Brain (1998), 121, 1545–1556
Brain–behaviour relationships
Some models and related statistical procedures for the study
of brain-damaged patients
O. Godefroy,1 A. Duhamel,3 X. Leclerc,2 T. Saint Michel,2 H. Hénon1 and D. Leys1
1Departments
3Biostatistics,
of Neurology, 2Neuroradiology and
University of Lille, France
Correspondence to: Dr O. Godefroy, Service de Neurologie
et Pathologie Neurovasculaire, F-59037 Lille, France.
E-mail: [email protected]
Summary
The study of brain-damaged patients provides the
opportunity to examine the anatomy of brain functions,
and has been renewed by the development of structural
neuroimaging. Despite the development of neuroimaging
and neuropsychological assessment, major uncertainties
persist on the exact delimitation of the brain areas
involved in specific processes, and these contribute to the
enduring controversies over the effective lesions associated
with neuropsychological disorders. These uncertainties
are mainly due to the methods used in the study of brain–
behaviour relationships, which frequently rely on a group
comparison design. The aim of this study was to provide
models for the study of brain–behaviour relationships and
to assess the reliability of related statistical procedures.
In the present work, four theoretical modes of brain–
behaviour relationship consistent with neuropsychological
data are put forward: unicity, equivalence, association
and summation. The first experimental study was based
on a simulated population of patients. Lesions associated
with the occurrence of a deficit were predetermined
according to modes of brain–behaviour relationship and
were compared with lesions selected by statistical analysis.
The study showed that (i) the group comparison design
did not allow determination of the effective lesion, (ii)
stepwise regression analysis was sensitive to the relative
frequency of lesions, especially when the occurrence of
a deficit depended on two lesions, but did not allow
determination of the mode of brain–behaviour
relationship, and (iii) the classification tree test described
the data very satisfactorily and permitted the
determination of the mode of brain–behaviour
relationships. In order to assess the validity of statistical
analyses, a second study was performed in which lesion
locations associated with motor weakness in stroke
patients were examined. Selected lesions were compared
with the anatomy of the human motor system. The study
mainly showed that (i) the stepwise regression analysis of
selected lesions was not related to the presence of a motor
deficit, and (ii) the classification tree test provided perfect
agreement with motor weakness predicted by lesion
locations and suggested an equivalence mode of brain–
behaviour relationship consistent with current neurological knowledge. These studies provide models of brain–
behaviour relationships and related statistical procedures
that may allow more precise documentation of the
anatomy of brain functions and its pathology, and further
investigation of the modalities of brain–behaviour
relationships.
Keywords: brain–behaviour study; neuropsychology; motor system; biostatistics
Abbreviations: ROI 5 region of interest; VIF 5 variance inflation factor
Introduction
Since its beginning, neuropsychology has been concerned
with the identification of cerebral structures that subserve
cognitive functions. The early description of neuropsychological syndromes was based on the confrontation of
neuropsychological deficit and post-mortem analysis. With
the advent of modern neuroimaging, concurrent brain imaging
and neuropsychological studies were possible, which allowed
considerable development of the study of brain–behaviour
relationships. For example, numerous reports have
© Oxford University Press 1998
documented the presence of language disorders not only in
patients with a focal lesion of a well-known region such as
Broca’s or Wernicke’s area, but also in patients with a lesion
in the thalamus, striatum or subcortical white matter of the
left hemisphere (Lecours and Lhermitte, 1979; Puel et al.,
1984; Alexander et al., 1987; Godefroy et al., 1994). Though
studies of patients have produced large series of data
documenting the roles of various cerebral regions in
perceptuomotor and cognitive operations, major uncertainties
1546
O. Godefroy et al.
persist about the exact delimitation of the brain areas involved
in specific processes. These uncertainties stem from two
main difficulties: (i) the characterization of processing stages
involved in a particular task, and (ii) the determination of
the minimal brain area within the damaged region accounting
for the deficit. The former difficulty has been alleviated by
a recent development in cognitive neuropsychology in which
a series of stages required for performing a task has been
proposed. Thus, it is now possible to evaluate in braindamaged and normal subjects the sequence of processes
in various domains such as language comprehension and
production, visual identification, attention, decision and
planning. Conversely, attempts to determine the minimal
damaged area responsible for the occurrence of a disorder
still rely on varied methodologies. This contrasts with the
development of a standardized methodology in functional
imaging studies which allows the accurate localization of
activation foci associated with each processing stage (Poline
et al., 1996). In the majority of brain damage studies, a
classical methodology based on a group comparison design
is used; imaging findings are used for grouping patients
according to the lesion location (e.g. left/right damage or
frontal/posterior lesion), and the interpretation obeys a
subtractive logic, i.e. the poor performance of one group
implies that the damaged region defining the group is required
for task completion. This classical approach has proved its
efficiency in delineating large cerebral regions associated
with the neuropsychological outcome at the level of
syndromes such as aphasia, hemineglect, visual agnosia and
frontal syndrome (Heilman and Valenstein, 1985). However,
the group comparison design provides only rough information
about which cerebral areas support each processing stage,
and this contributes to the enduring controversy on the
effective lesions associated with neuropsychological outcome
at an infra-syndrome level (i.e. based on the characterization
of impaired processes) such as the variety of aphasia, visual
agnosia or frontal syndrome (Puel et al., 1984; Shallice,
1988, 1994; De Renzi, 1991; Bogousslavsky, 1994; Démonet
and Puel, 1994; Caplan, 1995). The limitation of the group
comparison design probably stems from its methodology.
Lesion distribution obeys rules specific to the pathological
process (e.g. vascular territory for stroke, mode of
dissemination of infective agents, extent of degenerative
processes), and does not necessarily overlap the functional
organization of the brain. This results in a high degree of
variation in damaged structures even in studies in which
patients suffering from the same pathology or circumscribed
lesion are assessed (e.g. Godefroy et al., 1994, 1996;
Rousseaux et al., 1996; Vilkki et al., 1996). Thus, in the
analysis, the performances of groups of patients with variable
lesion extent and presumably variable deficits are compared,
and the finding of a deficit in one group cannot provide any
information on the minimal lesion responsible for the deficit.
This interpretation is supported by the few previous studies
that have been carried out, which include patients with the
same pathology and the assessment of the location of the
effective lesion (Godefroy et al., 1992, 1996; Kornhuber
et al., 1995; Vendrell et al., 1995; Rousseaux et al., 1996;
Rueckert and Grafman, 1996). These studies reliably show
that the lesion responsible for the deficit is circumscribed to
a smaller cerebral structure than the region used as a criterion
for grouping patients. A refinement frequently used to
establish the effective lesion site is to superimpose the
position of the lesions of all patients and to look for the site
where they overlap (e.g. Blunk et al., 1981). However, this
procedure may be misleading. First, when lesions of all
patients are used regardless of individual performance, the
procedure only determines the most frequent lesion, which
may differ from the effective lesion. Secondly, it implies that
the deficit is related to a common lesion location, but this
assumption is not supported by studies showing that a unique
neuropsychological disorder may be caused by damage to
different structures (Heilman and Valenstein, 1985; Vallar
and Perani, 1986). Thirdly, a lesion in area X may be strongly
correlated with a lesion in area Y because the two areas
share a common susceptibility to the pathology studied. Thus,
areas X and Y are liable to be included in the overlapping
area whereas only one of them could be responsible for the
deficit. Finally, the strength of association provided by this
procedure is not assessable using statistical analysis.
These considerations suggest that improving the
determination of brain–behaviour relationships requires the
development of a specific methodology, and this is now
possible owing to developments in neuropsychology,
neuroradiology and statistics. The present study used
procedures for inferring the locations of functions based on
systematic covariation of the deficit and the locus of the
lesion, as determined by analysis of structural neuroimaging.
Brain images are obtained for a sample of patients with a
focal lesion who have been given a neuropsychological test.
The outer perimeter of each lesion is related to an atlas
and the examiners determine whether the lesion includes
previously defined regions of interest (ROI). Before
examining the interaction of the brain lesion with the
neuropsychological outcome, general criteria regarding the
determination of performance and of the lesion location have
to be achieved. The deficit has to be due to the impairment
of specific processing stages required for task completion.
This necessitates control for measurement error and for the
role of extrinsic (e.g. hospitalization, fatiguability), nonneurological (e.g. depression, anxiety, severe general
conditions) or general cognitive factors (e.g. attention, speed
of processing and palliative strategy). The abnormality of the
imaging signal has to be associated with a major dysfunction
or the death of previously sane neurons (Anderson et al.,
1990) and to be focal, i.e. restricted to some cerebral structures
with sharp outlines.
Previous studies on most neuropsychological disorders,
such as aphasia, hemineglect and frontal syndrome, suggest
that the nature of the interaction between the brain lesion
and the neuropsychological outcome is variable, and this
requires the development of models of the brain–behaviour
Study of brain–behaviour relationships
relationship, which are still lacking. Brain–behaviour
relationships are frequently approached according to the
assumption of unicity, i.e. one deficit corresponds to a single
damaged area. However, the unicity approach may be an
oversimplification for multiple reasons. For example, most
neurological deficits (e.g. motor weakness) are caused by a
lesion which may be located in various parts of a functional
system (e.g. the pyramidal tract). Accordingly, a survey of
the literature shows that deficit in a neuropsychological test
frequently depends on one of several possible lesion locations
(Heilman and Valenstein, 1985; Shallice, 1988; Habib et al.,
1996). For example, naming may be impaired in patients
with a lesion of the left inferofrontal or temporal lobes,
thalamus, striatum or deep white matter (Alexander et al.,
1987; Mesulam, 1990; Kremin, 1994). The multiplicity of
lesion locations associated with an apparently similar deficit
may be observed because performance in complex tasks,
such as naming, depends on several perceptual, cognitive
and motor stages, where each stage is supported by a specific
structure (Mesulam, 1990). Another example is provided by
the interruption of tracts or association fibres by white matter
damage. Such lesions may lead to disconnection between
two areas, which was recognized early on as a situation in
which similar deficits may be induced by lesion of different
locations. Furthermore, the effect of multiple lesions may be
cumulative. For example, the occurrence of some deficits
requires the addition of several lesions such as the Balint
syndrome, reduplicative paramnesia and major frontal
syndrome in patients with striatal infarcts (Shallice, 1988;
Godefroy et al., 1992; Wolfe et al., 1994; Caplan, 1995).
According to available data, four basic modes of brain–
behaviour relationship may theoretically be observed: (i)
unicity, when the occurrence of a deficit depends on the
lesion of a single structure, i.e. one deficit, one lesion; (ii)
equivalence, when the occurrence of a deficit depends on a
single lesion within two possible structures; (iii) association,
when the occurrence of a deficit requires the combined lesion
of two different structures; and (iv) summation, when a single
lesion of two possible structures results in a minor deficit
and the combined lesion of both structures results in a major
deficit. These models provide strong predictions on the
interaction of brain lesion with neuropsychological outcome,
and such interaction has to be tested by statistical analysis.
Most recent attempts to delineate the minimal brain lesion
associated with a particular deficit have used analyses based
on linear models (Gur et al., 1988; Godefroy et al., 1992,
1996; Bigler, 1994; Kornhuber et al., 1995; Vendrell et al.,
1995; Rousseaux et al., 1996; Rueckert and Grafman, 1996).
Though linear models may adequately describe data where
the occurrence of a deficit is related to a single lesion
location, they may not fit situations where the deficit depends
on several lesions or on the interaction between lesions
(Cohen and Cohen, 1983; Glantz and Slinker, 1990). The
interpretation of linear models may be especially complicated
in situations where an interaction between lesions exists, i.e.
when the effect of a lesion is conditional on the presence of
1547
another lesion. Unicity implies one lesion, one deficit, and
equivalence implies that a lesion in area X or area Y is
sufficient to cause a deficit. In neither case is there an
interaction between the lesions in the two areas. For these
two modes of brain–behaviour relationship, a linear model
would be sufficient. However, the interpretation of the model’s
parameters may be ambiguous in the case of equivalence.
The next two modes, namely association and summation,
depend upon interaction between lesions in two areas. In
association both areas must be damaged before the deficit is
apparent, i.e. a conjunction of lesions is required. In
summation this interaction is present, but there is also a
simple main effect of lesions in either area. In other words,
lesions in either area will lead to mild deficits but conjoint
lesions produce a major deficit that is greater than the sum
of the mild deficits. A linear model may fail to describe
adequately these two modes of brain–behaviour relationship.
Conversely, non-linear statistical models such as classification
tree tests naturally deal with interactions (Breiman et al.,
1984). Such models may allow the examination of modes of
brain–behaviour relationship and the localization of the
effective lesion, but they have not been used for such a
purpose to our knowledge.
The aim of our study was to assess the reliability of
statistical procedures for the study of four basic modes of
brain–behaviour relationship. In the first experimental study
a simulated population of patients designed to reproduce the
main characteristics observed in brain pathology was used.
Areas associated with the occurrence of a deficit were
predetermined and compared with areas selected by statistical
analysis. In the second study the validity of the statistical
analyses was assessed and the lesion locations associated
with motor weakness in stroke patients were determined.
Selected areas were compared with the anatomy of the
motor system.
Brain–behaviour study on simulated patients
Subjects
The first step consisted of the re-examination of the lesion
distributions observed in patients from previous studies. We
pooled data on lesion locations observed in three previous
studies (Godefroy et al., 1994, 1996, 1997) in which disorders
of behaviour and frontal functions in patients with striatal
infarct (n 5 11), postaneurysmal frontal (n 5 21) and
vascular temporoparietal lesions (n 5 18) were assessed.
These studies were chosen because they used the same
neuropsychological and neuroradiological methods. The
presence of a lesion within six ROI (basal, medial and lateral
parts of the frontal lobes, head of the caudate nucleus, parietal
and temporal lobes) of each hemisphere was determined by
three observers according to a method providing significant
inter-examiner agreement (Godefroy et al., 1996). Association
between lesions of each ROI (Table 1) was examined using the
Pearson correlation test. Some lesions were highly correlated,
1548
O. Godefroy et al.
Table 1 Values for the Pearson R coefficient between lesion locations observed in our previous studies
FBa R
FBa L
FMe R
FMe L
FLa R
FLa L
CN R
CN L
Par R
Par L
Tp R
Tp L
FBa R
FBa L
FMe R
FMe L
FLa R
FLa L
CN R
CN L
Par R
Par L
Tp R
Tp L
1
0.82
0.29
0.27
0.67
0.41
0.22
0.44
–0.13
–0.09
–0.17
–0.28
1
0.32
0.31
0.59
0.47
0.13
0.51
–0.12
–0.06
–0.16
–0.25
1
0.7
0.14
0.18
–0.04
0.14
–0.04
–0.05
–0.05
–0.08
1
0.04
0.26
–0.06
0.19
–0.05
0.11
–0.07
–0.12
1
0.22
0.56
0.22
0.04
–0.16
–0.14
–0.23
1
0.21
0.52
–0.09
–0.01
–0.12
–0.01
1
–0.12
0.18
–0.09
–0.08
–0.13
1
–0.11
–0.05
–0.14
–0.07
1
–0.08
0.54
–0.12
1
–0.10
0.46
1
0.06
1
FBa 5 frontobasal; FMe 5 frontomedial; FLa 5 frontolateral; CN 5 caudate nucleus; Par 5 parietal lobe; Tp 5 temporal lobe; R 5
right, L 5 left.
Table 2 Number of lesions within each ROI and performance (%) of patients and controls on experimental studies 1 (Per
1) to 4 (Per 4)
n
ROI 1
ROI 2
ROI 3
ROI 4
ROI 5
ROI 6
L
L
R
L
R
L
R
L
R
L
R
Patients
30 17 18 5
8
6
8
10 8
7
5
6
4
Controls
30 0
0
0
0
0
0
0
0
0
R
0
0
0
P values
Per 1
Per 19
Per 2
Per 3
Per 4
90 6 13
(52–99)
96 6 3
(90–100)
0.08
72 6 20
(51–99)
95 6 3
(90–100)
0.0001
52 6 45
(1–99)
95 6 3
(90–100)
0.0001
50 6 46
(0–99)
95 6 3
(90–100)
0.002
52 6 38
(10–100)
95 6 3
(90–100)
0.0001
Performance (Per) is expressed as mean 6 SD and range (brackets). P values are for the Mann–Whitney test. R 5 right; L 5 left.
indicating that collinearity has to be taken into account before
examining the role of each lesion. The present correlations
were used as a guide for attributing the lesion locations of
the simulated population.
Secondly, one group of normal controls (n 5 30) and one
group of brain-damaged patients (n 5 30) were designed.
As in our previous studies, six ROI (ROI 1–6) within
each hemisphere were considered. Lesions were set by the
examiner in one or several ROI (Table 2). In order to
reproduce the main characteristics of lesion distribution
previously observed, lesions of ROI 1–4 were attributed to
the first 20 patients and lesions of ROI 5 and 6 to the last
10 patients. The resulting correlations between lesions within
each ROI did not differ from our previous studies
[Kolmgorov–Smirnov test: P . 0.2 (Kolmgorov, 1941;
Smirnov, 1948)], with 76% of absolute r values lower than
0.4, 15% between 0.4 and 0.6 and 9% higher than 0.6.
Thirdly, the performance of each subject was determined
by the examiner according to the four modes of brain–
behaviour relationship detailed below. The level of
performance in a hypothetical test was expressed as the
percentage of correct responses. It was set for each subject
with a random variation of 65%, in order to take into account
non-pathological sources of performance variability, such as
age, education level, premorbid ability and measurement
error. Performance variation of 65% seems to fit satisfactorily
the few data that have been obtained using normal subjects
and a normal reporting range, though considerable variation
is observed from test to test (Lezak, 1995). Normal
performance was set at 95% (65%) of correct responses.
Pathological performance was attributed by the examiner to
patients with a lesion or an association of lesions in specific
ROI. It was set at 55% (65%) in studies 1 and 19, 5%
(65%) in studies 2 and 3, and 75 and 15% (65%) in study
4. Preliminary analyses in which the level of pathological
performance was systematically varied between 0 and 80%
showed only a marginal effect on the main results.
Study design
Five studies were planned in order to test the efficiency of
statistical analyses applied to four modes of brain–behaviour
relationship: (i) studies 1 and 19: the lesion of one ROI was
responsible for the presence of a deficit (unicity); (ii) study
2: a single lesion within two possible ROI was responsible
for the presence of a deficit of the same magnitude
(equivalence); (iii) study 3: the conjunction of lesions of two
ROI was required for the occurrence of a deficit (association);
(iv) study 4: a single lesion within two possible ROI was
responsible for the presence of a mild deficit and the conjoint
lesions resulted in a major deficit (summation). The critical
areas responsible for the occurrence of a deficit were chosen
arbitrarily: study 1, ROI 6 right; study 19, ROI 1 left; study
2, ROI 4 left or right (n 5 10 and 8 subjects, respectively,
Study of brain–behaviour relationships
1549
Fig. 1 Distribution (number of subjects) of performance (%) in experimental studies 1 (Per 1) to 4 (Per 4). Dark bars indicate a deficit.
including 4 with both lesions); and studies 3 and 4, ROI 1
left and right (n 5 20 subjects, including 15 with both
lesions). The performance level of each subject was attributed
according to the presence of a lesion within the critical area:
for example, in study 1 subjects with a ROI 6 right lesion
had a performance level of 55 6 5% and others had a
performance of 95 6 5%. The resulting distributions of
performance (Per) are provided for the five studies (Fig. 1).
Performances of patients were significantly lower than those
of controls (Mann–Whitney test) except in study 1 (Table 2).
Statistical analysis
The effect of a lesion within each ROI was evaluated using
linear (linear regression with stepwise selection) and nonlinear (classification trees) tests. Linear regression with
stepwise selection is an iterative procedure to build the ‘best’
subset of predictive variables. The independent variable with
the largest correlation with the dependent variable is entered
first in the model. Then, the procedure adds the other
independent variables which maximize the multiple squared
correlation coefficients between the dependent variable and
each independent variable. The classification tree test used
the Classification and Regression Trees Method (Breiman
et al., 1984), which is based on a binary decision tree to predict
a nominal or ordinal dependent variable. The procedure is
iterative and the ‘splits’ computations are based on the
minimization of the number of misclassified observations.
The process is repeated on each subdivision of the tree until
the partition criterion is reached. For the present purpose,
both analyses differ mainly with regard to the description of
interactions between the independent variables, i.e. when the
1550
O. Godefroy et al.
effect of a lesion is conditional on the presence of another
lesion. The variance accounted for by interactions is not
directly available from linear regression analysis, and in
situations involving several independent variables it requires
a large number of computations and this compromises the
stepwise selection of the model. Moreover, the typical linear
relationship assumes that the dependent variable may be
expressed as the sum of independent variables multiplied by
a constant (Cohen and Cohen, 1983), and this relationship is
not meaningful when the dependent variable depends on one
or another of the independent variables, i.e. the equivalence
situation. Conversely, the classification tree analysis naturally
deals with interactions which are directly available from the
examination of the tree. Each vertex indicates the role of
each independent variable and the examination of the final
vertices indicates the relationships between independent
variables. In the present analyses, performance was used as
the dependent variable and the presence of a lesion within
the 12 ROI (0 5 normal; 1 5 lesion) as independent
variables. Linear regression and classification trees tests
automatically selected ROI associated with the occurrence
of the deficit. The efficiency of the statistical tests was
assessed by comparison between selected and effective ROI.
Statistical analyses were performed using only data on
patients. Whenever possible, analysis restricted to patient
data appears preferable since it reduces the variance accounted
for by extrinsic and general factors such as fatiguability and
general condition. Statistical analysis was performed using
SAS (SAS Institute, 1990) and SIPINA (Zhighed et al.,
1992) software. Values of P lower than 0.05 were regarded
as significant.
Results
Linear regression analysis
Among the assumptions underlying the use of linear
regression analysis, multicollinearity has to be checked since
it may affect the selection of factors (Glantz and Slinker,
1990). In the present study, the examination of
multicollinearity appeared especially relevant since some
lesions were correlated. Accordingly, the variance inflation
factor (VIF) indicated collinearity for three ROI (ROI 1 left
and right, VIF 5 11; ROI 5 left, VIF 5 13). Since the
present study examined the efficiency of statistical analyses
in real situations, each ROI was used as an independent
variable without the use of a correction procedure.
In study 1, the stepwise procedure selected the ROI 6 right
(P , 0.0001) (Per1 5 –38 3 ROI 6 right 1 95). In study
19, ROI 1 left (P , 0.0001) and 6 left (P , 0.007) were
selected (Per19 5 –38 3 ROI 1 left 14 3 ROI 6 left 193).
In study 2, ROI 4 left (P , 0.0001), 4 right (P , 0.0001)
and 2 right (P , 0.0001) were selected, leading to the
following equation: Per2 5 –56 3 ROI 4 left –47 3 ROI 4
right –29 3 ROI 2 right 191. In study 3, the stepwise
procedure selected ROI 1 left (P , 0.0001), 1 right (P ,
0.0001) and 2 left (P , 0.0001), with the following equation:
Per3 5 –47 3 ROI 1 left –44 3 ROI 1 right 144 3 ROI 2
left 195. In study 4, ROI 1 left (P , 0.0001), 1 right (P ,
0.0001) and 2 left (P , 0.0001) were selected, leading to
the following equation: Per4 5 –39 3 ROI 1 left –40 3 ROI
1 right 1 20 3 ROI 2 left 194. The number of predicted
performances deviating from observed values by ù5%
was low (study 19, n 5 0; studies 1 and 4, n 5 1; study 3,
n 5 2), except in study 2 (n 5 14).
These analyses showed that when a single lesion was
required for the occurrence of a deficit (studies 1 and 19),
the relevant ROI was selected and accounted for a large
amount of variance (Table 3). Conversely, when the effective
lesion included two areas (studies 2–4), ROI not responsible
for the occurrence of a deficit were also selected and usually
accounted for a small amount of variance. Moreover, large
differences in partial variance were observed between ROI
that had the same role in the occurrence of a deficit. Thus,
the linear regression procedure was reliable when the effective
lesion was unique, but when the occurrence of a deficit
depended on several lesions it included irrelevant factors,
leading to conflicting results. Moreover, it did not differentiate
among the equivalence, association and summation situations.
Classification tree analysis
This analysis initially required the transformation of a
continuous variable into an ordinal one. The transformation
was based on individual performance and was done by an
examiner blinded to performance computation. Performance
deviating from control means by 2 SDs was considered
significantly impaired. The number of impaired patients
differed according to the study (Fig. 1): study 1, 4 patients;
study 19, 17 patients; study 2, 14 patients; study 3, 15
patients. In study 4, 20 patients were impaired, with a bimodal
distribution: the first subgroup (n 5 5) deviated by 5–8 SDs
and the second subgroup (n 5 15) by 26–29 SDs. A score
was assigned to the performance of each patient and was
used as a dependent variable: studies 1–3, normal or deficit;
study 4, normal, minor deficit or major deficit.
The classification analysis, which was run automatically,
accurately selected the effective lesions in all studies (Fig.
2): study 1, ROI 6 right; study 19, ROI 1 left; study 2, ROI
4 left (first partition) and right (second partition); studies 3
and 4, ROI 1 left (first partition) and right (second partition).
Patients were classified with 100% accuracy. Furthermore,
the examination of trees indicated the modes of brain–
behaviour relationship. In studies 1 and 19 a single partition
achieved a correct classification of all impaired patients in
the right final vertex (Fig. 2), indicating a situation of unicity.
In study 2, the deficit was observed in patients with a lesion
of ROI 4 left (first partition, right final vertex) or ROI 4 right
(second partition, right final vertex), indicating a situation of
equivalence. In study 3, all impaired patients were grouped
in the right final vertex following the second partition, and
this corresponded to patients with conjoint lesions of ROI 1
Study of brain–behaviour relationships
1551
Table 3 Partial variances obtained in the five experimental studies (S1 to S4) for the 12 ROI
ROI 1
L
S1
S19
S2
S3
S4
ROI 2
R
L
ROI 3
R
L
ROI 4
R
L
ROI 5
R
L
ROI 6
R
L
Cp
R
0.95
0.98
0.77
0.82
0.004
0.12
0.14
0.08
0.1
0.04
0.57
0.24
0.6
–3
–2
2
4
Values in bold correspond to areas effectively responsible for the deficit. Cp 5 values of Mallows’ statistic for the five linear models.
Fig. 2 Clasification trees obtained in the five experimental studies (S1 to S4): the number of patients in each partition is according to the
presence of a lesion in ROI. N 5 normal performance; d 5 mild deficit; D 5 major deficit; L1 5 lesion; L– 5 no lesion; r 5 right;
l 5 left. Each vertex (box) represents the number of patients according to the presence of a deficit. Partitions are based on the presence
of selected lesions (indicated below each box). Each partition (first: top) is represented by two arrows (left: no lesion; right: lesion). The
final vertices (bottom boxes) indicate the final classification of the population.
left and right. This study showed that damage to both ROI
1 left and right was required for the occurrence of a deficit,
indicating a situation of association. In study 4, all patients
with a mild deficit were observed in both medial final vertices,
which corresponded to patients with either a ROI 1 right
(left medial vertex) or a ROI 1 left lesion (right medial
1552
O. Godefroy et al.
vertex). In addition, all patients with a major deficit were
grouped in the extreme right final vertex, which corresponded
to the conjunction of lesions of ROI 1 left and right. The
association of a mild deficit in patients with a lesion in either
area and of major deficit in patients with conjoint lesions
indicated a summation situation. Thus the classification
analysis selected the effective lesion location, and tree
examination allowed us to determine the four modes of brain–
behaviour relationship: unicity, equivalence, association and
summation.
Discussion
In the present study four basic modes of brain–behaviour
relationship consistent with neuropsychological data were
examined in order to assess the efficiency of linear and nonlinear statistical analyses for determining the effective lesions.
A simulated population designed to reproduce the lesion
distribution observed in real patient groups was used, and its
design was based on the usual procedures of neuropsychological study. Results relevant to the analysis of the functional
anatomy of the brain were obtained. First, the limitation of
the group comparison design for the evaluation of brain–
behaviour relationship was demonstrated. The group comparison analysis is sensitive to the proportion of impaired
patients and may provide negative results when a small
subgroup of the total sample is impaired (Clark and Ryan,
1993). This situation was illustrated in study 1, in which
only four patients were impaired. Though the performance
of the patient group did not differ significantly from that
of controls, the study of the brain–behaviour relationship
identified the four impaired patients and related impaired
performance to the presence of a ROI 6 right lesion. In
studies showing a significant difference between groups (all
except study 1), the group comparison did not allow us to
determine the ROI responsible for the occurrence of the
deficit. The conclusion that the most frequent lesion (i.e.
ROI 1 left and right) causes the deficit would be wrong, as
shown by study 2, in which the effective lesion was not the
most frequent one. Secondly, the brain–behaviour study using
linear regression analysis was found to be sensitive to the
relative frequency of lesions. This observation was prominent
in situations when the deficit depended on two lesions, and
was shown by a difference in variance that was accounted
for by lesions which had the same role. Though this difficulty
appeared to be minor in the present study, where partial
variances were high, it may be misleading in studies using
large ROI, which result in lower variance values. The
determination of the mode of brain–behaviour relationships
was not possible using linear analysis, and it was the main
limitation. The examination of partial variance and the
estimated parameters of the equation indicated whether unique
or multiple lesions were responsible for the deficit, but when
two lesions were selected, the nature of their interaction (i.e.
equivalence, association and summation) was not available.
Thirdly, results from classification tests were consistent with
the data. The effective lesion locations were correctly selected
and tree examination allowed us to separate the four modes
of brain–behaviour relationship. In this test the continuous
variable is transformed into an ordinal variable. The
transformation was easily achieved in the present study, but
may raise some problems when the neuropsychological test
results in high variability of normal performance. However,
this difficulty is not specific to such statistical tests and all
analyses of pathological disorders are compromised by nonpathological sources of performance variation.
This study demonstrates that: (i) the group comparison
design is not relevant to the assessment of brain–behaviour
relationships, at least when the lesion is not circumscribed
to a single cerebral structure, which is usual in brain
pathology; (ii) linear models may provide conflicting findings
and fail to identify the mode of brain–behaviour relationship
when several lesions account for the presence of a deficit; and
(iii) the classification tree test provides the most appropriate
analysis for the evaluation of brain–behaviour relationships.
The statistical analyses of the present study were designed
to examine a common concern in neuropsychology, i.e. the
location of cognitive functions, but could also be used in
other domains, such as perception and motor disorders.
Validation study
This study aimed to assess the validity of these statistical
procedures in a real patient group. We examined lesion
locations responsible for the occurrence of motor weakness
in stroke patients and the results were examined in relation
to the anatomy of the human motor system. The motor
domain was chosen because the anatomy of the pyramidal
system is known.
Subjects
The study included consecutive patients admitted to the acute
stroke unit of the Lille University Hospital during a 7 month
period (November 1995 to May 1996). These patients were
enrolled in another study on dementia in stroke patients
(Hénon et al., 1997), and for the present evaluation we
selected patients (i) with a first cerebral infarct, (ii) without
bilateral motor deficit, (iii) examined using MRI, and (iv)
without bilateral small infarcts of the centrum semiovale or
without a periventricular hyperintensity score higher than 1
(Blennow et al., 1991). Thus, only 29 patients were included
in the present study. All patients were examined at admission
by a board-certified neurologist (Leys et al., 1997) and the
severity of neurological deficit was scored according to
Orgogozo’s rating scale (Orgogozo and Dartigues, 1986).
The presence of a unilateral motor deficit (motor score ø
50) involving the face or/and upper or/and lower limb was
observed in 23 patients.
Method
MRI was used to determine lesion locations. Two independent
examiners blinded to neurological examination rated the
Study of brain–behaviour relationships
signal intensity using axial and coronal slices (T2-weighted
turbo spin-echo sequences) as 0 (no lesion) or 1 (lesion).
Reconstructions were performed using the method of
Talairach and Tournoux (1988). The centrum semiovale was
divided into the anterior part and the central-posterior part
according to the projection of the precentral sulci. The
following 21 ROI were evaluated on each side: prefrontal,
premotor, precentral and postcentral gyri, parietal (except
postcentral gyrus), temporal, occipital, anterior part and
central-posterior part of the centrum semiovale, anterior arm,
posterior arm and genu of the internal capsule, lenticular
nucleus, caudate nucleus, thalamus, cerebellum, anterolateral
part and medial part of the mesencephalon and pons, and
medulla oblongata. This method provided a very good and
significant inter-examiner agreement (κ 5 0.96, P , 0.0001).
Lesions were observed in the following regions: prefrontal
(n 5 7), premotor (n 5 10), precentral (n 5 9) and postcentral
(n 5 9) gyri, parietal (n 5 12), temporal (n 5 9), occipital
(n 5 7), centrum semiovale (anterior part, n 5 12; centralposterior part, n 5 20), internal capsule (anterior arm, n 5
5; posterior arm, n 5 9; genu: n 5 3), lenticular nucleus
(n 5 16), caudate nucleus (n 5 8), thalamus (n 5 9),
cerebellum (n 5 3), pons (anterolateral part, n 5 1; medial
part, n 5 8), and lateral part of the medulla (n 5 3). Lesions
of the precentral gyrus and of the genu of the internal capsule
were always associated with other lesions, especially in the
centrum semiovale and internal capsule. Since the motor
deficit was unilateral, neuroradiological data for both sides
of the brain were used, leading to 58 observations. Lesion
correlations were similar to those observed in previous
studies, with 64% of the absolute r values lower than 0.4,
22% between 0.4 and 0.6, and 14% higher than 0.6.
The same general procedure was used for statistical analysis
as in the experimental study. The statistical tests included a
linear regression analysis with stepwise selection and a
classification tree analysis. Independent variables were the
presence of a lesion (lesion 5 1; normal 5 0) in the 42 ROI.
The dependent variable was the motor score of Orgogozo’s
scale for the regression linear analysis and the presence of
motor weakness (deficit 5 1; normal 5 0) for the classification
tree analysis. The statistical analyses automatically selected
the ROI associated with a poor motor score (linear regression
test) or the presence of a motor deficit (classification tree
test). The validity of the statistical tests was assessed by the
comparison between selected ROI and ROI known to include
the pyramidal tract (Brion and Guiot, 1964; Lazorthes et al.,
1976; Talairach and Tournoux, 1988).
Results
First, the stepwise linear regression was performed using the
score on motor subtests of Orgogozo’s scale as the dependent
variable. The motor score was found to depend on the
presence of a lesion of the central-posterior part of the
centrum semiovale (R2 0.5, P , 0.0001), caudate nucleus
(R2 0.13, P , 0.0001), lenticular nucleus (R2 0.04, P , 0.01)
1553
and anterior arm of the internal capsule (R2 0.03, P , 0.04)
with the following regression equation: motor score 5
–12 3 central-posterior part of the centrum semiovale –28 3
caudate nucleus –10 3 lenticular nucleus 119 3 anterior
arm of the internal capsule 154. Multicollinearity was high
for three factors not included in the equation: premotor
(VIF 5 26), precentral gyrus (VIF 5 16) and temporal
(VIF 5 11). Omitting the premotor lesion was found to be
the most appropriate correcting procedure (all VIFs ,10),
and the repeated analysis provided exactly the same result.
Nineteen (33%) predicted values of motor score deviated
from the observed score by 10% or more. Using a cut-off
value of predicted motor score of 50 (predicted score ø50,
deficit; predicted score .50, absence of motor deficit), the
present model misclassified six patients; three patients with
a normal motor status were predicted to have a motor
weakness and three patients with a deficit were predicted to
have normal motor status.
Secondly, the classification tree analysis was performed
with the presence of a motor deficit as a dependent variable.
The presence of a motor deficit was found to depend on
lesions (Fig. 3) located in the central-posterior part of the
centrum semiovale (classification accuracy 91.4%), in the
posterior arm of the internal capsule (accuracy 94.8%), and
in the anterolateral part of the pons (accuracy 96.6%). Other
factors (thalamus, caudate nucleus and anterior part of the
centrum semiovale) were included in the model because we
used a strict criterion for partition (set size 5 1) but they
did not provide a gain in accuracy (accuracy 96.6%). The
most conservative model was achieved using only the first
three factors (central-posterior part of the centrum semiovale,
posterior arm of the internal capsule and antero-lateral part
of the pons), as shown by the lack of gain in accuracy after
the addition of other lesions. Using this three-factor model,
only two patients were misclassified (Fig. 3): the patient with
a thalamic lesion and motor deficit and the patient with a
lesion of the central-posterior part of the centrum semiovale
without motor deficit. Comparison of the predicted and
observed values of motor deficit did not reveal a significant
difference (χ2 goodness of fit test, P . 0.5). Tree examination
showed that motor weakness was associated with a lesion of
the central-posterior part of the centrum semiovale, the
posterior arm of the internal capsule or the anterolateral part
of the pons, suggesting an equivalence mode of brain–
behaviour relationship.
Finally, the validity of the linear regression and
classification tree tests was assessed by comparison of the
motor deficit predicted by statistical analyses with that
predicted by lesion locations. This procedure was used to
minimize the role of measurement error in the
neuroradiological examination. According to the Talairach
and Tournoux atlas (1988), ROI including the pyramidal tract
were the gyrus precentralis (n 5 9), the central-posterior part
of the centrum semiovale (n 5 20), the posterior arm (n 5
9) and genu (n 5 3) of the internal capsule, the antero-lateral
part of the mesencephalon (n 5 0) and pons (n 5 1) and the
1554
O. Godefroy et al.
Fig. 3 Classification tree of the validation study: the number of patients in each partition is according to the presence of a lesion.
N 5 normal motor examination; D 5 motor deficit; L1 5 lesion; L– 5 no lesion; CN 5 caudate nucleus; CSO a 5 anterior part of the
centrum semiovale; CSO cp 5 central and posterior parts of the centrum semiovale; PAIC 5 posterior arm of the internal capsule; Pons
al 5 antero-lateral part of the pons; Th 5 thalamus. * Two patients misclassified by the three factors model (CSO cp, PAIC, Pons al).
anterior part of the medulla oblongata (n 5 0). Thus, all
patients with a lesion within these critical ROI were predicted
to have a motor deficit (Melo and Bogousslavsky, 1995).
Among the 23 patients with a lesion of these critical ROI,
22 had a deficit; one patient with normal motor examination
had a small infarct of the central-posterior part of the centrum
semiovale which presumably spared the pyramidal tract. In
addition, one patient without lesion of the critical ROI had
a deficit: he suffered from a lesion of the thalamus extending
to the border of the internal capsule which was rated as
normal on neuroradiological examination. The agreement
between the motor deficit predicted by lesion location and
statistical analyses was perfect for the classification tree test
(χ2 goodness of fit test 5 0, P 5 1) and moderate for the
linear regression test (χ2 goodness of fit test, P . 0.5). The
discrepancy in the latter test was due to four patients: two
patients with a normal motor status and a lesion of the
lenticular nucleus were predicted to have a deficit since the
lenticular lesion was included in the linear regression, and
two patients with a deficit related to a lesion of the pons and
the posterior arm of the internal capsule were predicted to
have a normal motor status since neither lesion was selected
by the linear regression. Thus, the linear regression analysis
selected irrelevant lesions and omitted important lesions, and
this resulted in the misclassification of patients. Conversely,
the classification tree analysis fitted the data very satisfactorily
since the misclassification of two patients was due to a
measurement error in the neuroradiological examination.
General discussion
The two statistical tests gave different results, although both
selected the lesion of the central-posterior part of the centrum
semiovale. No analysis selected the precentral gyrus and the
genu of the internal capsule; this was due to the absence of
an isolated lesion of these areas in the present population.
The linear regression analysis gave poor results since lesions
not related to the presence of a motor deficit were also
selected, and this resulted in misclassification of six patients.
The best account was provided by the classification tree
analysis: brain lesions known to include the pyramidal tract
and known to induce a motor deficit were selected (Melo
and Bogousslavsky, 1995). Only two patients were
misclassified, and this misclassification was related to
measurement error in the neuroradiological examination.
Moreover, tree examination suggested an equivalence mode
of brain–behaviour relationship, i.e. a single lesion localized
at various sites of the pyramidal tract was responsible
for motor weakness, and this is consistent with current
neurological knowledge.
The validation study provides some information relevant
to the anatomy of the human motor system. First, the results
support the view that motor weakness due to brain damage
is mainly related to a lesion of the pyramidal tract (Melo
and Bogousslavsky, 1995). Secondly, the analysis was able
to locate the pyramidal tract in parts of the centrum semiovale,
internal capsule and pons, and thus allowed us to draw the
anatomy of the motor system. Analysis based on ROI of
Study of brain–behaviour relationships
lower size may improve the determination of the functional
anatomy, and we are currently investigating image analysis
methods that permit a quantitative analysis of the signal at
the level of voxels. It was not possible to assess the role of
the precentral gyrus and mesencephalon in the present study
group, and this emphasizes the need for checking for lesion
distribution and collinearity. Finally, the present study
provides an example of the equivalence mode of brain–
behaviour relationship, which may be the most frequent mode
(Heilman and Valenstein, 1985). However, the possibility of
a summation mode, i.e. a mode in which the intensity of
motor weakness depends on the number of lesions of the
pyramidal tract, cannot be excluded since the motor status
was graded according to a binary score. Though this point
was beyond the scope of the present study, it may be
examined using the same methodology.
The present study puts forward four basic modes of brain–
behaviour relationship which are consistent with the available
data, and the validation study illustrates the equivalence
mode. The other modes appear very likely to be able to
account for some disorders previously reported, and this
point requires formal examination. The scarcity of available
data also prevents us from drawing any conclusion on
the exhaustiveness of the present classification of brain–
behaviour relationships, and more complex interactions
between lesions are possible. Previous data and the validation
study suggest that some disorders depend on multiple lesions
whereas the highest complexity of the experimental study
was achieved using variable relationships (equivalence,
addition and summation) between only two lesions. Though
these points require further investigation, two considerations
suggest that the present approach may provide a good account
of more complex brain–behaviour relationships. First, the
classification tree test is able to deal with numerous
interactions of various natures within the data (Breiman
et al., 1984). Secondly, it appears likely that most complex
relationships may be approached as a combination of the
four basic modes put forward in the present study. For
example, if a disorder is observed in patients with a lesion
of area X or in patients with conjoint lesions of areas Y and
Z, then the classification tree analysis will provide a mixed
pattern of equivalence (X versus Y 1 Z) and association
(Y 1 Z).
Conclusion
This study shows that statistical analysis based on the
systematic covariation of deficits and lesion locations of
brain-damaged patients provides an accurate estimation of
the localization of functions. The present approach is based
on models of brain–behaviour relationship which are now
assessable using the appropriate statistical analysis, and this
may allow the examination of a large variety of disorders of
brain function. The development of such procedures may
allow more precise documentation of the anatomy of brain
1555
functions and its pathology, and further investigation of the
modalities of brain–behaviour relationships.
Acknowledgements
We wish to thank Patricia McBride for reviewing the
manuscript. This study was supported by grants from the
Direction de la Recherche et des Etudes Doctorales (no.
000639), Faculté de Médecine de Lille and from Laboratoires
Schering SA.
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