# Variability in fMRI: a re-examination of inter-session differences.

**ABSTRACT** We revisit a previous study on inter-session variability (McGonigle et al. [2000]: Neuroimage 11:708-734), showing that contrary to one popular interpretation of the original article, inter-session variability is not necessarily high. We also highlight how evaluating variability based on thresholded single-session images alone can be misleading. Finally, we show that the use of different first-level preprocessing, time-series statistics, and registration analysis methodologies can give significantly different inter-session analysis results.

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Page 1

Variability in fMRI: A Re-Examination of

Inter-Session Differences

Stephen M. Smith,1*Christian F. Beckmann,1Narender Ramnani,1

Mark W. Woolrich,1Peter R. Bannister,1Mark Jenkinson,1

Paul M. Matthews,1and David J. McGonigle2

1Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB), Department of

Clinical Neurology, Oxford University, John Radcliffe Hospital, Headington,

Oxford, United Kingdom

2Laboratoire de Neurosciences Cognitives et Imagerie Ce ´re ´brale, Ho ˆpital de la Salpe ˆtrie `re,

CNRS UPR 640-LENA, Paris, France

?

?

Abstract: We revisit a previous study on inter-session variability (McGonigle et al. [2000]: Neuroimage

11:708–734), showing that contrary to one popular interpretation of the original article, inter-session

variability is not necessarily high. We also highlight how evaluating variability based on thresholded

single-session images alone can be misleading. Finally, we show that the use of different first-level

preprocessing, time-series statistics, and registration analysis methodologies can give significantly differ-

ent inter-session analysis results. Hum Brain Mapp 24:248–257, 2005.

© 2005 Wiley-Liss, Inc.

Key words: fMRI; session variability; reproducibility; longitudinal studies

?

?

INTRODUCTION

The blood oxygenation level-dependent (BOLD) effect in

functional magnetic resonance imaging (fMRI), a marker of

neuronal activation, is often only of similar magnitude to the

noise present in the measured signal. To increase power and

to allow conclusions to be made about subject populations,

it is common practice to combine data from multiple sub-

jects. It is also common to take multiple sessions from each

subject, again to increase sensitivity to activation, or for

other experimental design reasons such as tracking changes

in function over time. It is therefore important that inter-

session variability present in fMRI data is understood, and

in response, McGonigle et al. [2000] presented an in-depth

study of this issue.

In designing both multi-subject and single-subject multi-

session studies, it is critical for the experimenter to have

some idea of the relative sizes of within-session variance and

inter-session variance. For example, if inter-session variance

is large, it could be difficult to detect longitudinal experi-

mental effects (e.g., in studies of learning [Ungerleider et al.,

2002] and poststroke recovery [Johansen-Berg et al., 2002]).

If fMRI is to be used in presurgical mapping [e.g., Fernandez

et al., 2003], which by its nature will involve only a single

subject, correct interpretation will be dependent on an ap-

preciation of the potential uncertainty due simply to a ses-

sion effect. In multi-subject studies, it is advantageous to

have some idea of the expected inter-session variance, as this

will contribute to the observed inter-subject variance.

To investigate how well a single-session dataset from a

single subject typified the subject’s responses across multi-

ple sessions, McGonigle et al. [2000] carried out the same

Contract grant sponsor: Medical Research Council (UK); Contract

grant sponsor: Engineering and Physical Sciences Research Council

(UK); Contract grant sponsor: EPSRC Medical Images and Signals

Collaboration; Contract grant sponsor: GSK.

*Correspondence to: Stephen M. Smith, FMRIB (Oxford Centre for

Functional Magnetic Resonance Imaging of the Brain), Department

of Clinical Neurology, Oxford University, John Radcliffe Hospital,

Headington, Oxford OX3 9DU, United Kingdom.

E-mail: steve@fmrib.ox.ac.uk

Received for publication 21 January 2004; Accepted 7 July 2004

DOI: 10.1002/hbm.20080

Published online in Wiley InterScience (www.interscience.wiley.

com).

? Human Brain Mapping 24:248–257(2005) ?

© 2005 Wiley-Liss, Inc.

Page 2

fMRI protocol on 33 separate days. On each day, three

paradigms were run (visual, motor, and cognitive), and the

variation in activation was studied. The study drew three

main conclusions: (1) the use of voxel-counting on thresh-

olded statistical maps was not an ideal way to examine

reproducibility in fMRI; (2) a reasonably large number of

repeated sessions was essential to properly estimate inter-

session variability; and (3) the results of a single session

from a single subject should be treated with care if nothing

was known about inter-session variability.

Although McGonigle et al. [2000] noted the presence of

between-session variability in their experiment, they did not

attempt to assess systematically the causes of this variance.

There are a number of potential contributors, such as phys-

iologic variance (subject), acquisition variance (scanner), and

differences in analysis methodology and implementation.

As noted in their original article, “it is possible that spatial

preprocessing (for example) may affect inter-session vari-

ance quite independently of underlying physical or physio-

logical variability.” This view is supported by Shaw et al.

[2003], where analysis methodology is shown to affect ap-

parent inter-session variance. In the present study, we revisit

the analysis of data from McGonigle et al. [2000] and con-

sider session variability in the light of the effects that differ-

ent first-level processing methods can have.

Others have taken from McGonigle et al. [2000] the simple

broadbrush conclusion that there was a “large amount of

session variability” [e.g., Beisteiner et al., 2001; Chee et al.,

2003]. One of the purposes here is to address this miscon-

ception; for example, we show that for this dataset, inter-

session variability was of similar magnitude to within-ses-

sion variability.

We start with a brief theoretical overview of the compo-

nents of variance present in multiple-session data. We then

describe the original data and analysis, as well as the new

analyses carried out for this study, with explanation of the

measures used in this study to assess session variability. We

then present the variability results as found from these data,

centering around the use of mixed-effects Z values in rele-

vant voxels as the primary measure of interest. We also

show qualitatively why it is dangerous to judge variability

through the use of thresholded single-session images.

Variance Components

Researchers often refer to different group analyses, the

most common being fixed-effects and mixed-effects. What

these terms are actually referring to are different inter-ses-

sion (or inter-subject) noise (variance) models. We now sum-

marize what the terms and associated models mean.

We start with the equation for the t-statistic:

t ?

mean effect

?variance?mean effect?,(1)

i.e., we are asking how big the mean effect size is compared

to the noise (the mean’s standard deviation1). The standard

deviation is the square root of either the fixed-effects vari-

ance of the mean or the random-effects variance of the mean.

With fixed-effects modeling, we assume that we are only

interested in the factors and levels present in the study, and

therefore our higher-level fixed-effects variance FV is de-

rived from pooling2the first-level (within-session) variances

(of first-level effect size mean) FVi, according to:

FV ???FVi?

n2

, DoFFV??DoFFVi, (2)

where DoF is the degrees of freedom, which is usually large

in the case of fMRI time series. This modeling therefore

ignores the cross-session (or cross-subject) variance com-

pletely and the results cannot be generalized outside of the

group of sessions/subjects involved in the study.

With simple mixed-effects3modeling, we derive the

mixed-effects variance MV directly from the variance of the

first-level parameter estimates PEi(effect sizes) or contrasts

of parameter estimates:

MV ?var?PEi?

n

, DoFMV? n ? 1,(3)

with a (normally) much smaller DoF than with fixed-effects.

The modeling thus uses the cross-session (or cross-subject)

variance, and the results (which are generally more conservative

than with a fixed-effects analysis) are relevant to the whole pop-

ulation from which the group of sessions/subjects was taken.

The mixed-effects variance is the sum of the fixed-effects

(within-session) variance and random-effects (pure inter-

session) variance, although simple estimation methods cal-

culate this directly, as above, and do not explicitly use the

fixed-effects variance. The estimated mixed-effects variance

therefore should in theory and in practice be larger than the

fixed-effects variance. We expect that when there is large

inter-session variance, there will be a large difference be-

tween fixed- and mixed-effects analyses.

There have been recent significant developments in group-

level analysis. For example, it has been shown [Beckmann et

al., 2003a] that there is value in carrying up lower-level vari-

ances to higher-level analyses of mixed-effects variance, and

one implementation of this using Bayesian modeling/estima-

tion methodology has been reported [Woolrich et al., 2003].

Whereas the dataset used in this study may well prove useful

1Note that in the simplest cases the variance of the mean is the

variance of the residuals divided by the number of data points.

2The first factor of 1/n in FV comes from taking the mean of the

first-level variances, i.e., pooling them, and the second factor comes

from converting this higher level variance from a variance of resid-

uals into the variance of the (higher-level) mean [for more detail, see

Leibovici and Smith, 2000].

3Note that the terms “mixed effects” and “random effects” are often

(incorrectly) used interchangeably.

?Inter-Session Variability in fMRI?

? 249 ?

Page 3

in investigating these developments further, this is beyond the

scope of this article. Instead, we concentrate primarily on two

other questions, namely the magnitude of session variability,

and the effect that first-level analysis methodologies can have

on its apparent magnitude. For mixed-effects analyses in the

present work, we therefore have only used ordinary least-

squares (OLS) estimators (see equation [3] and [Holmes and

Friston, 1998]).

MATERIAL AND METHODS

Original Experiments and Analysis

We describe here the experiment and original analysis car-

ried out by McGonigle et al. [2000]. A healthy, 23-year-old,

right-handed male was scanned on 33 separate days (over 2

months) with as many factors as possible held constant. On

each day, three block-design paradigms were run (all using

block lengths for rest ? 24.6 s and activation ? 24.6 s): visual

(8-Hz reversing black-white checkerboard, 36 time points after

deleting the first two); motor (finger tapping, right index finger

at 1.5 Hz, 78 time points); and cognitive (0.66-Hz random

number generating vs. counting, 78 time points), with the

paradigm order randomized. The data were collected on a

Siemens Vision at 2 T (repetition time [TR] ? 4.1 s, 64 ? 64

? 48, 3 ? 3 ? 3 mm voxels). A single T1-weighted 1.5 ? 1 ? 1

mm structural scan was taken.

Original analysis was carried out using SPM99 (online at

http://www.fil.ion.ucl.ac.uk/spm). All 99 sessions were re-

aligned (motion-corrected) to the same target (the first scan

of the first session of the first day) and then a mean over all

99 sessions was created. This was used to find normalization

(to a T2-weighted target in MNI space [Evans et al., 1993])

parameters for all 99 sessions (using 12-parameter affine

followed by 7 ? 8 ? 7 basis-function nonlinear registration).

Sinc interpolation on final output was used.

Sessions containing “obvious movement artefacts” were

identified by eye and removed from consideration (three

motor, two visual, and three cognitive). Cross-session anal-

ysis was carried out for voxels in standard space that were

present in all sessions. Spatial filtering with a Gaussian

kernel of full-width half-maximum (FWHM) 6 mm was

applied. Each volume of each session was intensity normal-

ized (rescaled) so that all had the same mean intensity.

Voxel time-series analysis was carried out using general

linear modeling (GLM). The data was first precolored by

temporally smoothing the data with a Gaussian of 6 s

FWHM. Slow drifts in the data were removed by including

drift terms in the model (a set of cosine basis functions

effectively removing signals of period longer than 96 s).

For presentation of within-session results, voxel-wise

thresholding (P ? 0.05) was used, correcting for multiple

comparisons using Gaussian random field theory (GRF)

[Friston et al., 1994].

Both fixed- and mixed-effects analyses were carried out to

examine the effects of using different variance components,

and an extra-sum-of-squares (ESS) F-test was performed

across all sessions of each paradigm to assess the presence of

significant inter-session variance.

Methods Tested

We now describe the analysis approaches used for this arti-

cle. The two packages used for our investigations were

SPM99b (Statistical Parametric Mapping) and FSL v1.3 (FMRIB

Software Library; online at http://www.fmrib.ox.ac.uk/fsl,

June 2001). Both are available freely and used widely.

SPM includes a motion-correction (realignment) tool, a

tool for registration (normalization) to standard space,

GLM-based time-series statistics [Worsley and Friston,

1995], and GRF-based inference [Friston et al., 1994]. SPM

carries out standard-space registration before time-series

statistics. The SPM99b time series statistics correct for tem-

poral smoothness by precoloring [Friston et al., 2000].

GLM-based analysis in FSL is carried out with the fMRI

Expert Analysis Tool (FEAT), which uses other FSL tools

such as Brain Extraction Tool (BET [Smith, 2002]), an affine

registration tool, FMRIB’s Linear Image Registration Tool

(FLIRT [Jenkinson and Smith, 2001; Jenkinson et al., 2002]),

and a motion-correction tool based on FLIRT (MCFLIRT

[Jenkinson et al., 2002]). FEAT carries out standard-space

registration after time-series statistics. FSL time-series statis-

tics correct for temporal smoothness by applying prewhit-

ening [Woolrich et al., 2001].

Six different, complete analyses were carried out with

various combinations of preprocessing and time-series sta-

tistics options to allow a variety of comparisons to be made.

In tests A, C, and G, FSL was used for preprocessing and

registration whereas in tests D, E, and F, SPM was used. For

tests A, D, and G, FEAT time-series statistics was used

whereas for C, E, and F, SPM time-series statistics was used.

In tests A–E, the various controlling parameters were kept as

similar as possible, both to each other and to default settings in

the relevant software packages. Tests A versus D and C versus

E hold the statistics method constant while comparing spatial

methods, therefore showing the relative merits of the spatial

components (motion correction and registration). Tests A ver-

sus C and D versus E hold the spatial method constant while

comparing statistical components, thus showing the relative

merits of the statistical components (time-series analysis). A

versus E tests pure-FSL against pure-SPM. F and G test pure-

SPM and pure-FSL, respectively, with these analyses set up to

match the specifications of the original analyses in McGonigle

et al. [2000] as closely as possible, including turning on inten-

sity normalization in both cases. For a summary, see Table I.

(For B, model-free independent component analysis (ICA) was

carried out; the model-free results are not included here but

will be presented elsewhere.)

Because the methods for high-pass temporal filtering in

FSL and SPM are intrinsically different, they cannot be set to

act in exactly the same way (within A–E and within F and G)

by choosing the same cutoff period in each; instead, the

cutoff choices were made to match as closely as possible the

extent to which the relevant signal and noise frequencies

were attenuated by the different methods. For the purposes

of the present work, high-pass temporal filtering is consid-

ered part of the temporal statistics, where it fits most natu-

?Smith et al.?

? 250 ?

Page 4

rally. The non-default “Adjust for sampling errors” motion-

correction option in SPM was not used.

Eight sessions (of the 99) were excluded from the original

analysis in McGonigle et al. [2000] due to “obvious move-

ment artefacts.” These were included in our analyses, how-

ever, as we did not consider that there was sufficient objec-

tive reason to exclude them. The estimated motions for these

sessions were not, in general, significant outliers relative to

the average motion across sessions and any apparent (acti-

vation map) motion artefacts were not in general signifi-

cantly different from most of the sessions. The quantitative

results below were in fact recalculated without these eight

sessions, i.e., reproducing the same dataset as used in

McGonigle et al. [2000], but without any significant change

in results, and therefore are not reported here.

Inter-Session Evaluation Methods

For all paradigms and analysis methods, simple fixed-

effects (FE) and OLS mixed-effects (ME) Z-statistics were

formed. For each paradigm, a mask of voxels that FE con-

sidered potentially activated (Z ? 2.3) was created. This

contains voxels in which an ME analysis is potentially inter-

ested (given that ME generally gives lower Z-statistics than

does FE4). This mask was averaged over A, C, D, and E to

balance across the various methods, and then eroded

slightly (2 mm in 3D) to avoid possible problems due to

different brain mask effects.

We initially investigated the size of inter-session variance

by estimating the ratio of random-effects variance to fixed

effects, averaged over the voxels of interest as defined

above. Given that ME variance is the sum of FE and RE

variance, we estimated the RE (inter-session) variance by

subtracting the FE variance from the ME variance. We then

took the ratio image of RE to FE variance, and averaged over

the masks described above. This ratio would be 0 if there

were no inter-session variability and rises as the contribu-

tion by inter-session variability increases. A ratio of 1 occurs

when inter- and intra-session variabilities make similar con-

tributions to the overall measured ME variance.

We next investigated whether session variability is indeed

Gaussian distributed. If it is not, then inference based on the

OLS method used for ME modeling and estimation in the

present work would need a much more complicated inter-

pretation (as also would be the case with many other group-

level methods used in the field). We used the Lilliefors

modification of the Kolmogorov-Smirnov test [Lilliefors,

1967] to measure in what fraction of voxels the session effect

was significantly non-Gaussian.

The variance ratio figures do not take into account estimated

effect size, which in general will vary between methods, and so

the primary quantification in this study uses the mixed-effects

Z (ME-Z). This is roughly proportional to the mean effect size

and inversely proportional to the inter-session variability. This

makes ME-Z a good measure with which to evaluate session

variability; it is affected directly by the variability while being

weighted higher for voxels of greater interest (i.e., voxels con-

taining activation). We are not particularly interested in vari-

ability in voxels that contain no mean effect. We therefore base

our cross-subject quantitation on ME-Z comparisons within

regions of interest (defined above).5

If one of the analysis methods tested here results in in-

creased ME-Z, then this implies reduced overall method-

4We are attempting to identify voxels of potential interest in ME-Z

images.GiventhatME-ZcanbethoughtofasbeingrelatedtoFE-Zbut

scaled down by a factor related to session variance, this seems like a

good way of choosing voxels which have the potential to be activated

in the ME-Z image, depending on the session variance. To investigate

the dependency of this approach on the FE-Z threshold chosen, we

re-ran the tests leading to the ME-Z plots presented in Figure 8, having

determined the regions of interest using a lower FE-Z threshold (Z

?1.64,i.e.,afactorof5moreliberalinthesignificancelevel).Themean

ME-Zresultswereallscaleddown,asexpected,butthequalitative(i.e.,

relative) results were identical to those presented in Figure 8.

5Although we are primarily investigating analysis efficiency and ses-

sion variance by looking at regions of potential activation, note that it

is also necessary to ensure that the non-activation (null) part of the ME

distribution is valid, i.e., not producing incorrect numbers of false

positives. This investigation/correction of the ME null distribution is

addressed below and uses the whole ME-Z image, not just the regions

of potential activation.

TABLE I. Different analyses carried out

TestPreprocessing StatisticsRegistration

A

C

D

E

F

G

FSL (MCFLIRT spat ? 5 intnorm ? n)

FSL (MCFLIRT spat ? 5 intnorm ? n)

SPM (SPM-mc&norm spat ? 5 intnorm ? n)

SPM (SPM-mc&norm spat ? 5 intnorm ? n)

SPM match [18] (SPM-mc&norm spat ? 6 intnorm ? y)

FSL match [18] (MCFLIRT spat ? 6 intnorm ? y)

FSL (FEAT) (hp-FSL ? 40)

SPM (hp-cos ? 72)

FSL (FEAT) (hp-FSL ? 40)

SPM (hp-cos ? 72)

SPM (hp-cos ? 98.4)

FSL (FEAT) (hp-FSL ? 53)

FSL (FLIRT)

FSL (FLIRT)

SPM (done in preproc)

SPM (done in preproc)

SPM (done in preproc)

FSL (FLIRT)

Spat, spatial filtering with full-width-half-maximum given in mm.

intnorm, intensity normalization (the intensity rescaling of each volume in a 4-D fMRI dataset so that all have the same mean within-brain intensity).

hp-FSL, FSL’s high-pass temporal filtering with cutoff period given in seconds.

hp-cos, high-pass temporal filtering (in seconds) via cosine basis functions.

preproc, preprocessing.

?Inter-Session Variability in fMRI?

? 251 ?

Page 5

related error (increased accuracy) in the method, because

unrelated variances add. Although a single-session analysis

cannot eliminate true inter-session variance intrinsic to the

data, it can add (induce) variance to the effective inter-

session variance due to failings in the method itself (for

example, poor estimates of first-level effect/variance, or reg-

istration inaccuracies). The best methods should therefore

give ME-variance that approaches (from above) the true,

intrinsic inter-session ME-variance. Recall that the same sim-

ple OLS second-level estimation method was used for all

analyses carried out, and it is only the first-level processing

that is varied.

Mean ME-Z was then calculated within the FE-derived

masks. As well as reporting these uncorrected mean ME-Z

values, we also report the mean values after adjusting the

ME-Z images for the fact that in their histograms (suppos-

edly a combination of a null and an activation distribution)

the null part, ideally a zero mean and unit standard devia-

tion Gaussian, was often significantly shifted away from

having the null peak at zero. This makes Z-values incompa-

rable across methods, and needed to be corrected for. The

causes of this effect include spatially structured noise in the

data and in differences in the success between the different

methods for correcting for temporal smoothness, a problem

enhanced potentially for all methods given the unusually

low number of time points in the paradigms.

We used two methods to correct ME-Z for null-distribu-

tion imperfections, and report results for both methods.

With hand-corrected peak shift correction, the peak of the ME-Z

distribution was identified by eye and assumed to be the

mean of the null distribution; the ME-Z image then had this

value subtracted. With mixture-model-based null shift correc-

tion, a nonspatial histogram mixture model was automati-

cally fitted to the data using expectation-maximization. This

involved a Gaussian for the null part, and gammas for the

activation and deactivation parts [Beckmann et al., 2003b].

The center of the Gaussian fit was then used to correct the

ME-Z image. The advantage of the hand-corrected method

is that it is potentially less sensitive to failings in the as-

sumed form of the mixture components; the advantage of

the mixture-model-corrected fit is that it is fully automated

and therefore more objective.

It is not yet standard practice (with either SPM or FSL) to

correct for null-Z shifts in ME-Z histograms; the most com-

mon method of inference is to use simple null hypothesis

testing on uncorrected T or Z maps (typically via Gaussian

random field theory). By correcting for the shifts, we are able

to investigate the effects of using the different individual

analysis components in the absence of confounding effects

of null distribution imperfections.

Figure 1 shows an example ME-Z histogram including the

estimates (by eye and mixture-modeling) of the null mode.

The estimated ME-Z shifts that were applied to the mean

ME-Z values before comparing methods are plotted for all

analysis methods and all paradigms in Figure 2. The shift is

clearly more related to the choice of time-series statistics

method than to the choice of spatial processing method

(motion correction and registration), but there is no clear

indication of one statistics method giving a greater shift

extent than another. The two correction methods are largely

in agreement with each other.

RESULTS AND DISCUSSION

Fixed-Effects Activation Maps

The FE-based mask images (used to define the voxels used

in the quantitative analyses reported below) are shown in

Figure 3 as overlaid onto the MNI152 standard head image.

Inter-Session Effect Size Plots

For analysis methods A and E, we now show the effect size

and its (fixed-effects, within-session) temporal standard devi-

ation, as a function of session number. Both the effect size and

the temporal standard deviation are estimated as means over

interesting voxels, as defined above. The plots were normal-

izedbyestimatingthemeaneffectsizeoverallsessions,scaling

this to be unity, scaling the standard deviation by the same

factor, and demeaning the effect size plot (Figs. 4 and 5). These

plots show (as does the following section) that the within-

session variance has similar magnitude to the inter-session

variance. They also show that variability in effect size is higher

than variability in its standard deviation (although the impli-

cation of this fact is not necessarily important to the primary

points in the present work). The results presented here corre-

spond to the uncorrected plot in Figure 8.

Quantification of Inter-Session Variance

To quantitate better the size of inter-session variance, we

estimated the mean ratio of RE (ME minus FE) to FE vari-

ance. Any comparison between the RE and FE variance will

be dependent on the number of time points in each session,

with a larger number of time points leading to an increase in

the RE:FE ratio.

Figure 1.

Example ME-Z histogram showing null-distribution shift, from

analysis A of the visual paradigm.

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The results are shown in Table II. The interpretation of this is

simple yet important: in these datasets, inter-session variability

is not large compared to within-session variability.6

We cannot make very useful interpretations of the varia-

tions across methods of the variance ratio, particularly with-

out also taking into account the estimated effect size; hence

the use of mixed-effects Z for the main method comparison

results shown below.

Test for Gaussianity of Inter-Session Variability

Using the results of analysis A, for each paradigm we

tested whether the session variability was Gaussian. At each

voxel in standard space, we took the (first-level) parameter

estimates (effect sizes) from the relevant voxel in each of the

33 relevant first-level analyses, (i.e., the same data that was

fed into the group-level ME analysis). The variance of these

is the ME variance. For each set of 33 first-level parameter

estimates, we ran the Lilliefors modification of the Kolmog-

orov-Smirnov test [Lilliefors, 1967] for non-Gaussianity,

with a significance threshold of 0.05. In null data, we would

therefore expect rejection of the Gaussianity null hypothesis

at this 5% rate by random chance.

We calculated the fraction of voxels failing the normality

test across the whole brain and within the FE-derived masks

described above. In both cases and for all three paradigms,

the fraction of failed tests was less than 7.5% (range, 4.5–

7.3%), which is very close to the expected 5% rate of null

hypothesis rejections if in fact all the data is normal. This

provides strong quantitative evidence for the normality of

the session variability in this data. Qualitatively, the voxels

where the null hypothesis was rejected were scattered ran-

domly through the images, not clumped, again suggesting

that they were rejected by pure random chance rather than

because of some true underlying non-Gaussian process.

On (Not) Drawing Conclusions About Session

Variability Based on Thresholded

Single-Session Images

McGonigle et al. [2000] does not include any such state-

ment as “session variability is high,” or even any quantifi-

cation explicitly suggesting in a simple way that session

6Noting the much greater variability (across methods) in these ratios

than in the plots in Figure 8, and by looking in detail at separate ME

and FE variances, it is clear that the variation in these figures across

methods is due primarily to variation in FE variance. This is possi-

bly caused by methodologic differences in correcting for temporal

autocorrelation at first level.

Figure 2.

Estimated ME-Z null distribution shifts. Different tasks: C, cogni-

tive; M, motor; V, visual. Different correction methods: h, hand-

shifted; m, mixture-model-shifted.

Figure 3.

Masks of potentially activated voxels, within which mean ME-Z was calculated for each analysis

method. Red, visual; orange, motor; yellow, cognitive.

?Inter-Session Variability in fMRI?

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Page 7

variability is a serious problem. Nevertheless, unfortunately,

many researchers [e.g., Beisteiner et al., 2001; Chee et al.,

2003] seem to have taken these messages from the study.

One of the causes of this is the apparent variability in Fig-

ures 2–4 in McGonigle et al. [2000], which show for each

paradigm each session’s thresholded activation image (as a

single sagittal slice maximum intensity projection). All three

figures give the impression of large inter-session variability,

even for the strong visual paradigm.

The most important point to make with respect to this

issue is that it is not safe to judge inter-session variability by

looking at variability in thresholded statistic images. It is

perfectly possible for two unthresholded activation images

to not be significantly different statistically and yet one

contains activation just over threshold and the other just

under, giving the false impression of large variability. The

fact that thresholds are in any case chosen arbitrarily in-

creases the weakness of this method of judging variability.

To illustrate these issues, Figures 6 and 7 show single-

session thresholded images from analysis F of the visual

experiment. Figure 6 is created using the same threshold

as that used in McGonigle et al. [2000], namely P ? 0.05,

corrected for multiple comparisons using Gaussian ran-

dom field theory [Friston et al., 1994]. In contrast, Figure

7 is created using a reduced threshold (the t threshold

used in Figure 6 is reduced by 33%). Obviously there is

more apparent activation when the threshold is reduced

(although it has clearly not been reduced so far that there

is generally a huge amount of spatially variable noise

activation caused by this). The interesting point, however,

is that the subjective impression of inter-session variabil-

ity is much reduced.

Finally, a question arises as to why Figure 6, which

should match the original figure in McGonigle et al. [2000]

having been processed in the same manner, seems to

show less variability than that in the original figures. This

was found to be because suboptimal timing was used in

the original model generation (caused by a particular

default setting of the point within a TR that the model is

sampled, which also corresponds to the point during a TR

when that time point’s whole fMRI volume is assumed to

have been sampled instantaneously; this default was

changed between SPM99 and SPM99b). The reanalysis

was more efficient at estimating activation as better-

matched models were used, causing less apparent inter-

session variability.

As part of the investigation of this effect, we tested the

variability in peak Z-values as the model timing was changed

slightly. The mean-across-sessions (max-across-space[Z]) value

for five different phase shifts of the model (?1 TR to ?1 TR)

were found to be 6.6, 7.5, 7.9, 7.5, 6.9 (model timing running

from earlier to later, respectively). This is quite a large effect for

these phase shifts, given that the paradigm is a block design.

Figure 4.

Mean first-level effect size and its (within-session) standard devi-

ation, as a function of session number, for analysis A.

Figure 5.

Mean first-level effect size and its (within-session) standard devi-

ation, as a function of session number, for analysis E.

TABLE II. Mean estimated ratio of RE (inter-session)

variance to FE (within-session pooled) variance

Paradigm

Test

ACDEFG

Cognitive

Motor

Visual

1.0

0.9

1.4

0.3

0.3

0.3

1.5

1.4

1.9

0.5

0.6

0.8

0.6

0.6

0.8

1.0

1.1

1.7

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Page 8

This is another illustration of the danger of judging variability

solely based on thresholded results.

Mean ME-Z plots

Mean ME-Z plots are shown in Figure 8. Higher ME-Z

implies less analysis-induced inter-session variance, or

viewed another way, greater robustness to session effects.

Before discussing these plots it is instructive to get a

feeling for what constitutes significant difference in the

plots. Suppose that in these figures, two ME-Z maps were

separated by a Z difference of 0.25. This would correspond

to a general relative scaling between the two maps of ap-

proximately 0.25/6 ? 4%. We are interested in the effect that

this difference has on the final thresholded activation map.

We can therefore estimate this effect by thresholding an

ME-Z map at a standard level and at this level scaled by 4%.

Thresholding at P ? 0.05, when corrected (using Gaussian

random field theory) for multiple comparisons, corresponds

to a Z threshold of approximately 5. We therefore thresh-

olded the three ME-Z images from analysis F at levels of

Z ? 5 and Z ? 5.2. For the cognitive, motor, and visual ME-Z

images, this resulted in reductions in suprathreshold voxel

counts by 11, 8, and 6%, respectively. These are not small

percentages; we conclude that a difference in 0.25 between

the various plots can be considered significant in terms of

the effect on the final reported mixed-effects activation

maps. Note that these different thresholdings were carried

out with two threshold levels on the same ME-Z image for

each comparison, hence the previous criticism of not com-

paring thresholded maps is not relevant here.

We consider here plots A, C, D, and E, the various tests

that attempted to match all settings both to each other and to

default usage. Firstly, consider comparisons that show the

relative merits of the spatial components (motion correction

Figure 7.

Visual paradigm; analysis F single-session thresholded maximum intensity projections, thresholded

with the t threshold reduced from the “P ? 0.05 GRF-corrected” level by 33%. Note that as well

as the obvious increase in reported activation, “apparent variability” is decreased significantly.

Figure 6.

Visual paradigm; analysis F single-session thresholded maximum intensity projections, P ? 0.05

GRF-corrected. Each image corresponds to a different day’s dataset.

?Inter-Session Variability in fMRI?

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Page 9

and registration): A versus D and C versus E hold the

statistics method constant while comparing spatial methods.

Next, consider comparisons that show the relative merits of

the statistical components (time-series analysis): A versus C

and D versus E hold the spatial method constant while

comparing statistical components. Finally, A versus E tests

pure-FSL against pure-SPM.

Plots F and G test pure-SPM and pure-FSL, respectively,

with these analyses set up to match the specifications of the

original analyses in McGonigle et al. [2000], including turn-

ing on intensity normalization in both cases.

The results show that both time-series statistics and spa-

tial components (primarily head motion correction and reg-

istration to standard space) add to apparent session variabil-

ity. Overall, with respect both to spatial alignment

processing and time-series statistics, FSL induced less error

than did SPM, i.e., was more efficient with respect to higher-

level activation estimation.

The experiments used a block-design, and as such are not

expected to show up the increased estimation efficiency of

prewhitening over precoloring [Woolrich et al., 2001]. In a

study similar to that presented here [Bianciardi et al., 2003],

first-level statistics were obtained using SPM99 and FSL (i.e.,

only time-series statistics were compared, not different

alignment methods). The data were primarily event related

and, as in this work, simple second-level mixed-effects anal-

ysis was used to compare efficiency of the different methods.

The results showed that prewhitening was not just more

efficient at first-level, but also gave rise to increased effi-

ciency in the second-level analysis.

Intensity Normalization

FEAT offers the option of intensity normalization of all

volumes in each time series to give constant mean volume

intensity over time; however, this option is turned off by

default, as it is considered that this is an oversimplistic

approach to a complicated problem [see for example De

Luca et al., 2002].

We investigated the effect on inter-session variance of

turning intensity normalization on. It was found that this

preprocessing step does reduce the overall fixed- and ran-

dom-effects variance (on average by about 10%), and there-

fore slightly increases the fixed- and random-effects Z-val-

ues (again giving on average approximately a 10% increase

in the number of suprathreshold voxels).

One- or Two-Step Registration

FEAT does not transform the fMRI data directly into

standard space but carries all statistics out in the original

(low-resolution) space and then transforms the final statis-

tics images into standard space. The transformation from

original space into standard space is carried out normally

(automatically) in a two-step process. First, an example func-

tional image (the one used as the reference in the motion

correction) is registered to the subject’s structural image

(normally a T1-weighted image that has been brain-ex-

tracted using BET [Smith, 2002]) and then the structural

image is registered to a standard space template (normally

the MNI152). The two resulting transformations are concat-

enated resulting in a single transform that takes the low-

resolution statistic images into standard space. This is the

default FEAT registration procedure and is what was used

for the analyses presented above.

We investigated whether for this data FEAT’s two-step

process (using FLIRT) is an improvement over registering

the example functional image directly into standard space

(using FLIRT). The two-step registration resulted in a slight

decrease in cross-session fixed- and random-effects overall

variance (by approximately 3%). The number of activated

voxels in general stayed the same, but the peak Z-statistic

improved (again by approximately 3%) when two-step reg-

istration was used and the activation seemed qualitatively to

Figure 8.

Mean mixed-effects Z-values, uncorrected and with both Z-shift correction methods.

?Smith et al.?

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Page 10

contain more structural detail (i.e., was less blurred). The

conclusion therefore is that even for this within-subject

across-session analysis, the two-step registration approach

was of value in the FEAT analyses.

CONCLUSIONS

Inter-session variability is an important consideration in

power calculations for the design of fMRI experiments. It is

also a critical issue for interpretation of studies that allow for

only single observations, e.g., in many clinical applications

of fMRI. We have provided here quantitative data confirm-

ing that inter-session variability in fMRI is not large relative

to within-session variability. We also emphasize that inter-

session variability should not be judged by apparent vari-

ability in thresholded activation maps.

There are several mechanisms by which inter-session vari-

ability can be minimized. Although considerable attention

has been paid in the past to hardware and experimental

design factors, we have shown here that additional benefits

can come with optimization of analysis methodology, as

analysis methods add extra variance to the true inter-session

variance, causing an apparent increase in inter-session vari-

ance. It was found that with respect both to spatial align-

ment processing and time-series statistics, FSL v1.3 induced

less error than did SPM99b, i.e., was more efficient with

respect to higher-level activation estimation.

ACKNOWLEDGMENTS

We thank C. Freemantle for retrieval and transfer of the

data from the Functional Imaging Lab, London, UK.

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