<s>
Dynamic	B-Algorithm
causal	I-Algorithm
modeling	I-Algorithm
(	O
DCM	O
)	O
is	O
a	O
framework	O
for	O
specifying	O
models	O
,	O
fitting	O
them	O
to	O
data	O
and	O
comparing	O
their	O
evidence	O
using	O
Bayesian	B-General_Concept
model	I-General_Concept
comparison	I-General_Concept
.	O
</s>
<s>
In	O
this	O
setting	O
,	O
differential	O
equations	O
describe	O
the	O
interaction	O
of	O
neural	O
populations	O
,	O
which	O
directly	O
or	O
indirectly	O
give	O
rise	O
to	O
functional	O
neuroimaging	O
data	O
e.g.	O
,	O
functional	B-Algorithm
magnetic	I-Algorithm
resonance	I-Algorithm
imaging	I-Algorithm
(	O
fMRI	B-Algorithm
)	O
,	O
magnetoencephalography	B-Algorithm
(	O
MEG	O
)	O
or	O
electroencephalography	B-Application
(	O
EEG	B-Application
)	O
.	O
</s>
<s>
Bayesian	B-General_Concept
model	I-General_Concept
comparison	I-General_Concept
is	O
used	O
to	O
compare	O
models	O
based	O
on	O
their	O
evidence	O
,	O
which	O
can	O
then	O
be	O
characterised	O
in	O
terms	O
of	O
parameters	O
.	O
</s>
<s>
The	O
evidence	O
for	O
each	O
model	O
is	O
used	O
for	O
Bayesian	B-General_Concept
Model	I-General_Concept
Comparison	I-General_Concept
(	O
at	O
the	O
single-subject	O
level	O
or	O
at	O
the	O
group	O
level	O
)	O
to	O
select	O
the	O
best	O
model(s )	O
.	O
</s>
<s>
Functional	O
neuroimaging	O
experiments	O
are	O
typically	O
either	O
task-based	O
or	O
examine	O
brain	B-Application
activity	I-Application
at	O
rest	O
(	O
resting	B-Algorithm
state	I-Algorithm
)	O
.	O
</s>
<s>
These	O
experimental	O
variables	O
can	O
change	O
neural	O
activity	O
through	O
direct	O
influences	O
on	O
specific	O
brain	O
regions	O
,	O
such	O
as	O
evoked	B-Algorithm
potentials	I-Algorithm
in	O
the	O
early	O
visual	O
cortex	O
,	O
or	O
via	O
a	O
modulation	O
of	O
coupling	O
among	O
neural	O
populations	O
;	O
for	O
example	O
,	O
the	O
influence	O
of	O
attention	O
.	O
</s>
<s>
Resting	B-Algorithm
state	I-Algorithm
experiments	O
have	O
no	O
experimental	O
manipulations	O
within	O
the	O
period	O
of	O
the	O
neuroimaging	O
recording	O
.	O
</s>
<s>
The	O
DCM	O
framework	O
includes	O
models	O
and	O
procedures	O
for	O
analysing	O
resting	B-Algorithm
state	I-Algorithm
data	O
,	O
described	O
in	O
the	O
next	O
section	O
.	O
</s>
<s>
The	O
neural	O
model	O
in	O
DCM	O
for	O
fMRI	B-Algorithm
is	O
a	O
Taylor	O
approximation	O
that	O
captures	O
the	O
gross	O
causal	O
influences	O
between	O
brain	O
regions	O
and	O
their	O
change	O
due	O
to	O
experimental	O
inputs	O
(	O
see	O
picture	O
)	O
.	O
</s>
<s>
DCM	O
for	O
resting	B-Algorithm
state	I-Algorithm
studies	O
was	O
first	O
introduced	O
in	O
Stochastic	O
DCM	O
,	O
which	O
estimates	O
both	O
neural	O
fluctuations	O
and	O
connectivity	O
parameters	O
in	O
the	O
time	O
domain	O
,	O
using	O
Generalized	O
Filtering	O
.	O
</s>
<s>
A	O
more	O
efficient	O
scheme	O
for	O
resting	B-Algorithm
state	I-Algorithm
data	O
was	O
subsequently	O
introduced	O
which	O
operates	O
in	O
the	O
frequency	O
domain	O
,	O
called	O
DCM	O
for	O
Cross-Spectral	O
Density	O
(	O
CSD	O
)	O
.	O
</s>
<s>
Another	O
recent	O
development	O
for	O
resting	B-Algorithm
state	I-Algorithm
analysis	O
is	O
Regression	O
DCM	O
implemented	O
in	O
the	O
Tapas	O
software	O
collection	O
(	O
see	O
Software	O
implementations	O
)	O
.	O
</s>
<s>
DCM	O
for	O
EEG	B-Application
and	O
MEG	O
data	O
use	O
more	O
biologically	O
detailed	O
neural	O
models	O
than	O
fMRI	B-Algorithm
,	O
due	O
to	O
the	O
higher	O
temporal	O
resolution	O
of	O
these	O
measurement	O
techniques	O
.	O
</s>
<s>
Convolution	B-Language
models	O
were	O
introduced	O
by	O
Wilson	B-Algorithm
&	I-Algorithm
Cowan	I-Algorithm
and	O
Freeman	O
in	O
the	O
1970s	O
and	O
involve	O
a	O
convolution	B-Language
of	O
pre-synaptic	O
input	O
by	O
a	O
synaptic	O
kernel	O
function	O
.	O
</s>
<s>
Convolution	B-Language
models	O
:	O
</s>
<s>
DCM	O
for	O
evoked	B-Algorithm
responses	I-Algorithm
(	O
DCM	O
for	O
ERP	O
)	O
.	O
</s>
<s>
The	O
first	O
operator	O
transforms	O
the	O
pre-synaptic	O
firing	O
rate	O
into	O
a	O
Post-Synaptic	O
Potential	O
(	O
PSP	O
)	O
,	O
by	O
convolving	B-Language
pre-synaptic	O
input	O
with	O
a	O
synaptic	O
response	O
function	O
(	O
kernel	O
)	O
.	O
</s>
<s>
The	O
second	O
operator	O
,	O
a	O
sigmoid	B-Algorithm
function	I-Algorithm
,	O
transforms	O
the	O
membrane	O
potential	O
into	O
a	O
firing	O
rate	O
of	O
action	O
potentials	O
.	O
</s>
<s>
A	O
version	O
of	O
the	O
CMC	O
has	O
been	O
applied	O
to	O
model	O
multi-modal	O
MEG	O
and	O
fMRI	B-Algorithm
data	O
.	O
</s>
<s>
Whereas	O
DCM	O
for	O
fMRI	B-Algorithm
and	O
the	O
convolution	B-Language
models	O
represent	O
the	O
activity	O
of	O
each	O
neural	O
population	O
by	O
a	O
single	O
number	O
-	O
its	O
mean	O
activity	O
-	O
the	O
conductance	O
models	O
include	O
the	O
full	O
density	O
(	O
probability	O
distribution	O
)	O
of	O
activity	O
within	O
the	O
population	O
.	O
</s>
<s>
Hypotheses	O
are	O
tested	O
by	O
comparing	O
the	O
evidence	O
for	O
different	O
models	O
based	O
on	O
their	O
free	O
energy	O
,	O
a	O
procedure	O
called	O
Bayesian	B-General_Concept
model	I-General_Concept
comparison	I-General_Concept
.	O
</s>
<s>
There	O
are	O
two	O
predominant	O
approaches	O
for	O
group-level	O
analysis	O
:	O
random	O
effects	O
Bayesian	B-General_Concept
Model	I-General_Concept
Selection	I-General_Concept
(	O
BMS	O
)	O
and	O
Parametric	O
Empirical	O
Bayes	O
(	O
PEB	O
)	O
.	O
</s>
<s>
This	O
has	O
included	O
testing	O
against	O
iEEG	O
/	O
EEG	B-Application
/	O
stimulation	O
and	O
against	O
known	O
pharmacological	O
treatments	O
.	O
</s>
