www.elsevier.com/locate/ynimg
NeuroImage 29 (2006) 1224 – 1230

A curvature-based approach to estimate local gyrification on
the cortical surface
E. Luders,a P.M. Thompson,a K.L. Narr,a A.W. Toga,a,* L. Jancke,b and C. Gaser ca

Laboratory of Neuro Imaging, Department of Neurology, UCLA School of Medicine, 710 Westwood Plaza,
4238 Reed, Los Angeles, CA 90095-1769, USAb
Department of Neuropsychology, University of Zurich, SwitzerlandcDepartment of Psychiatry, University of Jena, Germany
Received 5 February 2005; revised 23 August 2005; accepted 31 August 2005
Available online 11 October 2005

Using magnetic resonance imaging and a new method to analyze local
surface shape, we examined the effects of gender on gyrification in alarge and well-matched sample of healthy subjects. Unlike traditional
2D methods that produce whole-brain measurements of corticalcomplexity or more sophisticated 3D parametric mesh-based techniques that allow only different sections (lobes) of the cortex to beinvestigated, we employed a novel approach with increased spatial
resolution. Although our method is sensitive to similar cortical features
like the classic whole-brain gyrification index (depths of sulci andheights of gyri), we are now able to provide detailed and regionallyspecific estimates of cortical convolution at thousands of points acrossthe cortical surface without introducing any bias through the rater orthe selected orientation of the slices. We revealed pronounced genderdifferences, showing increased gyrification in frontal and parietal
regions in females compared to males that agree with recent regions-ofinterest findings. In addition, we detected higher female gyrification in
temporal and occipital cortices that was not previously identified instudies using more global measures. No cortical area was significantly
more convoluted in males compared to females. Our results demonstrate the sensitivity of this automated approach for identifying very
local changes in gyrification. This technique may serve to isolate
regionally specific changes in fissuration/gyrification in neurodevelopmental or neuropsychiatric disorders.
D 2005 Elsevier Inc. All rights reserved.
Keywords: Cortex; Sex; Gender; Mapping; MRI; Curvature

Introduction
Brain expansion is partly constrained by the size of theintracranial cavity during neurodevelopment (Hofman, 1989; Van
Essen, 1997; Courchesne et al., 2000), so gender-specific patternsof cortical folding are likely influenced by smaller female skull* Corresponding author. Fax: +1 310 206 5518.
E-mail address: toga@loni.ucla.edu (A.W. Toga).
Available online on ScienceDirect (www.sciencedirect.com).
1053-8119/$ - see front matter D 2005 Elsevier Inc. All rights reserved.
doi:10.1016/j.neuroimage.2005.08.049

sizes. Traditional postmortem and in vivo morphometric studies
have used several unique approaches to examine cortical complexity and to establish the presence and direction of gender differencesin sulcal/gyral convolutions. Measuring cortical folding in postmortem data with a 2D gyrification index (i.e. the ratio between
deep and superficial cortex in coronal sections) revealed nodifferences between men and women (Zilles et al., 1988).
Similarly, no gender differences were identified in an in vivo
study defining whole-brain surface complexity as the ratio of total
cortical surface area to overall brain volume, raised to the 2/3
power (Nopoulos et al., 2000). However, another MRI investigation used surface-to-volume ratios to calculate a fissurizationindex for the hemispheres and cingulate cortices. This study
detected a hemisphere by gender interaction, reflecting increased
asymmetries of fissurization in male brains (Yucel et al., 2001).
Moreover, using a sophisticated 3D parametric mesh-based
approach (Thompson et al., 1996a,b) applied to five functionally
relevant cortical regions, our group demonstrated that females
exhibit greater cortical complexity than males in frontal andparietal regions (Luders et al., 2004).
Overall, empirical data concerning sex-related differences incortical complexity or gyrification are sparse, and findings lackconsistency, where discrepancies may stem from differences inmeasurement methods (e.g. postmortem vs. in vivo, 2D vs. 3D).
Available data, however, suggest that the ability to detect genderspecific differences in gyrification increases by shifting focus fromglobal (e.g. whole brain) to more regional examinations (e.g.
frontal lobe). Region-of-interest (ROI) analysis appears to be themost spatially detailed method used to date. However, using ROIs
defined a priori limits the identification of changes elsewhere in thecortex, may introduce user bias and makes it impractical to study
large populations given that manual delineations are laborintensive.
In order to circumvent these potential limitations, we applied arefined and automated whole-brain approach for estimating
regional differences in cortical surface convolution. Specifically,
we computed the degree of convolution across the entire cortex at

E. Luders et al. / NeuroImage 29 (2006) 1224 – 1230

thousands of surface points in order to provide color-coded maps
indexing the local gyrification. We hypothesized that genderspecific differences in gyrification would exist in numerous corticalregions that would complement and extend existing knowledge
from studies using less spatially detailed methods. In order toconfirm correspondences with results achieved through a lower
resolution parametric mesh-based approach (Thompson et al.,1996a,b), we examined local gyrification in the same sample as
analyzed in a previously published study (Luders et al., 2004).

Materials and methods
Subjects
We analyzed the brain scans of 60 young and right-handed
subjects that were selected from a database of high-resolution
anatomical MR images acquired at the Center for Neuroscientific
Innovation and Technology (ZENIT), Magdeburg. Subjects werematched for biological sex (30 women, 30 men) and age (women:
24.32 T 4.35 years; men: 25.45 T 4.72 years). Handedness wasdetermined by referring to self-reports of hand preference. Subjects
were healthy volunteers and included university students fromdifferent fields who were recruited via notice board and/or Internet
advertisements. All subjects gave informed consent according toinstitutional guidelines (Ethics Committee of the University of
Magdeburg).
MRI acquisition
Images were obtained on a 1.5-T MRI system (General Electric,
Waukesha, WI, USA) using a T1-weighted spoiled gradient echopulse sequence with the following parameters: TR = 24 ms,
TE = 8 ms, 30- flip angle, FOV = 250  250 mm2, matrix size =256  256  124, voxel size = 0.98  0.98  1.5 mm.
Cortex extraction
Image volumes passed through a number of preprocessing steps
using mostly automated procedures. First, we created an intracranialmask of the brain using a brain surface extraction algorithm tool(BSE) that is based on a combination of non-linear smoothing, edge
finding and morphologic processing (Shattuck and Leahy, 2002).
Any small errors in the masks were corrected manually to isolate
intracranial regions from surrounding extracranial tissue and extracortical cerebrospinal fluid (CSF). Brain masks and anatomical
images were corrected for head position and individual differencesin brain size by using an automatic 12-parameter linear registration(Woods et al., 1998) to transform each brain volume into the target
space of the ICBM-305 average brain created by the International
Consortium for Brain Mapping (Mazziotta et al., 1995). To
eliminate intensity drifts due to magnetic field inhomogeneities in
the anatomical brain images, we employed radio-frequency bias
field corrections (Sled et al., 1998). Finally, we applied thenormalized brain masks (that include cerebral tissue only) to thenormalized anatomical brain images and created a sphericallyparameterized mesh model of the cortical surface using signal
intensity information. Each of these individual meshes in ICBM305 space was continuously deformed to fit the threshold intensity
value which best differentiated extra-cortical cerebrospinal fluid
from underlying cortical gray matter (MacDonald et al., 1994).

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Measures of local gyrification
The local gyrification is revealed through estimations of‘‘smoothed absolute mean curvature,’’ based on averaging
curvature values from each vertex of the spherical surface meshwithin a distance of 3 mm followed by calculating the absolutevalue of the resulting number within this region and smoothingover 25 mm. A detailed explanation is given in the following
paragraphs and Fig. 1.
The meshes model the cortical surface of the brain consisting ofgyri and sulci. We used these meshes to calculate the mean
curvature (do Carmo, 1976) at thousands of points across thecortical surface. Mean curvature is an extrinsic surface measureand gives information about the change in normal direction along
the surface (normals are vectors pointing outwards perpendicular tothe surface). Mean curvature at a given point is defined asnv

Tcurvature ¼ ~

v¼1



!2

x̄v  x̃x v I ÑNv
Bv

where x̃ v is the centroid of its neighbors of vertex v, B v is theaverage distance from the centroid of each of the neighbors, and I is
the vector product operator (MacDonald: A Method for Identifying
Geometrically Simple Surfaces from Three Dimensional Images.
PhD Thesis McGill University, Montreal). The resulting values ofthe mean curvature measurement can be expressed either in radiansor degrees ranging from 180 to 180 (we will use degrees
throughout this paper). Large negative values correspond to sulci
and large positive values to gyri. To increase the signal to noise
ratio for the curvature measure at a given vertex, we averaged thecurvature values within a distance of 3 mm on the cortical surface
and calculated the absolute value of the resulting number within
this region. The absolute values of mean curvature (hereafterreferred to as absolute mean curvature) are always above zero forboth gyri and sulci and express the local amount of gyrification.
Finally, absolute mean curvature values were smoothed using asurface-based heat kernel smoothing filter (Chung et al., 2005) offull width at half maximum (FWHM) of 25 mm, where the widthof the smoothing filter was chosen according to the matched filter
theorem. That is, the spatial frequency of the sulcus – gyrus patternsuggests a filter that optimally enhances features in the range of the
distance between sulci and gyri, which is about 20 – 30 mm.
Furthermore, we calculated the total surface area and the total
absolute mean curvature of the mesh models in ICBM-305 space(after spatial normalization). In order to approximate the impact of
spatial normalization on our curvature-based measurements, we
calculated absolute mean curvature and smoothed absolute mean
curvature of one brain in its native dimension (unscaled image) andafter spatial normalization (scaled image). For this purpose, we
simulated the scaling of the brain by using a scaling factor of 1.25
along the x, y, and z dimensions, which resulted in a change ofvolume of almost 200% and a change in surface area of about
150%.
Statistical analyses
We linearly averaged the curvature values from each surface
mesh point in the male and female group followed by computing
the mean difference between males and females (Fig. 2). Statisticaldifferences of local curvature values between male and female
group were obtained using a general linear model applied to each

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E. Luders et al. / NeuroImage 29 (2006) 1224 – 1230

Fig. 1. Estimation of local gyrification. The left column demonstrates the computation of local gyrification using a simulated folded surface, where themagnitude of the folding increases from proximal to distal and the wavelength from left to right. The calculation of the mean curvature results in large positive
values for local maxima (corresponding to gyri) and large negative values for local minima (corresponding to sulci), where curvature values are expressed indegrees. By calculating the absolute mean curvature, all values are converted into positive values. Finally, curvature values are smoothed using a surface-basedheat kernel filter with FWHM = 25 mm. As demonstrated, increases in the amplitude and frequency of the simulated folding are reflected in increased values ofsmoothed absolute mean curvature. The right column illustrates the process of estimating local gyrification on a single subject brain selected from the sample
analyzed in this study. In the first step, the mean curvature is calculated using the 3D mesh of the cortical surface. Sulci can be identified through large negativevalues (displayed in dark green, blue and purple), while gyri are characterized by large positive values (displayed in light green, yellow and red). Aftercalculating the absolute mean curvature, all values are transformed into positive values regardless of whether they represent gyri or sulci. Final surface
smoothing with a heat kernel (FWHM = 25 mm) reveals higher values for areas with pronounced gyrification.

corresponding mesh point of the cortical surface. The resulting t
values were thresholded at a P value of P < 0.05 and corrected for
multiple comparisons using False Discovery Rate (Benjamini and
Hochberg, 1995). In addition, we compared the total surface areaof the cortex in ICBM-305 space between females and males using
a one-tailed two-sample t test. Finally, we computed the Spearman
correlation coefficient between total surface area and total absolutemean curvature.

Results
Fig. 2 shows the average distributions of local gyrification in
ICBM-305 stereotaxic space for females (first row) and males(second row). The highest local gyrification in both men andwomen appears to be located in the left and right parietal lobes
between midline and intraparietal sulcus, as well as in the left
superior frontal cortex and bilaterally along the precentral sulcus in

women, and to a lesser degree also in men. Another small region
exhibiting extremely high gyrification was detected at the inferior
part of the central sulcus (in both hemispheres and sexes). The
lowest gyrification in the left and right hemispheres appears
surrounding the occipital poles and expanding into the inferior
temporal gyrus, with lower mean gyrification values in males thanin females.
As further illustrated in Fig. 2 (third and fourth row), the largest
differences between males and females are found in anterior
regions of the frontal lobe, with more pronounced gender effects inthe left hemisphere than in the right. Large clusters showing
significantly increased gyrification in females were also detected inanterior and posterior parts of the left and right temporal lobes, aswell as in the occipital lobes (appearing slightly more pronounced
in the right hemisphere than in the left). In addition, two regions in
the parietal lobes (covering inferior parts of the right postcentral
sulcus and superior parts of the left and right postcentral gyrus)
appeared more convoluted in females compared to males. We did

E. Luders et al. / NeuroImage 29 (2006) 1224 – 1230

1227

Fig. 2. Results of local gyrification measurements. The two upper rows (a, b) demonstrate the average distribution of local gyrification in males and females,
where curvature values are expressed in degrees. The third row (c) reveals the mean differences between males and females. Areas with higher gyrification infemales than males appear in yellow and red, whereas blue and purple would indicate lower gyrification in females. The fourth row (d) illustrates regions ofsignificantly increased gyrification in females compared to males (P < 0.05), corrected for multiple comparisons using False Discovery Rate (FDR).

not detect any cortical region showing significantly increased
gyrification in men compared to women.
The total surface area of the cortex was significantly larger infemales compared to males (P < 0.007, females: 1051.41 T 42.75
cm2, males: 1026.07 T 34.24 cm2) after transforming images into
standard ICBM-305 space by applying 12-parameter transformations. The Spearman correlation coefficient between total surface
area and absolute mean curvature for the whole sample was 0.917(P < 0.001) (Fig. 3). The simulated scaling of one brain resulted ina change of absolute mean curvature by a factor of 0.812, whilesmoothed absolute mean curvature changed by a factor of 0.895.
That is, a volume increase of almost 200% would be accompanied
by an 11% decrease in curvature.

Discussion
In this study, we present a new method for estimating a local
gyrification index. Our approach is related to formerly describedcalculations of curvature indices (CI) (Magnotta et al., 1999;

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E. Luders et al. / NeuroImage 29 (2006) 1224 – 1230

Fig. 3. Correlation between total surface area and total absolute mean
curvature. This plot shows the strong relationship between total surface areaof the cortical mesh model and the average of the absolute mean curvaturesfrom each vertex of the mesh.

contrast, our newly proposed method works almost fully automatically without introducing any bias from the rater or sliceorientation. Because of the excellent spatial resolution, our new
method furnishes extremely local measures of convolution thatclearly distinguish males from female subjects in a young andhealthy group. Moreover, as demonstrated in Fig. 1, there is a goodcorrespondence between mean curvature and cortical folding;increases in the amplitude and frequency of the folding arereflected in increased values of smoothed absolute mean curvature(Fig. 1). Our approach may also serve to identify regional changes
in gyrification that occur during neurodevelopment (Blanton et al.,2001) or that manifest as the result of disease (Narr et al., 2004). In
addition, gyrification measures may be associated with othermeasures made point-wise throughout the cortex, such as graymatter (GM) distribution or cortical thickness (Good et al., 2001;
Sowell et al., 2004; Narr et al., 2005), that may further elucidate
sex differences in brain morphology or neuropathological processes in individuals with neurodegenerative or neuropsychiatricdisorders. In fact, a recent study revealed a positive correlation
between cortical thickness and whole-brain cortical complexity innormal subjects (Thompson et al., 2005).
Potential confounds

Nopoulos et al., 2000). However, in contrast to measuring wholebrain sulcal and gyral CIs as implemented previously, we
computed the degree of convolution across the entire cortex at
thousands of surface points. Our approach further complements
traditional methods that produce global measures of gyrification(Zilles et al., 1988; Yucel et al., 2001) and our previously reported
approach providing only regional measures of cortical complexity
for lobar regions of the cortex (Thompson et al., 1996a,b; Luders etal., 2004).
Relation to other approaches
Usually, the classic whole-brain gyrification index is estimatedby calculating the ratio between the lengths of the inner and outer
contour of the cortex in coronal slices (Zilles et al., 1988; Yucel etal., 2001). The inner contour exactly follows the peaks and troughsof the sulci and gyri, while the outer contour connects the tops ofthe gyri using the convex contour with least enclosed area (without
following the sulci). The relation of our approach to the classicalversion of the whole-brain gyrification index can be described asfollows: analogous to the inner and outer contours establishing theclassic gyrification index, our cortical mesh models comprise innerand outer surfaces. More specifically, the inner surface isapproximated by the total surface area of our cortical meshes,
while the outer surface is assumed to be relatively constant over all
subjects after spatial normalization. Consequently, the total surface
area (the inner surface of the cortex) is suggested to be proportional
to the 3D extension of the gyrification index (the ratio between the
inner and outer contour of the cortex). Such a relationship between
total surface area and gyrification index not only exists on a global
level of the whole cortex but also on a local level at each point of
the cortical surface. Given that the present analysis revealed astrong correlation between total surface area and total absolutemean curvature (Fig. 3), absolute mean curvature appears to be asuitable means to estimate gyrification on a global and local level.
The classical approach requires manual tracing that is highly
time-consuming, and the gyrification measurement is affected by
the orientation of brain slices selected for tracing the contours. In

The problem of Fburied cortex_ is discussed extensively in
Magnotta et al. (1999), emphasizing the difficulty to accurately
extract the cortical surface when deep infolding occurs or whensulcal invaginations are filled with cerebrospinal fluid. Clearly,
sophisticated surface extraction tools that better reach the bottomof sulci will improve the accuracy of ‘‘mean curvature’’ as a valid
indicator for the convolution of the surface. Given that there are
multiple approaches that are viable and commonly used, futurestudies remain to be conducted to establish whether group-specificoutcomes are altered significantly in dependence of the applied
surface modeling. For example, using the WM surface versus theGM surface might lead to different results. Notwithstanding, since
one of the primary goals of the present manuscript was to validate
the newly developed voxel-wise approach, we decided to use
exactly the same cortical surface models as in a former ROI
analysis (Luders et al., 2004), which was based on the algorithm
developed by MacDonald et al. (1994).
Another potential confound could result from the analysis of
gyrification in scaled spherical meshes of the cortical surface in
ICBM-305 space. Here, we provide evidence that spatial transformations into ICBM-305 space, using 12 parameters, alter thevolume and surface area of the brains, but not significantly the
degree of gyrification. Notably, volume increases as large as almost
200% would be accompanied by curvature decreases of only 11%.
Thus, our findings indicate that mean curvature is relatively
invariant to affine transforms, and differences between groups
would be similar in native space and dimensions.
Correspondence with previous findings
In this study, by comparing local differences in gyrification
between men and women, we found pronounced gender differences. Although these findings conflict with some previous
examinations that failed to detect significant gender differencesin gyrification or fissurization indices (Zilles et al., 1988; Nopoulos
et al., 2000; Yucel et al., 2001), our findings corroborate otherrecently published results demonstrating increased complexity inE. Luders et al. / NeuroImage 29 (2006) 1224 – 1230

females (Luders et al., 2004). The earlier studies that detected no
gender differences only assessed cortical convolution or complexity by investigating the whole brain or the hemispheres individually. But, pronounced gender effects in the magnitude ofcomplexity and gyrification appear detectable in later studies
where more regional analyses are performed at a lobar or voxel
level spanning the whole cortical surface. In our prior lobar
analysis (Luders et al., 2004), we detected an increased complexity
in females in the frontal and parietal lobes. These genderdifferences were also evident in the current study. However, ourstatistical maps demonstrating sex-related differences in gyrification (Fig. 2) showed improved regional specificity for gyrificationdifferences surrounding the frontal pole and inferior/superior
frontal sulci. Similarly, larger clusters of significantly increased
gyrification were observed in the parietal lobe that appear restricted
to inferior parts of the right postcentral sulcus and superior parts of
the left and right postcentral gyrus. Interestingly, the present study
also revealed a higher female gyrification in cortical regions that
did not reach significance in our previous study examining
complexity collapsed over lobar regions (temporal and occipital
lobes). However, in the current analysis, increased gyrification was
predominantly observed in anterior and posterior parts of the left
and right temporal lobes that constitute only a portion of the whole
temporal lobe. Thus, since gyrification appears similar between
males and females for a substantial portion of the temporal cortex,
it is likely that global changes in gyrification were not detected
previously. Results therefore suggest that the current approach is amore powerful means to characterize highly localized differencesin gyrification. Our findings complement and refine previously
reported gender effects using whole-brain, hemisphere or lobar
level analyses where localized gender effects may have remained
undetected. Conversely, it is surprising that the present analysis
showed increased gyrification in large parts of the occipital lobe infemale compared to male brains, while previously no sex differences were observed in this lobar region overall (Luders et al.,2004). Methodological differences may account for these discrepancies. While our earlier approach, described in detail elsewhere(Thompson et al., 1996a,b), reflects the fractal nature of gyral
folding and sulcal fissuration, the current approach appears to be
more sensitive to the magnitude of convolution (depths of sulci andheights of gyri) (Fig. 1). Nevertheless, both approaches confirm
that numerous regions in female brains show an increased
gyrification, while males show no regional increases compared tofemales.
Functional implications and morphogenesis
Sulcal/gyral formation is influenced by the underlying
cytoarchitecture of the cortex (Rademacher et al., 1993; Watson
et al., 1993; Roland and Zilles, 1994). Furthermore, gyrification isthought to be influenced by neural connectivity (Caviness, 1975;
Goldman-Rakic, 1981; Rakic, 1988) and to change as a function of
the volumetric ratio between outer and inner cortical layers(Richman et al., 1975); greater folding complexities accompany
higher intracortical connectivities (originating in outer corticallayers) and smaller descending projections (originating in innercortical layers) (Rilling and Insel, 1999). Sexually dimorphic
information processing strategies might develop as a result ofdifferences in the underlying cytoarchitecture and neural connectivity of specific brain regions. Thus, it is possible that different
gyrification patterns have functional significance and may account1229

for gender-specific abilities and/or behavioral differences between
men and women (Halpern, 1992; Kimura, 1999).
Regardless of the functional implications or significance ofincreased gyrification, there remains the challenging question ofits morphogenesis. Several theories implicate factors intrinsic tothe cortex in the primary mechanism of folding. For example, it
was proposed that greater expansion of outer vs. inner corticallayers causes gyrification (Richman et al., 1975). Another theory
suggests that cortical folding results from the development of
intracortical connections (Rakic, 1988). Finally, tension alongaxons was proposed to produce gyri between strongly connectedcortical regions and sulci between weakly connected regions (Van
Essen, 1997). Gyral formation begins around 16 weeks in utero,and most cortical folding is principally defined in the late second
and third trimesters of fetal life (Richman et al., 1975; Chi et al.,
1977; Armstrong et al., 1995). Gender-specific rates of brain
maturation (Geschwind and Galaburda, 1985) may partly accountfor present findings of sexual dimorphism in local gyrification,although the details of this relationship require further examination. Genetic determination and/or the differential effects ofgonadal hormones during brain growth are likely to affect thegender-specific emergence of local gyrification (Arnold andGorski, 1984; Breedlove, 1994; Goldstein et al., 2001; Thompson
et al., 2001). However, given that brain growth is partly confinedby the size of the intracranial cavity (Hofman, 1989; Van Essen,
1997; Courchesne et al., 2000), increased gyrification in female
brains might alternatively (or additionally) be caused by a greater
constraint of brain expansion due to smaller skull sizes inwomen.

Acknowledgments
This work was supported by research grants R01 LM005639(funded by the NLM and NIA) and P01 EB001955 (funded by the
NIBIB, NINDS, and NIMG), an NIMH NRSA Training Grant(MH14584) and a Daniel X. Freedman NARSAD Young Investigator Award (to KLN) and R21 grants RR19771 and EB01561 (toPMT). Additional support was provided by U54 RR021813(funded by the NCRR, NCBC and NIGMS), P41 RR013642 and
M01 RR000865 (funded by the NCRR). We thank Karen Schrock
for proof reading the manuscript.

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