.
Hamalainen
and
Ilmoniemi
(1994)
Lin et al.
(2006)
PascualMarqui et al.
(1994)
to noise.
LASSO Least absolute shrinkage
selection
operator
(LASSO) is obtained with
P( j )
¼kjk
, where the l1-
1
norm enforces sparse
solutions.
It is good for
recovering
and localized
solutions.
focal
It has an iterative
solution, thus
usually more
expensive to
compute than
other closed-form
Tibshirani
(1996)
solution algorithms. It is sensitive to noise.
ENET Elastic net (ENET) is
obtained
P jðÞ¼ M
where M
with
2
j
þ M2j
kk
1
2
and M2 are lin-
1
k
ear operator. ENET is also
found in the literature as
MxNE (Mixed-norm
Estimate).
Combines l1 and
2 norms to pro-
l
mote solutions
,
k
1
that are smooth
and
non-overlapping,
therefore limiting
the excessive
Like Lasso, it is
solved
iteratively.
VegaHernández
et al. (
2008)
and
Gramfort
al. (
2012)
et
smoothness
sometimes
exhibit by
LORETA while
enforcing local
correlations.
See Paz-Linares et al.
(2017) and Vega-Hernández et al. (2008) for a more in-depth exposition
comes from a prior density, and the regularization parameters, known as
hyperparameters, are estimated within the same probabilistic framework. Although
an exposition of Bayesian approaches is beyond the scope of this chapter, it is worth
briefly mentioning that the Sparse Bayesian Learning (SBL) family of algorithms