cortical surface mapping using topology correction, partial flattening and 3d shape context-based...
TRANSCRIPT
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Journal of Neuroscience Methods 205 (2012) 96– 109
Contents lists available at SciVerse ScienceDirect
Journal of Neuroscience Methods
journa l h omepa g e: www.elsev ier .com/ locate / jneumeth
omputational Neuroscience
ortical surface mapping using topology correction, partial flattening and 3Dhape context-based non-rigid registration for use in quantifying atrophy inlzheimer’s disease
scar Acostaa,n,o,∗, Jurgen Frippa, Vincent Doréa, Pierrick Bourgeata, Jean-Marie Favreaul,m,aël Chételatc,d, Andrea Ruedaa,e, Victor L. Villemagned, Cassandra Szoekea, David Amesi,athryn A. Ellis j, Ralph N. Martinsk, Colin L. Masters f,g, Christopher C. Rowed,h, Erik Bonnera,lorence Grisa, Di Xiaoa, Parnesh Ranigaa, Vincent Barrab, Olivier Salvadoa
CSIRO Preventative Health National Research Flagship, ICTC, The Australian e-Health Research Centre – BioMedIA, Herston, AustraliaLIMOS, UMR 6158 CNRS, Université Blaise Pascal, Aubière, FranceINSERM-EPHE-Université de Caen/Basse-Normandie, Unité U923, GIP Cyceron, CHU Côte de Nacre, Caen, FranceDept. of Nuclear Medicine and Centre for PET, Austin Health, VIC, AustraliaBioIngenium Research Group, Universidad Nacional de Colombia, Bogotá, ColombiaThe Mental Health Research Institute, The University of Melbourne, VIC, AustraliaCentre for Neuroscience, The University of Melbourne, VIC, AustraliaDept of Medicine, Austin Health, University of Melbourne, VIC, AustraliaNational Ageing Research Institute, Melbourne, VIC, AustraliaAcademic Unit for Psychiatry of Old Age, Department of Psychiatry, The University of Melbourne, St. Vincents Aged Psychiatry Service, St. Georges Hospital, VIC, AustraliaCentre of Excellence for Alzheimers Disease Research Care, School of Exercise Biomedical and Health Sciences, Edith Cowan University, Joondalup, WA, AustraliaClermont Université, Université d’Auvergne, ISIT, BP10448, F-63000 Clermont- Ferrand, FranceCNRS, UMR6284, BP10448, F-63000 Clermont-Ferrand, FranceUniversité de Rennes 1, LTSI, Rennes, F-35000, FranceINSERM, U1099, Rennes, F-35000, France
r t i c l e i n f o
rticle history:eceived 22 July 2011eceived in revised form3 November 2011ccepted 20 December 2011
eywords:ortical mappingurface registrationartially inflated surfacesortical thicknessrain Atrophy
a b s t r a c t
Magnetic resonance (MR) provides a non-invasive way to investigate changes in the brain resulting fromaging or neurodegenerative disorders such as Alzheimer’s disease (AD). Performing accurate analysisfor population studies is challenging because of the interindividual anatomical variability. A large set oftools is found to perform studies of brain anatomy and population analysis (FreeSurfer, SPM, FSL). In thispaper we present a newly developed surface-based processing pipeline (MILXCTE) that allows accuratevertex-wise statistical comparisons of brain modifications, such as cortical thickness (CTE). The brainis first segmented into the three main tissues: white matter, gray matter and cerebrospinal fluid, afterCTE is computed, a topology corrected mesh is generated. Partial inflation and non-rigid registrationof cortical surfaces to a common space using shape context are then performed. Each of the steps wasfirstly validated using MR images from the OASIS database. We then applied the pipeline to a sample ofindividuals randomly selected from the AIBL study on AD and compared with FreeSurfer. For a population
hape contexttatistical analysis of populationslzheimer’s diseasereesurfer
of 50 individuals we found correlation of cortical thickness in all the regions of the brain (average r = 0.62left and r = 0.64 right hemispheres). We finally computed changes in atrophy in 32 AD patients and 81healthy elderly individuals. Significant differences were found in regions known to be affected in AD.We demonstrated the validity of the method for use in clinical studies which provides an alternative towell established techniques to compare different imaging biomarkers for the study of neurodegenerativediseases.
∗ Corresponding author. Tel.: +61 7 3253 3624; fax: +61 7 3253 3690.E-mail addresses: [email protected], [email protected],
[email protected] (O. Acosta).
165-0270/$ – see front matter © 2012 Elsevier B.V. All rights reserved.oi:10.1016/j.jneumeth.2011.12.011
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Non-invasive imaging techniques such as magnetic resonanceimaging (MRI) allow the investigation of many of the functionaland morphological changes in the brain occurring with age or dur-ing pathological processes. However, reliable statistical analysis of
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vailable data over a large number of individuals is required beforeetecting subtle differences over time or between individuals androups. The distribution differences of specific tissues such as whiteatter (WM), gray matter (GM) or cerebrospinal fluid (CSF), vol-
me changes, or any other signal coming from imaging devicesr intermediate pre-processing stages have been used in the past,nravelling some of the complex pathological changes. Statisti-al analysis per region (Lerch et al., 2005), voxels (Ashburner andriston, 2000; Ziolko et al., 2006) or vertices in a surface repre-entation of the brain (Dale et al., 1999; Fischl et al., 1999) can besed to assess the differences between groups using, for instance,
general linear model (GLM) to the available data (intensity dis-ribution, deformation, etc.) from all subjects at each region (voxelr vertex) with different covariates such as age, years of education,ender, diagnosis, cognitive scores, etc. Some of these techniquesave quantitatively demonstrated different biomarkers or predic-ors for Alzheimer’s disease (AD), showing a specific pattern oftrophy (Hua et al., 2008; Querbes et al., 2009), hypometabolismChételat et al., 2007), �-amyloid load (Mikhno et al., 2008) or com-ined hypometabolism and atrophy (Kawachi et al., 2006; Villaint al., 2008) and sulcal modifications (Zhan et al., 2009) using MRIr Positron Emission Tomography (PET).
Different software tools, grouping a wide range of methods toerform studies of cortical and subcortical anatomy are nowadaysvailable. Most of them are also able to carry out further popula-ion analysis. Statistical Parametric Mapping (SPM)1 or FreeSurferFS)2 represent two of those automated tools largely referenced inhe literature. Although they share the same goals, the comparisonsre performed in different ways. SPM is a voxel-based approach inhich the images are realigned, spatially normalized into a stan-ard space, and smoothed before performing statistical analysis at
voxel level (Ashburner and Friston, 2000). In contrast, FreeSurfers a surface-based approach performing first the reconstruction ofhe brain cortical surface from structural MRI data (Fischl et al.,999). FreeSurfer provides many anatomical analysis tools, includ-
ng the representation of the cortical surface, segmentation of therain, skull stripping, bias field correction, nonlinear registrationf the cortical surfaces into a standard space, labeling of regionsnd statistical analysis of populations. Comparison of those differ-nt tools has been performed in the past for specific tasks suchs segmentation (Klauschen et al., 2009). Overall, they face similarethodological challenges for interindividual comparisons.The primary issue for interindividual comparison is the map-
ing or registration of a given population to a common space.his is a particularly challenging task because of the brain convo-uted geometry and the high interindividual variability (Mangint al., 2004). Various registration approaches have been proposed,ncluding intensity-based in the voxel space (Rueckert et al., 1999;ercauteren et al., 2007) or shape-based in a surface representationf the brain (Yeo et al., 2008, 2010; Eckstein et al., 2007). Althoughntensity-based non-rigid registration methods work well in intra-ubject registration, cortical folds do not match well and may notffectively address the issues arising from the variability across aopulation (Hellier et al., 2003). Alternatively, cortical surfaces reg-
stration allows anatomically meaningful features to constrain theransformations (Tosun et al., 2004b), which improves the reliabil-ty of the registration and rather favors the alignment of functionalegions. Although variability in high level foldings, gyri and sulci,xists, the cortical shapes tend to present similar patterns at coarse
evels (Tosun et al., 2004a). A good matching may be consequentlyound by the alignment of the lobes and major folding patterns at a1 http://www.fil.ion.ucl.ac.uk/spm/.2 http://surfer.nmr.mgh.harvard.edu/.
ce Methods 205 (2012) 96– 109 97
coarse level across the brains, thereby registering cortical surfacesinstead of volumetric data.
Reliable cortical surface registration for statistical comparisonsraises different methodological questions which constrain anypre-processing step. The main issues are related with (i) the preser-vation of gyri and sulci and with (ii) the topology correction.Firstly, since the folding patterns correlate well with functionaland anatomical regions between individuals (Fischl et al., 2008)a reliable detection of gyri and sulci during the segmentation stepis required. Various methods have been proposed: Hutton et al.(2008) used a layering method in the voxel space based on math-ematical morphology to detect deep sulci. In Acosta et al. (2008),a method is proposed to improve sulci detection by using a dis-tance based cost function from WM in a post processing step,but no verification of topology is done. In Rueda et al. (2010) theapproach is improved by introducing topology constraints but alsoin a post-processing step, obtaining both reliable pure tissue andpartial volume images segmentations. In Cardoso et al. (2011) anexplicit model of partial volume classes is introduced within thesegmentation step and a locally varying MRF-based model is usedto locally modify the priors for enhancement of gyri, but the topol-ogy is not guaranteed yet. Secondly, the GM can be considered asa folded sheet built upon the WM and it is often assumed that ifthe midline hemispheric connections were artificially removed, thecortex would have the topology of a hollow sphere (neither han-dles nor tunnels). This assumption must be preserved throughoutall the processing pipeline. Topological operators and constraintshave to be used to correct and achieve accurate cortical tissue rep-resentations either in the voxel space during the segmentation or inthe surface representations (Ségonne et al., 2007; Ségonne, 2008;Bazin and Pham, 2005; Han et al., 2002; Kriegeskorte and Goebel,2001). The main drawback of correcting topology in the voxelspace lies in the modifications introduced by adding or remov-ing voxels compared to the size of the structures, besides the nonunicity of the handle definition. Some other approaches used acombined voxel-based strategy (Jaume et al., 2005; Zhou et al.,2007) and, as we mentioned before, other operates directly withthe surfaces (CLASP (Kim et al., 2005), BrainVISA (Mangin et al.,1995), so as Freesurfer (Dale et al., 1999; Fischl et al., 1999; Fischland Dale 2000)). FreeSurfer incorporates mechanisms to preventself-intersection of surfaces or topology correction, additionallyimposing smoothness constraints, but at expense of computationalcost.
The goal of topology correction in surface-based methods is theelimination of defects appearing in the mesh such as tunnels andhandles after the mesh generation (Fischl et al., 1999; Ségonne et al.,2007; Jaume et al., 2005; Zhou et al., 2007; Hong et al., 2006). Someof them inflate the surface to detect the topological incoherences(Fischl et al., 1999; Ségonne et al., 2007). Nevertheless, the opti-mization step for spherical inflating is non-deterministic and itscomplexity cannot be evaluated. Moreover, the corrections are notoptimal from the topological point of view as the surfaces are notcorrected according to the shortest loops that corresponds to thehandles and tunnels. In this paper we addressed the issue of topol-ogy correction with a method based on the detection and optimalcutting of non-separating loops in the mesh.
Concerning the surface based non-rigid registration, some of thepreviously proposed approaches have used a parametric represen-tation on a sphere, obtained either through iterative relaxation likein Freesurfer (Fischl et al., 1999) or conformal mapping (Angenentet al., 1999; Gu et al., 2004). In the spherical domain, the registra-tion strategy relies on features such as sulcal landmarks or mean
curvature, or convexity (Yeo et al., 2008, 2010; Ziolko et al., 2006).In those approaches the global shape information is not explicitand the registration is dependent on the selected features. Shi et al.(2007) proposed the computation of a direct map from the source
98 O. Acosta et al. / Journal of Neuroscience Methods 205 (2012) 96– 109
F tationp system
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ing each voxel to its most likely tissue type. This scheme has beenimproved in Bourgeat et al. (2009) allowing the use of multiple (n)atlases for subsequent segmentations and parcellations, in order
ig. 1. Overall pipeline for cortical mapping with MILXCTE. After WM/GM segmenerformed (6) and eventually surfaces are registered toward a common coordinate
o the target constrained by the sulcal landmark curves avoidingny parameterization. It assumes nevertheless that the sulcal land-arks curves are known and can be matched, which is not always
he case. An intermediate unfolded (inflated) representation of therain provides an alternative to expose hidden sulci and to sim-lify the geometry for cortical mapping preserving its global shapet a coarse level such as the main lobes and folds. Known as par-ially flattened surfaces (PFS) (Drury et al., 1996; Fischl et al., 1999;ons et al., 2004) they can also provide an intermediate step to fur-her conformal mapping (Tosun et al., 2004a). In a previous worke compared different methods for obtaining PFS in terms of their
bility to preserve areas and angles (Bonner et al., 2009). Comparedo the original brain surface representations, the PFS simplifies theetermination of shape correspondences between subjects whilevoiding the spherical mapping procedure (Eckstein et al., 2007). Aeaningful descriptor of shape in terms of brain anatomy may be
sed, thereby, as a similarity criterion.In this paper we present a new cortical surface processing
ipeline for vertex-wise inter-individual analysis. We provide aomprehensive approach which performs the surface cortical map-ing steps through MRI segmentation, surface generation, topologyorrection, inflation and surface matching, yielding a represen-ation of a whole population in a common space. The matchingetween individuals’ flattened surfaces (PFS) is based on the highlyiscriminative scale-invariant properties of the shape context (SC)Belongie and Malik, 2000), previously explored in (Acosta et al.,010). The similarity between points is a combination of shape con-
ext and the information of sulci automatically extracted during annflation step (sulci depth). The interpolation is obtained with thehin Plate Spline (TPS) (Bookstein, 1989). The major contributionf the shape context lies in the global shape characterization at a(1–4), topology is corrected on each separated hemisphere (5), partial inflation is (7).
local level for each single point. Our method produces an anatom-ically meaningful and scale-invariant matching between the lobesand the major folding patterns.
The C++ code and binaries for segmentation, cortical thicknessestimation (CTE) proposed in (Acosta et al., 2009) and the topologycorrection are fully available at our CSIRO software website.3 Theproposed pipeline, allows also the comparison of different imagingbiomarkers for other neurodegenerative diseases. In the remainderof the paper we explain the following steps: generation of genuszero surfaces (Section 2.1), PFS (Section 2.2) and a description of theshape context (Section 2.3.1). The validation experiments using realMRI are then described and a clinical application in an Alzheimer’sdisease study is also presented (Section 3.4) where we tested theability of cortical thickness as a biomarker for atrophy to comparetwo populations (Fig. 1).
2. Materials and methods
The proposed method consists of several stages as summarizedin Fig. 1. Firstly, 3D T1-weighted MR images are classified into GM,WM and CSF in their original space using an expectation maximiza-tion segmentation (EMS) algorithm (Van Leemput et al., 1999), asdescribed in Bourgeat et al. (2009). The EMS computes probabilitymaps for each tissue type, which are then discretized by assign-
3 http://aehrc.com/research/biomedical-imaging/medical-image-analysis/milxview.
O. Acosta et al. / Journal of Neuroscience Methods 205 (2012) 96– 109 99
Fig. 2. Cutting and patching of non-separating loops. (a) Computation of the cut locus B associated to a point p on a 1-genus surface M. (b) Cut locus B associated to a point pon a 2-genus surface M. (c) Computation of the shortest non-separating loop associated to a point on the path SB , subpart of the cut locus B associated to the point p.
n of (
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Fig. 3. Example of topological correctio
o improve the reliability of the priors. Thus, each individual scans segmented n times, once for each of the n atlases. The result-ng n segmentations per patient are then combined using a votingcheme to provide consensus segmentation according to (Aljabart al., 2009). Similarly, for each patient, the n propagated Automatednatomical Labeling (AAL) (Tzourio-Mazoyer et al., 2002) and the
nternet Brain Segmentation Repository (IBSR) labeling,4 are alsoombined using the same voting scheme. This step ensures thatutliers resulting from poor spatial normalization are excluded, andnly regions of high confidence are preserved. Secondly, based onhese pure tissue segmentations, a further maximum a posteriorilassification of voxels into pure tissues WM, GM and CSF and mixedissues WM/GM and GM/CSF along the previously computed GM
nterface is performed, which results in a GM partial-volume coeffi-ients (GMPVC) image used for further cortical thickness estimationAcosta et al., 2009). Topology-constraints are introduced in the4 http://www.cma.mgh.harvard.edu/ibsr.
a and b) tunnel, (c and d) two handles.
voxel classification assuming that the GM is a continuous layer cov-ering a WM, homotopic to a filled sphere as presented previously in(Rueda et al., 2009). A topology preserving dilation of the WM overthe GM improves the robustness of delineation of mixed GM/CSFvoxels in deep sulci. The propagated IBSR labeling is then used as amask to separate left and right hemispheres, after which the gen-eration of 3D polygon meshes representing the WM/GM interfaceis performed with the marching cubes algorithm (Lorensen andCline, 1987). Tunnels and handles resulting from the meshing areremoved with a method based on the detection and correction ofnon-separating loops (Fig. 3). In order to reduce the surface con-volution and the inter-individual variability, the surfaces are theninflated to a similar shape (Fig. 4). The inflated surfaces, referred toas PFS, are finally elastically registered toward the common tem-plate using the shape context-based non-rigid registration (Fig. 5).
The registration imposes a standardized coordinate system on bothsurfaces, allowing the vertex-wise comparison of the whole popu-lation. In this paper, we detail and validate the steps 5–7 in Fig. 1and illustrate the results with an example of clinical application in
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hich the cortical thickness was computed using our voxel-basedpproach (Acosta et al., 2009) propagated to the registered meshes.e compared the differences in cortical thickness between a pop-
lation of Alzheimer’s disease (AD) patients and a control group ofealthy elderly individuals (HC).
.1. Correction of topology and generation of genus zero surfaces
After the surfaces are generated by the Marching Cubes algo-ithm (Lorensen and Cline, 1987) the topology is corrected to meethe assumed topological properties of the brain, homeomorphico a sphere. Handles and tunnels appear as topological defects toe removed. To this end, we implemented an iterative topologicalorrection inspired by (Erickson and Har-Peled, 2002) allowing toemove one by one the unwanted handles and tunnels.
Let g be the genus of the surface M, defined as the num-er of handles and tunnels in M. g can be easily computedsing the Euler’s characteristic �(M) as g = (2 − �(M))/2, where(M) = V(M) − E(M) + T(M) and V(M), E(M) and T(M) are respectively
he number of vertices, edges and triangles in M.The algorithm (Algorithm 1) iteratively corrects the topology,
educing the genus of M by one at each step. After g corrections,lling the tunnels and cutting the handles, the new surface is home-morphic to a sphere.
Observe that in a first step the global algorithm is applied aimedt closing all the possible boundaries of the original surface. Theemoval of a handle or a tunnel is performed by first computing anpproximation of the shortest non-separating loop at each topo-ogical defect (detailed below and summarized in Algorithm 2). Aon-separating loop is a connected path that does not divide theurface into two connected components. The surface M is cut alonghe n edges of this identified loop, therefore adding n edges and nertices to the mesh. At this step, two new boundaries are createdut the Euler’s characteristic is not modified. The final correction iserformed by sealing the created boundaries with small discs, thusdding n edges n triangles and one vertex (we add an umbrella).his increases the Euler’s characteristic by one, globally reducinghe genus by one.
Algorithm 2 describes the computation of the shortest non-eparating loop. We first compute a set of basepoints B byropagating a wavefront from a randomly selected vertex (a seedoint) in M. B is defined as the set of vertices where the two wave-ront boundaries meet (Fig. 2a). The complement of B in M is a disc,mplying that any non-separating loop on M contains at least oneoint of B. Fig. 2b is an example of cut locus on a 2-genus surface.
Using this property we compute the non-separating loops fromll the vertices contained in the path B. This has been proved byrickson and Har-Peled (2002) as a good approximation of thehortest non-separating loop in M. Unlike the original approach,n which each point of B is used to compute a non-separating loop,
e perform this computation using propagations from a non-trivialet of points, which speeds-up the computation. As illustrated inig. 2b, the cut locus B is subdivided into a finite (and small) num-er of paths, like SB in Fig. 2c. For each of these paths, we compute
wavefront using Dijkstra’s algorithm (Dijkstra, 1959) from theontained points into the complement of B in M. When the twooundaries of this wavefront meet, an associated loop is computedrom the junction point going back to the initial wavefront seed.his, at each side of the junction. The non-separating property ofhis loop is verified by checking the number of connected compo-ents of the complement. Selecting a good approximation of the
hortest non-separating loop at each step guarantees a minimaltructural modification of the surface M. Fig. 3 shows topologicalorrections applied to a tunnel (Fig. 3a and b) and to two handlesFig. 3c and d).ce Methods 205 (2012) 96– 109
2.2. Partially flattened surfaces
A number of methods have been proposed in the literature forunfolding or flattening cortical surfaces (Drury et al., 1996; Fischlet al., 1999; Pons et al., 2004). In order for a flattening to be useful,it must preserve local and global metrics such as triangle anglesand areas. For our purposes we implemented a method based uponCARET (Drury et al., 1996; Tosun et al. 2004a). This method wascompared with the method implemented in Freesurfer (Bonneret al., 2009). In our implementation, a cortical surface is itera-tively deformed at each vertex according to mt+1
i= (1 − �)mt
i+
�mti, where mt
iis the position of vertex i for iteration t, � is a scalar
in the range [0,1] and mti
represents the average vertex position ofmt
i, given by
mti = 1∑
Stj
∑
j ∈ Ni
Stj Ct
j (1)
where Ni is the set of all triangles containing mi, cj is the centerof triangle j and Sj is its area. Typically a factor of 0.9 is chosen for�, giving more weigh to the averaged vertex position. This processmoves all mesh vertices toward the weighted average of the centersof their surrounding triangles. The deformation progresses until theglobal mean curvature k drops below a predefined threshold (Tosunet al., 2004a) or in our case using a predefined number of iterations(we used typically 400), obtaining similar shapes between mov-ing and fixed surfaces. Fig. 4(top) shows the different steps in theevolution of the PFS with the sulcal depth maps computed at eachstep. The color-coded sulcal depth map allows the visual localiza-tion of the main folding patterns. The sulcal depth map is computedas the cumulative path length at each point i as
depthi =∑
t=[1,...,N]
[mt+1i
− mti ] (2)
where N is the number of iterations. Fig. 4 (bottom) depicts the com-parison of area distortion after inflation using CARET and Freesurfer.
2.3. Surface-based non-rigid registration
Surface based non-rigid registration methods face several chal-lenges including: (i) the choice of similarity criterion and (ii)the matching and global optimization procedure (Audette et al.,2000). The first one refers to the type of information extractedfrom the 3D surface, namely the description of local or globalshape to represent the similarity. The latter challenge concernsthe exploitation of the similarity information to find the bestmatching between the two surfaces. In this context, the goal ofthe registration is to determine the transformation such that fora finite set of control points, any control point of a moving sur-face M, is mapped onto the corresponding control point of a fixedsurface M.
Fig. 5 illustrates the method used to register the moving M ={mi}i=1...p and fixed F = {fj}j=1...q
. PFS surfaces, respectively. F maybe a template toward which we register the whole population.Let Ms = {mk}k=1...u and F = {fl}l=1...v be the corresponding simpli-fied surfaces, represented in two subsets of characteristic points(control points) of M and F, such that Ms ⊆ M, Fs ⊆ F. After estab-lishing bijective correspondences between the sets Ms and Fs,exploiting a given similarity metric (in this paper the shape con-text), the mapping is computed as a set of transformations T ={Tk}k=1...u(Tk ∈ R3 → R3) such that fk = Tk ◦ mk, ∀ mk.
2.3.1. Shape contextThe shape context is a shape descriptor that, for a single sur-
face, captures the distribution of points over relative positions of
O. Acosta et al. / Journal of Neuroscience Methods 205 (2012) 96– 109 101
Fig. 4. Top: original cortical mesh is flattened to a PFS and color coded sulcal depth. (Eq. (2)) is mapped over each point in the surface as inflation progresses (20, 50 and 100iterations). (a) Original mesh, (b) 20 iterations, (c) 50 iterations, and (d) 100 iterations. Bottom: local area distortion map after inflation using CARET and Freesurfer.
Fig. 5. Finding correspondences between two individuals. After PFS are obtained, the surface M is registered toward the fixed F target. Ms and Fs are the control points tomatch.
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subjects met the Petersen criteria (Petersen et al., 1999) of subjec-tive and objective cognitive difficulties, in the absence of dementiaor significant functional loss. The remaining participants in thestudy were healthy elderly volunteers. All patients were recruited
5 http://aehrc.com/research/biomedical-imaging/medical-image-
02 O. Acosta et al. / Journal of Neur
he global shape points. This characterization is invariant to scalend rigid transformations, naturally leading to a highly discrimina-ive and robust score for measuring shape similarities. The shapeontext was first introduced in Belongie and Malik (2000) withinhe 2D pattern recognition field, and aimed to match point cloudsepresenting similar patterns. Further modifications to the methodppeared in Mori et al. (2005) and 3D matching of features haveeen extended to work with thoracic images (Urschler and Bischof,004). A first implementation of 3D Shape Context for brain regis-ration was presented in Acosta et al. (2010).
Let Ms and Fs the two simplified PFS surfaces corresponding tohe meshes M and F to be registered. Ms and Fs constitute the uontrol points (typically u = 3000 points) of the moving and fixedurfaces, respectively, to be matched and for which the shapeontext is computed (Fig. 5). Here, they are obtained using anlgorithm that iteratively contracts vertex pairs while minimizingeometric errors (Garland and Heckbert, 1997). For a given pointmk}k=1...u ∈ Ms, its shape context is the 3D histogram of the rela-ive 3D polar coordinates (�r, �, �) of the remaining u − 1 points. Asn Belongie et al. (2002), in order to be more sensitive to nearbyoints, we use a log-polar coordinate system. In our case we build
3D histogram with R�r equally spaced log-radius bins and u� andϕ equally spaced angle bins. Since the intracranial volume mayonsiderably differ across a population, an additional normaliza-ion of the shape context is performed to obtain scale invariance.o this end, all the radial distances dist(mk, ml)k,l=1...u, {k /= l}, areormalized by the mean distance between all the point pairs in thehape:
1u
∑
k, lk /= l
dist(mk, ml) (3)
.3.2. Cost function and matchingThe shape context cost CSC
i,jof matching the point mi from the
implified surface Ms with the point fj from Fs is given by the �2
tatistic as
SCi,j = 1
2
K∑
k=1
[hi(k) − gj(k)]2
hi(k) + gj(k)(4)
here hi(k) and gj(k) are the histograms (shape context) at theoints i and j of the moving Ms and fixed Fs shapes, respectively,nd K is the total number of bins.
In addition to the description given by the shape context, we usehe sulcal depth map computed at each point according to Eq. (2)o enrich the matching between the points with local informationbout sulci and gyri. Thus, in a second iteration we recompute theepth map cost function CSD
i,jas:
SDi,j = |sj − rj|
N(5)
here si and rj are the sulcal depths at points i and j of the moving Ms
nd fixed Fs shapes, respectively. Both are normalized by the brainize. N is the highest difference between the floating and the fixedormalized sulcal depths; this enables the comparison between theulcal depth and the shape context cost. The global cost functionecomes then:
i,j = CSCi,j + ˇCSD
i,j (6)
here = 1 − ˛, and in practical terms = 0.8, resulting in the best
rade-off for a good matching of the folds. Given the individualosts Ck,l ∈ [0, ..., 1] between all pairs of points, the next step iso find the perfect matching by minimizing the total cost of theijective correspondences H =∑C. This is done within a one to one
ce Methods 205 (2012) 96– 109
point matching step with the Hungarian algorithm (Kuhn, 1955).After the correspondences are found, the set of transformationsT = {Tk}k=1,..,u for each point are computed. Finally, a transfor-mation using a thin plate spline model (TPS) (Bookstein, 1989)calculated from the control points, achieves the interpolation ofthe corresponding moving shape M onto F. In our implementation,the number of points in Ms is lower than in Fs to avoid miscorre-spondences or topological errors due to crossing points betweenMs and Fs. Fig. 6 shows an example of labeling, propagated froma template to a single individual’s surface after registration of thecorresponding PFS.
3. Experiments and results
This section describes the experiments performed to validateeach step of the pipeline using real data and shows with an exam-ple the application on clinical data for quantifying atrophy inAlzheimer’s disease using cortical thickness. We also compared theresults with Freesurfer (Dale et al., 1999; Fischl et al., 1999; Fischland Dale, 2000). All the methods were implemented in C++, incor-porated in a plugin called MILXCTE devised to compute the corticalthickness as described in (Acosta et al., 2009), and MILXCTESurfacedevised to perform the surface analysis presented in this paper, andis part of our downloadable software platform MILXView®,5 andTAGLUT (Topological And Geometrical Library – a Useful Toolkit)6
(Favreau, 2009), which provides the topological and geometricaltools for genus zero mesh generation. MILXview utilises the opensource ITK7 and VTK8 libraries.
3.1. Data
3.1.1. Cross sectional MR scansFrom the Open Access Series of Imaging Studies (OASIS)
database (Marcus et al., 2007),9 we randomly selected 30 younghealthy individuals. The scans were T1-weighted MagnetizationPrepared RApid Gradient Echo (MP-RAGE) in sagittal orienta-tion with isotropic 1 mm3 resolution (256 × 256 × 128 pixels). Forthe first set of experiments, inflation and registration parts, thesegmentations of the WM/GM interface were computed usingFreesurfer. Thus, for each individual we obtained separated surfacerepresentations for left and right hemispheres. The SC was used toregister the surfaces to a common template, which was obtainedafter segmentation of the Colin atlas (Collins et al., 1998) withFreesurfer. The resulting meshes contained an average of 300,000vertices.
3.1.2. Clinical data in Alzheimer’s disease: the AIBL studyFor the application of the proposed method to the study of
Alzheimer’s disease, MR images from AD patients, individuals withmild cognitive impairment (MCI), and HC were included. They wererandomly selected from the individuals enrolled in the AlzheimerImaging Biomarkers and Lifestyle longitudinal (AIBL) study (EllisKathryn et al., 2009). The AD participants met NINCDS-ADRDA cri-teria for probable AD (McKhann et al., 1984) while all the MCI
analysis/milxview.6 http://www.jmfavreau.info/?q=en/taglut.7 http://www.itk.org/.8 http://www.vtk.org/.9 www.oasis-brains.org.
O. Acosta et al. / Journal of Neuroscience Methods 205 (2012) 96– 109 103
atient
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For the experiments using clinical data a different template wasobtained as an average surface representation of the populationbeing studied.
Table 1Average percentage of vertices with MA in range [0.8, 1.2].
Hemisphere CARET FreeSurferLeft
Frontal 49.31 38.67Temporal 45.77 37.69Occipital 39.94 31.92Parietal 46.67 32.86Total 42.41 32.94
RightFrontal 49.59 39.00
Fig. 6. Propagated labels from the template (d) to the p
rom the Austin Health Memory Disorders and Neurobehaviourallinics. All of the subjects were scanned with a standardized pro-ocol. Thus, sagittal T1 weighted MR images were acquired using
standard 3D MPRAGE sequence at 3T, with in-plane resolution × 1 mm, slice thickness 1.2 mm, TR/TE/T1 = 2300/2.98/900, flipngle 9◦ and field of view of 240 × 256 voxels and 160 slices.he protocol of acquisition and demographics are fully detailed inBourgeat et al., 2009). The SC was used to register the surfaces to
template, which was obtained as an average of a subsample (20ndividuals) randomly selected from the whole population.
.2. Partially inflated surfaces
Using the 30 young healthy individuals randomly selected fromhe OASIS database (Marcus et al., 2007), we first compared theesults of the inflation step with Freesurfer. In this experiment,egmentations of the WM/GM interface were computed usingreesurfer. Thus, for each individual we obtained separated sur-ace representations for left and right hemispheres. We evaluatedhe computation of PFS separately in terms of area preservation. Ahorough comparison of different methods using local and globalrea, angle and length distortions was presented in Bonner et al.2009). In this paper we only report the measured local metric dis-ortion in the 1-neighbourhood surrounding each mesh vertex. Theocal area distortion was defined for each vertex i as
ˆ A(i) =∑
t ∈ T A(t)∑t ∈ T A0(t)
(7)
nd the length distortion as
ˆ D(i) =∑
j ∈ N1dij∑
j ∈ N1d0
ij
(8)
here T is the set of triangles containing vertex i, N1 is the setertices in the 1-neighbourhood of i, A(t) is the area of triangle tnd A0(t) is the area of triangle t on the original mesh. This is a
easure of the average absolute change in area per triangle on theesh. d0in and din are the distances between vertex i and n on theriginal and modified surfaces, respectively. In our experiments,he implemented method for computation of PFS has been proven
(c) after the registration of both PFS surfaces (a and b).
(Bonner et al., 2009) to perform better than FreeSurfer (Fischl et al.,1999). Fig. 4 (bottom) depicts a comparison of the local area dis-tortion after inflation using CARET and Freesurfer. Averaging overthe 30 individual brains surfaces, it produced substantially fewerarea and distance distortions. 45.89% of vertex distortions rangedwithin [0.8, 1.2] (1.0 represents no distortion), compared to 34.83%for FreeSurfer. Table 1 shows the average portion of vertices withinthis range for each method, computed for all 30 subjects in the sam-ple space per lobe. Overall, the distance metric was distorted nearlyequally by both CARET and FreeSurfer (23.03 ± 0.86% for CARET vs23.11 ± 1.05% for FreeSurfer) whereas the area was distorted by32.7 ± 1.42% using CARET vs. 39.09 ± 1.71 with Freesurfer.
3.3. Shape context-based non rigid registration
The overall method was used to register the obtained surfaces toa common template. For the experiments described using OASIS thetemplate was obtained as a surface representation of the Colin atlas(Collins et al., 1998). This template was obtained with Freesurferapplying the segmentation pipeline to the initial Colin’s T1-W MRI.
Temporal 45.13 37.49Occipital 39.50 32.91Parietal 46.76 32.44Total 42.47 32.91
104 O. Acosta et al. / Journal of Neuroscience Methods 205 (2012) 96– 109
Table 2Averaged Hausdorff distance (HD), mean absolute distance (MAD) and area relation (% A M–F) betweeen moving M and fixed F surfaces after shape context registration. Mean(standard deviation), as the number of sampling control points varies. 30 left and 30 right hemispheres.
Left h Right h
NPts 500 1000 2000 500 1000 2000HD [mm] 8.45 (1.9) 7.25 (1.97) 6.29 (1.71MAD [mm] 0.74 (0.05) 0.49 (0.04) 0.35 (0.03% A 98.08% 98.45% 98.72%
Table 3Averaged (standard deviation) jaccard coefficient on some anatomical labels com-puted after registration with Shape Context (SC) and with Freesurfer (FS).
Region Hemisphere SC FS
Average St. Dev. Average St. Dev.
5 cuneus Left 0.54 0.08 0.66 0.065 cuneus Right 0.62 0.08 0.55 0.187 fusiform Left 0.55 0.10 0.58 0.137 fusiform Right 0.60 0.08 0.58 0.1010 isthmuscingulate Left 0.36 0.10 0.46 0.0910 isthmuscingulate Right 0.54 0.11 0.51 0.0811 lateraloccipital Left 0.66 0.04 0.63 0.0611 lateraloccipital Right 0.62 0.06 0.53 0.0812 lateralorbitofrontal Left 0.77 0.03 0.68 0.0612 lateralorbitofrontal Right 0.76 0.05 0.71 0.0417 paracentral Left 0.69 0.06 0.71 0.0717 paracentral Right 0.65 0.08 0.68 0.1220 parstriangularis Left 0.42 0.09 0.60 0.0920 parstriangularis Right 0.46 0.12 0.59 0.0924 precentral Left 0.71 0.06 0.82 0.0324 precentral Right 0.73 0.05 0.68 0.1425 precuneus Left 0.69 0.05 0.78 0.0425 precuneus Right 0.71 0.05 0.70 0.0830 superiortemporal Left 0.69 0.05 0.77 0.0330 superiortemporal Right 0.67 0.06 0.72 0.05
ttqe
TA
34 transversetemporal Left 0.56 0.11 0.76 0.0734 transversetemporal Right 0.43 0.11 0.70 0.11
In the first experiment using the OASIS database, we inves-
igated the effect of the number of control points (u) employedo represent the simplified surfaces Ms and Fs on the registrationuality. Mean absolute (MAD) and Hausdorff (HD) distances (Gerigt al., 2001) between moving and target surfaces were used toable 4verage (standard deviation) cortical thickness, computed with MILXCTE and Freesurfer
Structure MILXCTE F
Average (mm) St. Dev. A
Supramarginal L 2.38 0.20 2Supramarginal R 2.38 0.17 2Superiorfrontal L 2.49 0.17 2Superiorfrontal R 2.54 0.20 2Rostralmiddlefrontal L 2.32 0.18 2Rostralmiddlefrontal R 2.36 0.18 2Rostralanteriorcingulate L 2.62 0.32 2Rostralanteriorcingulate R 2.67 0.29 2Precuneus L 2.53 0.27 2Precuneus R 2.45 0.26 2Precentral L 2.21 0.28 2Precentral R 2.26 0.27 2Posteriorcingulate L 2.57 0.24 2Posteriorcingulate R 2.49 0.21 2Pericalcarine L 2.29 0.29 1Pericalcarine R 2.2 0.25 1Pars triangularis L 2.41 0.15 2Pars triangularis R 2.3 0.16 2Inferior temporal L 2.87 0.36 2Inferior temporal R 2.76 0.29 2Inferior parietal L 2.48 0.24 2Inferior parietal R 2.35 0.22 2Superiorfrontal L 2.45 0.17 2Superiorfrontal R 2.50 0.20 2
) 14.97 (7.13) 13.24 (7.83) 13.11 (8.25)) 1.17 (0.58) 0.86 (0.61) 0.74 (0.83)
97.02% 97.72% 98.8%
assess the accuracy of our method to register two PFSs. Table 2presents a summary of these results. By Increasing u from 500 to1000 control points the accuracy in terms of mean absolute distance(MAD) was improved by 33% (p < 0.0001) and by 32% (p < 0.0001)when varying from 1000 to 2000 points for the left hemisphereand 23% (p < 0.0001) and 27% (p < 0.01), respectively, for the righthemisphere. As expected, surface alignment is better when usingmore control points. A trade-off between computational require-ments and accuracy exists and must be defined depending on theapplication.
3.3.1. Overlap with Freesurfer labelingIn this experiment, we compared the localization of Freesurfer
labeled regions (obtained as described in Desikan et al. (2006)) afterregistration to the same template (Fig. 6). The Jaccard coefficientmeasured as the relation between the intersection and union ofareas of labeled regions was used as the similarity metric. Over-all, our method is comparable with the registration provided withFreesurfer. Averaging for the 30 individuals, in 6 regions of the lefthemisphere and 6 of the right hemisphere the overlap (Jaccard)obtained with our method was higher than with Freesurfer. In otherregions the accuracy was lower than with Freesurfer but in mostof them these differences they were not statistically significant,except for the entorhinal cortex, middle temporal, pars triangularisand transverse temporal (Desikan et al., 2006) in both hemispheres.Table 3 shows some examples of the jaccard coefficient averaged
on the 30 individuals. The worst values were obtained in the small-est regions, where the overlap is highly affected by misregistrationerrors. Conversely in larger areas the overlap was fairly good, andthe main folds were well aligned. It is important to notice that theand correlation between both methods in the AAL Regions.
reesurfer Comparison
verage (mm) St. Dev. Difference (mm) r
.45 0.13 0.07 0.69
.45 0.14 0.07 0.65
.59 0.12 0.01 0.64
.54 0.11 0 0.73
.28 0.11 −0.04 0.72
.25 0.10 −0.11 0.67
.64 0.21 0.02 0.68
.52 0.18 −0.15 0.78
.28 0.15 −0.25 0.79
.28 0.14 −0.17 0.8
.43 0.13 0.22 0.72
.38 0.15 0.12 0.83
.38 0.14 −0.19 0.57
.33 0.12 −0.16 0.72
.74 0.12 −0.55 0.65
.76 0.12 −0.44 0.72
.32 0.11 −0.09 0.65
.34 0.12 −0.04 0.62
.67 0.15 −0.2 0.6
.77 0.18 −0.01 0.55
.38 0.14 −0.10 0.86
.39 0.15 0.04 0.86
.59 0.12 0.14 0.80
.54 0.11 0.04 0.75
O. Acosta et al. / Journal of Neuroscience Methods 205 (2012) 96– 109 105
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Fig. 7. Regional mapping of the correlation (r) between cortical thickness co
tatistical analysis will be performed later at a voxel basis. Fig. 6llustrates an example of propagated labels between an individualnd the template. It can be observed that although there is a highnterindividual variability, the regions are well transferred throughll the foldings representing different anatomical regions.
.4. Clinical data: AIBL study
Following the procedure detailed in Section 2, consensus seg-entations were obtained as described in Bourgeat et al. (2009)
sing nine atlases for initialization. Subsequently, cortical thick-ess maps were computed using our voxel-based approach (Acostat al., 2009). The individuals’ Automated anatomical labelingAAL) (Tzourio-Mazoyer et al., 2002) and cortical thickness wereropagated to the resulting mesh and then to the average templatefter the SC registration.
As an example to describe the matching of similar regions of therain, we randomly selected 26 individuals. Their consensus AAL
abelings, obtained in the previous step, were propagated towardhe template applying the whole pipeline. The labelings were thenombined in a voting scheme to obtain a final AAL labeling in theemplate space (Fig. 9). After the registration, consistency in the
ig. 8. Example of correlations in some regions left/right hemispheres. (a and b) SFG: supright H), r = 0.75] [IPG (left H), r = 0.86] [IPG (right H), r = 0.86] (corrected values).
ed with both methods: MILXCTE and Freesurfer, left and right hemispheres.
coincidence of the major folding patterns was obtained across theindividuals.
3.4.1. Cortical thickness comparison with FreesurferCortical thickness maps from 50 individuals obtained with FS
and MILXCTE (Acosta et al., 2009) were compared. After registra-tion and mapping to the common template, the thickness mapswere regionally compared. Cortical thickness was comparable inall the regions. Similar patterns for thickness in gyri and sulci wereobtained. Overall, a strong correlation between the results usingboth methods FS and MILXCTE was found. In average, for all theregions the absolute computed difference was 0.23 mm (r = 0.63)for the left hemisphere and 0.17 mm (r = 0.65) for the right. Table 4shows the results for some of the regions, left and right hemi-spheres.
Fig. 7 shows the results of the correlations (r) for all the regions.Similar results were obtained in both hemispheres. Some examplesof the individuals’ thickness computed with MILXCTE and FS are
depicted in Fig. 8. As suggested in Klauschen et al. (2009) Fresurfertends to underestimate gray matter, therefore the computed thick-ness with our method tends to be higher. Although the slope inFig. 8 is leaning toward the higher values of CTE, the correlationserior frontal gyrus, (c and d) IPG: inferior parietal gyrus [SFG (left H), r = 0.80] [SFG
106 O. Acosta et al. / Journal of Neuroscience Methods 205 (2012) 96– 109
F commt ent. Tt
ampabStca
ig. 9. Top: resulting AAL labeling after voting using a population labels mapped to ahickness mapped onto a common template: a HC individual, bottom: an AD patiemporal areas.
re still high as shown in Table 4. In MILXCTE the thickness esti-ation is entirely voxel-based with a sub-voxel initialization using
artial volume maps (Acosta et al., 2009). This makes it very fast andccurate whereas FS is based on meshes deformations which maye computationally expensive. Not surprisingly, larger regions:
upramarginal (2400 vertices), Inferior parietal (4200), superioremporal (2600), superior frontal (4500) presented the highestorrelations as opposed to smaller regions such as rostralnterior cingulate (400), frontal pole (60) or caudal anteriorFig. 10. Top: vortex-wise differences in averaged cortical thickness between the two
on template. Right and left hemispheres, lateral and medial views. Middle: corticalhe pronounced generalized atrophy in AD compared to a HC is visible, mainly in
cingulate (813) where small overlap differences may affect themeasure.
3.4.2. Study of cortical thickness in Alzheimer’s diseaseWe also investigated the ability of our method to detect cortical
thickness differences between 81 healthy elderly individuals HC,and 32 AD patients. Fig. 9 shows an example of cortical thicknessmaps from two individuals, one from each group, propagated to thecommon template.
groups AD and HC. Bottom: statistical p-values map after two-sampled t-test.
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O. Acosta et al. / Journal of Neur
After applying the whole pipeline to all the individuals, vertex-ise t-tests were performed between NC and AD to identify regionshere a significant atrophy existed. The cortical thickness valuesere corrected for age and False Discovery Rate (FDR) corrected
-values were obtained (5% threshold). In our experiments, thenalysis was performed using the thickness maps with a Lapla-ian smoothing (5 mm full width at half of the maximum – FWHM)ver the scalar cortical thickness maps to reduce the effects ofiscontinuities. The obtained differences between the two groupsre illustrated in Fig. 10 and demonstrated qualitatively the con-istency of the results. The results show significant differencesetween the two groups, with lowest thickness for the AD groupith both methods. Significant differences were found in the hip-ocampus, parahippocampus, cingulate and in the temporal androntal lobes between the two groups. In average, the absolute dif-erences in cortical thickness for some regions were higher by usingur method, as it can be seen in Fig. 10 and in Table 4. These resultsorroborate what has been previously reported in the literature forlzheimer’s disease (Lerch and Evans, 2005; Querbes et al., 2009).
. Conclusion
In this paper we presented a new cortical surface processingipeline, MILXCTE, for accurate statistical regional analysis. It offersn alternative to traditional methods using surface representationsf the brain such as Freesurfer. It involved several steps, namely MRIegmentation, surface generation, topology correction, inflationnd surface matching, yielding a representation of a whole pop-lation in a common space. In addition to the shape context whichrovides a global description at a local level, we included additional
ocal landmarks, such as the sulcal depth map, to iteratively adjusthe registration, yielding a meaningful matching between lobes. Anpdate of the binary distribution of MILXCTE, MILXCTESurface andILXView® is available.10
We demonstrated the validity of the method for use in clinicaltudies, by evaluating each step separately on real data, and thenomparing the overall technique against Freesurfer. This compari-on showed that the labeling of major folding patterns is preservednd the cortical thickness computed by using our method is region-lly consistent. In average, with Freesurfer the obtained values ofortical thickness were lower than with MILXCTE for single indi-iduals. This is not a surprising finding as it has been previouslyhown and reported in larger studies. Our method performs theomputation of cortical thickness in the voxel domain, which isery fast. Additionally, it uses advantageously the partial volumenformation to initialize at a subvoxel level, thereby yielding a veryccurate result. However, a good correlation between both mea-ures were found and different experiments comparing averagedortical thickness between two populations allowed to measure theelative differences of atrophy. This preliminary study on clinicalata showed regional differences between healthy elderly individ-als and Alzheimer’s disease patients. The most significant atrophyas measured in the temporal lobe, which is consistent with theublished literature.
We intend to perform longitudinal clinical studies onlzheimer’s disease and other neurological disorders. As similaresults were found in regional comparisons with Freesurfer, ourethod represents an alternative for the study of cortical thickness
stimation across a population.
As the method allows the mapping of a whole population in aommon space, in future work we will perform multi-feature com-arison of additional imaging biomarkers for Alzheimer’s disease.
10 http://aehrc.com/research/biomedical-imaging/medical-image-nalysis/milxview.
ce Methods 205 (2012) 96– 109 107
Thus, not only cortical thickness is compared but also other featuresfrom different modalities such as sulcal depth, WM/GM MRI con-trast, GM volume, �-amyloid burden or WM integrity in the samevertex-wise common space.
Algorithm 1. Topological correction
Data: a mesh MResult: M homeomorphic to a sphereForeach b∈boundaries (M) do
b∈boundaries (M) Close the surface on b by adding a disc;While genus (M) /= 0 do
l = an approximation of the shortest non-separating loop;Cut M according to l;Close the surface on each side of the created boundaries by
adding a disc;
Algorithm 2. Non-separating loop detection
Data: a mesh M non homeomorphic to a sphereResult: a non-separating loop l
B reduced cut locus;Foreach: path p ⊂ B do
lp = shortest no-separating loop containing p;if l not defined or length (lp) < length (l) then
l = lp;
Appendix A. Supplementary data
Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.jneumeth.2011.12.011.
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