Supplemental Methods
Clinical Measures: Additional clinical assessments of depression severity (Hamilton
Rating Scale of Depression-17 Item (HRSD-17; (Hamilton, 1967)) and anxiety (Beck Anxiety
Inventory; BAI; and State-Trait Anxiety Scale; STAI; (Spielberger, 1983), temperament
(Retrospective Self Report of Inhibition (RSRI; (Reznick, 1992), current stress (Perceived
Stress Scale; PSS-14; (Cohen, 1983), recent life stressors (Recent Life Events; RLE (Brugha,
1985) were performed. Group comparisons are included in Table 1.
UCS duration: To address questions that were not the focus of the present analysis,
participants were assigned to either a Controllable or Uncontrollable group. Participants in the
Condition (CC) were informed that the UCS would last between 0.5-6.0 s, and that they had the
ability to control the duration of the UCS. They were informed that they could terminate the
UCS by pressing a button on the joystick. In doing so, CC participants determined the duration
of the UCS for themselves as well as their matched Uncontrollable Condition (UC) counterpart.
UC participants were also informed that the UCS would last between 0.5-6.0 s. Given that UC
participants did not have the ability to control the UCS, they were instructed to make a button
press when the UCS ended, to control for motor activity associated with the button presses
made by their match in the CC group.
Imaging Analysis: Functional data were analyzed using Statistical Parametric Mapping
(SPM8, Wellcome Department of Cognitive Neurology, London, UK). Functional data were
analyzed using Statistical Parametric Mapping (SPM8, Wellcome Department of Cognitive
Neurology, London, UK). Echo-planar time series data were subsequently slice time and motion
corrected (ArtRepair; [Mazaika, 2009], realigned and unwarped. High-resolution T1 images
were coregistered with the mean EPI image and segmented using the New Segment routine in
SPM8. Tissue-reclassification for gray, white matter and CSF were performed using DARTEL
to create structural templates derived from all study participants as well as individual flow fields
(Ashburner, 2007). Flow fields were then used to spatially normalize the EPI images into
standard Montreal Neurological Institute (MNI) space.
Granger Causality Modeling
Let j fMRI time series be represented as X(t) = [x1(t) x2(t) … xj(t)]. A dynamic statespace model can be described as follows.
 nj   f (nj1 , uj1 ,  j1 )  X j1 
  
  j 
n~ j  uj   
uj1
   Y 1 
j
j
  
  Z j1 
 1
  
 

Where n is the neuronal state
variable, u is the exogenous input and θ are
the parameter variables. The current neuronal state is linked to the previous neuronal states,
exogenous inputs and parameters by function f. The subscript τ indicates continuous time and
the superscript j indicates the number of time series in the model. X, Y and Z are zero mean
Gaussian state noise vectors. The observation equation, which links the state to observation
variables, is as follows.
~ j ) 
x j (t )  h(n
t
t 1
Where h is the measurement function which links the state variables to measurement
variables, t is discrete time and η is the measurement noise. The inputs to the model are
a (0) ... a (0)  n (t)
 a (m) a (m) ... a (m)  n (t - m)   e (t)
 n1(t)  0
12
1j
12
1j 
1
 11


 1
 1 
n (t) a (0)
n (t)
0
a
(0)
a
(m)
a
(m)
a
(m)
n
(t
m
)


 e2 (t)
 2   21
2j   2 
22
2j   2
  21


 .  .
.
.  .     .
.
.  .    . 
 
0
 .  
 m  1
  .   . 
.
.   . 
.
.
.

  .


 
 
n j (t)  a j1(0) a j2(0) ... 0  n j (t)
 a j1(m) a j2(m) ... a jj(m)  n j (t - m)  e j (t)




exogenous inputs u, which is the experimental boxcar function, and xj(t) is the observed fMRI
signal. As shown earlier, blind hemodynamic deconvolution using cubature Kalman filter is
very efficient in performing a joint estimation of the hidden neuronal variables and parameters
(Havlicek et al, 2011). In addition, by using a time step up to 10 times smaller than the TR
while discretizing the continuous time model, higher effective temporal resolution can be
obtained. As a result, the efficiency of the connectivity analysis is improved. The neuronal state
varia
a (0,t) ... a (0,t)  n (t) 
 a (m, t) a (m, t) ... aj(m,t)   n (t - m)   e (t) 
 n1(t)   0
12
1j
12
1
 11
  1
  1 

n (t) a (0,t)
a (m, t) a (m, t)
a (m, t)  n (t - m) e (t)
0
a (0,t) n (t)


21
22
2j
 2 
 2 
2 
21
2j
2
 
 
 . 
.
 .  .
.
.
.

.
.  .    



 
0
 .  
 m  1
 
  . 
.
.
.
.
.
.   . 

  .




 
0  n j (t)
n j (t)  a j1(0,t) a j2(0,t) ...
 a j1(m, t) a j2(m, t) ... a jj (nmt) n j (t - m) e j (t)




bles
nj(t)
can
be input into the MVAR as follows:
Where ρ is the order of the model determined by the Akaike/Bayesian information
criterion(Deshpande et al, 2009), e is the model error and a are the model coefficients. Here a
(0) represents the instantaneous influences between time series while a(m), m=1 .. j represent
the causal influences between time series. As shown previously, the effect of instantaneous
correlation on the causal metrics can be minimized by modeling both causal and instantaneous
terms in a single model(Deshpande et al, 2010). The MVAR model can be made dynamic by
allowing the model coefficients to vary as a function of time as given below.
The model coefficients a (m,t) were taken as the state vector of a Kalman filter and
adaptively estimated using the algorithm proposed by Arnold and colleagues(Arnold et al,
1998). Dynamic Granger causality (DGC) was then obtained as follows
DGC pq (t ) 

 [a
m 1
pq ( m, t )]
 p  1 j, q  1 j
Several earlier studies have used these MVAR models based on the GC framework to
study the predictive relationship between time series from different brain regions (Roebroeck et
al., 2005, Abler et al., 2006, Deshpande et al., 2008, Deshpande et al., 2009). However it was
shown that using raw fMRI time series in GC analysis could lead to confounds in the estimated
causal connectivity metrics (David et al., 2008, Deshpande et al., 2010), which can be attributed
to the spatial variability of the hemodynamic response (HRF) which may in part be of nonneural origin (Handwerker et al., 2004). Consequently, blind deconvolution of the
hemodynamic response and subsequent GC analysis in the latent neuronal space has been
employed (Deshpande et al., 2011, Grant, 2014). In the current study, we obtained condition
specific connectivity values by applying the dynamic MVAR model to the latent neuronal
variables estimated by blind hemodynamic deconvolution using a cubature Kalman filter as
described below (Havlicek et al., 2011).
ANOVA
A group [ELS vs non-ELS] x region of interest [CeA, BLA, SF] ANOVA was employed
to determine whether the groups differed in response to the UCS in any of the three a priori
defined amygdala subregions.
Results
Stimulus Duration
No group differences were observed with regard to stimulus duration across the two
runs, (t=.087, p=.93; ELS Mean= 3.7 sec, Non-ELS Mean=3.6 sec). Thus, no further analysis
based on duration of stimulus was performed.
Group differences in BOLD response
Bilateral differences were observed between regions [right: F(2,64)=15.62, p<.001;
SF>CeA, p<.00, SF>BLA, p<.001] and [left: F(2,64)=9.51, p<.001; SF>BLA, p<.001 and
CeA>BLA,p<.01] but no group (p=.10-.15) or group by region differences were observed
(p=.17-.65), respectively.
Granger Causality
Group Differences in Intra-Amygdaloid GC. The comparison of non-ELS > ELS
elicited robust activity in paths primarily originating from right BLA (Fig. S2a; Table S1)
to bilateral SF, left BLA, and right CeA. Less robust paths originating from right SF were
also observed. In contrast, ELS> non-ELS exclusively demonstrated connectivity for
paths originating in bilateral CeA to left BLA and bilateral SF, although notably they
were less robust than the BLA paths observed for non-ELS > ELS Fig. S2b).
Group Differences in Extra-Amygdaloid GC: Between-group comparisons for non-ELS>
ELS for CeA and the implicit regulation of emotion network elicited a pattern of causal
connectivity from right BA 11 to bilateral CeA (Table 4), in addition to a mutual pathway
between left CeA and left hippocampus. In contrast, the comparison ELS> non-ELS elicited
robust connectivity for a number of distributed paths originating in right CeA to BA 11, BA 32
or right hippocampus, in addition to paths from left hippocampus, right DLPFC and right BA
32. Between-group comparison for extra-amygdaloid connectivity of BLA demonstrated
primary paths; right BA 11 predicted bilateral BLA and right BLA to all other regions included
in the implicit regulation model (Table 5). In contrast, the comparison of ELS > non-ELS
elicited two primary paths, one originating in right BA 32 to bilateral BLA and right DLPFC to
bilateral BLA. Between group comparison for SF for non-ELS > ELS demonstrated paths
originating in either right OFC to bilateral SF or from right SF to BAs 24, 25 and 32 (Table S1).
In contrast, causal paths for the comparison of ELS > non-ELS were more distributed,
originating in right BA, right DLPFC and left hippocampus to bilateral SF. Paths originating in
SF projected to BA 11, 24, 25 and 32.
BIBLIOGRAPHY
Arnold M, Miltner W, Witte H, Bauer R, Braun C (1998). Adaptive AR modeling of
nonstationary time series by means of kalman filtering. IEEE transactions on biomedical
engineering 45(5): 553-562.
Deshpande G, LaConte S, James G, Peltier S, Hu X (2009). Multivariate granger causality
analysis of brain networks. Human Brain Mapping 30(4): 1361-1373.
Deshpande G, Sathian K, Hu X (2010). Effect of hemodynamic variability on granger causality
analysis of fMRI. NeuroImage 52(3): 884-896.
Havlicek M, Friston K, Jan J, Brazdil M, Calhoun V (2011). Dynamic modeling of neuronal
responses in fMRI using cubature Kalman filtering. NeuroImage 56(4): 2109-2128.
Table S1. Between Group Intra-Amygdala Granger Causality Paths
Non-ELS
ROI
Coordinates mean conn
mean
> ELS
(Non-ELS)
conn(ELS)
R BLA
R CeA
22 -4 -11
0.070
-0.017
L BLA
-22 -3 -14
0.085
-0.032
L SF
-22 0 -15
0.093
-0.037
R SF
26 0 -12
0.085
-0.045
R SF
L BLA
-27 -1 -20
0.062
-0.047
R SF
R SF
R BLA
26 -3 -17
0.049
-0.025
t-score
3.885
5.299
5.887
6.061
5.520
3.788
ELS > Non-ELS
Coordinates
mean conn
(Non-ELS)
mean
conn(ELS)
t-score
-22 -3 -14
26 0 -12
-0.035
-0.029
0.046
0.046
-4.084
-3.808
L CeA
L BLA
R SF
R CeA
L BLA
-27 -1 -20
-0.024
0.067
-4.279
L SF
-22 0 -15
-0.017
0.072
-4.137
R SF
26 -3 -14
-0.012
0.078
-4.198
Note. Group comparison of causal paths between amygdala subregions in which Non-ELS > ELS
or ELS>Non-ELS. Abbreviations basolateral nucleus (BLA); central nucleus (CeA); superficial
nuclei (SF); Right hemisphere; Left hemisphere; coordinates are in Montreal Neurological
Institute (MNI); Mean connectivity coefficient (mean conn). Coordinates indicate location of
local maxima. p-values >.05, FDR corrected.
Table S2. Between Group Extra-Amygdaloid Granger Causality Paths (CeA)
Non-ELS>
MNI
mean conn
mean conn
ELS
Coordinates
(Non-ELS)
(ELS)
R BA 11
L CeA
-21 -9 -11
0.090
-0.013
R CeA
22 -4 -11
0.091
-0.023
L CeA
L Hipp
-22 -24 -8
-0.043
0.039
t-score
4.837
5.204
-4.157
ELS > Non-ELS
Coordinates
mean conn
(Non-ELS)
mean conn
(ELS)
t-score
L CeA
R CeA
-21 -9 -11
22 -4 -11
-0.055
-0.051
0.070
0.094
-6.283
-7.239
L CeA
R CeA
-22 -4 -12
22 -4 -11
-0.014
-0.026
0.076
0.080
-4.137
-4.702
L CeA
R CeA
-21 -9 -11
22 -4 -11
0.030
0.029
-0.057
-0.059
4.122
4.268
R BA 32
R DLPFC
L Hipp
R CeA
L BA 11
-24 48 -6
-0.024
0.061
-3.955
L BA 32
-4 23 31
-0.028
0.080
-4.951
R Hipp
25 -28 -9
-0.007
0.075
-3.885
Note. Group comparison of Granger causality paths between central nucleus (CeA) and implicit
regulation of emotion network; mean conn; mean connectivity coefficients. Abbreviations:
dorsolateral prefrontal cortex (DLPFC); Hippocampus (Hipp); Brodmann’s Area 11 (BA11);
Brodmann’s Area 24 (BA24); Brodmann’s Area 25 (BA25); Brodmann’s Area 32 (BA32); Right
hemisphere; Left hemisphere. Coordinates are in Montreal Neurological Institute (MNI); Mean
connectivity coefficient (mean conn). Coordinates indicate location of local maxima. p-values
>.05, FDR corrected.
Table S3. Between Group Extra-Amygdaloid Granger Causality Paths (BLA)
Non-ELS >
ELS
R BA 11
MNI
Coordinates
mean conn
(Non-ELS)
mean conn
(ELS)
t-score
L BLA
R BLA
-22 -3 -14
28 -4 -12
0.075
0.084
-0.030
-0.035
4.719
5.677
L BA 11
R BA 11
L BA 24
R BA 24
L BA 25
R BA 25
L BA 32
R BA 32
L DLPFC
R DLPFC
L Hipp
R Hipp
-24 48 -6
22 42 -15
-4 21 28
4 24 28
-6 20 -2
4 3 -5
-4 23 31
4 20 37
-54 8 39
43 30 36
-22 -24 -8
26 -28 -9
0.067
0.081
0.068
0.057
0.052
0.060
0.074
0.097
0.079
0.056
0.065
0.084
-0.038
-0.043
-0.027
-0.041
-0.039
-0.029
-0.028
-0.036
-0.024
-0.033
-0.038
-0.028
4.859
5.623
4.316
4.520
4.099
4.167
4.662
6.139
4.678
4.073
4.758
5.044
R BLA
ELS > Non-ELS
Coordinates
mean conn
(Non-ELS)
mean conn
(ELS)
t-score
-0.027
-0.055
0.080
0.078
-5.307
-6.529
R BA 32
L BLA
R BLA
-27 -1 -20
26 -3 -17
R DLPFC
L BLA
-27 -1 -20
-0.052
0.097
-6.945
R BLA
26 -3 17
-0.011
0.090
-4.637
Note. Group comparison of Granger causality paths between basolateral nucleus (BLA)
and implicit regulation of emotion network; mean conn; mean connectivity coefficients.
Abbreviations: dorsolateral prefrontal cortex (DLPFC); Hippocampus (Hipp); Brodmann’s Area
11 (BA11); Brodmann’s Area 24 (BA24); Brodmann’s Area 25 (BA25); Brodmann’s Area 32
(BA32); Right hemisphere; Left hemisphere. Coordinates are in Montreal Neurological Institute
(MNI); Mean connectivity coefficient (mean conn). Coordinates indicate location of local
maxima. p-values >.05, FDR corrected.
Table S4. Between Group Extra-Amygdaloid Causal Paths (SF)
Nonmean conn
mean conn
ELS>ELS
(Non-ELS)
(ELS)
R BA 11
L SF
0.069
-0.016
R SF
0.102
-0.011
R SF
R BA 24
0.048
-0.038
R BA 25
0.047
-0.030
L BA 32
0.054
-0.029
t-score
3.981
5.219
4.261
3.861
4.103
ELS> Non-ELS
mean conn
(Non-ELS)
mean conn
(ELS)
t-score
L SF
R SF
-0.042
-0.045
0.067
0.072
-5.485
-5.795
L SF
R SF
-0.030
-0.020
0.075
0.082
-4.830
-4.653
L SF
0.036
-0.058
4.425
R BA 32
R DLPFC
L Hipp
R SF
L BA 11
0.035
-0.046
4.026
L BA 24
0.029
-0.046
3.803
R BA 25
0.042
-0.047
4.516
R BA 32
0.034
-0.048
4.107
Note. Group comparison of Granger causality paths between basolateral nucleus (BLA) and
implicit regulation of emotion network; mean conn; mean connectivity coefficients.
Abbreviations: dorsolateral prefrontal cortex (DLPFC); Hippocampus (Hipp); Brodmann’s Area
11 (BA11); Brodmann’s Area 24 (BA24); Brodmann’s Area 25 (BA25); Brodmann’s Area 32
(BA32); Right hemisphere; Left hemisphere. Coordinates are in Montreal Neurological Institute
(MNI); Mean connectivity coefficient (mean conn). Coordinates indicate location of local
maxima. p-values >.05, FDR corrected.
Figure Legend
Fig. S1. Granger Causality Analysis Schematic. Schematic illustrating the directional
connectivity analysis pipeline.The time series extracted from different ROIs were first
deconvolved using a cubature Kalman filter without any assumptions about the shape of the
underlying hemodynamic response. As this is a continuous time model, a time step of TR/10
was used to discretize it. The resulting latent neuronal variables were input
into the dynamic multivariate autoregressive model to obtain time-varying directional
connectivity between the ROI time series. The connectivity values corresponding to negative
and neural valence conditions were populated into different samples to find
the paths which were greater during negative valence. Among these paths, the connectivity
values for negative valence were compared across the two groups to determine those which
differed between groups.
Fig. S2. Group Comparison of Intra-Amygdaloid Granger Causality Paths. (A) The contrast
Non-ELS> ELS elicited right BLA-dominant causal paths that predicted robust relationships
with bilateral SF and left BLA and less robust relationship with right CeA. Right SF predicted
response to bilateral BLA. (B) The contrast ELS>Non-ELS elicited parallel response in bilateral
CeA-dominant causal paths that predicted response in bilateral SF as well as left BLA.
Fig. S1. Granger Causality Schematic
Fig. S2. Intra-Amygdala Network Group Comparison
A. Non-ELS > ELS
B. ELS > Non-ELS
R CeA
L CeA
R BLA
R SF
L SF
L SF
L
BLA
L
BLA
R SF
R
CeA
.0001
1 x 10-4
p-value
4 x 10-8