Aging is generally thought to be accompanied by reduced neuronal plasticity and a
loss of neuronal processes that accounts for a loss of grey matter, which progresses
gently with age –. Many concomitants of physiological aging have been studied.
In particular, studies of the mismatch negativity (MMN) speak to a decline in sensory
learning or memory , . For example, elderly subjects show a significant reduction
in superior temporal gyrus responses, which has been interpreted as “an aging-related
decline in auditory sensory memory and automatic change detection” . In this work,
we examine the physiological basis of attenuated mismatch responses using dynamic
causal modeling in a large cohort of human subjects. However, we motivate the present
study using an alternative – and slightly more optimistic – model of normal aging.
Our basic premise is that aging reflects a progressive refinement and optimization
of generative models used by the brain to predict states of the world – and to facilitate
an active exchange with it. Evidence that the brain learns to predict its environment
has been demonstrated in the perceptual , motor  and cognitive domains .
These studies are motivated by formal theories – such as the free energy principle
and predictive coding – that appeal to the Bayesian brain hypothesis –. In
this theoretical framework , the quality of the brain's model is measured by Bayesian
model evidence. Crucially, model evidence can be expressed as accuracy minus complexity.
This means that as the brain gets older – and maintains an accurate prediction of
the sensorium – it can progressively improve its performance by decreasing its complexity.
This provides a normative account for the loss of synaptic connections and fits intuitively
with the notion that as we get older we get wiser, more sanguine and ‘stuck in our
ways’. Formally, under the Free Energy Principle, the brain supports active exchanges
with the environment in order to minimize the surprise associated with sensory inputs.
Over time, learning optimizes brain connectivity to support better predictions of
the environment . These ‘better’ models must conform to Occam's razor by providing
accurate predictions with minimal complexity . In Figure 1 we illustrate model
qualities prescribed by the Free Energy Principle, potential age effects and their
context or environmental sensitivity. This formulation of Free Energy minimization
is based on hierarchical message passing and predictive coding. Neuronal implementations
of predictive coding have been proposed as the mechanisms underlying the MMN ,
. In the present study, we address the corollary of model complexity minimization;
namely, less reliance on Bayesian updating through sensory learning and underlying
neuronal plasticity. Mathematically, an attenuation of Bayesian learning precludes
overfitting of sensory data; thereby minimizing complexity and ensuring that explanations
for those data generalize. In other words, as we age, we converge on an accurate and
parsimonious model of our particular world (Figure 1B) - whose constancy we actively
strive to maintain (Figure 1B). Its neuronal implementation would be consistent with
a large literature on synaptic mechanisms in aging and a progressive decline in neuromodulatory
(e.g., dopaminergic , ) activity that underwrites changes in synaptic efficacy
Hypotheses – explanations for sensory input.
A) The Negative Free Energy (F) is maximized by the brain (model, m) to ensure homeo/allostasis.
An optimal model can accurately predict incoming sensory signals s, (this accuracy
term is the expected log-likelihood of the sensory signal s, under the conditional
density, q ie.
) while ensuring generalization, when inferring new sensory causes (θ represented
through their sufficient statistics μ). This complexity penalty
is revealed during the presentation of the oddball. Given changes in synaptic efficacy
of forward connections; i.e. learning the standard tone - the Kullback-Leibler (KL)
divergence between the learned prior, p and the posterior, q under these new (oddball)
data will be high. These effects, indicating brittle models, were hypothesized to
be less pronounced in older subjects. B) An illustration of how model optimality depends
on the environment. Left-most panels: In a constant environment both young (top) and
old (bottom) brains have connections that convey accurate predictions (blue arrows).
The sensory input, s, will result in prediction error messages (red arrows) that are
cancelled by the appropriate prediction. A change in the environment (e.g., from a
dog bark to a human voice) will result in prediction error signals along the human
voice pathway until human voice predictions are made and cancellation occurs. This
type of predictive coding scheme has been proposed as the mechanism underlying the
mismatch negativity . In this scenario, both young and old brains generate accurate
predictions with similar complexity. Centre Left panels: repeated sensory input from
a specific human voice results in new prediction and error pathways for that particular
vocalization in a younger brain. For this environment, the younger brain is more accurate
(at the penalty of higher complexity) and may outperform the older brain in terms
of model quality. Centre Right panels: on return to the original environment, the
older brain – that has maintained a less complex model – outperforms the younger brain.
Right-most panels: In a novel environment that persists, younger brains – that support
more flexible Bayesian updating – will outperform older brains. In this context, the
degrees of freedom subtended by effective connections in the older brain are not sufficient
to simulate the environment and provide accurate predictions.
The implications for the neurobiology of aging are that – over the years – cortical
message passing may become more efficient (providing accurate predictions with a less
redundant or complex hierarchical model) and increasingly dominated by top-down predictions.
This is consistent with reports of age-induced shifts in neuronal activation from
sensory to prefrontal regions . The hypothesis addressed in the present study
was that the Bayesian updating implicit in the sensory learning of standard stimuli
in the MMN paradigm would fall progressively with age. In particular, we predicted
that changes in effective connectivity during the processing of repeated stimuli (namely,
changes in forward connections to superior temporal cortex) would be attenuated as
a function of age.
Here, we examined age-related attenuation of sensory learning by quantifying synaptic
coupling or effective connectivity changes using the mismatch negativity (MMN) paradigm
and dynamic causal modeling (DCM). There is a large literature on DCM and the MMN
–, where changes in coupling during repetition of standard stimuli are revealed
by differential responses to oddball stimuli – producing the MMN (oddball minus standard)
difference in event related potentials that peaks around 150 msec. These connectivity
changes (plasticity) are expressed in both intrinsic connections within auditory sources
and in an increase in the effective connectivity from auditory to superior temporal
sources during the processing of oddball relative to (learned) standard stimuli .
These changes have been interpreted in terms of predictive coding, in which bottom-up
or ascending prediction errors (under modulatory gain control) adjust representations
at higher levels in the cortical hierarchy – that then reciprocate descending predictions
to cancel prediction error at lower levels.
Recent studies of age-related changes in functional connectivity provide evidence
for changes in long-range coupling with age . Our hypothesis rests on changes
in (directed) effective connectivity that produces the functional connectivity or
dependencies in measured activity . To quantify changes in effective connectivity
we used DCM  to model magnetoencephalographic (MEG) recordings. DCM uses forward
models of evoked responses based on neuronal mass formulations that account for the
laminar specificity of forward and backward connections . These models have been
previously validated using animal  and human recordings , and provide subject-specific
measures of intrinsic (within source) and extrinsic (between source) synaptic coupling.
Dynamic Causal Modeling of Sensory Evoked Responses
We measured event-related MEG responses in 97 subjects, aged 20 to 83 and applied
DCM to quantify the underlying synaptic coupling producing observed responses. We
used an auditory oddball paradigm to elicit the mismatch negativity or MMN . Our
stimuli comprised pseudo-random tone sequences, with standard (frequent) tones interspersed
with infrequent oddball tones (with a presentation frequency of 88% and 12% respectively).
Consistent with previous studies of MMN generation , , source localization
revealed hierarchical responses (Figure 2A), with large magnitude responses in auditory,
temporal and inferior frontal sources (p<0.05 family-wise error corrected; Figure
2A). A prominent MMN (oddball – minus standard) was observed, as expected, around
150 msec post stimulus (Figure 2B).
A) Statistical parametric mapping of mismatch (standard – oddball) effect across subjects
(p<0.05 FWE corrected) sharing a color-coded F statistic on a semi-transparent canonical
cortical inflated mesh. This SPM compares the power (in frequencies from 0–30 Hz,
over 60–300 msec of peristimulus time), evoked by oddball stimuli with the equivalent
power evoked by standard stimuli. B) Auditory evoked responses recorded at one MEG
sensor over right frontal cortex. Plotted are the grand averaged evoked measurements
across all sessions (shaded areas represent their standard deviation) in response
to standard tones (blue) and oddball tones (green). The difference in these responses
constitutes the mismatch negativity (MMN); seen here as the negative differences from
100–200 msec (white inset) – as predicted from the literature. Both types of trials
were fitted for each subject in the DCM analysis. C) In the DCM, we modeled the transmission
of neuronal activity from primary sensory to frontal regions using three sources reciprocally
connected in each hemisphere; source location priors were as follows: left HG: x = −42,
y = −22, z = 7; right HG: x = 46, y = −14, z = 8; left STG: x = −61, y = −32, z = 8;
right STG: x = 59, y = −25, z = 8; left IFG: x = −46, y = 20, z = 8; right IFG: x = 46,
y = 20, z = 8. Inputs entered Heschl's gyrus bilaterally and were passed via forward
connections to STG within each hemisphere. STG sent top-down backward connections
to HG. STG also sent forward connections up to IFG and received backward connections
from IFG. Each source is modeled in the DCM with a neural mass model. The parameters
of synaptic interactions within each source, as well as the extrinsic connections
between sources were optimized during model inversion. The extrinsic connectivity
was equipped with an additional parameter that allowed for different connection strengths
during standard or oddball stimulus processing.
Following previous DCM studies of the MMN, we used a six–source model to characterize
age effects within the MMN network (Figure 2C). For each subject, we inverted the
ensuing DCM to obtain subject-specific measures of (changes in) connectivity based
on their evoked responses to standards and oddballs. In this DCM, auditory input enters
bilaterally at Heschl's gyrus (HG), these primary auditory sources were connected
via forward connections to superior temporal gyrus (STG) sources, which in turn sent
forward connections to the inferior frontal gyrus (IFG). Reciprocal backward connections
were included to allow signal propagation down the hierarchy from IFG to STG and from
STG to HG (Figure 2C). Each source was modeled with a neural mass model comprising
three neuronal populations, with distinct receptor types and intrinsic connectivity
. Specifically, the model contains synaptic parameters that encode the contribution
of AMPA, NMDA and GABAa receptor mediated currents in three populations: comprising
pyramidal cells, inhibitory interneurons and granular-layer spiny-stellate cells.
These populations are connected intrinsically and receive extrinsic inputs according
to their laminar disposition: forward connections drive spiny stellate cells and backward
connections drive pyramidal cells and inhibitory interneurons . Crucially, we
included stimulus-specific parameters that changed the strength of extrinsic connections
when responding to standard and oddball inputs. This enabled us to test our hypothesis
of age-related differences in connectivity changes. Specifically, we hypothesized
that the learning or repetition-dependent increase in sensitivity to extrinsic forward
afferents – conveying prediction errors induced by the oddball events – would be attenuated
in older subjects.
An analysis of model fits confirmed that DCM provided an accurate account of the evoked
responses (193 data sets were inverted in total), accounting for 81%±12% (mean ± std)
of the empirical variance (for a representative example see Figure 3A). We found no
evidence for age-dependent differences in model fit (p>0.1, Pearson correlation of
age and proportion of variance explained).
Age Effects from DCM's Neuronal Parameters.
A) Representative example of data fit shown as a sensor space image for all MEG channels
(along the x-axis) over peristimulus time (0–300 msec along the y-axis). Data are
normalized to arbitrary units according to color bar. B) Subjects age as predicted
by a linear regression on the DCM neuronal parameters. C) Left: Contribution of each
parameter to the regression: negative log p-value for all 38 regression coefficients
(37 DCM parameters and a constant; Table 1) as assessed using the appropriate t-statistic.
The horizontal line depicts the Bonferroni-corrected significance level. One parameter
has a significant p-value: this parameter encoded the difference in forward connectivity
to right STG, between oddballs and standard and had a negative correlation with age.
Right: Red is the forward connectivity parameter, illustrated within the DCM architecture,
where age was predicted. D) Individual DCM parameter estimates. Left: the parameter
controlling changes in connectivity from right HG to right STG identified above, plotted
according to an adjusted (for the effect of remaining parameters in the regression
model} age ranking. Right: a similar plot illustrating the latent connectivity strength
from right HG to right STG, plotted according to age rank, adjusted as above.
Neuronal Parameters Predicting Age
Having established the accuracy of the DCM, we then asked whether the subjects' age
could be predicted by neuronal parameters that included: i) the strength of forward
and backward extrinsic connections, ii) changes in these connections during oddball
(compared to standard) tones, iii) the strength of intrinsic connections within each
source, iv) parameters controlling synaptic adaptation; namely, time constants of
AMPA, NMDA and GABAa receptors, membrane capacitance, subcortical input strength and
axonal delays (37 parameters and a constant term see Table 1). Electromagnetic lead
field parameters were optimized for each DCM but not included in this predictive analysis
Neuronal parameters of the DCM – description and prior values presented in Figure
Parameter (Parameter Index in Figure 3C)
Parameter controlling covariance amongst states (optimized for all sources)
Average synaptic time-constant AMPA-like channels (optimized per source)
NMDA like channels
Intrinsic Excitatory Connectivity (optimized per source)
Extrinsic Forward Connection
Extrinsic Backward Connections
Modulations of Extrinsic Connection
Input Strength of volley from Thalamus to Left and Right Primary Auditory Cortex
Controls the size of the input volley (a Gaussian bump function) from the thalamus,
onset: 64 msec
Controls the duration of the input volley
Intrinsic conduction delay
Extrinsic conduction delay
Background Synaptic Input
Note parameters are log-scaling parameters:
. These operate on variables with the following prior mean – and can be found in spm_fx_nmda.m,
part of the DCM_MEG toolbox in SPM (http://www.fil.ion.ucl.ac.uk/spm/).
(* indicates age-predictive parameter).
Using a multiple linear regression, we found that the neuronal DCM parameters could
predict age with a high degree of reliability (R2
= 0.56; F37,59 = 2.06; p = 0.006; Figure 3B). Post-hoc t-tests were used to identify
the parameters with the greatest predictive ability. Across all regression coefficients,
the largest and only significant regression coefficient (correcting for 38 tests)
was associated with the learning dependent increase in forward connectivity from the
right primary auditory cortex to the right superior temporal gyrus (β = −36.41; p<0.05
Bonferroni corrected, Figure 3C). This increase was attenuated over the lifespan,
speaking to a reduced sensitivity of STG responses to ascending (prediction error)
afferents from primary auditory cortex. This was in contradistinction to the latent
connectivity strengths from right primary auditory to superior temporal gyrus - that
do not reflect learning – which were consistent across the lifespan population (Figure
Complexity Minimization under the Free Energy Principle
The Free Energy Principle  provides a description of neurobiological circuit processing
that attributes specific computational roles to forward, backward, lateral (extrinsic)
connections and intrinsic connections and their neuromodulation . Each level of
a processing hierarchy transmits predictions to the level below, which reciprocates
with bottom-up prediction errors. Bayes optimal perception and action is achieved
by maximising the Negative Free Energy (F):
Maximising this functional at every point in time ensures homeo/allostasis , by
minimising the surprise (the negative log model evidence
) of incoming sensory signals s caused by states of the world
, represented in the brain with their sufficient statistics μ. It renders the current
prediction of states of the environment;
, close to the true probability of those states;
(where the distance measure is the Kullback-Leibler divergence KL). This process is
dependent on the model the brain instantiates, m. Rearranging this equation, we see
that the quality of this model can be decomposed into two components; representing
accuracy and complexity.
In our connectivity analysis, the only consistent aging effect was manifest in trial-by-trial
updates and revealed during the presentation of the oddball. This is represented mathematically
as the KL-divergence from the approximate posterior to the prior, ie. the complexity
penalty; which reduced over the lifespan (Figure 1). Over-learning of the standard
tone by younger subjects is indicative of brittle models. These effects were significantly
less pronounced as our cohort (cross-sectionally) aged. In contrast, accuracy was
equivalent across the lifespan on a trial-average basis, since younger subjects learned
the standard tone; indicating poor predictions to early standard and all deviant tones
with better predictions to later standard tones; while age induced greater baseline
predictions overall, that were generalizable to auditory deviants.
These results are interesting for two reasons. First, the ability of subject-specific
DCM parameters to predict age in such a reliable way suggests that the coupling estimates
have a high degree of predictive validity. Second, it is remarkable that the most
predictive parameter encoded a sensory learning effect – as opposed to a connection
engaged by the predictive coding of standard or oddball stimuli per se. Furthermore,
the particular connection implicated – the forward primary auditory afferent to STG
– has been found to increase in previous DCM studies of the MMN . The present
study is the largest DCM study reported to date and underscores a general point; namely,
that biologically grounded models of evoked responses can disclose important associations
between quantitative estimates of functional brain architectures and the behavioral
or clinical phenotype. In particular, we used our data to estimate the underlying
causes of evoked responses – and did not simply look for correlations between age
and a particular data feature (e.g., the MMN magnitude). This means that we could
account for a range of potentially age-related confounds (e.g., intersubject differences
in lead fields) that would otherwise obscure structure-function relationships of interest.
In conclusion, our results suggest that effective connectivity in the human brain
does not undergo indiscriminate age-related decline but shows a selective and specific
attenuation of plasticity in the face of short-term sensory learning or memory. In
other words, there were no systematic age-related changes in effective connectivity
when processing auditory stimuli per se. This is consistent with the conjecture that
older brains are more efficient (less complex) models of the sensorium and are less
predisposed to short-term (Bayesian) updating.
The present study was motivated by recent perspectives provided by theoretical neurobiology
 that offer a principled explanation for the reduction in connectivity (complexity)
with progressive optimization of the generative models the brain uses for hierarchical
Bayesian inference. A corollary of this complexity minimization is decreased Bayesian
updating and neuroplasticity that we confirmed experimentally with a sensory learning
(oddball) paradigm. Our results may call for a reinterpretation of aging neuroimaging
studies; in particular, the compensation hypothesis that has been provided as explanation
for age-related changes in the pattern of cortical activations , , . Indeed,
a reinterpretation has been offered from a cognitive perspective  where a shift
from bottom-up to top-down processing has been proposed to explain better cognitive
performance in older individuals . These performance gains have been shown to
accrue in unconventional (generalized) re-test circumstances; e.g. using distractors
that should have been ignored in one task, to complete later tasks . From the
perspective of task performance, complexity reduction would similarly support reliability,
as exhibited by older participants in a recent study of performance consistency across
multiple cognitive domains . The complexity minimization perspective may also
account for de-differentiation in cortical specialization – and cognitive
structure ,  due to age - in the sense that simpler generative models require
fewer degrees of freedom (functional specialization) to predict sensorimotor contingencies.
While our results focus on functional connections, structural changes commensurate
with complexity reduction have recently been demonstrated in a non-aged but practiced
cohort of ballerinas. In their study , highly trained ballet dancers - who show
improved stability in response to spinning - exhibited grey matter reductions in cerebellar
grey matter compared to controls. Furthermore, controls showed enhanced vestibular
perception that was positively correlated with cortical white-matter measures, an
effect absent in the dancers, effects summarized by the authors as “training-related
Interestingly, the schema presented in Figure 1 was supported by learning effects
in early sensory cortex. These were constrained to the right hemisphere, where classical
MMN effects are most pronounced . Complexity reduction could potentially evolve
over the lifespan, providing a balance of metabolic cost  to allow for an elaboration
of model components in multi-modal regions. It could also contribute directly to the
poor discriminability of (unimodal) sensory inputs observed in older adults ,
which in turn may preface as a ‘common cause’, age-related cognitive disruption .
From a physiological perspective, predictive coding may provide a useful process theory
for neuronal computations in aging. For example, simulations of the mismatch negativity
paradigm predict a rapid trial-by-trial suppression of evoked responses that rests
on the neuromodulation of superficial pyramidal cells reporting prediction error.
Previously, we confirmed this prediction empirically using dynamic causal modeling
and a placebo-controlled study of cholinesterase inhibition . In a complementary
simulation study of frequency-based MMN, NMDA mediated synaptic plasticity has been
shown to underpin model reorganization at the predictive cell population . Given
the therapeutic benefit of cholinesterase inhibition , and the role of NMDA receptors
 in dementia further modeling of non-invasive psychopharmacological studies may
provide important insights into the synaptic basis of age-related changes in perceptual
We studied 97 healthy volunteers, 55 female, who were cognitively normal with no neurological
or psychiatric illness or serious medical history. Subjects were aged 20 to 83 and
all completed the recording paradigm.
Subjects were paid for their participation and consented to all procedures, which
were conducted in accordance with the Declaration of Helsinki (1991). Protocols were
approved by the South-East Strategic Health Authority Regional NHS Ethics Committee.
Experimental Paradigm and MEG Data Acquisition
MEG recordings were made in a magnetically shielded room using a 275-channel CTF system
with SQUID-based axial gradiometers (VSM MedTech Ltd., Couquitlam, BC, Canada). Recordings
were obtained during two sessions with a small rest period between scanning, during
which time subjects remained in the MEG scanner. Head localisation was performed at
the beginning of each session.
Auditory responses were elicited by stimuli comprising pure tones presented binaurally
over headphones. Two stimuli, at 500 Hz and 800 Hz were presented in a pseudo-random
sequence for 70 msec with 10 msec rise and fall times. The first tone served as the
standard and was presented on 88% of trials, while the second, which served as the
oddball, was presented on 12% of trials. The sequence ensured that the minimal interval
between oddballs was 2 trials and the maximum was 25 trials. The ISI was fixed at
1100 msec. Loudness was adapted to each subject's auditory threshold to be clearly
audible binaurally – as measured in a test run while in the scanner. We collected
data over two sessions for 96 subjects. For one subject we recorded just one session.
Sessions were 6 minutes in length.
Data Pre-processing and Source Localization
MEG data were first filtered off-line (band-passed from 0.5–30 Hz), down-sampled (to
200 Hz), epoched (from −150 ms to 350 ms peri-stimulus time), baseline corrected to
0 ms peristimulus time, artefact corrected (peak-to-peak threshold 5pF) and averaged
to obtain event related fields (ERFs). The analysis routines we used are available
in the academic freeware SPM8 (http://www.fil.ion.ucl.ac.uk/spm/).
For source localization, multiple sparse priors were used to estimate the cortical
sources of the sensor recordings, using standard settings . Multiple sparse priors
employs several hundred patches of activation that are iteratively reduced until an
optimal number and location of active patches are found using a greedy Bayesian search.
A tessellated cortical mesh set in canonical Montreal Neurological Institute (MNI)
anatomical space – as implemented in SPM8 – served as a brain model . This dipole
mesh was used to calculate the forward solution using a spherical head model. Source
activity measures were then interpolated into MNI voxel space and analysed using statistical
parametric mapping – at the between subject level – using an F test: A contrast of
standard vs deviant stimuli was computed at p<0.05 family-wise error corrected (Figure
2) based on the evoked power over frequencies from 0–30 Hz and from 60 to 300 msec
Dynamic Causal Modeling
For dynamic causal modeling, we used source location priors as described in previous
DCM analyses of the mismatch negativity (MMN) paradigm , . These included
sources in Heschl's gyrus, superior temporal cortex and inferior frontal gyrus and
were consistent with the source localisation analyses. The MNI coordinates were as
follows: left HG: x = −42, y = −22, z = 7; right HG: x = 46, y = −14, z = 8; left
STG: x = −61, y = −32, z = 8; right STG: x = 59, y = −25, z = 8; left IFG: x = −46,
y = 20, z = 8; right IFG: x = 46, y = 20, z = 8. These prior locations were optimised
at an individual level during DCM inversion using distributed dipoles and the forward
solution from the above source localisation .
In DCM, event related fields are modelled as the response of a dynamic input–output
system to exogenous (experimental) inputs . The DCM generates a predicted ERF
as the response of a network of coupled sources to sensory (thalamic) input – where
each source corresponds to a neural mass model of three neuronal populations. Our
dynamic causal models comprised hierarchical sources with prior locations as defined
above, extrinsic input to primary sensory regions and extrinsic connections of forward
and backward type :
MEG sensor data were fitted over 0–300 msec peristimulus time, with the following
model: auditory input (modelled as a Gaussian bump-function, with a prior onset of
64 msec) entered bilateral Heschl's gyrus, which provided forward connections to STG
within each hemisphere. STG sent top-down backward connections to HG. STG also sent
forward connections up to IFG and received backward type connections from IFG. To
accommodate trial-dependent differences, stimulus specific parameters were included
for all extrinsic connections. The neural mass model describing the activity of each
source comprised three subpopulations, each assigned to three cortical layers – which
determine how they receive external inputs . Spiny stellate cells receive input
via forward and thalamic inputs and are located in layer IV. Pyramidal cells and inhibitory
interneurons are located outside of layer IV. These receive inputs from backward connections.
Extrinsic output cells are the pyramidal cell subpopulation in each region.
The neuronal dynamics were based on a conductance based model with intrinsic AMPA
receptors (at all cell populations), GABAa receptors (at pyramidal cell populations
and inhibitory interneurons) and NMDA receptors (at pyramidal cell populations and
inhibitory interneurons)  (specified as the “NMDA” model in the SPM interface).
The DCM generates a predicted ERF as the response of the network of coupled sources
to sensory input. This input takes the form of a narrow (16 msec) Gaussian impulse
function, which accounts for some temporal smoothing in thalamic volleys.
For computational expediency, DCMs were computed following dimensionality reduction
to eight channel mixtures or spatial modes. These were the eight principal modes of
a singular value decomposition (SVD) of prior predictive covariance based upon the
prior source locations. Note that data are normalized prior to model inversion and
the forward model which accounts for source transmission to the MEG sensors is also
parameterised and optimised during inversion.
Analyses of Conditional Model Parameters
Where data were collected over multiple trial runs (96 out of 97 subjects), DCMs were
fitted for each run separately and post-hoc conditional parameter means were computed
using Bayesian parameter averaging (BPA). These were used for the regression models
and lifespan correlation. BPA involves a weighted average where each model's posterior
mean (in DCM.Ep) is weighted with its relative precision, where precisions are obtained
from the inverse of the posterior covariance.