Prediction of Motor Recovery Using Initial Impairment and fMRI 48 h Poststroke
Eric Zarahn1, Leeor Alon2, Sophia L. Ryan2, Ronald M. Lazar2, Magnus-Sebastian Vry3, Cornelius Weiller3, Randolph S. Marshall2and
John W. Krakauer4
1The Neurological Institute, New York, NY 10032, USA,2Department of Neurology, Columbia University College of Physicians and
Surgeons, New York, NY 10032, USA,3Department of Neurology, University of Freiburg and4Department of Neurology, Johns
Hopkins University, Baltimore, MD 21287, USA
Address correspondence to Eric Zarahn. Email: email@example.com.
There is substantial interpatient variation in recovery from upper
limb impairment after stroke in patients with severe initial
impairment. Defining recovery as a change in the upper limb
Fugl-Meyer score (DFM), we predicted DFM with its conditional
expectation (i.e., posterior mean) given upper limb Fugl-Meyer
initial impairment (FMii) and a putative functional magnetic
resonance imaging (fMRI) recovery measure. Patients with first
time, ischemic stroke were imaged at 2.5 6 2.2 days poststroke
with 1.5-T fMRI during a hand closure task alternating with rest
(fundamental frequency 5 0.025 Hz, scan duration 5 172 s).
Confirming a previous finding, we observed that the prediction of
DFM by FMii alone is good in patients with nonsevere initial
hemiparesis but is not good in patients with severe initial
hemiparesis (96% and 16% of the total sum of squares of DFM
explained, respectively). In patients with severe initial hemiparesis,
prediction of DFM by the combination of FMiiand the putative fMRI
recovery measure nonsignificantly increased predictive explanation
from 16% to 47% of the total sum of squares of DFM explained. The
implications of this preliminary negative result are discussed.
Keywords: fMRI, prediction, recovery, stroke
Stroke is the leading cause of long-term disability among adults,
and hemiparesis is the most common impairment after stroke
(Wolfe 2000; Krakauer 2005). Recovery from hemiparesis can
be considered from the perspectives of recovery of function
(i.e., regaining the ability to perform a given task, but not nec-
essarily through the same pattern of muscle activation as used
to perform it prestroke) and recovery from impairment (i.e.,
regaining the ability to perform a given task through the same
pattern of muscle activation as used to perform it prestroke).
We are concerned here with prediction of recovery from
impairment (Fugl-Meyer et al. 1975) rather than of recovery of
function. This is because though recovery of function is of great
socioeconomic importance, it is influenced by compensatory
strategies (Lyle 1981; van der Lee et al. 1999; Kwakkel et al. 2004).
A substantial proportion of initial impairment is recovered in
patients with first time, nonsevere hemiparesis by 3 months
poststroke. Using the Fugl-Meyer scale, for example, we pre-
viously observed that a change in measure of recovery (meas-
ured as the change from initial impairment to impairment at 3
months poststroke) in such patients was well described as
0.70?initial impairment (Prabhakaran et al. 2008) (‘‘proportional
recovery’’). Also, recovery at this time point tends to be near
(say within 10% of) asymptotic recovery in this patient sub-
population (Duncan et al. 1992, 1994; Nakayama et al. 1994;
Jorgensen et al. 1995, 1999; Kwakkel et al. 2004, 2006; Swayne
et al. 2008; Verheyden et al. 2008; van Kuijk et al. 2009). The
degree of regularity of the magnitude and time course of this
recovery and its seeming robustness to rehabilitation dose
(reviewed by Kwakkel et al. 2004) have suggested that it is
mediated by a common, ‘‘spontaneous’’ mechanism.
In contrast to patients with nonsevere initial hemiparesis,
~50% of stroke survivors that have severe initial hemiparesis
remain so in the chronic state (Nakayama et al. 1994; Jorgensen
et al. 1999; Hendricks et al. 2002; Kwakkel et al. 2003;
Prabhakaran et al. 2008; van Kuijk et al. 2009). Motor-evoked
potentials (MEPs) at the abductor digiti minimi using trans-
cranial magnetic stimulation (TMS) 1 week poststroke in
patients with severe initial impairment have a positive pre-
dictive value of ~0.95 for recovery of some criterion dexterity
at 3--6 months poststroke but tend to have less impressive
negative predictive value (Hendricks, Pasman, Merx, et al. 2003;
Hendricks, Pasman, van Limbeek, et al. 2003; Swayne et al.
2008; van Kuijk et al. 2009). This might 1) be an artifact of MEP
threshold choice, 2) indicate that MEPs assayed within 1 week
poststroke inherently cannot detect all usable, residual cortico-
spinal (CST) connections early poststroke (perhaps due to
diaschisis corticospinalis; Kwakkel et al. 2004), or 3) indicate
that recovery from hand impairment can be effected through
non-CST, cortical reorganization mechanisms. Furthermore, the
positive predictive value of TMS-evoked MEPs has been ob-
served to act through a delay of a few weeks such that a patient
can be MEP positive while still having substantial recovery in
front of him (Swayne et al. 2008; van Kuijk et al. 2009), which
suggests that cortical reorganization is sometimes also re-
quired, above and beyond CST physiological integrity, to effect
or complete recovery. For these reasons, if functional neuro-
imaging measures cortical reorganization, then it might provide
information about subsequent recovery.
To wit, a multivariate correlation has been reported between
early poststroke, task-related functional magnetic resonance
imaging (fMRI) activation and subsequent recovery in a sample
evincing a wide range of initial impairment (Marshall et al.
2009). However, the magnitude of this correlation does not
directly (or at least simply) imply the accuracy of prediction of
recovery based on fMRI. Here we formally assessed prediction
of the same measure of recovery that we have assessed pre-
viously (Prabhakaran et al. 2008) from its posterior mean given
the combined measurement of initial impairment and fMRI. We
were particularly interested in the contribution of fMRI to
prediction of recovery in patients with severe initial impair-
ment as proportional recovery already seems to provide
accurate prediction of recovery in patients with nonsevere
initial impairment (Prabhakaran et al. 2008).
Among all possible functions of the random variables that are
available as predictors (here, initial impairment and fMRI), the
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Cerebral Cortex Advance Access published April 28, 2011
posterior mean minimizes the expectation of the squared
prediction error (SPE) of the random variable to be predicted
(here, recovery) (Shao 2003). Computation of a posterior mean
requires a conditional probability density of recovery given
initial impairment and fMRI; the form of this density is thus
a hypothesis being assessed by the quality of the prediction.
Moreover, the free parameters of this density need in practice
to be estimated. Part of this report involves describing the form
of this density and the estimation of its parameters.
Materials and Methods
Patients signed informed consent forms as approved by either Columbia
University’s or University of Freiburg’s Institutional Review Boards.
Two nonoverlapping patient samples were used in this study: 1) an
imaged patient sample for which prediction of recovery was performed
and 2) a nonimaged patient sample from which parameters for the joint
density of recovery, initial impairment, and fMRI were obtained (Fig. 1).
Both samples comprised patients with first time, ischemic stroke with
some degree of clinical hemiparesis (NIH stroke scale for the arm >1
for both the patients studied at Columbia Medical Center and those
studied at the University of Freiburg).
The patients of the imaged sample (N = 30; age = 60.3 ± 9.9 years; 21
male, 28 right handed) were recruited as part of Columbia’s Specialized
Program of Translational Research in Acute Stroke, an National Institute
of Neurological Disorders and Stroke-funded national network to
investigate new pathophysiological, diagnostic, and clinical approaches
in acute stroke. Fourteen of these 30 patients were part of a sample
used in a previous report that did not concern imaging (Prabhakaran
et al. 2008). fMRI results from 23 of these 30 patients were reported
previously in a paper that did not examine prospective prediction of
recovery(Marshall et al. 2009).
The nonimaged patient sample (N = 64; age = 61.6 ± 11.6 years; 38 M,
59 right handed) comprised 24 patients from the University of Freiburg
and 40 patients from Columbia Medical Center. Twenty-seven of these
64 patients were part of a sample used in a previous report that did not
concern imaging (Prabhakaran et al. 2008). Patients with prior
symptomatic subcortical stroke or any prior cortical stroke were
excluded. Also excluded were patients with seizure at stroke onset,
aphasia, neglect, any other cognitive impairment that precluded
training on the fMRI task, or any contraindication to MRI. At Columbia
Medical Center, aphasia was assessed with the Western Aphasia Battery
(spontaneous speech, repetition, naming, and comprehension); neglect
was assessed with line bisection, letter cancellation, and line judgment;
and apraxia was assessed by pantomiming scissors. At the University of
Freiburg, aphasia was assessed with part 9 of the NIH stroke scale and
neglect was assessed with part 11 of the NIH stroke scale; apraxia was
not assessed at the University of Freiburg.
fMRI Data Acquisition
T, 64 3 64 matrix, field of view = 19 cm, 21 slices, slice thickness/skip =
4.5 mm/0 mm, TR = 4000 ms, TE = 52 ms, flip angle = 60?) while
performing the repetitive hand closure task described below. One
session (43 volumes o ´ 2 min 52 s) was performed per hand. fMRI data
preprocessingwas performedas described previously(Marshalletal.2009).
Motor Task Used during fMRI
The motor task comprised alternations of 20-s epochs for which
patients had been instructed to attempt hand closure (the first such
epoch beginning 12 s after initiation of scanning) with 20-s rest
epochs. Four cycles were performed per hand. The instruction for hand
closure blocks was to close the hand gently from a resting position to
a fist in synchrony with a 1-Hz metronome click that was played
continuously (during both attempted hand closure and rest epochs) via
MRI-compatible headphones in the scanner. Auditory ‘‘start’’ and ‘‘stop’’
commands were given via the headphones at the beginning and end of
each 20-s attempted hand closure block. Separate runs were performed
for the affected hand and unaffected hand (only the data corresponding
to use of the affected hand were used in the current analysis). For
patients with complete hand plegia, instructions were to ‘‘do exactly
what you did with your good hand.’’ That instructions were varied with
initial impairment was understood to be an experimental design error
Figure 1. Schematic of patient sample composition.
Page 2 of 10
fMRI and Prediction of Recovery
Zarahn et al.
in hindsight. Nevertheless, we could not conceive of any mechanism
for how any confound of scanning design with initial impairment could
artifactually improve prediction of recovery over initial impairment
alone. Task performance was not measured, but grip force dynamom-
etry score obtained on the day of scanning was included as a covariate
in the second-level fMRI analyses (to prevent any task-related fMRI
activation linearly related to dynamometry from contributing to
prediction of recovery). Patients were familiarized with the task
outside of the scanner. No formal assessment of mirror movements was
performed; the potential effect of mirror movements on prediction is
taken up in the Discussion section.
Measure of Impairment
We used the upper limb Fugl-Meyer score (FM) (Fugl-Meyer et al. 1975)
as the upper limb impairment measure. The FM is a valid (Gladstone
et al. 2002; Platz et al. 2005; Woodbury et al. 2008) and highly reliable
(Duncan et al. 1983; Gowland et al. 1993; Gladstone et al. 2002; Platz
et al. 2005; Prabhakaran et al. 2008) measure of upper limb impairment
with a maximum score of 66 (higher score corresponds to less
impairment). FM was assessed both at ~2 days poststroke (FMinitial) and
~3 months poststroke (FM3 months); more specifically, FMinitial(as well as
grip force dynamometry score) was assessed in the imaged sample on
the day of fMRI scanning (2.5 ± 2.2 days poststroke). FM3 monthswas
assessed in the imaged sample at 96 ± 17 days poststroke. FMinitialwas
assessed in the nonimaged sample between 1 and 3 days poststroke
(average not available). FM3 months was assessed in the nonimaged
sample between 81 and 176 days poststroke (108± 25 days poststroke).
We chose 3 months as the intended endpoint because it has been
shown that recovery from impairment tends to be near asymptote <3
months poststroke (Duncan et al. 1992; Jorgensen et al. 1995, 1999;
Kwakkel et al. 2004, 2006; Swayne et al. 2008; van Kuijk et al. 2009).
Initial impairment was defined as FMii= 66 – FMinitial.
Measure of Recovery
Our recovery measure was DFM = FM3 months– FMinitial. We chose DFM
as opposed to FM3 months as the recovery measure because, from
a physiological perspective, the process of recovery is not reflected in
the final level of patient performance per se but is instead the
mechanism that takes a patient from initial to final level of performance
(Kwakkel et al. 2006; Prabhakaran 2008).
Dichotomous Categorization of Stroke Severity
A previous study of variability in stroke recovery (Prabhakaran et al.
2008) suggested to us that, up to some suitably high value of FMii, DFM
was approximated well by the proportional recovery relationship:
with b = 0.70. At higher (i.e., more severe) values of FMii, however, this
relationship qualitatively failed, with a nontrivial proportion of patients
with severe FMiishowing a much smaller DFM than that predicted by
equation (1). Here, we consider the threshold FMiithat determines this
dichotomy in the relationship between DFM and FMiias a demarcation
between nonsevere versus severe FMii. To get a reasonable estimate of
this demarcation to be used for subsequent modeling steps, Rj(the
correlation coefficient between DFM and FMii computed using the
lowest value of FMiiup to FMii,j, where j is an index of the ordered FMii
values) was computed using the nonimaged sample and plotted against
FMii,j. If equation (1) (for any fixed b) held throughout the entire range
of FMii, then the resulting Rjversus FMii,jplot would tend to stabilize
around a decelerating (but increasing) curve as FMii,j increased. In
contrast, if there was a dichotomy as described above in the
relationship between DFM and FMii, then the plot, after an initial
period of stabilization, would begin to appreciably decrease in the
neighborhood of some FMii,j. The plot showed this latter pattern of
behavior (Fig. 2) and subjectively suggested FMii> 56 (5FMinitial< 10)
as a reasonable definition of severe FMii. A patient with an FM of 10 in
the upper limb would have a dense hemiparesis with some proximal
movement but no distal movement. Using this criterion on the
nonimaged sample itself yielded 46/64 patients with nonsevere FMii
and 18/64 patients with severe FMii. Though it was determined in
a completely different way, this criterion closely corresponds to the
value of FMinitial chosen by one other group to define severe
hemiparesis (Shelton and Reding 2001), but it is more inclusive than
that used by another group, which defined as severe those patients
with FMinitial= 0 (van Kuijk et al. 2009).
Model for Recovery versus Initial Impairment
The conditional probability density of DFM given FMii, fDFMjFMii; is
required for computing the posterior mean of DFM (see Posterior mean
of DFM). Motivated by the previous finding described by equation (1),
we assumed fundamentally a proportional recovery model,
with proportionality constant b and unexplained interpatient variation
required that patients with nonsevere and severe FMiihad the same b
class had the same b or r2
the data from a previous report (Prabhakaran et al. 2008), which
suggested that b in patients with severe FMiitook on more than one
value (e.g., say 2: ~0.70 and ~0). These assumptions are formalized by
stating that separate mixtures of proportional recovery models were
allowed for patients with nonsevere and severe FMii; this implicitly
defines fDFMjFMii: For each severity category, the number of proportional
recovery models K was varied from 1 to 6 and maximum likelihood
sample (pl is the weight for the lth component). The Akaike
Information Criterion (AIC) (Stone 1977; Burnham and Anderson
2002) was used to select among fDFMjFMii. Details are provided in Section
3 of the Supplementary Material.
/. Second, it was not required that all patients within a severity
/. These modeling features were motivated by
/) but with 2 flexible model features: First, it was not
were obtained from the nonimaged
fMRI-Based Measurement of DFM
We obtained an fMRI-based measurement (Zj) of DFM in the jth patient
in the imaged sample to serve as the fMRI information in computing the
posterior mean of DFMj(see Posterior Mean of DFM). Zjis a corrected
and normalized inner product of the jth patient’s fMRI ‘‘task-related
activation pattern’’ ( ˆ aj; a standard first-level statistical parametric T-map
Figure 2. Cumulative correlation coefficient (see text for description) versus FMiifor
the nonimaged sample. The arrow marks where we specified the (inclusive) threshold
(which corresponds to FMii$ 56) for defining severe FMiibased on where the
cumulative correlation coefficient begins to decrease. We chose to place this
threshold slightly before the apparent decrease so as to be less likely to misclassify
severe strokes as nonsevere.
Cerebral Cortex Page 3 of 10
(SPM) representing task-related activation) and a ‘‘recovery pattern’’
(ˆd–j; a standard second-level SPM [t] representing correlations between
fMRI and DFM). For those unfamiliar with inner products, one can
heuristically think of a regression model in which ˆ aj acts as the
dependent variable and ˆd–j acts as the independent variable. Then Zj
can be thought of as a regression coefficient of this model that is
corrected for biases. A proof that Zj is an asymptotically unbiased
estimator of DFMj(given the existence of some linear relationship
between fMRI task-related activation and DFM) is provided in Section 2
of the Supplementary Material. This means that asˆd–jitself is estimated
(see next paragraph) from more and more fMRI data sets, the
difference between E <Zj> and DFM gets closer to zero. The formula
for Zjis provided in Section 1 of the Supplementary Material.
ˆd–j itself is estimated from standard linear regression based on
½ð ˆ ai;hi;DFMiÞ?i2A–j, where A–j is an index set and hiis an optional
vector of nuisance variables from patient i (see Section 1 of
Supplementary Material); here hicomprised a constant term and grip
force dynamometry score. To avoid artifactual contributions to the
statistical relationship between Zjand DFMj, it is necessary that the
not contribute to the computation of ˆd–j.
Therefore, j 2 A–j(hence the motivation for the choice of subscript for
d–j), which makes Zja cross-validatory (CV) estimator of DFMj(Stone
1974, 1977). This type of CV (known as either leave-one-out or N-fold
CV) has the same purpose as split-half CV (Strother et al. 2002): to
determine the prediction error for a dependent variable (in this case,
DFMj) when applying model parameters (in this case, d–j) estimated
from an independent sample. CV is not to be confused with
bootstrapping (the purpose of the latter being estimation of the
variance of an estimator ˆ l of a model parameter l by computing ˆ l
repeatedly via a resampling scheme; Efron and Tibshirani 1981). The
principle of CV is fundamentally related to the idea behind the AIC
(Stone 1977; Burnham and Anderson 2002). If ˆd–jwere not estimated
using CV, then estimation of SPE would be biased downward (i.e., it
would lead to an overly optimistic assessment of prediction accuracy in
future patients). The reason we used leave-one-out instead of split-half
is that the former uses the maximum possible sample size for parameter
estimation (ˆd–jbeing a multidimensional parameter) with no drawback
in terms of prediction validity. Software written in MATLAB used in
conjunction with SPM5 (Wellcome Department of Imaging Neurosci-
ence) to compute Zjas well as the fMRI data set are available from the
authors upon request.
In addition to fDFMjFMii(see Model for Recovery Versus Initial
Impairment), fZjDFM is also required for the computation of the
posterior mean of DFM (see Posterior mean of DFM). It follows from
the asymptotic unbiasedness of Z that (asymptotically)
where ejis a zero mean random variable. For expedience, we assume
that ej has a Gaussian density, which implies that asymptotically
the poorer the accuracy of this assumption the poorer will be the
prediction DFM. The maximum likelihood estimator of r2
is a Gaussian density with mean DFMjand variance r2
Posterior Mean of DFM
Given information about a realization of a random variable, the
predictor (or, equivalently, estimator) of that random variable that
minimizes the expected squared error is the expectation of that
random variable with respect to the conditional density of the random
variable given the information (Shao 2003). This density is called the
‘‘posterior density’’ in the context of Bayes’ theorem, and the
expectation with respect to it is called ‘‘the posterior mean.’’ Here,
we wished to predict DFM given the information about it contained in
FMiiand/or Z, and so we computed the appropriate posterior means.
Assuming that Z is conditionally independent of FMiigiven DFM, the
posterior mean of DFM given FMiiand Z can be shown to be (see
Section 3 of Supplementary Material)
where u and v are dummy variables of integration corresponding to the
random variable DFM, which was approximated numerically. In
addition to this model, 3 additional posterior means of DFM were
computed: (conditioning on) FMii, Z and dichotomous stroke severity,
or dichotomous stroke severity (formulae for these posterior means are
provided in Supplementary eqs S3.7, 3.9, and S3.10, respectively, in
Section 3 of the Supplementary Material).
For subject i of the imaged sample, the SPE of DFM
whereˆDFMi, the prediction of DFMi, was computed under each model
as the posterior mean. The critical test was the comparison of SPE
under conditioning on FMiialone versus that under conditioning on
FMiiand Z in the severe subgroup. A 1-tailed, paired t-test was used for
this comparison; the rationale for using a 1-tailed test is that the
alternative hypothesis is that including fMRI improves prediction (i.e.,
lowers SPE) over using initial impairment alone.
Age (average ± standard deviation = 60.3 ± 9.9 years), time
between stroke and assessment of FMii(2.5 ± 2.2 days), lesion
location, FMii (28.9 ± 23.1), DFM (14.9 ± 13.8), and acute
dynamometry (12.3 ± 13.3 kg) for the individual patients of the
imaged sample are presented in Table 1. Patients in the imaged
sample were assessed for FMiiand scanned with fMRI at 2.5 ±
2.2 days poststroke for 2 minutes 52 seconds per hand during
the same MRI session as their clinical exams. Patients had been
instructed just prior to scanning to attempt hand closure (for
a specified hand) at an auditorily cued 1-Hz pace (alternating
with rest epochs with matched auditory stimuli). Only fMRI
data from the affected hand were used in this analysis. Follow-
up for assessment of DFM in the imaged patient sample was at
93 ± 17 days poststroke.
Twelve out of 30 patients of the imaged sample had an acute
dynamometry score of 0 kg (Table 1) and thus are likely to have
been unable to execute the instructions of the motor task.
Formally, however, the experimental condition was not the
performance of the task but was rather the instruction to
perform the task: behavior is never directly under experimental
control and so cannot be properly thought of as an
experimental variable. Behavior was not measured, but acute
dynamometry score was used as a covariate in the estimation of
CV fMRI recovery pattern expression (Z), and so any task-
related fMRI activation linearly related to dynamometry could
not contribute to prediction of recovery through Z. For
example, if task-related activation was simply a reflection of
dynamometry score, then Z would be pure noise with respect
to DFM, even though dynamometry and DFM are correlated
(R = 0.56, 2-tailed P = 0.001).
Z was computed in a CV fashion by essentially taking the
inner product of a given patient’s task-related fMRI activation
data with an estimated fMRI recovery pattern whose compu-
tation involved neither that patient’s fMRI data nor their DFM. Z
was significantly correlated with DFM in the net imaged sample
(R = 0.56, 1-tailed P <0.001; it is not a typo that this is the same
R value as immediately previous). While this result is more
robust than a correlation between non-CV recovery pattern
expression and DFM, it still does not directly indicate the
accuracy of prediction. Thus, we also assessed SPE (squared
Page 4 of 10
fMRI and Prediction of Recovery
Zarahn et al.
prediction error, an explicit measure of prediction accuracy) in
the imaged sample for posterior means of DFM given FMiiand/
or Z. To facilitate appreciation of the magnitude of SPE relative
to the range of the FM (0--66), below we will express SPE in the
form of ‘‘x2,’’ where x is thus in FM units.
The posterior mean of DFM given FMiirequired an estimated
fDFMjFMii(which was allowed to be a mixture of K proportional
recovery models for each severity category) and fZjDFM. Based
on fitting using the nonimaged sample, the minimum AIC
fDFMjFMiifor the patients with nonsevere FMii was K = 3
minimum AIC model for the patients with severe FMiiwas K = 1
prised that a 1-component model fit best for the severe FMii
group given our previous findings suggesting a mixture of 2
proportional recovery models (one with b ~ 0.7 and one with b
~ 0) (Prabhakaran et al. 2008). Visual inspection of the
nonimaged sample data confirmed, however, that there was
a more even distribution of DFM in the patients with severe
FMii from the University of Freiburg (who were not repre-
sented in that study) than from Columbia University (who
were); we proceeded regardless. The sole parameter of fZjDFMis
DFM in the imaged sample: ˆ r2
A preliminary remark is that it is not a mathematical
necessity that SPEs decrease (just as the AIC need not
decrease) as more information is added to the prediction
algorithm; this can be contrasted with the necessary increase of
R2for a linear regression model as the rank of the design matrix
increases. We now present the (average) SPE in the net imaged
sample for the various posterior means of DFM: The SPE of the
/;3;nonsevere=1:22) and the
/;1;severe=376:22). We were sur-
e. Its maximum likelihood estimator was obtained from Z and
posterior mean of DFM given dichotomous stroke severity was
162. The SPE given FMiiwas 102, while the SPE given FMiiand Z
was 82. The decrease in SPE in the net imaged sample from
using FMiito using FMiiand Z was not significant (t(29) = 1.14,
1-tailed P = 0.13).
A more meaningful understanding of the effect of condi-
tioning is provided by looking at SPE separately in the
nonsevere (N = 23) and severe (N = 7) FMiipatient subgroups
of the imaged sample (Table 2; Fig. 3). SPE tends to be much
greater in all models in the patients with severe FMii. Relative to
conditioning on dichotomous stroke severity alone, condition-
ing on FMiiimproves SPE only in the patients with nonsevere
FMii(nonsevere FMii: DSPE = 132, t(22) = 5.89, 1-tailed P <
0.0001; severe FMii: DSPE = –22, t(6) = –0.66, 1-tailed P = 0.73).
Relative to conditioning on FMii, conditioning on FMiiand Z
improves SPE meaningfully, although not significantly, only in
the patients with severe FMii(nonsevere FMii: DSPE = 22, t(22) =
0.98, 1-tailed P = 0.17; severe FMii: DSPE = 122, t(6) = 1.03, 1-
tailed P = 0.17).
A way of reexpressing SPE for a given predictive model is in
terms of the percentage of the total sum of squares of DFM
explained by that model, which equals 100?(1 – [mean SPE for
that model]/[mean DFM2]). Unlike R2, this value need not be
positive. For patients with nonsevere FMii, this value was 96%
and 97% when conditioning on FMiiand [FMii, Z], respectively.
For patients with severe FMii, this value was 16% and 47% when
conditioning on FMiiand [FMii, Z], respectively.
Our opinion is that one focus of stroke research should be the
development of novel, early poststroke treatments (Turton and
Pomeroy 2002; Biernaskie et al. 2004) for those patients likely
Basic information for imaged sample
Patient ID Age on date of stroke Time between stroke and FMii(days) Lesion sideLesion locationFMii
DFMAcute dynamometry (kg)
Note: CR, corona radiata; IC, internal capsule; M1, primary motor cortex; S1, primary sensory cortex; R, right; L, left side; B, bilateral.
Cerebral Cortex Page 5 of 10
to remain severely hemiparetic under current standard care.
Such treatments might include noninvasive brain stimulation
(Williams et al. 2009) and robotics-based rehabilitation (Huang
and Krakauer 2009). However, as such alternative treatments
are likely to be more costly in terms of patient effort and
healthcare resources than standard care, one ideally wants to
exclude patients who would recover substantially under
standard care from such alternative treatments. For this
purpose, early poststroke prediction should have high sensi-
tivity for recovery. But of course, a high specificity would be
desired as well in order to have a low chance of mistakenly
excluding patients who will not sufficiently recover. Thus,
a generally accurate prediction algorithm would be useful for
developing and applying new treatments. An alternative
rationale for early prediction of recovery that is more relevant
for the current state of treatment is to inform patients and
family about expected outcomes and also to direct physical and
occupation therapists to focus on compensatory strategies
rather than recovery from impairment. A promising prediction
finding in this regard is that the presence of finger extension
and shoulder abduction 72 h poststroke yielded positive and
negative predictive values for some recovery of upper limb
dexterity using the action research arm test (ARAT) (for a brief
description of the ARAT, which assesses function, see Van der
Lee et al. 2001) of 0.98 and 0.75, respectively (Nijland et al.
2010). Here we assessed the contribution of fMRI (through Z)
to prediction of recovery from impairment at 2--3 days
poststroke. The combination of Z and FMii led to a non-
significant increase from 16% to 47% of the total sum of squares
of DFM explained in patients with severe FMii. Assuming the
effect size observed here for patients with severe FMii, 42
patients with severe FMiiwould be required for power = 0.80
(58 for power = 0.90; 73 for power = 0.95) to detect such
a reduction. However, these sample size calculations are
conservative in that as imaged sample size increases, r2
also decrease (and consequently decrease SPE when using Z),
while these sample size calculations assume it will remain
constant. Likewise, use of a larger sample size to estimate
fDFMjFMiiwould also tend to lower SPE, while these sample size
calculations do not account for such effects. Regardless, we
take our negative statistical result with regard to prediction as
inconclusive. The significant correlation between Z and DFM
could be taken as an impetus for sufficiently powered studies.
Such studies might also be performed at higher field strength
and acquire at larger voxel sizes to increase signal:noise ratio.
Another reason to consider the negative result inconclusive is
the nature of the samples used. We estimated fDFMjFMiifrom
a nonimaged sample combined from 2 institutions. Though the
samples were similar in terms of clinical inclusion and exclusion
criteria, they were unlikely to be matched genetically, educa-
tionally, or socioeconomically (factors which could conceivably
affect recovery). We qualitatively observed (after the decision
had been made to use the combined sample) that the patients
with severe initial impairment from the University of Freiburg
had a less stark dichotomy of DFM than those from Columbia
University. This made fDFMjFMiifor this severity a single broad
Gaussian rather than 2 well-separated, narrower ones (the latter
having been our hypothesis based on the results of a previous
study; Prabhakaran et al. 2008). As the imaged sample
(exclusively from Columbia University) manifested dichotomous
DFM, a speculative explanation for the unimpressive perfor-
mance of the posterior mean based on Z and FMii is that
fDFMjFMiiwas too far from ground truth for the population from
which the imaged sample was obtained. In hindsight, we
recognize that we were overeager to expand our sample size
for estimating fDFMjFMiiand consequently did not consider the
possibility of important systematic differences in populations
sampled by the 2 institutions; we hope to be more careful in our
Current Level of Impairment and Subsequent Recovery
Could Have Different Neural Correlates
While the purpose here was simply to predict DFM from FMii
and fMRI, rather than characterize the brain mechanisms of
recovery, it is important to make clear how the experimental
design we employed relates to those of previous relevant brain
Mean SPE of DFM for various prediction models (columns)
Z and severe/nonsevere
Net imaged sample (N 5 30)
Patients with severe FMii(N 5 7)
Patients with nonsevere FMii(N 5 23)
Figure 3. Predicted (posterior mean) versus observed DFM when using either 1)
FMii(patients with nonsevere FMii: white squares; patients with severe FMii: black
squares) or 2) FMiiand Z (patients with nonsevere FMii: red circles; patients with
severe FMii: blue circles) as the information in determining the posterior density of
DFM. The SPE for a given datum is the (vertical distance to the identity line)2. All data
plotted correspond to the imaged sample.
Page 6 of 10
fMRI and Prediction of Recovery
Zarahn et al.D ownloade
imaging studies of stroke. Previous such studies can be
dichotomized into longitudinal (Marshall et al. 2000; Calautti
et al. 2001; Feydy et al. 2002; Ward et al. 2003b,) and cross-
sectional (Ward et al. 2003a; Loubinoux et al. 2003; Loubinoux
et al. 2003; Loubinoux et al. 2007; Jang et al. 2004) designs; the
design of the current study was cross-sectional. Ward et al.
(2003a, 2004) have argued that the existence of positive cross-
sectional correlations between activation and impairment at
the time of scanning in both the early and chronic periods
indicates that patients with more severe impairment need to
utilize ‘‘secondary motor areas’’ to a greater extent than less
impaired patients in order to generate motor output (which is
nevertheless suboptimal). This hypothesis is supported by
a study that showed that the slowing of reaction time induced
by TMS applied to contralesional dorsal premotor cortex
correlates with the degree of impairment (Johansen-Berg
et al. 2002). However, it is not clear how the cross-sectional
correlations observed by Ward et al. (2003a, 2004) relate,
either in a causal sense or simply in a correlative sense, to
subsequent recovery (i.e., recovery that manifests behaviorally
after the time of imaging). Spatial signatures for these 2 types of
theoretical activation signals (considered at any fixed time
poststroke), those related to current level of impairment
(ostensibly reflected in the results of Ward et al. 2003a,
2004) and those related to subsequent recovery (ostensibly
contributing to the current prediction results and similarly to
the correlations from our previous imaging study), need not be
the same. This is because the failure of proportional recovery in
patients with severe initial impairment uncouples current level
of impairment and subsequent recovery; conversely, in the
absence of patients with severe initial impairment who recover
very little, it would not be possible to disambiguate the neural
correlates of current level of impairment and subsequent
recovery. It is therefore of note that the studies of Ward et al.
(2003b, 2004) seem not to have included any such patients,
which implies that their reported correlations from the early
period could be an admixture of those related to current level
of impairment and those related to subsequent recovery. This
could possibly be an explanation of their finding that certain
correlations detected early were not detected later poststroke
(the ones only detected early possibly being related to
subsequent recovery) (Ward et al. 2003b, 2004).
Three cross-sectional studies have concerned correlation
and/or prediction of future impairment level (as opposed to
change in impairment) (Loubinoux et al. 2003; Jang et al. 2004;
Loubinoux et al. 2007). Two of these studies from the same
group were correlative (i.e., not predictive) and yielded
inconsistent results with respect to one another (Loubinoux
et al. 2003, 2007). The third study (Jang et al. 2004) attempted
prospective prediction based on an arbitrary decision criterion
applied to voxel-wise activation data in a primary sensorimotor
cortical region of interest; the resulting prediction accuracy
was poor. This type of approach was not devised to be optimal
given the region of interest chosen, nor did it reasonably
weight all potential spatial sources of relevant functional
imaging signal (Kjems et al. 2002; Strother et al. 2002; O’Toole
et al. 2007). In contrast, the approach taken in the current
study was to use the posterior mean (which is an optimal
estimator given a conditional density) and also to use all the
linear information about DFM present in multivariate fMRI data
(not just that from a single region of interest). However,
neither study yielded impressive prediction.
MEPs and Recovery in Patients with Severe Initial
The volume of anatomical damage per se seems insufficient to
explain the majority of the variation in recovery in patients
with severe initial impairment (Binkofski et al. 2001; Shelton
and Reding 2001; Konishi et al. 2005; Cho et al. 2007). MEPs
ostensibly measure the functional nature of the damage
sustained to the CST (van Kuijk et al. 2005), as opposed to
the total lesion volume. Pooling data from 3 studies that
examined MEPs in hemiplegic patients within the first 10 days
poststroke (Hendricks et al. 1997; Hendricks, Pasman, Merx
et al. 2003; van Kuijk et al. 2009), positive predictive value for
recovery was 0.94 and negative predictive value was 0.83. Thus,
while it does seem that the degree of functional CST damage is
a critical determinant of recovery, recovery is possible in 15--
20% of cases where functional CST damage seems complete;
this recovery could depend on brain plasticity. Moreover,
patients MEP+at 1 week tend not to reach their recovery
endpoints until 1--3 months later (Swayne et al. 2008), which
suggests that even in the presence of residual monosynaptic
connections from primary motor cortex (M1) to spinal
motoneurons, some sort of plasticity mechanism which lasts
for several weeks poststroke is required to allow their effective
use. fMRI could be sensitive to these putative brain plasticity
mechanisms. It would therefore be of interest to specify
a conditional density (or better, several densities representing
different hypotheses) for recovery given initial impairment,
fMRI, and MEPs.
No behavioral measure was acquired during imaging. There-
fore, the correlation between Z and DFM could be due to
individual differences in behavior during imaging. Such
behavior can include, but is not limited to, mirror movements,
which have been estimated to occur 70% of the time during
repetitive squeezes using the affected hand and correlate with
severity of impairment of the affected hand (Nelles et al. 1998).
Activation of contralesional motor cortex correlates with
individual differences in mirror movements in hemiparetic
stroke patients (Wittenberg et al. 2000; Kim et al. 2003).
However, even if individual differences in the degree of mirror
movements during imaging were causal to the observed
correlation between Z and DFM, it would not invalidate
prediction of DFM based on fMRI using the current design.
This is because the metric for prediction is the magnitude of
prediction error; nothing more, nothing less (Akaike 1974). While
it is true that the inclusion of more controls at the experimental
design (e.g., clamp performance in the scanner) and/or analysis
stages (e.g., include a covariate for performance in the scanner)
could potentially improve prediction by reducing the variance of
dˆ, it is logically incorrect to say that a degree of prediction
obtained in the absence of such controls ‘‘does not count’’ or is
‘‘artificially too high.’’ This is an important difference between
predictive and causal modeling, and this was a prediction study.
If the correlation between Z and DFM were caused only by
correlations between 1) FMii and the degree of mirror
movements (Nelles et al. 1998), 2) mirror movements and
contralesional M1 activation (Wittenberg et al. 2000; Kim et al.
2003), and 3) FMiiand DFM (Prabhakaran et al. 2008), then
(assuming the measurement noise of FMiiis negligible) Z would
not improve the prediction of DFM over that provided by FMii
Cerebral Cortex Page 7 of 10
alone. The empirical result was that while recovery pattern
expression was significantly correlated with recovery, its
contribution to the prediction of recovery over that provided
by initial impairment alone was not statistically significant.
Thus, the result is on its face consistent with mirror move-
ments having contributed to recovery pattern expression. In
future studies, mirror movements could be measured quanti-
tatively and included as a covariate in recovery pattern
estimation (see fMRI-based Measurement of DFM); this would
eliminate any (linear) contribution of mirror movements to Z.
Doing so could 1) reduce unexplained variability in the fMRI
data (good for prediction, as it ceteris paribus decreases the
variance of the recovery patternˆd and hence decreases r2
reduce the amount of variation in the fMRI data uniquely
attributable to DFM (bad for prediction, as it ceteris paribus
increases variance ofˆd and hence increases r2
the complexity of the model by adding more parameters
(which is bad for prediction, as it ceteris paribus increases r2
The net effect on the accuracy of prediction of DFM would
depend on the balance of these effects.
It is possible that some patients did not perform the
instructed movement with the affected hand at all during
imaging. Indeed, 12/30 patients in the imaged sample had
a grip force dynamometry score (of the affected hand) of 0 on
the day of scanning; recovery was heterogeneous in this
subgroup (Table 1). In the prediction algorithm, both the
estimation of d and the computation of Z use dynamometry
score as a covariate such that any systematic component of the
fMRI signal that is linearly dependent on grip force dynamom-
etry has no effect on the prediction of DFM. Thus, if the
intensity of movement (say the across-click average of the
maximal torque produced by the effector per metronome
click) during scanning is linearly related to dynamometry score,
then whether subjects actually moved or not is irrelevant to
prediction of DFM in this model. If instead, the intensity of
movement during scanning is only weakly correlated with
dynamometry score (or not correlated at all) and if the pattern
of brain activation associated with intensity of movement is
strongly ‘‘spatially’’ correlated with the recovery pattern, then
this would reduce the signal:noise of Z (as the random,
unmodeled variations across subjects in intensity of movement
during scanning would lead to activations similar to those
associated with recovery and hence add noise to Z) and hence
worsen prediction. If this were the case, then measurement of
the intensity of movement within the scanner would allow for
improved prediction. A third possibility is that brain activation
correlates of recovery are modulated by the intensity of
movement; if so, failure (as in the current study) to account
for this modulation (i.e., interaction) would lead to a worsened
prediction. It is again worth noting that there is no way that
failure to account for movement (or anything else) could lead
to an artificially good prediction of DFM.
The patients in the imaged sample had predominantly sub-
cortical strokes. It is an empirical question as to whether fMRI
would contain predictive information about recovery for large
cortical strokes. If the cortical regions damaged were critical for
case, the predictive information of Z would be preserved).
e), and 3) increase
In conclusion, we found that prediction of recovery in patients
with nonsevere initial impairment was accurate based on initial
impairment alone. In contrast, prediction of recovery in
patients with severe initial impairment was poor based on
initial impairment alone and was not statistically significantly
improved by the inclusion of fMRI acquired at 2 days
poststroke. However, the significant correlation between fMRI
and recovery might provide a motivation for further assessment
of prediction using adequately powered studies and more
carefully considered samples.
material canbefoundat: http://www.cercor
National Institute of Health (grant numbers NIH K02NS048099
and NIH R01 NS052804 to J.W.K., NIH 5P50NS049060 to R.S.M.);
Gatsby Initiative in Brain Circuitry to E.Z.
We thank Katherine O’Brien for helping in data collection, Allison
Speizer and Brandon Minzer for assisting in patient recruitment and
collection of experimental data, and Dr Joy Hirsch for providing
technical and experimental support. Conflict of Interest : None
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