Content uploaded by Prantik Kundu
Author content
All content in this area was uploaded by Prantik Kundu
Content may be subject to copyright.
An Integrated Strategy for Improving Functional
Connectivity Mapping Using Multi-Echo EPI
Prantik Kundu ∗ † , Noah D. Brenowitz ∗Valerie Voon †Yulia Worbe †Petra E. V´
ertes †Souheil J. Inati ‡, Ziad S. Saad
§, Peter A. Bandettini ∗ ‡ and Edward T. Bullmore † ¶ k
∗Section on Functional Imaging Methods, National Institute of Mental Health, Bethesda, MD, USA,†Behavioural and Clinical Neuroscience Institute, University of
Cambridge, Cambridge, UK,‡Functional MRI Core Facility, National Institute of Mental Health, Bethesda, MD, USA,§Statistical and Scientific Computing Core, National
Institute of Mental Health, Bethesda, MD, USA,¶NIHR Cambridge Biomedical Research Centre, Cambridgeshire & Peterborough National Health Service Foundation
Trust, and kClinical Unit Cambridge, GlaxoSmithKline, Cambridge, UK
Submitted to Proceedings of the National Academy of Sciences of the United States of America. *P.A.B. and E.T.B. contributed equally to the preparation of this
manuscript.
Functional connectivity analysis of resting state BOLD fMRI is
widely used for non-invasively studying brain functional networks.
Recent findings have indicated, however, that even small (≤1 mm)
amounts of head movement during scanning can disproportion-
ately bias connectivity estimates, despite various preprocessing
efforts. Further complications for interregional connectivity es-
timation from time domain signals include the unaccounted re-
duction in BOLD degrees of freedom related to sensitivity losses
from high subject motion. To address these issues, we describe
an integrated strategy for data acquisition, denoising, and con-
nectivity estimation. This strategy builds on our previously pub-
lished technique combining data acquisition with multi-echo (ME)
echo planar imaging (EPI) and analysis with spatial independent
component analysis (ICA), called ME-ICA, which distinguishes
BOLD (neuronal) and non-BOLD (artifactual) components based
on linear echo-time (TE) dependence of signals - a characteris-
tic property of BOLD T∗
2signal changes. Here we show for 32
control subjects that this method provides a physically principled
and nearly operator-independent way of removing complex arti-
facts such as motion from resting state data. We then describe
a new estimator of functional connectivity based on interregional
correlation of BOLD independent component coefficients. This
estimator, called independent components regression (ME-ICR),
considerably simplifies statistical inference for functional con-
nectivity since degrees of freedom equals the number of indepen-
dent coefficients. Compared to traditional connectivity estimation
methods, the proposed strategy results in 4-fold improvements
in signal-to-noise ratio, functional connectivity analysis with im-
proved specificity, and valid statistical inference with nominal con-
trol of type 1 error in contrasts of connectivity between groups
with different levels of subject motion.
multi-echo |resting state fMRI |functional connectivity |human neu-
roimaging |time series |preprocessing
Abbreviations: BOLD, blood oxygenation level dependent; fMRI, functional mag-
netic resonance imaging; EPI, echo planar imaging; ICA, independent compo-
nents analysis; TE, echo-time; T∗
2, succeptibility-weighted traverse relaxation
time; S0, initial signal intensity
Resting state experiments typically involve a short period (i.e.
10 minutes) of BOLD fMRI scanning while participants lie in
the scanner without experimental control over brain function. The
data show low frequency (f≤0.1 Hz) oscillations indicative of spon-
taneous brain activity. Functional connectivity between brain regions
is then typically estimated by the correlation between time series [1].
Unfortunately, resting state fMRI is highly susceptible to artifacts.
It has recently been shown that small (≤1mm) and transient move-
ments of the subject’s head during scanning can bias estimates of time
series correlation for long distance anatomical connections, even af-
ter the data have been preprocessed by traditional methods [2, 3, 4].
The effects of head motion and related artifacts are problematic espe-
cially for studies of very young or elderly subjects, or patients with
neuropsychiatric disorders, all of whom demonstrate a greater extent
of head movement than healthy adults.
Current proposals for solving problems related to motion arti-
fact involve elaborating traditional methods for "denoising" the blood
oxygenation level dependent (BOLD) fMRI signal time series ac-
quired at one "optimized" echo time (TE) [5]. One denoising step
that has been widely adopted is to regress the "raw” fMRI time series
to the series of head motion parameters estimated post hoc as trans-
lations and rotations in 3 spatial dimensions to geometrically align
all fMRI volumes to a reference volume. Additional "nuisance” re-
gressors are often included in regression models, such as the global
mean fMRI time series and/or time series representing presumably
non-neuronal signal of the white matter or cerebrospinal fluid (CSF)
[6, 7]. Before or after regression analysis, time series are typically
also band-pass filtered to remove higher frequency signals consid-
ered less likely to represent functionally related variance [8]. Some
groups prefer to use independent component analysis (ICA) to de-
compose the time series into spatially independent components and
remove components identified as artifacts by user-dependent evalu-
ation of anatomical localization and/or time series. Finally, it has
been suggested that in extreme cases, time points that are severely
contaminated by otherwise intractable movement effects may be sim-
ply deleted or "scrubbed” from the time series [2]. Although some
permutation of these preprocessing steps can indeed substantially re-
duce contamination of the data by non-neuronal sources, this is not
achieved without cost. All of these denoising operations will have a
major impact on the statistical properties of the data by varying the
degrees of freedom in a poorly controlled way or introducing time se-
ries artifacts due to preprocessing. Altogether, traditional preprocess-
ing often implements several arbitrary operator-dependent choices
and yet may be incompletely effective.
Here, we advocate a more radical departure from conventional
resting state fMRI methodology using an integrated procedure for
data acquisition, BOLD denoising, and connectivity estimation and
statistical inference. Using our previously published method com-
bining multi-echo EPI and ICA, called ME-ICA, fMRI signals are
acquired at multiple TEs and BOLD signals are identified as inde-
pendent components having linearly TE dependent percent signal
changes, which is a distinctive characteristic of BOLD T∗
2(transverse
susceptibility-weighted relaxation rate) signal [9, 10, 11]. Compo-
nent level TE-dependence of BOLD signals is measured using the
pseudo-F statistic κ; components which scale strongly with echo
time, indicating BOLD weighting, will have high κscores. In con-
trast, component level TE-independence can be used to identify non-
BOLD signal changes, measured using the pseudo-F statistic ρ(see
SI section 1.2-1.5 for theory summary). In this framework, denoising
involves removing low-κ/high-ρcomponents from data, which the-
Reserved for Publication Footnotes
http://www.pnas.org/content/110/40/16187.short PNAS Issue Date Volume Issue Number 1–7
Figure 1 (a) Comparison of two datasets (subjects 1 and 2) with increasing levels of in-scanner head motion. For each subject, four panels show (from top to
bottom): rigid-body motion parameter (MP) traces in millimeter units; framewise displacement (FD) traces; a comparison of DVARS for raw data (black trace) and
motion regressed data; comparison of DVARS for raw data (black trace) and high and low-κ time series (blue and red traces respectively) from ME-ICA. The MP
traces show that subjects have (left to right): repeated small movements atop a more substantial tilt (>3mm maximum); and a series of large abrupt head
movements of >3mm in some directions and >1-2mm in FD. Subject 2 is a ‘worst case’ dataset that would ordinarily be discarded, but is studied here as a test
case. For all subjects, DVARS traces show that linear regression of motion parameters (and first derivatives) does not effectively remove most motion related
signals. In contrast, low-κ time series capture the majority of motion related signals, leaving a comparatively flat DVARS trace from high-κ time series without the
use of motion parameter regression or band pass filtering. (b.i) Comparison of acquisition parameters and signal quality after preprocessing for conventional
methods versus ME acquisition and ME-ICA denoising. ME acquisition has larger voxels and longer TR, but (ii) T2* weighted combination and conventional
preprocessing along gives greater than expected increases in tSNR (190 theoretical based on voxel size increases). ME-ICA denoising nearly quadruples tSNR
while explaining nearly all (97%) combined ME variance. (iii) Number of high-κ components differs significantly between high and low motion subject groups.
i. Acquisition Parameters
i. Acquisition Parameters
Voxel Size
TR
Single-Echo
3x3x3.75
2.26
Multi-Echo (ME)
3.75x3.75x4.4
2.47
ii. Signal Quality
ii. Signal Quality
Preprocessed
tSNR
ICA % Var.
Exp.
κ
Single-Echo
130±14%
76±3%
-
Comb. ME
285±10%
85±5%
-
ME-ICA
517±9%
97±1%
80±4%
iii. ME-ICA : Low vs. High Motion
iii. ME-ICA : Low vs. High Motion
iii. ME-ICA : Low vs. High Motion
Comb. ME
tSNR1
ME-ICA
tSNR
BOLD
DOF2
Low-Motion
297±7%
548±4%
40±6%
High-Motion
235±4%
529±5%
33±8%
Significant difference between high and low movers:
1p<0.03 2p<0.02
Significant difference between high and low movers:
1p<0.03 2p<0.02
Significant difference between high and low movers:
1p<0.03 2p<0.02
Significant difference between high and low movers:
1p<0.03 2p<0.02
B
Motion
FDDVARSDVARS
Subject 1 Subject 2
Raw Motion Regression
Raw Low-κHigh-κ
A
Fig. 1. (a) Comparison of two datasets (subjects 1 and 2) with increasing levels of in-scanner head motion. For each subject, four panels show (from top to bottom):
rigid-body motion parameter (MP) traces in millimeter units; framewise displacement (FD) traces; a comparison of DVARS for raw data (black trace) and motion
regressed data; comparison of DVARS for raw data (black trace) and high and low-κtime series (blue and red traces respectively) from ME-ICA. The MP traces show
that subjects have (left to right): repeated small movements atop a more substantial tilt (>3mm maximum); and a series of large abrupt head movements of >3mm in
some directions and >1-2mm in FD. Subject 2 is a worst case dataset that would ordinarily be discarded, but is studied here as a test case. For all subjects, DVARS
traces show that linear regression of motion parameters (and first derivatives) does not effectively remove most motion related signals. In contrast, low-κtime series
capture the majority of motion related signals, leaving a comparatively flat DVARS trace from high-κtime series without the use of motion parameter regression or band
pass filtering. (b) Comparison of acquisition parameters and signal quality after preprocessing for conventional methods versus ME acquisition and ME-ICA denoising.
ME acquisition has larger voxels and longer TR, but T∗
2weighted combination gives greater than expected increases in tSNR (190 theoretical based on voxel size
increases). ME-ICA denoising nearly quadruples tSNR while explaining nearly all (97%) combined ME variance. Number of high-κcomponents differs significantly
between high and low motion subject groups.
oretically includes all non-BOLD signals including motion artifacts
(see Supp. Fig. 2 for selection example). This approach enables com-
prehensive denoising with minimal operator intervention and without
additional arbitrary preprocessing steps. We then describe a new es-
timator of functional connectivity based on interregional correlation
between the coefficients of BOLD independent components. Because
these components are, by construction, independent, this means that
the BOLD degrees of freedom for inference are known and can be
used to appropriately normalize correlation values. [12, 13] This nor-
malization also controls for variability in BOLD degrees of freedom
due to varying BOLD sensitivity with subject motion [14]. We show
that this approach, called multi-echo independent components regres-
sion (ME-ICR), supports valid hypothesis testing of functional con-
nectivity for individual subject data and groups of data. By analyzing
data from healthy volunteers exhibiting a wide variety of noncom-
pliant motion, we show that ME-ICA denoising leads to substantial
improvements in signal-to-noise ratio over conventional single-echo
techniques. We then show that ME-ICR yields valid statistical infer-
ence with nominal type 1 error control and the generation of plausible
and specific maps of functionally connected brain regions at multiple
levels of analysis.
Results
ME-ICA Motion Artifact Removal.We first assessed the capability
of ME-ICA denoising to attenuate movement-related effects on time
series. ME-ICA denoising involved separating a "raw" (optimally
combined, see SI section 2.4 and Supp. Fig. 1) ME-fMRI time series
dataset into separate BOLD (high-κ) and non-BOLD (low-κ) time
series datasets [11] (see SI section 2.6). Theoretically, and on the
basis of prior results, we expected that the high-κtime series would
represent functional activity generating BOLD contrast (see Supp.
Fig. 3 for functional component maps); whereas the low-κtime se-
ries would represent other sources of non-BOLD variance such as
head movement artifact (see Supp. Fig. 4 for denoised time series).
ME-ICA denoising and conventional denoising are compared for the
same ME datasets. Conventional denoising involved regression of
motion parameters (MP), high-pass filtering, and de-spiking (see SI
section 2.5 for ordering). Denoising performance is demonstrated for
two individual datasets exhibiting different patterns of noncompliant
head movement (Figure 1a). Head motion parameters for subject 1
(low motion) show a prolonged, gradual drift in head position over
the course of scanning; subject 2 (high motion) moved to a greater
extent (up to 8mm total displacement) and more abruptly at times.
Additional diagnostics from other studies were used here to char-
acterize in more detail the extent of transient head movements, their
impact on fMRI signal variance, and denoising performance in terms
of uncoupling BOLD signals from transient, non-linear head arti-
facts. Framewise displacement (FD), computed as the sum of mo-
tion parameter first derivatives, measured the occurrence of transient
movements. Delta-variation-signal (DVARS), computed as the root-
mean-square average of the first derivatives of all fMRI signals, iden-
tified time points with rapidly changing fMRI signal [2]. Correspon-
dence or coupling of DVARS and FD traces indicated contamination
of fMRI signals with motion artifacts (see SI section 2.7). For ex-
ample, the high motion dataset is affected by numerous transient in-
creases in FD (at 50 s and 420 s, for example) that are associated with
increases in DVARS, indicating that subject motion produced bursts
of rapidly changing fMRI signal. By the same token, uncoupling of
FD and DVARS traces indicated effective denoising for movement
effects. DVARS processes for conventionally denoised data closely
overlapped with DVARS processes for raw data, indicating that lin-
ear motion parameter regression was ineffective. Since most mo-
tion artifact remains in data after linear regression, this suggests that
most motion artifacts are non-linear manifestations of head motion
parameters. In comparison, DVARS traces for high κtime series
are essentially flat, indicating the removal of both linear and non-
linear effects of motion. On the other hand, DVARS traces for low κ
time series closely match DVARS traces for raw data. This indicates
that ME-ICA specifically isolates motion artifacts as non-BOLD sig-
nals. These results illustrate that removing non-BOLD signals is a
more effective means of removing motion artifact than linear regres-
sion of head movement parameters, while also reiterating that other
2http://www.pnas.org/content/110/40/16187.short Footline Author
Right Hand
Network
Default Mode
Network
Subject 1 Subject 2
Conventional FC
R>0.5
ME-ICR
P<0.05
Subject 1 Subject 2
Figure 2 (a) Maps for seed-
based correlation analysis
after: conventional denoising
and fu nctional connectivity
estimation (top row) and ME-
ICR (bottom row).
Con ve nt io na l con ne ctivity
maps are thresholded to
R>0.5 and ME-ICR maps are
thresholded to p<0.05.
Connectivity is shown for the
default mode network (left)
and right hand area (right) in
two subjects with moderate
and high levels of motion
respectively (1 and 2 from Fig.
1). (b) Probability densities of
functional connectivity values
(Z) for seed-based
connecti vity analysis after
conventional (blue), ME-ICA
analysis (green), and a
standard normal distribution
(red) for comparison.
Gaussianity 1, so that ME-ICA can identify informative low variance
components for inclusion within a stable high dimensional ICA .
We previously showed that ME-ICA denoising can remove mo-
tion artifacts without regressing motion parameters. The removal of
cardiac pulsation artifacts without physiological traces was demon-
strated as well. Here we compare ME fMRI acquisition and ME-ICA
denoising versus conventional unaccelerated single-echo fMRI ac-
quisition and denoising by motion regression (with zeroth and first
derivatives), despiking, and high pass filtering (Table 1). Conven-
tional denoising of the T2* weighted combination of ME data leads
to 50% greater tSNR than expected by voxel size increases alone.
ME-ICA denoising results in twice that, quadrupling the tSNR of
gray-matter voxels over conventional methods.
Enhanced ME-ICA denoising split ME data into separate BOLD
(high-) and non-BOLD (low-) datasets. Framewise displacement
(FD) and delta-variance (DVARS) traces were computed to detect ar-
tifacts, for conventionally denoised time series versus split BOLD
and non-BOLD time series (Figure 1a) [2]. DVARS traces for high
time series are essentially flat, indicating the removal of linear and
non-linear effects of motion. DVARS traces for low time series
match FD traces and DVARS traces for raw data, indicating that mo-
tion artifacts have been isolated from BOLD signals. FD and DVARS
traces were originally used to argue that motion regression is ineffec-
tive and that scrubbing is necessary for seed-based functional connec-
tivity analysis of resting state fMRI. An obvious reason why scrub-
bing is problematic is that a variable number of points are removed
depending on subject motion and threshold. Traces for subject 1, for
example, may suggest removal of the majority of points, but ME-
ICA denoises data without removing data points. Traces for sub-
ject 2 show that signal from even extreme motion (4mm movements,
8mm total displacement), unrecoverable by conventional means, is
removed by ME-ICA. Removing motion artifacts by denoising non-
BOLD signals makes scrubbing unnecessary, which avoids the many
problems associated with this approach.
The tSNR and BOLD DOF of ME data was compared for high
movers versus low movers (Table 1b). Total movement was mea-
sured as the sum of FD, and groups were defined by median split.
tSNR of conventionally denoised ME data was higher than the tSNR
estimate for comparable single-echo data. This suggests that using
acceleration to acquire ME data does not increase susceptibility to
nuisance effects (such as motion) to the extent of losing a tSNR ad-
vantage [18]. In conventionally denoised ME data, tSNR of low mo-
tion subjects is significantly higher than tSNR for high motion sub-
jects. In ME data after ME-ICA denoising, tSNR of high and low mo-
tion subjects does not differ significantly. However, ME-ICA shows
that high motion subjects have significantly lower BOLD DOF. The
low and high motion subjects 1 and 2 have for example 32 and 13
BOLD DOF, respectively. This suggests that high motion subjects
have lower BOLD variability due to sensitivity losses from spin his-
tory effects and related physical limitations on acquiring T2* signals
due to motion (See Supplemental Figure 2). It also indicates that the
conventional assumption of a fixed standard error for connectivity
will produce overestimated standard scores for high motion subjects,
and lead to spurious connectivity differences between groups with
different motion.
Subject Level ME-ICR Seed Connectivity Estimation. Seed based
functional connectivity estimation by ME-ICR was compared to es-
timation with Pearson correlation of time series after motion re-
gression, despiking, bandpass filtering (0.01Hz-0.1Hz), followed by
Fisher transformation of correlation values using fixed standard er-
ror (based on 82 nominal DOF). These two connectivity estimators
were compared for the high-movement data represented in Figure 1
using thresholded connectivity maps (Figure 2a) and probability den-
sity histograms (Figure 2b). A posterior cingulate cortex seed was
used to map the default mode network and a right hand area seed was
used to map the right hand network.
Conventional connectivity histograms were strongly weighted to
high positive values. In contrast, ME-ICR connectivity histograms
are centered about the standard normal distribution. One reason for
applying global signal regression is for explicitly centering the con-
ventional correlation distribution [19]. ME-ICR achieves regularized
estimates of seed connectivity at subject level based on spatial ICA
whitening and using a data-driven estimate of standard error based
on the effective BOLD degrees of freedom.
The unbiased distribution of ME-ICR connectivity indicated that
subject level connectivity maps could be thresholded by statistical
inference, so ME-ICR maps are thresholded p<0.05. The positive
bias of conventional connectivity values meant that inference for con-
ventional connectivity at subject-level was not appropriate, so maps
are thresholded R>0.5. The limitation of a Pearson’s R threshold is
its variable interpretation across datasets depending on the extent of
collinearity and autocorrelation in BOLD signals and the effect of
preprocessing steps applied. The advantage of thresholding by sig-
nificance value using ME-ICR is that the connectivity p-values incor-
porate the statistical variability of resting state datasets. While con-
nectivity inference is regularly made at group level, inference on sub-
Footline Author PNAS Issue Date Volume Issue Number 3
BA
non-BOLD artifacts such as cardiac pulsation can be removed equiv-
alently [11].
To evaluate the denoising performance of ME-ICA more rigor-
ously, gray matter temporal signal-to-noise (tSNR) was measured to
assess BOLD sensitivity (Figure 1b.i-ii, see SI section 2.7.2 for com-
putation details). High-κtime series were compared to correspond-
ing conventionally denoised optimally combined ME time series (as
above). In addition, the tSNR of standard single-echo fMRI (with-
out parallel imaging) was also assessed using conventional denois-
ing. This experiment was conducted for 3 representative subjects.
ME-ICA high-κtime series had mean tSNR of 517 with 9% uncer-
tainty. Since ME-ICA decomposition explained 97% of dataset vari-
ance on average, this significantly increased tSNR fairly represented
acquired signals (see SI section 1.5). Conventionally denoised ME
data had approximately half that tSNR, at 285, with similar uncer-
tainty. Finally, conventionally denoised single-echo data had tSNR
of 130 with 14% uncertainty. Importantly, these results show that
the pulse sequence techniques utilized to acquire multi-echo fMRI,
such as parallel imaging, ultimately lead to improved signal quality
for ME data over single-echo data. In conjunction with ME-ICA, ac-
quiring ME data leads to a 4-fold improvement in data quality over
conventional fMRI acquisition and standard denoising techniques.
The hypothesis that subject motion reduced BOLD sensitivity
and effective BOLD degrees of freedom was assessed next. BOLD
sensitivity was assessed in terms of tSNR and degrees of freedom was
estimated as the number of high-κcomponents. In this experiment,
the main cohort of 32 subjects was divided into high and low mo-
tion groups by median split according to a measure of "total" motion,
computed as the sum of FD. The tSNR of conventionally prepro-
cessed ME data was compared between groups to estimate the effect
of motion without ME-ICA (Figure 1b.iii). Results showed that even
in high tSNR data such as combined ME data, high motion datasets
had approximately 25% lower tSNR than low motion datasets, which
was a significant difference (p<0.03). Based on the DVARS experi-
ment, this limitation to BOLD sensitivity can be attributed to resid-
ual motion artifact signals in data. In the high-κtime series result-
ing from ME-ICA denoising, there was no significant difference in
tSNR, due to comparable artifact removal from datasets with differ-
ent levels of motion. However, high motion ME data still had sig-
nificantly fewer degrees of freedom according to ME-ICA (p<0.02),
likely due to the physical processes underlying artifacts interfering
with the BOLD contrast mechanism and thus reducing functionally
related BOLD signal variability.
Subject Level ME-ICR Seed Connectivity Estimation.After ME-
ICA selected functionally related BOLD independent components
and counted BOLD degrees of freedom, ME-ICR was used to esti-
mate functional connectivity. For each dataset, ME-ICR estimated
functional connectivity as the Pearson correlation of high-κ, BOLD-
weighted independent component (IC) coefficients. These IC coef-
ficient correlations were converted to standard scores (Z) using the
Fisher transform for the appropriate degrees of freedom, i.e., sim-
ply the number of BOLD independent component coefficients (see
SI section 2.8 for further detail). ME-ICR connectivity was com-
pared to conventional seed-connectivity mapping using Pearson cor-
relation of time series that were conventionally denoised (motion pa-
rameter regression, de-spiking, 0.02 Hz-0.1 Hz bandpass filtering).
Conventional correlation values were converted to standard scores
using the Fisher transform for 82 nominal degrees of freedom. Since
valid inference is not ordinarily expected of conventional functional
connectivity analysis of individual resting fMRI datasets, conven-
tional connectivity maps were thresholded to R>0.5. In contrast,
valid inference was expected for ME-ICR connectivity, so these maps
were thresholded to nominal p<0.05 based on Z-score . Corrections
for multiple comparisons using stronger thresholds (FDR q<0.01)
yielded similar maps, indicating the robustness of the present con-
nectivity estimation method (Figure 2a).
ME-ICR connectivity estimation was expected to produce more
consistent connectivity maps than conventional connectivity estima-
tion across datasets with varying subject motion. This was demon-
strated using the low and high motion datasets referenced in Figure
1a. Subject 1 (low motion) expressed 32 BOLD degrees of freedom,
while subject 2 (high motion) expressed 13, emphasizing the deleteri-
ous effect of motion on BOLD sensitivity. For both subjects, a poste-
rior cingulate cortex seed was used to map the default mode network,
and a right hand area seed was used to map the right hand motor net-
work. For each seed, results compare connectivity maps across sub-
ject and method. Using conventional connectivity estimation, maps
across low and high motion subjects are not clearly comparable. In-
creased correlation across gray and white matter and apparent under-
thresholding for subject 2 are associated with residual motion arti-
fact and decreased effective degrees of freedom. In comparing con-
ventional and ME-ICR connectivity for subject 1, maps were simi-
lar except for the right hand network having attenuated contralateral
sensory cortex connectivity. For subject 2, ME-ICR estimation gen-
erated maps with much lower noise than conventional connectivity
maps. Finally, comparing ME-ICR connectivity for subjects 1 and
2 shows consistent ME-ICR maps despite significant differences in
subject motion and BOLD degrees of freedom.
The capability for inference using ME-ICR was further examined
using probability density histograms for correlation values (Figure
2b). One histogram is given per subject and per seed. Each histogram
compares a standard normal distribution with ME-ICR and conven-
tional connectivity distributions. It is apparent that across subject
and seed, ME-ICR follows the standard normal distribution, varying
Footline Author PNAS Issue Date Volume Issue Number 3
ME-ICR
DL-PFC Seed - Cortical Conn.
S1 S2 S3 S4 S5
Conventional
Cerebellum Seed - Subcortico-cortical Conn.
S1 S2 S3 S4 S5
ME-ICRConventional
A
Group Connectivity Mean
DL-PFC Seed Cerebellum Seed
ME-ICR Conventional ME-ICR Conventional
Consistency Analysis
B
C
ICC
Consistency (ideal ICC=1) Specificity (ideal ICC=0)
Figure 3 (a) Unthresholded maps of ME-ICR and conventional connectivity
maps using seeds: right DL-PFC and left cerebellar motor area seeds, to
assess cortical and subcortical-cortical connectivity respectively. (b) Mean
connectivity maps for both estimators and both seeds. (c) Consistency
analysis of ME-ICR and conventional connectivity. Consistency is assessed
using ICC of connectivity for individual seeds over 32 subjects. ICC=1 is
ideal, indicating seed-connectivity is identical over subjects. Specificity is
assessed using ICC of connectivity for individual subjects over 32 random
seeds. ICC=0 is ideal, indicating random connectivity maps are not
consistent.
Fig. 3. (a) Unthresholded maps of ME-ICR and conventional connectivity maps
using seeds: right DL-PFC and left cerebellar motor area seeds, to assess
cortical and subcortical-cortical connectivity respectively. (b) Mean connectivity
maps for both estimators and both seeds. (c) Consistency analysis of ME-ICR
and conventional connectivity. Consistency is assessed using ICC of connectivity
for individual seeds over 32 subjects. ICC=1 is ideal, indicating seed-connectivity
is identical over subjects. Specificity is assessed using ICC of connectivity for
individual subjects over 32 random seeds. ICC=0 is ideal, indicating random
connectivity maps are not consistent.
with heavy right tails and differences in kurtosis. In contrast, con-
ventional connectivity distributions are more variable and result in
right-shifted distributions [6]. The centered distribution of ME-ICR
connectivity is expected because spatial ICA components are uncor-
related, and the standard variance of the distribution indicates that the
number of independent component coefficients is indeed an appropri-
ate estimator of the degrees of freedom in BOLD signals. Altogether,
ME-ICR distributions indicate that conventional statistical inference
for individual subject connectivity is valid in this mode of functional
connectivity estimation.
Consistency and Specificity of ME-ICR Connectivity.The consis-
tency of seed connectivity maps from ME-ICR versus conventional
connectivity was compared. Connectivity maps were computed for
individual subjects using right dorsolateral prefrontal cortex (DL-
PFC) and left cerebellar motor area seeds; unthresholded maps from
both estimators are shown for 5 random subjects (Figure 3a). These
particular seeds were chosen because they have lateralized connectiv-
ity (useful for inferring specificity). Cerebellar motor area connectiv-
ity is particularly informative since it is between contralateral cortical
and subcortical areas, which have signficantly different tSNR. In ME-
ICR maps across subjects, consistent DL-PFC connectivity is seen
between middle frontal gyrus and ipsilateral inferior parietal cortex,
showing near-0 connectivity for other regions. Right cerebellar mo-
tor area connectivity is seen to the contralateral cortical motor area
with similar specificity. In contrast, conventional connectivity maps
vary from showing the aforementioned regionally specific connectiv-
ity to showing diffuse connectivity across the brain. Mean connectiv-
ity maps (across all subjects) indicated overall that conventional con-
nectivity had low functional contrast (Figure 3c). This is highlighted
by connectivity between right cerebellar motor area and contralateral
cortical motor area. Where contralateral subcortical-cortical connec-
tivity cannot be seen in conventional connectivity maps, it is clearly
shown by ME-ICR.
ME-ICR and conventional connectivity were assessed for con-
sistency and specificity (Figure 3d) in subject-level connectivity for
random seeds using the intraclass correlation coefficient (ICC, see
SI section 2.9) [15]. Consistency was assessed by computing ICC
of connectivity maps for the same seed over subjects. In this com-
parison, ideal ICC=1, but lower is expected due to random error and
intersubject variability. Specificity was assessed by computing ICC
of maps for the same subject over random seeds. In this compari-
son, ideal ICC=0, since random maps should have little consistency.
32 random gray-matter seeds were analyzed to match the number of
subjects in the analysis. Conventional connectivity showed no sig-
nificant difference in ICC across maps from random subjects versus
maps from random seeds, indicating poor specificity. ME-ICR con-
nectivity, in contrast, showed significant difference between the two
factors. ME-ICR and conventional connectivity maps across subjects
did show nominally similar consistency according to ICC values, but
since conventional connectivity had the same mean ICC over random
maps, its apparent consistency is not significant. The ratio of mean
ICC values shows that ME-ICR at least doubles specificity over con-
ventional seed-connectivity analysis.
Group Level Connectivity. After confirming the statistical condition-
ing of subject-level connectivity values from ME-ICR and their con-
sistency across subjects, ME-ICR group analysis was conducted us-
ing 1-sample t-tests of ME-ICR connectivity maps across subjects,
for 4 commonly studied seed regions: posterior cingulate cortex,
right hand area, Broca’s area and left V1 (Figure 4a). Similarly,
conventional group analysis was conducted using 1-sample t-tests of
conventional connectivity maps across subjects for the same seeds
(see SI section 2.10). Group connectivity maps were thresholded
according to t-value. When thresholding conventional connectiv-
ity maps, all common significance values (p < 0.05−10−5) led to
essentially fully populated maps. Conventional group connectivity
maps had to be thresholded p < 10−7before interpretable maps were
produced; this p-value corresponded to a false discovery rate (FDR)
corrected significance of q < 10−6, suggesting overestimated sta-
tistical significance. Moreover, thresholded conventional group con-
nectivity maps often appeared globally significant, reflecting the non-
specificity of conventional connectivity estimates shown in Figure
3c. In contrast, group-level ME-ICR connectivity maps at thresholds
corresponding to p < 0.001 (FDR q < 0.005) were comparable to
maps observed in subject level analysis, were consistent with con-
nectivity known from neuroanatomy and task-based fMRI, and indi-
cated comparable levels of plausible connectivity for different seeds.
For example, Broca’s area connectivity shows the lateralized lan-
guage network involving left inferior frontal gyrus, Wernicke’s area
(superior temporal gyrus) and supramarginal gyrus. Conventional
connectivity maps show bilateral connectivity without indicating the
supramarginal gyrus. Left V1 connectivity specifically follows the
temporal-parieto-occipital junction and clearly shows bilateral pulv-
inar, whereas conventional connectivity is highly unspecific, indicat-
ing connectivity to almost all gray matter.
4http://www.pnas.org/content/110/40/16187.short Footline Author
Figure 4 (a) Group level connectivity
maps using ME-ICR (p<0.001, FDR
q<0.005) and conventional connectivity
(p<10-7, FDR q<10-6) for four different
seeds: posterior cingulate, right hand,
Broca’s area, left V1. ME-ICR
connectivity shows: for the PCC, the
canonical default mode network; for the
right hand, ipsilateral motor and
prem ot or ar eas, b il atera l sen so ry
cortices, ipsilateral thalamus, and
contralateral cerebellum; for Broca’s
area, premotor, middle temporal,
supramarginal areas, and ipsilateral
dorsal striatum; and for visual seed,
bilateral visual cortices bounded by
parieto-occiptal junction and the
pulvinar of the thalamus (black arrow).
Convenional connectivity shows: for
PCC, connectivity to the motor cortex;
for the right hand to the insula; for
Broca’s area, bilateral connectivity; for
primary visual cortex, the whole cortex.
(b) For regions in (a), plus dorsolateral,
ventromedial prefrontal cortices,
caudate, and insula, type I error control
for contrasts between subgroupings:
random (left); motion biased (middle);
high vs. low movers (right). For each
seed, observed error (y-axis) compared
to expected error (x-axis). Comparisons
are made at a series of significance
values (lines, 0.0001-0.05), for ME-ICR
(blue) and conventional (yellow)
connectivity. Lines below and above
y=x (black line) denote nominal and
failed type I error control, respectively.
ME-ICA consistently demonstrates
nominal type I error control, whereas in
biased and extreme cases conventional
connectivity fails with up to 5 times
greater type I error than expected. (c)
Maps of false positive connectivity
differences between high vs. low
movers after thresholding to p<0.01 and
family wise error (cluster) correction to
ɑ<0.05. All conventional FC maps are
populated by false positive clusters. All
ME-ICR maps are empty.
ME-ICR / 1-sample T-test Conventional FC / 1-sample T-test
Posterior
Cingulate
Right
Hand
Broca’s
Area
Left
V1
Posterior
Cingulate
Right
Hand
Broca’s
Area
Left
V1
Conventional
FC
ME-ICA
FC
Posterior Cingulate Broca’s Area Left V1
False Positive Connectivity Differences (High vs. Low Movers)
A
Expected (p<=x) Expected (p<=x)
Random Groupings Motion Biased Groupings
Expected (p<=x)
High vs. Low Movers
BNull Hypothesis Test For Type I Error Control
Observed (p<=y)
Observed (p<=y)
Observed (p<=y)
C
Type 1 Error Testing of Group Level ME-ICA Functional Connec-
tivity . ME-ICR and conventional connectivity were assessed for false
positive (type 1) error control in group contrasts (see SI section 2.11)
[16]. A null hypothesis test was used, based on computation of func-
tional connectivity contrasts (2-sample t-tests) between equally sized
permuted subgroups of the healthy volunteers, for 6 seed regions.
Three subgroupings were assessed: random (50 permutations), par-
tially motion biased (at least half of subjects with greater motion,
50 permutations), and fully motion biased (high vs. low movers).
Since subgroups were drawn from the same normal sample, all pos-
itive tests were type 1 error, and the number of false positive tests
was not expected to exceed the number of false positive tests (FP)
predicted under the null hypothesis, i.e., F P =p×N, where N
is the number of tests and pis the probability of type 1 error. False
positive counts were made at 20 thresholds spanning p=0.0001-0.05
(Fig. 4b). False positive counts were pooled over permutations and
expressed as an observed false positive rate, then compared to the
expected false positive rates (p).
For contrasts without motion bias, ME-ICR produced clear and
consistent nominal type 1 error control, for all seeds. Conventional
functional connectivity had more varied performance, in that ob-
served rates could exceed expected rates by small but notable mar-
gins. In subgroupings biased by motion, ME-ICR continued to ex-
ercise nominal type 1 error control. In contrast, conventional con-
nectivity contrasts clearly failed in error control, with observed error
rates up to twice the expected rate. Lastly, in the extreme case of
contrast between functional connectivity maps for high movers ver-
sus low movers (Fig. 4c), ME-ICR again maintained nominal type 1
error control, whereas observed false positive rates for conventional
connectivity testing were up to 5 times the expected rate. Results
therefore show the crucial finding that group level ME-ICR connec-
tivity contrasts have nominal type 1 error control that is highly robust
to biases in subject motion.
Discussion
Eliminating spurious seed-connectivity findings requires both robust
BOLD denoising and valid statistical estimation and inference. Con-
ventional functional connectivity methodology works within the lim-
itations of single-echo fMRI to achieve specific goals in denois-
ing or connectivity estimation. Isolating BOLD signals with ME-
ICA allows several established goals to be achieved simultaneously.
tSNR of signal was greatly increased over conventional methods us-
ing widely available MRI hardware. Motion artifacts were removed
without motion parameter regression or scrubbing. Bandpass fil-
tering was removed from analysis and spatial ICA transformation
represented the full frequency spectrum of BOLD signals for seed-
connectivity analysis with ME-ICR. The positive bias of conventional
subject level connectivity did not affect ME-ICR, so the problems
of distribution centering with global signal regression were avoided
[6]. Subject level connectivity inference with ME-ICR was consis-
tent across datasets with significant differences in motion. The poor
specificity of conventional seed-connectivity was characterized, and
ME-ICR doubled specificity, at least. Conventional group-level seed-
connectivity maps were characterized as having diffuse and neuro-
anatomically inaccurate global connectivity. This limitation of con-
ventional analysis was due to its poor specificity in mapping anatom-
ically predictable patterns of cortical-cortical and cortical-subcortical
connectivity. Conventional connectivity differences between groups
with different motion were associated with up to 5-fold greater type
1 error than expected under the null hypothesis. In contrast, ME-ICR
produced precise and plausible connectivity maps based on valid sta-
Footline Author PNAS Issue Date Volume Issue Number 5
tistical inference across subject and group levels of analysis, critically
culminating in type 1 error rates predicted by the null hypothesis for
explicitly motion-biased group contrasts. Altogether, preprocessing
was greatly simplified and made more effective, and valid hypothesis
testing was enabled for the study of connectivity differences between
groups with motion differences.
The present study leveraged many benefits of ICA for resting
state fMRI analysis. To date, ICA has been applied in both spatial
and temporal domains to produce connectivity maps [17]. Spatial
ICA has shown common components across subjects and has been
used to find the common set of components across groups. Dual-
regression of spatial ICA maps also enables the study of group differ-
ences in shared components [18]. Here we use spatial ICA as a trans-
formation of BOLD signals for ME-ICR. This method essentially is
principal component regression in the space of the BOLD-weighted
independent components. Functional connectivity estimation and in-
ference with ME-ICR is an important contribution to ICA method-
ology because it enables subject and group-level hypothesis testing
without expert knowledge for component selection or a shared ba-
sis of connectivity maps. These attributes make ME-ICR well suited
to studying patient populations with poorly characterized functional
networks and in computing connectivity differences between healthy
volunteers and patients that may not share the same basis of func-
tional networks.
The limitations of ME-ICR relate to ME acquisition, ICA, and
TE-dependence analysis. Current ME fMRI implementations use
parallel imaging to acquire images at multiple TEs. Parallel imaging
may increase susceptibility to motion artifacts, but we have shown
that the proposed approach improves tSNR and reduces artifacts over
conventional methods regardless. ME acquisition achieves better sig-
nal quality at the cost of lower temporal and spatial resolution than
conventional acquisition. Single-echo multi-band imaging may allow
also denoising and tSNR increases with better resolution [19, 20].
However, approaches that do not isolate BOLD signals would still
require the application of various filters for denoising and would not
solve problems of seed-connectivity inference.
Materials and Methods
Functional MRI Data Acquisition. This study was approved by the Local Re-
search Ethical Committee at the University of Cambridge (LREC 11/EE/0198).
Resting state fMRI data was acquired from 35 normal consenting volunteers (18
males, 17 females, mean age 33±13). Data were acquired with a Siemens
Trio 3T MRI Scanner and a 32-channel receive-only head coil (Siemens Medical
Solutions, AG, Erlangen, Germany). Functional images were acquired with a
multi-echo EPI sequence with online reconstruction (TR 2.47 s, flip angle 78,
matrix size 64x64, in-plane resolution 3.75 mm, FOV 240 mm, 32 oblique slices,
alternating slice acquisition slice thickness 3.75 mm with 10% gap, iPAT factor 3,
bandwidth 1698 Hz/pixel, TE=12,28, 44,60 ms) [9]. For 3 subjects, an additional
single-echo EPI scan was acquired (repetition time TR=2.26 s, flip angle 78,
matrix size 64x64, in-plane resolution 3.0 mm, field of view 192 mm, 32 oblique
slices, alternating slice acquisition slice thickness 3.75, iPAT factor 3, TE=30
ms) Anatomical images were acquired using a T1-weighted MPRAGE sequence
(magnetization prepared rapidly acquired gradient echo) 176x240 FOV, 1mm in-
plane resolution, inversion time TI=1100 ms). Preprocessing and ME-ICA for
denoising and BOLD component identification was performed with the AFNI tool
meica.py[11, 21]. Anatomical and functional data were nonlinearly warped to
the MNI template using FSL FNIRT [22]. See SI sections 2.1-2.3 for further
processing details.
Multi-Echo Independent Components Regression (ME-ICR). Subject level
seed-based connectivity analysis for ME-ICA processed BOLD component coef-
ficients was based on computing Pearson correlation of spatial ICA component
coefficients. The ICA mixing matrix was fit to the T∗
2weighted combination of
multi-echo data [9], and the coefficient maps corresponding to high-κcompo-
nents comprised the component coefficient dataset. Following computation of
correlation between vectors of component coefficients, Pearson’s R values were
converted to standard (Z) scores using the Fisher R-Z transform with degrees of
freedom counted as the number of high-κcomponents.
ACKNOWLEDGMENTS. P.K. is supported by the NIH-Cambridge Scholars Pro-
gram. V.V. is a Wellcome Trust Clinical Fellow. FMRI data collection was sup-
ported by the National Institute of Health Research (NIHR) Cambridge Biomedical
Research Centre.
1. Biswal, B., Yetkin, F.Z., Haughton, V.M., Hyde, J.S. (1995) Functional connectivity
in the motor cortex of resting human brain using echo-planar MRI. Magn. Reson.
Med. 34(4):537-541.
2. Power, J.D., Barnes, K.A., Snyder, A.Z., Schlaggar, B.L. Petersen, S.E. (2012) Spuri-
ous but systematic correlations in functional connectivity MRI networks arise from
subject motion. NeuroImage 59(3):2142-2154.
3. Satterthwaite, T.D., Wolf, D.H., Loughead, J., Ruparel, K., Elliott, M.A., Hakonarson,
H., Gur, R.C. Gur, R.E. (2012) Impact of in-scanner head motion on multiple mea-
sures of functional connectivity: Relevance for studies of neurodevelopment in
youth. NeuroImage 60(1):623-632.
4. van Dijk, K.R.A., Sabuncu, M.R. Buckner, R.L. (2012) The influence of head motion
on intrinsic functional connectivity MRI. NeuroImage 59(1):431-438.
5. Satterthwaite, T.D., Elliott, M.A., Gerraty, R.T., Ruparel, K., Loughead, J., Calkins,
M.E., Eickhoff, S.B., Hakonarson, H., Gur, R.C., Gur, R.E. Wolf, D.H. (2013) An
improved framework for confound regression and filtering for control of motion ar-
tifact in the preprocessing of resting-state functional connectivity data. NeuroImage
64(1):240-256.
6. Murphy, K., Birn, R.M., Handwerker, D.A., Jones, T.B. Bandettini, P.A. (2009) The
impact of global signal regression on resting state correlations: Areanti-correlated
networks introduced? NeuroImage 44(3):893-905.
7. Saad, Z. S., Gotts, S. J., Murphy, K., Chen, G., Jo, H. J., Martin, A., & Cox, R.W. (2012)
Trouble at rest: how correlation patterns and group differences become distorted
after global signal regression Brain connectivity:2(1), 25-32.
8. Salvador, R., Martinez, A., Pomarol-Clotet, E., Gomar, J., Vila, F., Sarr ´
o, S., Capdev-
ila, A. Bullmore, E. (2008) A simple view of the brain through a frequency-specific
functional connectivity measure NeuroImage 39(1):279-289.
9. Poser, B.A., Versluis, M.J., Hoogduin, J.M. Norris, D.G. (2006) BOLD contrast sen-
sitivity enhancement and artifact reduction with multiecho EPI: Parallel-acquired
inhomogeneity-desensitized fMRI. Magn. Reson. Med. 55(6):1227-1235.
10. Peltier, S.J. Noll, D.C. (2002) T∗
2dependence of low frequency functional connec-
tivity NeuroImage 16(4):985-992.
11. Kundu, P., Inati, S.J., Evans, J.W., Luh, W.M. Bandettini, P.A. (2012) Differentiating
BOLD and non-BOLD signals in fMRI time series using multi-echo EPI NeuroImage
60(3):1759-1770.
12. Hyv¨
arinen, A. Oja, E. (2000) Independent component analysis: Algorithms and
applications Neural Networks 13(4-5):411-430.
13. Beckmann, C.F. Smith, S.M. (2004) Probabilistic Independent Component Analysis
for Functional Magnetic Resonance Imaging IEEE Transactionson Medical Imaging
23(2):137-152.
14. Friston, K.J., Holmes, A.P., Poline, J.B., Grasby, P.J., Williams, S.C.R., Frackowiak,
R.S.J. Turner, R. (1995) Analysis of fMRI time-series revisited NeuroImage 2(1):45-
53.
Poser, B.A., Barth, M., Goa, P., Deng, W. Stenger, V.A. (2013) Single-shot echo-
planar imaging with Nyquist ghost compensation: Interleaved dual echo with ac-
celeration (IDEA) echo-planar imaging (EPI) Mag. Reson. Med. 69(1):37-47.
15. Bartko, J.J. (1966) The intraclass correlation coefficient as a measure of reliability.
Psychological Reports 19(1):3-11.
16. Bullmore, E.T., Suckling, J., Overmeyer, S., Rabe-Hesketh, S., Taylor, E. Brammer,
M.J. (1999) Global, voxel, and cluster tests, by theory and permutation, for a differ-
ence between two groups of structural MR images of the brain , IEEE Trans. Med.
Im. 18(1):32-42.
17. Smith, S.M., Miller, K.L., Moeller, S., Xu, J., Auerbach, E.J., Woolrich, M.W., Beck-
mann, C.F., Jenkinson, M., Andersson, J., Glasser, M.F., Van Essen, D.C., Feinberg,
D.A., Yacoubb, E.S. Ugurbil, K. (2012) Temporally-independent functional modes
of spontaneous brain activity Proc. Nat. Acad. Sci. USA 109(8):3131-3136.
18. Filippini, N., MacIntosh, B.J., Hough, M.G., Goodwin, G.M., Frisoni, G.B., Smith,
S.M., Matthews, P.M., Beckmann, C.F. Mackay, C.E. (2009) Distinct patterns of
brain activity in young carriers of the APOE-4 allele Proc. Nat. Acad. Sci. USA
106(17):7209-7214.
19. Setsompop, K., Gagoski, B.A., Polimeni, J.R., Witzel, T., Wedeen, V.J. Wald, L.L.
(2012) Blipped-controlled aliasing in parallel imaging for simultaneous multislice
echo planar imaging with reduced g-factor penalty Magn. Reson. Med. 67(5):1210-
1224.
20. Feinberg, D.A., Moeller, S., Smith, S.M., Auerbach, E., Ramanna, S., Glasser, M.F.,
Miller, K.L., Ugurbil, K., Yacoub, E. (2010) Multiplexed Echo Planar Imaging for
Sub-Second Whole Brain FMRI and Fast Diffusion Imaging Plos One 5(12):e15710.
21. Cox, R.W. (1996) AFNI: Software for analysis and visualization of functional mag-
netic resonance neuroimages Computers and Biomedical Research 29(3):162-173.
22. Klein, A., Andersson, J., Ardekani, B.A., Ashburner, J., Avants, B., Chiang, M.C.,
Christensen, G.E., Collins, D.L., Gee, J., Hellier, P., Song, J.H., Jenkinson, M.,
Lepage, C., Rueckert, D., Thompson, P., Vercauteren, T., Woods, R.P., Mann, J.J.
Parsey, R.V. (2009) Evaluation of 14 nonlinear deformation algorithms applied to
human brain MRI registration NeuroImage 46(3):786-802.
6http://www.pnas.org/content/110/40/16187.short Footline Author
