ACCURATE NONLINEAR MAPPING BETWEEN MNI152/COLIN27 VOLUMETRIC AND FREESURFER SURFACE COORDINATE SYSTEMS

Transcription

1 ACCURATE NONLINEAR MAPPING BETWEEN MNI152/COLIN27 VOLUMETRIC AND FREESURFER SURFACE COORDINATE SYSTEMS WU JIANXIAO (B.Eng. (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2018 Supervisor: Dr. Yeo Boon Thye Thomas Examiners: Associate Professor Ong Sim Heng Dr. Yen Shih-Cheng

2 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Wu Jianxiao 7 Feburary 2018

3 ACKNOWLEDGEMENT I would like to thank Bin Bin Tang for assistance with testing several algorithms. This work was supported by Singapore MOE Tier 2 (MOE2014-T ), NUS Strategic Research (DPRT/944/09/14), NUS SOM Aspiration Fund (R ), Singapore NMRC (CBRG/0088/2015), NUS YIA and the Singapore National Research Foundation (NRF) Fellowship (Class of 2017). Data were also provided by the Brain Genomics Superstruct Project of Harvard University and the Massachusetts General Hospital (Principal Investigators: Randy Buckner, Joshua Roffman, and Jordan Smoller), with support from the Center for Brain Science Neuroinformatics Research Group, the Athinoula A. Martinos Center for Biomedical Imaging, and the Center for Human Genetic Research. Twenty individual investigators at Harvard and MGH generously contributed data to the overall project. Our research also utilized resources provided by the Center for Functional Neuroimaging Technologies, P41EB and instruments supported by 1S10RR023401, 1S10RR019307, and 1S10RR from the Athinoula A. Martinos Center for Biomedical Imaging at the Massachusetts General Hospital. Additional support was provided by the NIH Blueprint for Neuroscience Research (5U01-MH093765), as part of the multi-institutional Human Connectome Project.

4 TABLE OF CONTENTS SUMMARY... I LIST OF FIGURES... II 1. INTRODUCTION THESIS STRUCTURE BACKGROUND MAGNETIC RESONANCE IMAGING BRAIN ATLASES IMAGE REGISTRATION METHODS METHODS DATA AND PRE-PROCESSING RECOMMENDED FREESURFER METHODS REGISTRATION FUSION METHOD Index volumes Volumetric registration Average mapping ASYMMETRY IN MAPPING EVALUATION MNI152/COLIN27-TO-FSAVERAGE EVALUATION FSAVERAGE-TO-MNI152/COLIN27 EVALUATION INVERSE CONSISTENCY EVALUATION RESULTS MNI152-TO-FSAVERAGE RESULTS FSAVERAGE-TO-MNI152 RESULTS INVERSE CONSISTENCY RESULTS DISCUSSION CONCLUSION BIBLIOGRAPHY APPENDIX A. LIST OF PUBLICATIONS... 63

5 SUMMARY The results of most neuroimaging studies are reported in volumetric or surface coordinate systems. Accurate mappings between them can facilitate many applications, such as projecting fmri group analyses in volume to a surface space for visualisation, or projecting surface resting-state fmri parcellations to a volumetric space for analysis of new data. However, there has been surprisingly little research on this topic. Here we evaluated three approaches for mapping data between MNI152/Colin27 volumetric and fsaverage surface coordinate systems by simulating the above applications. Two of the approaches are currently widely used. A third approach (registration fusion) was proposed a number of years ago, but has not been widely adopted. Two implementations of the registration fusion (RF) approach were considered, with one implementation utilising the Advanced Normalisation Tools (ANTs). We found that RF-ANTs performed the best, even for new subjects registered using a different software tool (FSL FNIRT). i

6 LIST OF FIGURES FIGURE 1 LEFT SUPERIOR TEMPORAL SULCUS IN THREE SUBJECTS' BRAINS, SHOWN IN SAGITTAL VIEW... 1 FIGURE 2 WHITE AND GREY MATTER SEGMENTATION FOR THREE SUBJECTS CORTEX. GREEN LINES ARE THE BOUNDARIES OF WHITE MATTER, WHILE BLUE LINES ARE THE BOUNDARIES OF GREY MATTER... 6 FIGURE 3 THE TALAIRACH ATLAS... 7 FIGURE 4 THE 6TH GENERATION NONLINEAR MNI152 TEMPLATE... 8 FIGURE 5 THE COLIN27 TEMPLATE... 9 FIGURE 6 EUCLIDEAN DISTANCE DOES NOT REFLECT THE FUNCTIONAL SIMILARITY, ESPECIALLY BETWEEN POINTS ON OPPOSITE BANKS OF A SULCUS. GEODESIC DISTANCE ALONG THE CORTICAL SURFACE IS MORE SUITABLE FOR MEASURING FUNCTIONAL PROXIMITY FIGURE 7 THE SPHERICAL COORDINATE SYSTEM OF FSAVERAGE TEMPLATE, OVERLAY ON (FROM LEFT TO RIGHT) THE SPHERICAL SURFACE, THE PIAL SURFACE, THE INFLATED WHITE SURFACE, AND THE FLATTENED SURFACE FIGURE 8 ILLUSTRATION OF HOW THE DEMONS GUIDE THE MOVING IMAGE INTO THE STATIC (TARGET) IMAGE FIGURE 9 ILLUSTRATION OF HOW SYN ACHIEVES DIFFEOMORPHISM. THE TWO IMAGES, I AND J ARE REGISTERED TO THE MEAN SHAPE BETWEEN THEM BY 1 AND 2. A FULL MAPPING FROM I TO J CAN BE OBTAINED BY CONCATENATING 1 AND THE INVERSE OF FIGURE 10 THE REGISTRATION FUSION (RF) PROCEDURE. EACH SUBJECT IS MAPPED TO (A) THE MNI152 OR COLIN27 TEMPLATE, AND (B) THE FSAVERAGE SURFACE. BY CONCATENATING THE TWO MAPPINGS, WE OBTAIN AN INDIVIDUAL MAPPING BETWEEN MNI152/COLIN27 AND FSAVERAGE THROUGH EACH SUBJECT FIGURE 11 THE X-INDEX VOLUME SHOWN IN FREEVIEW. THE TOP ROW SHOWS THE AXIAL VIEW. THEO BOTTOM ROW SHOWS, FROM LEFT TO RIGHT, THE SAGITTAL VIEW, THE CORONAL VIEW, AND THE 3D VIEW FIGURE 12 PROCEDURE FOR THE 2011 IMPLEMENTATION FIGURE 13 (A) TIGHT CORTICAL MASK, (B) LOOSE CORTICAL MASK, AND (C) THE DIFFERENCE BETWEEN LOOSE AND TIGHT MASKS, OVERLAY ON MNI152 BRAIN ii

7 FIGURE 14 PROJECTED PARCELLATION BEFORE GROWING (LEFT) AND AFTER GROWING (RIGHT) FIGURE 15 (A) GROUND TRUTH FSAVERAGE PROBABILISTIC MAP FOR SUPERIOR TEMPORAL SULCUS (B) ANTS-DERIVED MNI152 PROBABILISTIC MAP FOR SUPERIOR TEMPORAL SULCUS FIGURE 16 (A) FSAVERAGE WINNER-TAKES-ALL PARCELLATION (B) "GROUND TRUTH" MNI152 WINNER-TAKES-ALL PARCELLATION FIGURE 17 VISUALISATION OF PROJECTED ANTS-DERIVED MNI152 PROBABILISTIC MAPS IN MIDDLE POSTERIOR CINGULATE, POST DORSAL CINGULATE GYRUS, CENTRAL SULCUS, AND SUPERIOR PRECENTRAL SULCUS. THE BLACK OUTLINES CORRESPOND TO THE "GROUND TRUTH" FSAVERAGE PARCELLATION. THE VALUE BELOW EACH BRAIN SHOWS THE NAD VALUE OF THAT PROJECTION, WITH THE BEST ACROSS ALL APPROACHES IN BOLD FIGURE 18 VISUALISATION OF PROJECTED FNIRT-DERIVED MNI152 PROBABILISTIC MAPS IN MIDDLE POSTERIOR CINGULATE, POST DORSAL CINGULATE GYRUS, CENTRAL SULCUS, AND SUPERIOR PRECENTRAL SULCUS. THE BLACK OUTLINES CORRESPOND TO THE "GROUND TRUTH" FSAVERAGE PARCELLATION. THE VALUE BELOW EACH BRAIN SHOWS THE NAD VALUE OF THAT PROJECTION, WITH THE BEST ACROSS ALL APPROACHES IN BOLD FIGURE 19 NAD RESULTS FOR ANTS-DERIVED AND FNIRT-DERIVED MNI152 MAPS. EACH BAR REPRESENTS THE MEAN NAD VALUE ACROSS ALL AREAS IN LEFT HEMISPHERE (BLACK) AND RIGHT HEMISPHERE (RIGHT). THE ERROR BARS REPRESENT STANDARD ERROR FIGURE 20 VISUALISATION OF PROJECTED FSAVERAGE WINNER-TAKES-ALL PARCELLATION, COMPARED AGAINST ANTS-SIMULATED WINNER-TAKES- ALL "GROUND TRUTH" (BLACK OUTLINE) FIGURE 21 VISUALISATION OF PROJECTED FSAVERAGE WINNER-TAKES-ALL PARCELLATION, COMPARED AGAINST FNIRT-SIMULATED WINNER-TAKES- ALL "GROUND TRUTH" (BLACK OUTLINE) FIGURE 22 DICE RESULTS FOR PROJECTED WINNER-TAKES-ALL PARCELLATION IN COMPARISON TO ANTS-SIMULATED AND FNIRT-SIMULATED "GROUND TRUTH" SEGMENTATION. EACH BAR REPRESENTS THE MEAN DICE VALUE ACROSS ALL AREAS IN LEFT HEMISPHERE (BLACK) AND RIGHT HEMISPHERE (RIGHT). THE ERROR BARS REPRESENT STANDARD ERROR FIGURE 23 NAD RESULTS FOR ANTS-DERIVED AND FNIRT-DERIVED COLIN27 MAPS. EACH BAR REPRESENTS THE MEAN NAD VALUE ACROSS ALL AREAS IN LEFT HEMISPHERE (BLACK) AND RIGHT HEMISPHERE (RIGHT). THE ERROR BARS REPRESENT STANDARD ERROR iii

8 FIGURE 24 DICE RESULTS FOR PROJECTED WINNER-TAKES-ALL PARCELLATION IN COMPARISON TO ANTS-SIMULATED AND FNIRT-SIMULATED "GROUND TRUTH" SEGMENTATION. EACH BAR REPRESENTS THE MEAN DICE VALUE ACROSS ALL AREAS IN LEFT HEMISPHERE (BLACK) AND RIGHT HEMISPHERE (RIGHT). THE ERROR BARS REPRESENT STANDARD ERROR FIGURE 25 MEAN EUCLIDEAN DISTANCE MEASURE IN MM, FOR LEFT HEMISPHERE (BLACK) AND RIGHT HEMISPHERE (WHITE) iv

9 1. INTRODUCTION A powerful imaging technique, Magnetic Resonance Imaging (MRI) has been widely used in medical diagnosis and research. This non-invasive technique can produce images with high spatial resolution without exposing the subject to ionizing radiation. In the neuroscience field specifically, the structural MRI (smri) images generated can be used to study brain anatomy under healthy condition or deformation for subjects with brain diseases. For studies of brain activity, functional MRI (fmri) techniques are commonly used. Specifically, the Blood Oxygenation Level Dependent (BOLD) signal offers both great spatial resolution and great temporal resolution. For both structural and functional MRI studies, it is common to report results in a standard coordinate system [1] [2] [3] [4] [5] [6] [7]. This is because brain anatomy can differ drastically between different individuals; the same coordinate in different brains may be in different brain structures. As a result, data obtained in an individual s brain cannot be compared directly to those in another individual s brain. For example, the superior temporal sulcus regions in three different indivisual brains are shown in Figure 1. It is obvious that the coordinate of voxels in the superior temporal sulcus are not comparable across the three individuals. In order to generalise research results across individuals, Figure 1 Left superior temporal sulcus in three subjects' brains, shown in sagittal view 1

10 many brain atlases have been created to be used as standard coordinate systems. By warping individual brain image to a brain atlas, data in the individual brain can be mapped to the atlas coordinate system and be analysed using the atlas coordinate system with data from other individuals brains. For example, a brain activation study can report the coordinates of peak activations in a standard coordinate system, making it much easier for comparison with other studies and for meta-analysis. Image registration between brain atlases, hence, is crucial in facilitating neuroscience studies. Numerous image registration tools have been developed for warping brain image of individuals to a common template [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]. In general, nonlinear deformation algorithms can achieve reasonable accuracy within the resolution limits of screening equipment. Nevertheless, it should be noted that there are two types of standard coordinate system, volumetric and surface (see Section 2.2 for more details about brain coordinate systems). While there have been tremendous research efforts on mapping data from individual subjects into common coordinate systems, there is significantly less work on mappings between coordinate systems [20] [21], especially between volumetric and surface coordinate systems. Importance for the latter type of mappings should not be overlooked as it has many useful applications. Specifically, it would help to connect research done exclusively in volumetric space and those done exclusively in surface space, both of which are common in the field. A reason behind the lack of mappings between volumetric and surface coordinate systems is that there is usually no optimal way to do it. As analysis 2

11 conducted in a volumetric coordinate system requires data from individuals to be projected to and averaged in the standard coordinate space. This means that irreversible errors would have been incurred during the projection and averaging process. Therefore, any mapping from volumetric space to surface space directly cannot possibly be perfect. Indeed, if analysis in a surface coordinate system is needed, the optimal way is to project individual data to the standard surface coordinate space and average them. As surface-based registration generally incurs negligible errors by respecting the 2D topology of the cerebral cortex [22] [23] [24] [25] [26] [27] [28] [29], this ensures almost perfect data for analysis in surface space. Nevertheless, we should be aware that a large amount of research results has already been analysed and reported in volumetric coordinate space. Since optimal methods would not be available in dealing with these findings (or legacy data), an accurate mapping between volumetric and surface coordinate system would be extremely useful in this case. Possible applications include mapping existing data in volumetric coordinate space to surface for visualisation [30] [31] [32], or mapping surface parcellation (or network) [33] [34] [35] [36]to a volumetric coordinate space to aid analysis of these existing data. In this thesis, we evaluate three different approaches for mapping between volumetric and surface coordinate systems; specifically, we evaluate mappings between MNI152/Colin27 volumetric coordinate system and fsaverage surface coordinate system (also known as the Freesurfer surface coordinate system). In particular, we consider a previously proposed 3

12 registration fusion (RF) approach [37] [33] and implement it using two powerful registration tools, FreeSurfer [38] and Advanced Normalisation Tools (ANTs) [39]. We test these two variants of the RF approach against two existing approaches commonly recommended by experts in the field. By simulating actual applications of such mappings, our evaluation of these approaches provide error bounds on common procedures in the literature and guide the adoption of best practices. 1.1 THESIS STRUCTURE The thesis is organised as follows. Chapter 2 introduces the background of this research, including MRI techniques, brain atlases and image registration methods. This chapter focuses on image registration between individual brain and standard template. Chapter 3 describes existing methods and the method proposed in this study for image registration between volumetric and surface coordinate systems. This includes two approaches commonly recommended by experts and two variants of our proposed methods. Chapter 4 describes the evaluation tests used to compare the existing and new methods. Besides testing the registration accuracy, an inverse consistency test is also carried out to assess the robustness of the methods. Chapter 5 presents the results of the evaluation tests. Chapter 6 presents the discussion and identifies future research direction. 4

13 2. BACKGROUND 2.1 MAGNETIC RESONANCE IMAGING MRI is a non-invasive clinical scanning technique, which can be used to obtain 3-dimensional (3D) images of the human brain. The MRI machine creates strong electromagnetic field that can interact with atomic nuclei with an odd number of protons and neutrons [40]. Such nuclei act as magnetic dipoles and will align their spin axes to external magnetic field. The scanner in the MRI machine measures the time for the spin axes to align with the electromagnetic field, and the time for them to fall back to random state when the electromagnetic field is switched off [40]. For example, hydrogen atoms in water and fats contain single-proton nuclei that will interact with the magnetic field. The human brain consists of ventricles and two main type of tissues, grey matter and white matter. Macroscopically, the human brain can also be divided into the cerebrum, the cerebellum and the brain stem. The main subject of neuroscience studies, the cerebrum, consists of two hemispheres, each of which consists of four lobes. The hemispheres contain mainly white matter interior and is covered by a sheet of grey matter called the cerebral cortex. An advantage of MRI is that it can make use of different measurements to generate images with good contrast between different tissue types, as the tissues contain different proportion of water and fat [41]. For example, structural MRI studies usually make use of T1-weighted images which shows grey matter as dark grey and white matter as light grey. This type of images shows the longitudinal relaxation time (T1 time) at each 5

14 part of the brain, which measures how long the spin axes take to realign with the electromagnetic field after switching off and on again. As carbon molecules in fatty acid provide more efficient energy transfer, causing neighbouring hydrogen atoms to realign spin axes faster, T1 time in fat is shorter compared to that in water [40]. The smri images are reconstructed from the measurements by multiplication with sine and cosine function for demodulation [40]. The signals are then processed by low-pass filtering and inverse Fourier transform [40]. The final result is a 3D image in the form of 2-dimensional (2D) slices. These images can have resolution of down to 1mm, making them suitable for studying the brain anatomy. Furthermore, due to the clear contrast, the T1-weighted images are often used for segmentation of brain into substructures. Figure 2 shows the white and grey matter segmentation, using FreeSurfer [38] [22] [5], for the three individual brains shown in Figure 1, based on their T1-weighted images. The intensity difference between white and grey matter can be clearly observed in all three brains. Figure 2 White and grey matter segmentation for three subjects cortex. Green lines are the boundaries of white matter, while blue lines are the boundaries of grey matter. Based on the MRI techniques, the functional MRI techniques have been developed and widely used by neuroscience researchers, the most popular of which is the BOLD contrast imaging. The BOLD signal tracks the blood 6

15 oxygenation level in the brain by making use of the haemoglobin s magnetic properties [42]. The variation of blood oxygenation level has been found to reflect onsets and offsets of activities in the cerebral cortex, since such activities in a brain region cause increased blood flow to that region [43]. Hence the BOLD signals can be used to study cerebral activities in different parts of the brain, with fine temporal resolution. 2.2 BRAIN ATLASES As aforementioned, group studies in neuroscience usually report their findings in a common coordinate system, so that results across individuals and across studies can be comparable. Brain coordinate systems based on brain atlases (or templates) are developed to this end. The first brain atlas was created by Talairach and Szikla in 1967 [1]. In 1988, Talairach and Tournoux created the second edition of this atlas, known as the Talairach-Tournoux system (see Figure 3) [2], based on a single post-mortem brain. This brain template has Figure 3 The Talairach atlas 7

16 become widely used since then; many studies report their results in the form of coordinates in Talairach space. Brain templates developed later are usually linearly registered to the Talairach space for better compatibility. However, an inevitable problem with the Talairach brain is that it uses only one brain to construct the template. This means the template would not be representative of the population [44]. As a result, a new type of brain atlas was created, based on average brain across individuals. In 1993, the Montreal Neurological Institute (MNI) created a brain template by averaging 305 individual brains [45]. This atlas is named MNI305, which became the standard template to map to for years. In 2001, an improved version of MNI305 template was generated as part of a project by the International Consortium of Brain Mapping (ICBM) [46] [47]. This new template used 152 scans of different subjects with higher resolution and was hence called the MNI152 template (see Figure 4). This template has since become the most popular template, distributed in many Figure 4 The 6th generation nonlinear MNI152 template 8

17 standard software and toolboxes, like FMRIB s Software Library (FSL) [48]. Among the many version distributed, most are linearly or nonlinearly registered to the MNI305 space. In this study, we make use of the 6th generation nonlinear MNI152 template from FSL version [49]. Despite the popularity of population-average templates like MNI152, templates based on single brain are preferred in certain areas. Specifically, the population-average templates tend to have abnormal anatomy and insufficient anatomical details, due to averaging across subjects. A commonly used singlesubject template is Colin27 (or sometimes known as MNI single subject, see Figure 5), which was based on 27 scans of an individual [50]. The average image of the 27 scans was registered to the MNI305 space, resulting in a highresolution template with clear anatomical details. In this study, we make use of the Colin27 template from the Statistical Parametric Mappings (SPM) Anatomy Toolbox version 2.2c (see Figure 5) [51]. Figure 5 The Colin27 template Finally, a very different type of brain atlas is a surface atlas, compared to MNI152, Colin27, etc. which are volumetric atlases. The motivation for constructing surface atlas is to facilitate study of cerebral activities. The volumetric systems are inadequate because they are 3-dimensional (3D) spaces, where the distance between two points are measured by 3D Euclidean distance. 9

18 Such measure is inaccurate for points on the cortical surface, as more than half of the area of the cerebral cortex are buried in folds (also called sulci) [22]. For example, Figure 6 shows two points on opposite banks of a sulcus. They can seem close by Euclidean distance, but might belong to entirely different brain region. In order to characterise the topology of 2D cortical surface, surface Figure 6 Euclidean distance does not reflect the functional similarity, especially between points on opposite banks of a sulcus. Geodesic distance along the cortical surface is more suitable for measuring functional proximity. models need to be established, where geodesic distance along the surface can be calculated between points on the surface. The most popular surface atlas is the fsaverage template from FreeSurfer software [22] [5]. This atlas was created by registering and averaging across 40 subjects cortex. The FreeSurfer software also provides a surface reconstruction function (recon_all) which can extract and reconstruct the cortical surface of any individual brain. The reconstructed surface can then be registered to the fsaverage surface to be compared with other individual brains (mri_surf2surf; second surface in Figure 7). This is an optimal way of fmri data analysis as surface-based registrations generally incur very little registration errors [24] [26] 10

19 [29]. Besides, the fsaverage template has inflated and spherical forms [22]. The former is very useful for visualisation of data, as areas in sulci can be seen clearly (third surface in Figure 7). The latter provides a spherical coordinate system which situates points on the surface in 3D space, so that both geodesic and Euclidean operations can be performed on the points coordinates (first surface in Figure 7). Lastly, a flattened form is produced but rarely used (last surface in Figure 7). In this study, we make use of the fsaverage template from FreeSurfer version Figure 7 The spherical coordinate system of fsaverage template, overlay on (from left to right) the spherical surface, the pial surface, the inflated white surface, and the flattened surface. 2.3 IMAGE REGISTRATION METHODS Image registration is a technique of transforming one image (moving image) to conform to the shape of another image (fixed image). The registration process usually aims to minimise a cost function which describes dissimilarity between the two images. Dependent on the degree of freedom, the registration can be linear or nonlinear. In order to avoid being trapped in a local minimum, it is common practice to use linear registration followed by nonlinear registration [52]. Recently, multi-resolution scheme has also been utilised for such purpose; the image is registered with a coarse resolution before proceeding to use finer resolutions [39]. In brain image registration, it is not only important 11

20 to align the shapes of the two brain images, it is paramount that the brain structures in the moving image be transformed to their corresponding counterparts in the fixed image [11]. It is also debatable if brain image registration should result in the transformed image matching the target image exactly, since visible anatomical difference between individuals may be desirable even after mapping to a common space [40]. Therefore, evaluation of brain image registration methods can be hard to design, as different evaluation standards exist. Numerous image registration algorithms have been developed for registering individual brains to a volumetric atlas [8] [9] [10] [12] [13] [14] [15] [16] [17] [18] [19]. The earliest attempt was the Diffeomorphic Demons developed in 1998 [53]. Inspired by thermodynamic concepts, the algorithm was based on a diffusion model where an image can diffuse through boundaries of another image. The term diffeomorphic refers to the deformation function being invertible, both direction of registration being smooth, and deformation of both direction being differentiable. Nevertheless, the algorithm is only theoretically diffeomorphic and may not be so in real applications. Interpolations may be needed to forge symmetry. The name Demons is an analogy to Maxwell s Demons, which is able to differentiate particles of different nature. In the case of image registration, this means that the algorithm 12

21 differentiates pixels of different parts of an image, hence how they should diffuse (see Figure 8). Figure 8 Illustration of how the demons guide the moving image into the static (target) image Following the Diffeomorphic Demons, many toolboxes have been developed for image registration. For example, the Automatic Registration Toolbox (ART) [54] and Advanced Normalisation Tools (ANTs) [39] [55] contain image registration functions for various purposes. They were also found to be the two best registration algorithms in a 2009 comparative study [52]. Later in the 2010 study followed [56], Symmetrical Normalisation (SyN) from ANTs were shown to outperform ART, especially if custom template is used. On the other hand, the ART algorithm uses a homeomorphic deformation function, which aims to preserve the topological properties of the transformed image [54]. As nonlinear warps may cause distortion in the transformed image when trying to force the shapes to fit, this helps to prevent anatomical details to be lost during the transform. The SyN algorithm guarantees diffeomorphism, Figure 9 Illustration of how SyN achieves diffeomorphism. The two images, I and J are registered to the mean shape between them by $ and %. A full mapping from I to J can be obtained by concatenating $ and the inverse of %. 13

22 hence eliminating the interpolation needed to forge diffeomorphism in Demons (see Figure 9) [55]. Both ART and SyN uses cross-correlation (CC) as a similarity measure in their cost functions. It is argued that CC accounts for local variations in intensity better than other metrics like squared differences or mutual information. Some popular statistical or general toolboxes also include image registration methods, like FSL [48] and SPM [51]. The FSL software contains the FMRIB s Linear Image Registration Tool (FLIRT) [57] and FMRIB s Nonlinear Image Registration Tool (FNIRT) [12]. FLIRT is a popular linear registration method which is sometimes used by other registration methods to start the registration. In fact, using FNIRT requires that an affine registration through FLIRT be performed first. FNIRT itself uses a cubic B-spline function for nonlinear registration. On the other hand, SPM offers a rather simple registration model, which focuses on registering the shape of the brains [58]. However, it is mostly used as part of a pipeline consisting of segmentation, statistical analysis, etc. Hence it is commonly used to facilitate the other functions in SPM. Finally, there are also registration methods for mapping individual brain surface to a surface template. As mentioned previously, FreeSurfer provides a surface-based registration function to map reconstructed individual cortical surface to the fsaverage surface [38] [22]. This registration method has been shown to perform at least comparably to landmark-based registration methods [27]; the latter is not fully automatic like the former and relies on accurate landmark labelling to work. 14

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24 3. METHODS 3.1 DATA AND PRE-PROCESSING Data from 1490 subjects from the Brain Genomics Superstruct Project (GSP) were considered [59]. All imaging data were collected on matched 3T Tim Trio scanners using the vendor-supplied 12-channel phase-array head coil. Subjects were clinically normal, English-speaking young adults (ages 18 to 35). The structural MRI data consisted of one 1.2mm isotropic scan for each participant. Details of data collection can be found elsewhere [33] [59]. The subjects were split into train and test set, each containing 745 subjects. The T1 images of all 1490 participants, as well as the volumetric atlas templates (MNI152 and Colin27), were processed using FreeSurfer reconall procedure ( [60] [61] [62] [22] [5] [63]. FreeSurfer constitutes a suite of automatic algorithms that extract models of most macroscopic human brain structures from T1 MRI data. There are three outputs of the recon-all procedure that were important for subsequent analyses. First, FreeSurfer automatically reconstructs surface mesh representations of the cortex from individual subjects T1 images. The cortical surface mesh is inflated into a sphere, and registered to a common spherical coordinate system that aligned the cortical folding patterns across subjects [22] [5]. The outcome of this procedure is a nonlinear mapping between the subject s native T1 space and fsaverage surface space. Second, the recon-all procedure generates corresponding volumetric (aparc.a2009s+aseg.mgz) and surface (lh.aparc.a2009s.annot and rh.aparc.a2009s.annot) parcellations of 74 sulci and gyri for each subject [64] 16

25 [65] [66]. These anatomical segmentations will be utilized in our evaluation of various algorithms for mapping between MNI152/Colin27 and fsaverage. Third, the recon-all procedure performs a joint registrationsegmentation procedure that aligns the T1 image to FreeSurfer internal volumetric space 1, while classifying each native brain voxel into one of multiple brain structures, such as the thalamus and caudate [64] [67]. The outcome of this procedure is a nonlinear mapping between the subject s native T1 space and FreeSurfer internal volumetric space. The nonlinear mapping is represented by a dense displacement field (i.e., a single displacement vector at each 2-mm isotropic atlas voxel) and can be found in the file talairach.m3z (under the mri/transforms folder of the recon-all output). 3.2 RECOMMENDED FREESURFER METHODS As aforementioned, there is a very little work done in creating mapping between volumetric and surface coordinate systems. In fact, in most mailing list of popular software or toolbox, experts would suggest not to carry out such mapping at all. In the FreeSurfer mailing list, however, a suboptimal method is sometimes recommended for people who really needs a mapping between MNI152 and fsaverage surface. This method involves an affine registration between MNI152 space and the fsaverage volume; the warp was computed using FLIRT and provided in the FreeSurfer software. A similar affine transformation between Colin27 space and the fsaverage volume can be 1 Note that this internal volumetric space is different from fsaverage volume. 17

26 generated using FSL. This is followed by a registration between fsaverage volume and fsaverage surface; the warp is provided with the fsaverage template. Here we denote this method as Affine. There are two problems with this approach. Firstly, the MNI152 template and fsaverage volume have significant anatomical difference. An affine transformation is unlikely to eliminate the fine differences. Secondly, the fsaverage volume is a blurry image, constructed by averaging across 40 individual brains. The anatomical details have been lost during the averaging process. Although a previous implementation of the approach utilised nonlinear registration between MNI152 and fsaverage volume using FNIRT [28], we do not expect the resultant mapping to be sufficiently accurate. This is the method used by many current research, and would hence be a good baseline. We also considered another possible method using FreeSurfer software. By utilising the recon-all function in FreeSurfer, we can reconstruct the cortical surface of MNI152. As aforementioned, this would allow us to project any new data in MNI152 to the MNI152 surface space (mri_vol2surf), and then to fsaverage surface (mri_surf2surf). The same procedure can be applied to any other volumetric template. We denote this method as MNIsurf for MNI152- fsaverage mapping and Colinsurf for Colin27-fsaverage mapping. This approach is not essentially a correct usage of the recon-all function, which is designed to process single subject volume. As MNI152 is an average brain, the surface reconstruction and the resultant warps would not be optimal. However, this method is easy to implement; our implementation also shows that 18

27 it outperforms the Affine approach. Hence, we consider this a competing approach to our proposed approach. 3.3 REGISTRATION FUSION METHOD The RF method was first proposed Buckner and colleagues briefly [37] [33]. In this thesis, we implement two variants of the RF method and describe the procedures in detail. Note that our current implementation is different from the 2011 version in a few aspects (e.g. the format of index volume, the volumetric registration method used, etc.); we have tested and confirmed that the current implementation is at least comparable to the 2011 implementation. Figure 10 shows the general procedure of the RF method. The procedure involves registering the MNI152 (or Colin27) template to subject s native T1 space and then to fsaverage, or the reverse. A mapping between MNI152 (or Colin27) and fsaverage is hence obtained for each subject. Averaging across all subject s individual mapping then generates a single average mapping, which Figure 10 The Registration Fusion (RF) procedure. Each subject is mapped to (A) the MNI152 or Colin27 template, and (B) the fsaverage surface. By concatenating the two mappings, we obtain an individual mapping between MNI152/Colin27 and fsaverage through each subject. 19

28 can be used to project new data between MNI152 (or Colin27) and fsaverage. We describe the details of the procedures below INDEX VOLUMES For both directions of mapping between MNI152/Colin27 and fsaverage coordinate systems, the first step is to sample the starting space with index volumes. In other words, we construct volumes in an atlas space by representing each voxel/vertex by its coordinate in that space. During the registration stage, these index volumes are warped to the target space, offering a correspondence between voxels/vertices in the target space and coordinates in the starting space. Specifically, for volumetric spaces (MNI152 and Colin27), the Right- Anterior-Superior (RAS) coordinates are utilised. Three volumes are generated, corresponding to x, y, and z index. This is different from the 2011 implementation, where only one index volume is used; the single index volume represents each voxel by an arbitrary index number. The advantage of using x/y/z index volumes is that interpolation options like linear, cubic, spline, etc. are now feasible, whereas only nearest neighbours interpolation could be used when the single index volume was used. Figure 11 shows the x index volume loaded in Freeview. Note that the sagittal view shows no variation in intensity, since the x coordinates do not vary in the sagittal plane. For fsaverage space, the spherical coordinates are utilised. As aforementioned, the spherical form of the fsaverage surface helps to locate each vertex on the surface in Euclidean space. In our implementation, we directly used the spherical coordinates of fsaverage surface that are projected onto each individual subject s surface, which are provided by FreeSurfer s recon-all 20

29 function. This is equivalent to projecting the fsaverage spherical surface to the subject s surface with mri_surf2surf function. This is again different from the 2011 implementation, where vertices on fsaverage surface are assigned arbitrary indices, which causes interpolation option to be limited to nearest neighbours. Figure 11 The x-index volume shown in Freeview. The top row shows the axial view. Theo bottom row shows, from left to right, the sagittal view, the coronal view, and the 3D view VOLUMETRIC REGISTRATION Similar to the 2011 implementation, we consider a volumetric registration method that make use of FreeSurfer s recon-all function. During pre-processing, we obtained nonlinear mappings between the FreeSurfer internal volumetric space and each train subject s native T1 space. We also obtained such mappings for MNI152 and Colin27 templates. By concatenating the talairach.m3z from the recon-all of an individual subject (Figure 12B) and the talairach.m3z from the recon-all of the MNI152 (or Colin27) template (Figure 12A), a mapping between the subject s native T1 space and MNI152 21

30 (or Colin27) volumetric space was obtained. The concatenation of warps is possible due to the use of index volumes; the index volumes of MNI152 (or Colin27) are warped to the FreeSurfer internal volumetric space and then to each subject s native T1 space. The procedure is illustrated in Figure 12. Figure 12 Procedure for the 2011 implementation Visual inspection suggested that the resulting mappings between MNI152/Colin27 and individual subjects were of good quality. However, by concatenating two deformations, small registration errors in each deformation may be compounded to result in large registration errors. For example, a voxel on one bank of a narrow sulcus in the starting brain may be warped to become inside the sulcus, due to a small registration error, in the intermediate brain (FreeSurfer internal volumetric space in our case). Then, when mapping from the intermediate brain to the final target, another small registration error could cause the voxel to end up on the other bank of the sulcus. Furthermore, FreeSurfer is optimized for processing the brains of individual subjects, not an average brain like the MNI152 template. Therefore, we also considered the more standard approach of directly registering the individual subjects to 22

31 MNI152 (or Colin27) using ANTs. The procedure using ANTs would be identical to that illustrated in Figure 10. An example script for ANTs was provided by the developers for either quick implementation or standard production. As the production setting parameters used in the example script is equivalent to those used in Klein et al study, we find it optimal to base our implementation on the same parameters. We also experimented with slight tweak in parameters to balance performance and run time. We removed the translation and rigid stage, only keeping the affine and SyN stage, which we found to be sufficient. To further save time, we register the original MNI152 (or Colin27) template, instead of its larger normalised version, to each train subject s normalised T1 volume. This roughly halves the run time, while also ensuring good quality of warps. While registering subjects normalised T1 volume to the original MNI152 (or Colin27) templates would be even more convenient, the results were visually worse; this is because the MNI152 brain, being an average brain, does not have clearly delineated sulci and gyri to serve as registration target. This asymmetry in warps is caused by the asymmetric affine registration stage, despite the SyN stage being diffeomorphic. The inverse of the warp generated is then used to project the index volumes of MNI152 (or Colin27) to each subject s native T1 space (Figure 10A). Finally, we restricted the maximum iterations of affine registration as it should converge rather fast. While it is also possible to adjust the convergence criteria to ensure fast convergence, restricting maximum number of iterations is more generally used in the field. 23

32 3.2.3 AVERAGE MAPPING For each training subject, a mapping between the subject s native T1 space and the fsaverage surface is constructed by FreeSurfer s recon-all function (Figure 10B and Figure 12B). Following the volumetric registration, the index volumes projected to subject s native T1 space are then projected to fsaverage using this mapping. Now each set of index volume projected to fsaverage provides a set of corresponding coordinates in MNI152 (or Colin27) for each vertex in fsaverage. We call this an individual mapping from MNI152 (or Colin27) to fsaverage. A similar procedure is used for projection from fsaverage to MNI152 (or Colin27). As the index volumes of fsaverage spherical surface are already projected to each train subject s surface, the mappings provided by FreeSurfer s recon-all function are then used to project them to each train subject s native T1 space. The warps generated using FreeSurfer s talairach.m3z and ANTs can then be applied to project these index volumes to MNI152 (or Colin27) space. These index volumes hence provide corresponding spherical coordinates in fsaverage for each voxel in MNI152 (or Colin27). Each set of index volume projected is then an individual mapping from fsaverage to MNI152 (or Colin27). To reduce random errors that could be present in individual mappings, an average mapping (for each direction of projection) is generated by simply taking the mean coordinate at each vertex, across all 745 train subjects. The average mappings can then be used to sample new data in MNI152 (or Colin27) onto the fsaverage surface, or to sample new data on fsaverage surface into MNI152 (or Colin27) space. We denote the mappings obtained where 24

33 FreeSurfer s talairach.m3z transform was used as RF-M3Z, and the mappings obtained where ANTs was used for volumetric registration as RF-ANTs. 3.4 ASYMMETRY IN MAPPING It is important to note that an asymmetry is present in mappings generated. Specifically, the MNI152/Colin27-to-fsavaerage mapping is not a simple inverse of the fsaverage-to-mni152/colin27 mapping. For MNI152/Colin27-to-fsaverage mapping, every vertex in fsaverage correspond to a set of coordinates in MNI152/Colin27; some coordinates in MNI152/Colin27 would not have a corresponding vertex in fsaverage, since they may be outside the cortex. The average coordinate for each vertex is simply the sum of all sets of coordinates at the vertex divided by the total number of subject. On the other hand, for fsaverage-to-mni152/colin27 mapping, voxels inside the cortex correspond to a set of spherical coordinates in fsaverage. However, the individual mappings could have determined different voxels to be inside the cortex. As a result, many voxels do not have 745 set of corresponding spherical coordinates. This is especially a problem for MNI152, which is treated to have a thin cortical ribbon in FreeSurfer, due to its nature as an average brain. In cases where voxels have very few set of corresponding coordinates, averaging would not be very helpful with reducing random errors due to the small subject count. In order to account for voxels inside the cortex but with few set of corresponding coordinates, we implement a growing step to assign coordinates to them. A tight cortex mask consists of voxels where more than 50% of all 25

34 subjects have projected valid coordinates to. A loose cortex mask is defined with a lower threshold of 15%. Figures 13 shows the two masks and their difference, overlay on MNI152 brain. We consider voxels in the tight mask as those having accurate projections (50% is an arbitrary but sensible choice), and those in the loose mask but not in the tight mask as needing accurate projections. The threshold for the loose cortex mask is set such that the mask aligns well with the cortical ribbon of MNI152 brain (see Figure 13A). Each voxel that needs accurate projection is then assigned a set of coordinates of the voxel with accurate projection, that is closest to it. In other words, voxels with 15-50% subjects coordinate correspondence (Figure 13C) are assigned coordinates from more accurate neighbours, rather than using their own averaged coordinates. Figure 13 (A) Tight cortical mask, (B) loose cortical mask, and (C) the difference between loose and tight masks, overlay on MNI152 brain This growing step let the data sampled from fsaverage surface to fill up the loose cortex mask in MNI152 (or Colin27), resolving the issue with thin cortical ribbon in MNI152. Figure 14 shows an example, where the projected parcellation in MNI152 is grown to fill the loose cortical mask. Each colour region in the parcellation correspond to a brain region, which should roughly align with the black boundaries; the choice of colour has no particular 26

35 implication. We applied this step to all four approaches, Affine, MNIsurf (or Colinsurf), RF-M3Z and RF-ANTs. This also helps to restrict the results projected to MNI152 (or Colin27), so that the different approaches can be more easily compared to each other. Figure 14 Projected parcellation before growing (left) and after growing (right) 27

36 4. EVALUATION In this section, we describe evaluation tests for MNI152-fsaverage mappings, the procedure of which is also used for Colin27-fsaverage mapping evaluation. As aforementioned, a perfect mapping between MNI152 (Colin27) and fsaverage is not possible. This is because irreversible registration errors are always present in data analysed in MNI152 (or Colin27) space in real applications. Therefore, a good mapping should not only have good anatomical alignment between MNI152 (or Colin27) and fsaverage, but also should account for the presence of such errors. To this end, we designed simulations based on actual scenarios. The results are hence justified on practical grounds. 4.1 MNI152/COLIN27-TO-FSAVERAGE EVALUATION To evaluate MNI152/Colin27-to-fsaverage mappings, we consider a likely usage scenario. Researchers often project data (e.g., fmri) from subjects native spaces to MNI152 coordinate system for some form of group analysis. The outcome of the group analysis can be visualized in the volume, but is often projected to fsaverage surface for visualization. By contrast, data from subjects native space can be directly projected to fsaverage surface for group analysis. The latter is more optimal as surface-based registrations are less prone to errors, but the former has been a common practice in the community. In ideal scenario, the subjects-to-mni-to-fsaverage results should be close to the subjects-tofsaverage results. This would allow the researcher to align interpretation of data with visualisation more easily. To simulate the above scenario, we utilised the 745 GSP test subjects that were processed using FreeSurfer recon-all, yielding corresponding surface 28

37 (lh.aparc.a2009s.annot and rh.aparc.a2009s.annot) and volumetric (aparc.a2009s+aseg.mgz) parcellations of 74 sulci and gyri per cortical hemisphere. The volumetric parcellations were projected to MNI152 coordinate system and averaged across subjects, resulting in a volumetric probabilistic map per anatomical structure. The probabilistic maps simulated the group-average results from typical fmri studies. The probabilistic maps were produced using the warps from ANTs or FNIRT, resulting in ANTs-derived or FNIRT-derived MNI152 volumetric probabilistic maps. Figure 15B shows the ANTs-derived MNI152 map for superior temporal sulcus. Note the diffusion of intensity at boundaries of the map, representative of the irreversible errors present in the data. The MNI152 volumetric probabilistic maps can then be projected to fsaverage surface using the four MNI-to-fsaverage projection approaches (RF- M3Z, RF-ANTs, MNIsurf, Affine) for comparison with ground truth surface probabilistic maps. The ground truth surface probabilistic maps were obtained by averaging the surface parcellations across subjects in fsaverage surface space. Since the ground truth surface probabilistic maps were deriving (A) (B) Figure 15 (A) ground truth fsaverage probabilistic map for superior temporal sulcus (B) ANTs-derived MNI152 probablistic map for superior temporal sulcus 29

38 using FreeSurfer, they were the same for both ANTs-derived and FNIRTderived MNI152 volumetric probabilistic maps. Figure 15A shows the ground truth map for superior temporal sulcus. Note that diffusion at boundaries is much reduced here, since surface-based registration is less prone to errors. To quantify the disagreement between the projected probabilistic map and the ground truth surface probabilistic map of an anatomical structure, the Normalized Absolute Difference (NAD) metric was used. The NAD metric was defined as the absolute difference between the two maps, summed across all vertices and divided by the sum of the ground truth probabilistic map, as shown below. This metric measured the dissimilarity between the two maps, normalizing for the size of the anatomical structure. A lower NAD value indicates better performance. &'( = +,-./ For every pair of approaches, the NAD metric for each of the 74 anatomical structures were averaged between the two hemispheres and submitted to a paired-sample t-test. Since there were four approaches and two sets of volumetric probabilistic maps (M3Z-derived and ANTs-derived), there were a total of 12 statistical tests. Multiple comparisons were corrected using a false discovery rate (FDR) [68] of q < All the p values reported in Results section survived the false discovery rate. 4.2 FSAVERAGE-TO-MNI152/COLIN27 EVALUATION To evaluate the fsaverage-to-mni projection, we also consider a possible usage scenario. It is unlikely that researchers would directly project 30

39 individual subjects fmri data onto fsaverage surface space for group-level analysis, and then project their results into MNI152 space for visualization. A more likely scenario might be the projection of surface-based resting-state fmri cortical parcellations to MNI152 space. The projected resting-state fmri parcellation can then be utilized for analysing new data from individual subjects registered to the MNI152 coordinate system. In this scenario, it would be ideal if the projected fsaverage-to-mni resting-state parcellation were the same as a parcellation that was estimated from resting-state fmri data directly registered to MNI152 space. Note that, in this case, the existing data in MNI152 space are imperfect due to registration from subject to MNI152. Therefore, it is likely that the projected fsaverage-to-mni152 parcellation would be of better quality than the parcellation estimated from these data. This simulates the problem researchers would have in real applications. Despite the problem, a fsaverage-to-mni152 mapping is more useful if its projected parcellation can match the parcellation estimated from data in MNI152 better. We find it practically reasonable to evaluate the fsaverage-to-mni152 mappings by the extent of this matching. To simulate the above scenario, we again use the surface probabilistic maps of the 74 anatomical structures, which served as the ground truth for the MNI-to-fsaverage evaluation. In the current evaluation, the surface probabilistic maps were combined into a winner-takes-all parcellation. The surface-based winner-takes-all parcellation was then projected to the MNI152 coordinate system using the four fsaverage-to-mni projection approaches (RF-M3Z, RF- ANTs, MNIsurf, Affine) for comparison with ground truth volumetric 31

40 parcellations. Here the ground truth volumetric parcellations were obtained by combining the M3Z-derived (or ANTs-derived) MNI152 volumetric probabilistic maps (from the previous section) into winner-takes-all parcellations. Therefore in this scenario, we have two ground truth volumetric parcellations, one based on talairach.m3z and the other based on ANTs. Figure 16 shows the fsaverage and ground truth winner-takes-all parcellations. Each colour region correspond to one brain region in the parcellation; the choice of (C) (D) Figure 16 (A) fsaverage winner-takes-all parcellation (B) ground truth MNI152 winner-takes-all parcellation colour has no particular implication. To quantify the agreement between the projected parcellation and a ground truth parcellation, the Sorensen-Dice coefficient [69] [70] was computed for each of the 74 anatomical regions per hemisphere. The Dice coefficient is defined as two times the overlap between two regions, divided by the sum of their areas, as shown below. A higher Dice value indicates better matching between areas, hence better performance. (78 = 2 9 ; 9 + ; 32

41 For every pair of approaches, the Dice metric for each of the 74 anatomical structures were averaged between the two hemispheres and submitted to a paired-sample t-test. Since there were four approaches and two sets of ground truth volumetric parcellations (M3Z-derived and ANTsderived), there were a total of 12 statistical tests. Multiple comparisons were corrected using a false discovery rate (FDR) [68] of q < All the p values reported in subsequent sections survived the false discovery rate. 4.3 INVERSE CONSISTENCY EVALUATION Finally, inverse consistency evaluation [71] was carried out for each approach, for MNI152-fsaverage mappings. This concerns the symmetry of the mappings. For a location in the MNI152, it should be preferably mapped to and from about the same location in fsaverage, for MNI152-to-fsaverage and fsaverage-to-mni152 mappings respectively. The inverse consistency check does not directly measure the performance of the approaches, but is a sanity check. For FS-recon and FS-affine approaches, the x, y and z coordinates of vertices on fsaverage spherical surface are projected to MNI152 space and then back to fsaverage surface. For the RF approaches, the fsaverage-to-mni152 mappings already specify the corresponding x, y, z coordinates in fsaverage spherical space for each vortex in MNI152 space (within the liberal cortex mask defined in the growing step). Therefore, the inverse consistency check is performed by projecting the fsaverage-to-mni152 mappings for RF-FS and RF- ANTs back to fsaverage using their MNI152-to-fsaverage mappings respectively. Finally, the projected coordinates are compared against the original spherical coordinates of each vertex, by computing the Euclidean 33

42 distance between them. A smaller mean distance across all vertices (excluding the medial wall) means better consistency. The inverse consistency check was not performed for Colin27-fsaverage mappings, as we expect them to have similar inverse consistency as MNI152- fsaverage mappings. 34

43 5. RESULTS 5.1 MNI152-TO-FSAVERAGE RESULTS Figures 17 and 18 show the projections of ANTs-derived and FNIRTderived MNI152 probabilistic maps of four representative anatomical structures to fsaverage surface space. The black boundaries correspond to the winnertakes-all parcellation obtained by thresholding the ground-truth fsaverage surface probabilistic maps. Visual inspection of Figures 17 and 18 suggests that the projected probabilistic maps corresponded well to the ground truth for all approaches, although there was also clear bleeding to adjacent anatomical structures for the postcentral gyrus, middle temporal gyrus and central sulcus. The NAD evaluation metric is shown below each brain in Figures 17 and 18. A lower value indicates closer correspondence with the ground-truth probabilistic map. The NAD generally agreed with the visual quality of the projections, suggesting its usefulness as an evaluation metric. For example, the projection of the left ANTs-derived middle posterior cingulate probabilistic map using RF-ANTs visually matched the ground truth black boundaries very well, resulting in a low NAD of On the other hand, the corresponding projection using MNIsurf aligned well with the posterior, but not the anterior, portion of the ground truth black boundaries, resulting in a worse NAD of Figure 19 shows the NAD metric averaged across all anatomical structures within each hemisphere. When ANTs-derived MNI152 probabilistic maps were used, RF-ANTs was the best (p < 0.01 corrected, effect size > 0.2). RF-M3Z and MNIsurf showed comparable performance (effect size < 0.03) and 35

44 were both significantly better than Affine (p < 0.01 corrected, effect size > 0.4). Similarly, when FNIRT-derived MNI152 probabilistic maps were used, RF- ANTs showed comparable performance to RF-M3Z (effect size < 0.1), but outperformed the other two approaches (p < 0.01 corrected, effect size > 0.2). RF-M3Z and MNIsurf showed comparable performance (effect size < 0.1) and were both significantly better than Affine (p < 0.01 corrected, effect size > 0.5). It is worth noting that the ground truth fsaverage surface probabilistic maps were the same for both ANTS-derived and FNIRT-derived MNI152 probabilistic maps, so the two sets of results (left and right in Figure 19) were comparable. In general, the NAD was lower (i.e., better) for ANTS-derived MNI152 probabilistic maps compared with FNIRT-derived MNI152 probabilistic maps. This is not surprising since ANTs has been shown to be the top-performing registration tool. 36

45 Figure 17 Visualisation of projected ANTs-derived MNI152 probabilistic maps in middle posterior cingulate, post dorsal cingulate gyrus, central sulcus, and superior precentral sulcus. The black outlines correspond to the ground truth fsaverage parcellation. The value below each brain shows the NAD value of that projection, with the best across all approaches in bold. 37

46 Figure 18 Visualisation of projected FNIRT-derived MNI152 probabilistic maps in middle posterior cingulate, post dorsal cingulate gyrus, central sulcus, and superior precentral sulcus. The black outlines correspond to the ground truth fsaverage parcellation. The value below each brain shows the NAD value of that projection, with the best across all approaches in bold. 38

47 Figure 19 NAD results for ANTs-derived and FNIRT-derived MNI152 maps. Each bar represents the mean NAD value across all areas in left hemisphere (black) and right hemisphere (right). The error bars represent standard error. 5.2 FSAVERAGE-TO-MNI152 RESULTS Figures 20 and 21 illustrate the projections of the fsaverage winnertakes-all parcellation to MNI152 volumetric space, juxtaposed against black boundaries of ANTs-simulated and FNIRT-simulated ground truth segmentations respectively. Figures 20A and 21A show the fsaverage-to-mni projections before the dilation within the loose cortical mask (see Methods). Figures 20B and 21B show the fsaverage-to-mni projections after the dilation, with insets illustrating regions with obvious differences across methods. Figure 22 shows the Dice metric averaged across all anatomical structures within each hemisphere. When ANTs-simulated ground truth was considered, RF-ANTs was the best (p < 0.01 corrected, effect size > 0.4). The remaining three approaches showed comparable performance (i.e., difference not statistically significant; effect size < 0.2). Similarly, when FNIRT-simulated 39

48 ground truth was considered, RF-ANTs was the best (p < 0.01 corrected, effect size > 0.3). The remaining three approaches showed comparable performance (effect size < 0.1). Figure 20 Visualisation of projected fsaverage winner-takes-all parcellation, compared against ANTs-simulated winner-takes-all ground truth" (black outline). 40

49 Figure 21 Visualisation of projected fsaverage winner-takes-all parcellation, compared against FNIRT-simulated winner-takes-all ground truth (black outline). 41

50 Figure 22 Dice results for projected winner-takes-all parcellation in comparison to ANTs-simulated and FNIRT-simulated ground truth segmentation. Each bar represents the mean Dice value across all areas in left hemisphere (black) and right hemisphere (white). The error bars represent standard error. 5.3 COLIN27-TO-FSAVERAGE AND FSAVERAGE-TO-COLIN27 RESULTS Figures 23 show the NAD metric for Colin27-to-fsaverage projection results. Figures 24 show the Dice metric for fsaverage-to-colin27 projection. The results are generally consistent with the MNI152 results from the previous sections. RF-ANTs is the best-performing approach in general. Figure 23 NAD results for ANTs-derived and FNIRT-derived Colin27 maps. Each bar represents the mean NAD value across all areas in left hemisphere (black) and right hemisphere (right). The error bars represent standard error. 42

51 Figure 24 Dice results for projected winner-takes-all parcellation in comparison to ANTs-simulated and FNIRT-simulated ground truth segmentation. Each bar represents the mean Dice value across all areas in left hemisphere (black) and right hemisphere (white). The error bars represent standard error. 5.4 INVERSE CONSISTENCY RESULTS Figure 25 compares the Euclidean distance between projected coordinates and original coordinates across the four methods, where the bars represent average Euclidean distance across all vertices (excluding the medial wall). The RF approaches had similar consistency, with RF-ANTs having a slightly better consistency. Despite not having the best average inverse Figure 25 Mean Euclidean distance measure in mm, for left hemisphere (black) and right hemisphere (white). 43