Evoked brain responses are generated by
Marta I. Garrido*, James M. Kilner, Stefan J. Kiebel, and Karl J. Friston
Wellcome Trust Centre for Neuroimaging, University College London, London WC1N 3BG, United Kingdom
Edited by Steven Petersen, Washington University School of Medicine, St. Louis, MO, and accepted by the Editorial Board November 10, 2007
(received for review July 4, 2007)
Neuronal responses to stimuli, measured electrophysiologically,
unfold over several hundred milliseconds. Typically, they show
characteristic waveforms with early and late components. It is
thought that early or exogenous components reflect a perturba-
tion of neuronal dynamics by sensory input bottom-up processing.
Conversely, later, endogenous components have been ascribed to
recurrent dynamics among hierarchically disposed cortical process-
ing levels, top-down effects. Here, we show that evoked brain
responses are generated by recurrent dynamics in cortical net-
works, and late components of event-related responses are medi-
ated by backward connections. This evidence is furnished by
dynamic causal modeling of mismatch responses, elicited in an
oddball paradigm. We used the evidence for models with and
without backward connections to assess their likelihood as a
function of peristimulus time and show that backward connections
are necessary to explain late components. Furthermore, we were
able to quantify the contribution of backward connections to
evoked responses and to source activity, again as a function of
peristimulus time. These results link a generic feature of brain
responses to changes in the sensorium and a key architectural
component of functional anatomy; namely, backward connections
are necessary for recurrent interactions among levels of cortical
hierarchies. This is the theoretical cornerstone of most modern
theories of perceptual inference and learning.
connectivity ? dynamic causal modeling ? EEG ? predictive coding ?
cephalography (MEG) are among the mainstays of noninvasive
neuroscience. Typically, the response evoked by a stimulus
evolves in a systematic way, showing a series of waves or
components. Many of these components are elicited so reliably
that they are studied in their own right. These include very early
sensory-evoked potentials, observed within a few milliseconds;
early cortical responses such as the N1 and P2 components; and
later components expressed several hundred milliseconds after-
ward. Broadly speaking, ERP components can be divided into
early and late (1). Early- or short-latency stimulus-dependent
(exogenous) components reflect the integrity of primary affer-
ent pathways. Late stimulus-independent (endogenous) compo-
nents entail long-latency (?100 ms) responses thought to reflect
cognitive processes (1, 2). Early components have been associ-
ated with exogenous bottom-up stimulus-bound effects, whereas
late components have been ascribed to endogenous dynamics
involving top-down influences. Indeed, the amplitude and la-
tency of early (e.g., P1 and N1) and late (e.g., N2pc) components
have been used as explicit indices of bottom-up and top-down
processing, respectively (3). Here, we demonstrate that late
components are mediated by recurrent interactions among re-
mote cortical regions; specifically, we show that late components
rest on backward extrinsic corticocortical connections that en-
able recurrent or reentrant dynamics.
This enquiry has been enabled by recent advances in the analysis
of EEG data, specifically, dynamic causal modeling (DCM). A
vent-related potentials (ERPs) or event-related fields
(ERFs) in electroencephalography (EEG) and magnetoen-
detailed description of DCM can be found elsewhere (4–8). DCM
represents a departure from conventional source reconstruction or
forward model that embodies known constraints in the way EEG
sources are generated. Put simply, these constraints require that
electrical activity in one part of the brain be caused by activity in
another. This is modeled explicitly in terms of neuronal subpopu-
lations that influence each other through intrinsic and extrinsic
corticocortical connections. The parameters of these models cover
not only the expression of cortical sources at the electrodes but also
of sources. Model inversion by using DCM allows us to estimate
these key parameters.
The focus of this article is on the role of backward connections
in the elaboration of long-latency ERP responses. We compared
models with and without backward connections and looked at
the contribution of forward and backward connections to pre-
dicted responses at the source level, as a function of peristimulus
time. In brief, we recorded EEG from healthy subjects while
listening to a stream of auditory tones embedded in an oddball
paradigm. Here, we analyze only the ERP elicited by the deviant
stimulus and report our results at both the subject and group
levels, by using the ERP averaged over trials within-subject and
over all subjects. In all analyses, we compared two models; both
had the same source architecture but were distinguished by the
presence of backward connections among sources (see Fig. 1).
motivated by recent electrophysiological and neuroimaging stud-
ies looking at the sources underlying Mismatch Negativity
(MMN), an event-related response to violations in the regularity
of an auditory sequence (9, 10). We assumed five sources,
modeled as equivalent current dipoles (ECD), over left and right
primary auditory cortices (A1), left and right superior temporal
gyrus (STG), and right inferior frontal gyrus (IFG). Our mech-
anistic model attempts to explain the generation of responses to
deviants. Left and right A1 were chosen as cortical input stations
for processing auditory information. Opitz et al. (9) identified
sources for the differential response, with functional MRI
(fMRI) and EEG measures, in both left and right STG and right
IFG. Here, we use the coordinates reported in ref. 9 (for left and
right STG and right IFG) and in ref. 11 (for left and right A1)
as prior source location means, with a prior variance of 16 mm2
(see Fig. 1C). We converted these coordinates, given in the
literature in Talairach space, to MNI space by using the algo-
rithm described in http://imaging.mrc-cbu.cam.ac.uk/imaging/
Authors contributions: M.I.G., J.M.K., and K.J.F. designed research; M.I.G. and J.M.K.
performed research; S.J.K. and K.J.F. contributed new analytic tools; M.I.G., J.M.K., and
K.J.F. analyzed data; and M.I.G., J.M.K., and K.J.F. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. S.P. is a guest editor invited by the Editorial Board.
*To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
© 2007 by The National Academy of Sciences of the USA
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MniTalairach. The dipole moment parameters had prior mean
of zero and a variance of 256 mm2in each direction.
By using these sources and prior knowledge about functional
anatomy, we constructed the following DCM: An extrinsic input
entered bilaterally to primary auditory cortex (A1), which were
connected to their ipsilateral STG. Right STG was connected
with the right IFG. Given this connectivity graph, specified in
terms of its nodes and connections, we tested two models. These
differed in terms of the presence of reciprocal or recurrent
connections: model FB had reciprocal, i.e., forward and back-
ward connections, and model F lacked backward connections,
having forward connections only (Fig. 1 A and B). In other
words, model FB resembles recurrent dynamics or parallel
bottom-up and top-down processing, whereas model F emulates
a simple bottom-up mechanism.
ERPs and Bayesian Model Comparison. We modeled the ERP
elicited by the deviants by using a DCM with these five sources
(compare equivalent current dipoles), as in previous analyses of
mismatch differences (5, 8). The evoked response to the deviant
peaked on average at ?100 ms and had a widespread negative
topography at the frontal electrodes, in agreement with previous
studies (Fig. 2A). The free parameters of these models included
the location and orientation of each dipole, excitatory and
inhibitory rate constants, and postsynaptic densities for the
(three) subpopulations of neurons within each source, intrinsic
(within-source) coupling strengths and extrinsic (between-
sources) coupling. Extrinsic connections were divided into for-
ward and backward and conformed to the connectivity rules
described in refs. 7 and 12. These rules allow one to build a
network of coupled sources linked by extrinsic connections.
Within this model, bottom-up or forward connections originate
in the infragranular layers and terminate in the granular layer;
top-down or backward connections link agranular layers, and
lateral connections originate in infragranular layers and target
all layers. All these extrinsic corticocortical connections are
excitatory and are mediated through the axons of pyramidal
cells. To test the hypothesis that backward connections mediate
late components selectively, we evaluated the model-evidence
Li? p(y??, mi) ? exp(Fi) for models m1and m0, with and without
backward connections as a function of peristimulus time; FB and
F, respectively (see Fig. 2C). This involved inverting the model
by using data, from stimulus onset to a variable poststimulus
time, ranging from 120 to 400 ms, in 10 ms steps. A difference
in log-evidence of ?3 is usually taken as strong evidence for one
model over the other (i.e., the likelihood of one model is ?20
times the other). We compared the evidence, or marginal
likelihood (13), of the two models as a function of increasing
peristimulus time windows both for the grand average ERP
nected with backward (gray) and/or forward (dark gray) connections as
temporal gyrus. Two different models were tested within the same architec-
ture, with and without backward connections (A and B, respectively). (C)
Sources of activity, modeled as equivalent dipoles (estimated posterior mo-
ments and locations), are superimposed in an MRI of a standard brain in MNI
space and their prior mean locations are: lA1 [?42,?22, 7], rA1 [46, ?14, 8],
lSTG [?61, ?32, 8], rSTG [59, ?25, 8], rIFG [46, 20, 8], in millimeters.
Model specification. The sources comprising the network are con-
overlaid on a whole-scalp map of 128 EEG electrodes. (B) Overlapped ERP responses to deviant tones from all 128 sensors over the peristimulus interval [0, 400]
(in milliseconds). (C) Differences in negative free-energy or log-evidence comparing the model with backward connections (FB) against the model without (F).
The gray patch indicates the interval chosen to model the ERPs for each individual subject (see Fig. 3).
Bayesian model comparison among DCMs of grand mean ERPs. (A) Grand mean ERP responses, i.e., averaged over all subjects, to the deviant tone
www.pnas.org?cgi?doi?10.1073?pnas.0706274105Garrido et al.
across subjects and for each subject individually (Figs. 2C and 3,
respectively). Both analyses revealed the same result. The longer
evoked responses evolve, the more likely backward connections
appear. For the group data, this is evident in Fig. 2C, which
shows that the model with backward connections (FB) super-
venes over the model without (F). This is particularly clear later
in peristimulus time (220 ms poststimulus or later).
At the suggestion of one of our referees, we also evaluated a
backward connection-only model for completeness (and to fur-
ther ensure the validity of our model selection procedure). As
anticipated, this model had much lower evidence than either the
forward or forward and backward models considered here (over
all peristimulus times examined).
Motivated by these results, we selected a window of interest;
180–260 ms for expediency, to perform an identical analysis for
each subject. Our results for individual subjects recapitulated the
group analysis (Fig. 3). For the majority of subjects (8 of 11), the
forward model supervenes over the model with backward con-
nections, when explaining the data in the first half of peristimu-
lus time. Conversely, in the second half, for most subjects (8 of
11), the model with backward connections supervenes over the
model without. This means that forward connections are suffi-
cient to explain ERP generation in early periods, but backward
connections become essential in later periods. This effect occurs
after 220 ms and is more evident for longer latencies. In short,
backward connections are not necessary to explain early data
and only incur a complexity penalty, without increasing accu-
racy. This does not mean backward connections are ‘‘switched
off;’’ it simply means their effects are not manifest until later in
levels. At this point, backward connections become necessary to
explain the data. This can be seen quantitatively in a plot of the
log-evidence over time and qualitatively in terms of the number
of subjects supporting each model at larger peristimulus time
(Fig. 3 A and B, respectively).
Conditional Contribution of Extrinsic Coupling.Finally,weevaluated
the contribution of forward and backward connections to pre-
log-evidence differences over subjects [this is proportional to the log-group Bayes factor (Bf) or to the differences in the free energy of the two models (?F); see
Materials and Methods for details]. The points outside the gray zone imply very strong inference (?99% confidence that one model is more likely), i.e., model
FB supervenes over F for positive points and the converse for negative points. (B) Histogram showing the number of subjects in each of seven levels of inference
on models with and without backward connections across the peristimulus interval 180–260 ms.
Bayesian model comparison across subjects. (A) Comparison of the model with backward connections (FB) against the model without (F), across all
Garrido et al.
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dicted responses at the channel and source levels, by using the
conditional mean of the model parameters, ?, from the model
with backward connections for the group data (see Fig. 4). We
quantified the change in predicted responses, ?x(?,t)/??, at the
source level, x, for a change in ?, for selected forward or
backward connections. The model parameter ? quantifies the
extrinsic coupling in the forward or backward connections
area influences the activity of another. Fig. 4 C–E show traces of
how source activity would change at right A1, STG, and IFG,
because of increment changes in forward and backward connec-
tions. It can be seen that unit changes in forward connections
have a profound effect on responses throughout peristimulus
time, whereas backward connections show a temporal selectivity,
in that they modulate the expression of late components (dx/db
is mostly flat for early peristimulus time, ?200 ms). In other
words, an increment change in the connectivity of a forward
connection will cause the source activity to change throughout
the whole peristimulus time, whereas an increment change in a
backward connection will cause the source activity to change
considerably for long latencies but will have no effect early in
time. The idea that backward connections are necessary to
explain late ERP components is also supported by the remark-
able improvement of model fit later in peristimulus time for
model FB (afforded by backward connections). Conversely, both
models provide an equally good fit when modeling ERP re-
sponses at early latencies (see Fig. 4 A and B). This means the
backward connections add unnecessary complexity, which is why
the forward model has a greater log-evidence in, and only in,
early phases of the ERP (see Fig. 3A). These graphs show
predicted and observed responses with and without backward
connections projected onto the first eigenmode of a principal
component analysis (PCA). It is evident that the model fit
improves later in time, after ?200 ms, by adding backward
connections to the network. This is coincident with the time
interval for which Bayesian model comparison revealed that the
model with backward connections explains the data much better
at both group and individual subject levels.
Having established face (4) and predictive validity (8) of DCM,
we use it here to provide direct evidence for the theoretical
prediction that evoked brain responses are mediated by reen-
trant dynamics or top-down effects in cortical networks and
therefore rest on backward connections. This is an explicit
statistical test of the hypothesis that evoked responses depend on
top-down effects (1, 2). Furthermore, we hoped to quantify the
relative contribution of bottom-up and top-down effects under
a biologically informed model. Our results show that backward
connections are necessary to explain late neuronal responses.
This evidence was furnished by comparison of models of oddball
responses with and without backward connections. Bayesian
model comparison revealed that the model with backward
connections explains both group and individual data better than
the model with forward connections only. This was particularly
evident for long latencies (?200 ms; see Figs. 2 C and 3).
Furthermore, we were able to quantify the contribution of
backward connections to evoked responses (in both channel and
source space) as a function of peristimulus time. As expected,
on responses throughout peristimulus time, whereas backward
first spatial mode, which was obtained after projection of the scalp data onto eight spatial modes, for (A) FB model and (B) F model. The first mode accounts
for the greatest amount of observed variance. The improvement of model fit due to backward connections for later components is evident. Predicted responses
at each source (solid line) and changes in activity with respect to a unit change in forward (dotted line) and backward connection (dash-dotted line) for (C) right
IFG, (D) right STG, and (E) right A1. The gray bar covers the same period of peristimulus time as in Fig. 2.
Contribution of extrinsic coupling to source activity. The graphs show predicted (solid) and observed (broken) responses in measurement space for the
www.pnas.org?cgi?doi?10.1073?pnas.0706274105Garrido et al.
connections show a temporal specificity, in that they mediate the
expression of late components (?200 ms).
Backward connections are an important part of functional
brain architectures, both empirically and theoretically. The
distinction between forward and backward connections rests on
the notion of cortical hierarchies and the laminar specificity of
their cells of origin and termination (14). Anatomically, back-
ward connections are more abundant than forward connections
(in the proportion of ?1:10/20) and show greater divergence and
convergence. Forward connections have sparse axonal bifurca-
tions and are topographically organized, whereas backward
connections show abundant axonal bifurcation and diffuse to-
pography transcending various hierarchical levels. Functionally,
backward connections have a greater repertoire of synaptic
effects: whereas forward connections mediate postsynaptic ef-
by slow NMDA receptor, which are voltage-sensitive and there-
fore show nonlinear dynamics or modulatory effects (with time
constants ?50 ms) (15, 16). Furthermore, the deployment of
backward synaptic connections on the dendritic tree can endow
them with nonlinear and veto-like properties (17). Backward
connections play a central role in most theoretical and compu-
tational formulations of brain function (18, 19), ranging from the
role of reentry in the theory of neuronal group selection (20) to
recurrent neural networks as universal nonlinear approximators
(21). Several previous studies have highlighted the functional
role of backward connections, especially in the visual domain. It
has been suggested that visual perception or awareness emerges
from neuronal activity in ascending and descending pathways
that link multiple cortical areas (22). Accordingly, recurrent
processing or cortical feedback is necessary for object recogni-
tion (23) and has been found to be important in differentiation
of figure from ground, particularly for stimuli with low salience
(24). Modern-day formulations of Helmholtz’s ideas about per-
ception suggest that backward connections play a critical role in
providing top-down predictions of bottom-up sensory input (25).
Indeed, the hypothesis that the brain tries to infer the causes of
its sensory input refers explicitly to hierarchical models that may
be embodied by cortical hierarchies (26). In these formulations,
the brain suppresses its free energy or prediction error to
reconcile predictions at one level in the hierarchy with those in
neighboring levels. This entails passing prediction errors up the
hierarchy (via forward connections) and passing predictions
down the hierarchy (via backward connections), which is in
conformity with a predictive coding framework based on hier-
archical Bayes (25–27). Experimental evidence consistent with
predictive coding models has arisen from fMRI studies (28–30).
It has been shown that activity in early visual areas is reduced
through cortical feedback from high- to low-level areas, which
simplifies the description of a visual scenery (28) and facilitates
predictive coding models in the context of perceptual decisions
and found an increase in top-down connectivity from the frontal
cortex to face visual areas, when ambiguous sensory information
is provided (30). In predictive coding, evoked responses corre-
spond to prediction error that is explained away (within trial) by
self-organizing neuronal dynamics during perception and is
suppressed (between trials) by changes in synaptic efficacy
during learning. The recurrent dynamics that ensue are a plau-
sible explanation for the form of evoked responses observed
electrophysiologically and the theoretical cornerstone of most
modern theories of perceptual inference and learning.
Materials and Methods
Experimental Design. We chose to study evoked responses known to comprise
paradigm. In this report, we analyze only the responses to the oddball tones.
We acquired electroencephalographic data from 13 healthy volunteers aged
24–35 years (five female) while they were listening to a stream of auditory
tones at 1,000 HZ (standards, occurring 80% of the time for 480 trials).
Occasionally, the tone had a frequency of 2,000 Hz, corresponding to oddball
stimuli (deviant, occurring 20% of the time for 120 trials). The stimuli were
presented binaurally via headphones, in a pseudorandom sequence, for 15
min every 2 seconds. The duration of each tone was 70 ms, with 5-ms rise and
fall times. Subjects sat on a comfortable chair in front of a desk in a dimly
illuminated room and were instructed not to move, to keep their eyes closed,
and to count the deviant tones. We report our results at both the subject and
group levels, by using the ERP averaged over trials within-subject and the ERP
averaged over all subjects. Each subject gave signed informed consent before
the study, which proceeded under local ethical committee guidelines.
Data Acquisition and Processing. EEG was recorded with a Biosemi system with
and horizontal eye movements were monitored by using electrooculogram
of ?100–400 ms, down-sampled to 200 Hz, band-pass-filtered between 0.5
and 40 Hz, and rereferenced to the average of the right and left ear lobes.
Trials in which the absolute amplitude of the signal exceeded 100 ?V were
trials containing artifacts. In the remaining subjects, an average 18% of trials
was reduced to eight channel mixtures or spatial modes. These were the
principal modes of a singular-value decomposition of the channel data from
preserved ?90% of the variance in each subject.
Dynamic Causal Modeling. Most approaches to connectivity in the MEG/EEG
literature use functional connectivity measures, such as phase synchroniza-
tion, temporal correlations, or coherence, that establish statistical dependen-
cies between activities in two sources. Functional connectivity is useful, be-
cause it rests on an operational definition and is therefore independent of
how the dependencies are caused. However, there are cases where we are
precisely interested in the causal architecture of the interactions. Here, DCM
as opposed to functional connectivity. Effective connectivity refers explicitly
to the influence one neuronal system exerts over another and can be esti-
mated by perturbing the system and measuring the response by using Bayes-
ian model inversion (31). DCM is described elsewhere (4–8, 31). In brief, DCM
to make inferences about the parameters of the system and investigate how
these parameters are influenced by experimental factors. Furthermore, by
taking the marginal likelihood over the conditional density of the model
parameters, one can estimate the probability of the data, given a particular
model. This is known as the marginal likelihood or evidence and can be used
to compare different models.
In the context of EEG/MEG, DCM furnishes spatiotemporal, generative or
forward models for evoked responses (4, 5, 7). DCM entails specification of a
plausible model of electrodynamic responses. This model is inverted by optimiz-
ing a variational free energy bound on the model evidence to provide the
conditional density of the model parameters and the model evidence for model
comparison. This is an important advance over conventional analyses of evoked
in one source has to be caused by activity in another. DCMs for MEG/EEG use
neural mass models (6) to explain source activity in terms of the ensemble
based on the model of Jansen and Rit (32). This model emulates the activity of a
source by using three neural subpopulations, each assigned to one of three
cortical layers; an excitatory subpopulation in the granular layer, an inhibitory
subpopulation in the supragranular layer, and a population of deep pyramidal
cells in the infragranular layer. A hierarchical model described in ref. 7 uses
extrinsic connections among multiple sources that conform to the connectivity
rules reported in ref. 12. These rules allow one to build a network of coupled
connections originate in the infragranular layers and terminate in the granular
layer; top-down or backward connections link agranular layers, and lateral con-
nections originate in infragranular layers and target all layers. All these extrinsic
pyramidal cells. The exogenous input, u, models afferent activity to subcortical
same characteristics as forward connections, i.e., exogenous sensory input is
delivered to the granular layer.
The DCM is specified in terms of some state equations that summarize the
Garrido et al.
December 26, 2007 ?
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average synaptic dynamics in terms of spike-rate-dependent current and Download full-text
voltage changes, for each subpopulation
x ˙? f?x, u, ??.
This means that the evolution of the neuronal state, x, is a function (param-
eterized by ?) of the state itself and the input u. An output equation couples
specific states (the average depolarization of pyramidal cells in each source),
x0, to the MEG/EEG signals y by using a conventional linear electromagnetic
y ? L???x0? ?
Eq. 1 summarizes the state equations specifying the rate of change of the
potentials as a function of the current and how currents change as a function
of the currents and the potentials (see refs. 4, 6, and 7 for details). The state
parameters for forward, backward, and lateral connections and their modu-
states to observed channel data. In this application, the lead field L(?) was
parameterized in terms of the location and orientation of each source as
described in ref. 5.
Source Localization and DCM. Source localization refers to inversion of an
electromagnetic forward model that maps sources to observed channels. This
implicitly performs source localization. In practice, priors on dipole locations
or moments (i.e., spatial parameters) are derived from classical source recon-
struction techniques or the literature. The latter approach was taken in this
relatively informative priors; 16 mm2Gaussian dispersion) and orientation
(under uninformative or flat priors).
corresponds to approximating the posterior probability on the parameters,
which is proportional to the probability of the data (the likelihood) condi-
tioned on the model and its parameters, times the prior probability on the
p???y, m? ? p?y??, m?p???m?.
This approximation uses variational Bayes that is formally identical to expec-
tation-maximization (EM), as described in ref. 33. The EM can be formulated
F, of a system. The aim is to minimize the free energy with respect to a
variational density q(?). When the free energy is minimized q(?) ? p(??y,m),
the free energy F ? ?ln p(y?m) is the negative marginal log-likelihood or
negative log-evidence. After convergence and minimization of the free en-
ergy, the variational density is used as an approximation to the desired
conditional density, and the log-evidence is used for model comparison.
One often wants to compare different models and select the best before
making statistical inferences on the basis of the conditional density. The best
model, given the data, is the one with highest log-evidence ln p(y?m) (assuming
a uniform prior over models). Given two models, m1and m0, one can compare
log-evidences ln p(y?m1) ? ln p(y?m0). If this difference is greater than ?3 (i.e.,
their relative likelihood is ?20:1), then one asserts there is strong evidence in
favor of the first model.
ACKNOWLEDGMENTS. We thank David Bradbury for technical support and
the volunteers for participating in this study, Oliver Hulme for comments on
the manuscript, and Marcia Bennett for preparing the manuscript. This work
was funded by Wellcome Trust (J.M.K., S.J.K., and K.J.F.) and the Portuguese
Foundation for Science and Technology (M.I.G.).
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