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A framework for evaluating correspondence between brain images using anatomical fiducials

Accurate spatial correspondence between template and subject images is a crucial step in neuroimaging studies and clinical applications like stereotactic neurosurgery. In the absence of a robust quantitative approach, we sought to propose and validate a set of point landmarks, anatomical fiducials (AFIDs), that could be quickly, accurately, and reliably placed on magnetic resonance images of the human brain. Using several publicly available brain templates and individual participant datasets, novice users could be trained to place a set of 32 AFIDs with millimetric accuracy. Furthermore, the utility of the AFIDs protocol is demonstrated for evaluating subject-to-template and template-to-template registration. Specifically, we found that commonly used voxel overlap metrics were relatively insensitive to focal misregistrations compared to AFID point-based measures. Our entire protocol and study framework leverages open resources and tools, and has been developed with full transparency in mind so that others may freely use, adopt, and modify. This protocol holds value for a broad number of applications including alignment of brain images and teaching neuroanatomy.


Introduction 19
Establishing spatial correspondence between images is a crucial step in neuroimaging studies enabling 20 fusion of multimodal information, analysis of focal morphological differences, and comparison of within-21 and between-study data in a common coordinate space. Stereotaxy arose as a result of questions raised 22 by scientists and surgeons interested in the physiology and treatment of focal brain structures (A. C. 23 Evans, Janke, Collins, & Baillet, 2012;Horsley & Clarke, 1908;Peters, 2006). Jean Talairach played a 24 crucial role, observing consistent anatomical features on lateral pneumoencephalograms (Dandy, 1918), 25 or "air studies", that could be consistently localized, specifically the anterior commissure (AC) and 26 posterior commissure (PC) (Schaltenbrand & Wahren, 1977; J Talairach, David, Tournoux, Corredor, & 27 Kvasina, 1957), and could thus be mapped to prepared post-mortem brain sections in a 3D coordinate 28 system. The AC-PC line has remained important in the era since magnetic resonance imaging (MRI) has 29 risen to prominence for aligning brain images to create population atlases ( While these measures are effective for evaluating spatial correspondence on the macroscale, here we 47 argue that they remain relatively coarse measures of registration quality and are insensitive to focal 48 misregistration between images. In addition, they do not permit facile identification or description of 49 where these local biases are occurring. These issues are particularly critical as technical advancements 50 in both imaging and stereotaxy are enabling more accurate therapeutic modulation of brain regions 51 where several millimeters could represent the difference between optimal therapy and complications. 52 53 In this paper, we sought inspiration from classical stereotactic methods (Schaltenbrand & Wahren, 1977;54 J Talairach et al., 1957), and propose that point-based distances provide a more sensitive metric by 55 which brain image correspondence can be evaluated. Anatomical points have been referred to in the 56 literature using a variety of terms including fiducials, landmarks, markups (sometimes used in 57 combination) but ultimately involve representing an anatomical feature by a three-dimensional (x,y,z) 58 Cartesian coordinate. For this manuscript, we have chosen to use the term AFIDs, short for anatomical 59 fiducials, "fiducia" being Latin for trust or confidence. We argue that the advent of automatic 60 segmentation-based methods has led to a relative underemphasis of point correspondence between 61 brain structures. We first sought to determine whether we could define a set of AFIDs that were both 62 consistently identifiable across multiple datasets while also providing a distributed sampling about the 63 brain. Following this, we demonstrate how AFIDs are complementary to segmentation-based metrics for 64 providing a quantitative report of spatial correspondence between structural magnetic resonance images 65 of the brain using more intuitive distance-based measures of alignment. Central to this work was the 66 development of our protocol using an open source framework, enabling reproducibility across sites and 67 centers. The overall study organization is shown schematically in

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To compute the mean AFLE, the mean AFID coordinate for each brain image was used as an 129 approximation of the ideal coordinate location. Mean AFLE was calculated as the Euclidean distance 130 between the individual position and the group mean. We furthermore calculated intra-rater AFLE as the 131 mean pairwise distance between AFIDs placed by the same rater. The individual measures were 132 averaged across all raters as a summary metric. To calculate inter-rater AFLE, a mean coordinate was 133 computed by averaging the coordinates for each rater as an estimate of the ideal coordinate location for 134 the rater; the mean pairwise distance between AFIDs placed across raters was then calculated as a 135 summary metric. We summarized global and location-specific mean AFLE according to a number of 136 variables: template (group versus individual), rating session (1-4), rater, and AFID. Phase 3: Evaluating subject-to-template registration 169 We evaluated the quality of subject-to-template registration using the output provided as part of 170 fMRIPrep version 1.1.1 using conventional ROI-based metrics (i.e. voxel overlap) as well as distance 171 metrics derived from our manual AFID32 annotations from Phases 1 and 2. The default template for 172 fMRIPrep 1.1.1 was the MNI2009cAsym template. We started by visually inspecting the images 173 qualitatively from the output fMRIPrep html pages. For each individual subject scan, we used the mean 174 fiducial location as the optimal location calculated in Phase 2. The distance between the individual 175 subject AFID location and the corresponding mean AFID location in the template was computed and 176 defined as the anatomical fiducial registration error (AFRE) and computed for linear transformation alone 177 (lin) and combined linear and nonlinear transformation (nlin). Our definition of AFRE differs from the FRE 178 used by Fitzpatrick whose framework for neuronavigation was necessarily limited to rigid-body 179 transformations (Fitzpatrick et al., 1998). This was compared with ROI-based measures of spatial 180 correspondence, specifically, the Jaccard similarity coefficient (  Source code and data availability 204 All data analysis was performed using R-project version 3.5.1. The AFIDs protocol, raw and processed 205 data, processing scripts, and scripts used in this manuscript are available at: https://github.com/afids. 206

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Phase 1: Protocol validation for brain templates 208 The 8 raters had a mean experience of 11.5 +/-11.2 months in medical imaging (range: 0-24 months), 209 14.3 +/-17.0 months in neuroanatomy (range: 0-48 months), and 7.0 +/-8.8 months in 3D Slicer (range: 210 0-24 months). During the template validation phase, the raters placed a total of 3072 individual points 211 (number of sessions = 4; templates = 3; points = 32). Average AFID32 placement time was estimated at 212 between 20-40 minutes. Thus, a total of 1920-3840 minutes (or 32-64 hours) were logged in this phase 213 of the study. The mean, intra-rater, and inter-rater AFLE metrics are summarized in Table 1.  214   215 For the raw data, the mean AFLE was 1.27 +/-1.98 mm (1.10 +/-1.59 mm for Agile12v2016; 1.71 +/-216 2.78 mm for Colin27; 0.99 +/-1.11 mm for MNI2009bAsym). Using a threshold of mean AFLE greater 217 than 10 mm from the group mean, we identified 24 outliers out of 3072 independent points (0.78%). 218 20/24 (83.33%) of outliers were the result of variable placement in the bilateral ventral occipital horns (i.e. 219 AFID29 and AFID30) of the Colin27 template. One pair (2/24; 8.33%) of outliers was due to left-right 220 mislabeling (indusium griseum; AFID27 and AFID28). One additional point was mislabeled; i.e. the left 221 anterolateral temporal horn point (AFID22) was placed at the left inferior AM horn location (AFID26). 222 After quality control and filtering outliers, mean AFLE improved to 1.03 +/-0. and inter-rater AFLE for each AFID post-QC are summarized in the Supporting Information S1 File. 231 232 All subsequent analyses were performed using the mean AFLE metric. We performed a one-way 233 analysis of variance observing evidence of statistically different variance between templates (F-value = 234 7.88; p-value < 0.001). Differences in mean AFLE between templates were identified on subgroup 235 analysis for the right superior lateral mesencephalic sulcus (AFID06), culmen (AFID10), genu of the 236 corpus callosum (AFID19), and left superior anteromedial temporal horn (AFID24), suggesting 237 differences between templates that may contributing to errors in placement. The results for each AFID 238 are also summarized in the Supporting Information S1 File. 239 240 Furthermore, we observed several distinct patterns of AFID placement using K-means clustering of 241 fiducial locations (point clouds) relative to the mean fiducial location (see Fig 4). We identified three 242 different general patterns of point cloud distributions ranging from highly anisotropic to moderately 243 anisotropic to isotropic.

251
As a secondary analysis, we explored whether any evidence of learning over the 4 independent rating 252 sessions could be identified (Supporting Information S1 file). Using linear modeling, we identified a 253 general decrease in mean AFLE with increasing session number although this did not meet thresholds of 254 statistical significance (estimate = -0.02 mm/session; p-value = 0.11). These trends were explored on the 255 individual rater level. For two out of 8 raters, AFLE varied with session number. Rater04 demonstrated a 256 general linear improvement of -0.17 mm/session from an initial mean AFLE of 1.64 mm (i.e. the worst 257 performing initial session); however Rater02 worsened at a rate of 0.12 mm/session from an initial mean 258 AFLE of 0.59 mm (i.e. the best performing initial session). No significant effect with individual AFIDs was 259 identified. All subgroup analyses were multiple comparisons corrected using FDR (q-value < 0.05).   The following section uses the AFIDs to evaluate the quality of spatial correspondence between the 283 Phase 2 subject data with the MNI2009cAsym template as processed through fMRIPrep. Visual 284 inspection of the fMRIPrep generated reports revealed no gross misregistrations between MNI2009c and 285 the individual subject scans although a pattern of worse deformable registration in subjects with enlarged 286 ventricles was observed. The rest of this section is concerned with examining the comparative utility of 287 conventional voxel overlap (ROI-based) metrics against the point-based (AFRE) metric proposed in this 288 study (see Fig 5A).   (Table 3). Some heterogeneity in values was noted between ROIs with voxel overlap 302 measures observed to be lowest for the pallidum (the smallest structure evaluated). All Jaccard values 303 after nonlinear transformation were greater than 0.7 (greater than 0.8 for Dice kappa), generally 304 considered to represent good correspondence between two registered images. For simplicity, we report 305 the Jaccard coefficient as our measure of voxel overlap for all subsequent analyses. 306 307 Mean AFRE improved from 3.40 +/-2.55 mm with linear transformation alone to 1.80 +/-2.09 with 308 combined linear/nonlinear transformation (p-value < 0.001). AFRE was significantly decreased with 309 nonlinear registration for all AFIDs except the pineal gland (AFID14). AFRE was observed to be higher 310 than mean AFLE measures (see Phase 2: 0.93 +/-0.73 mm) across the same subjects providing 311 evidence that registration error is detectable beyond the limits of localization error. The number of outlier 312 AFIDs with AFRE > 3 mm (more than 2 standard deviations above the mean AFLE found in Phase 2 for 313 the same subjects) was 135/960 (14.06%), representing 22/32 (68.75%) unique AFIDs identified as 314 misregistered. Each independent OASIS-1 subject had at least one AFID with AFRE > 3 mm with a 315 mean maximum AFRE of 7.5 mm (Range: 3.16-32.78 mm). Although AFLE and AFRE were statistically 316 correlated, the effect size was small (Kendall tau = 0.15; p-value < 0.001; Supporting Information S3 file). histograms, AFRE demonstrated a more unimodal distribution peaking between 1-2 mm (Fig 5B) while 333 voxel overlap exhibited two peaks within the 0.8-0.9 range (Fig 5C). The AFRE plot also demonstrated a 334 longer tail up to 10 mm, thus permitting a broader dynamic range in which to judge the quality of 335 registration. In contrast, voxel overlap metrics were sparse in the lower range making interpretation more 336 difficult. Finally, we observed that even where voxel overlap was high, suggesting good spatial 337 correspondence, high AFRE values were also observed for certain AFIDs (see Fig 5D). These represent 338 focal AFID locations where two images are misregistered despite stable voxel overlap results (Fig 6). 339 340

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The mean AFRE between BigBrainSym and MNI2009bSym was 2.16 +/-1.99 mm and between 362 BigBrainSym and MNI2009bAsym was 2.30 +/-1.83 mm, both above threshold. The largest error was 363 9.27 mm (MNI2009bSym) and 9.38 mm (MNI2009bAsym), found at the culmen (AFID10). Out of the 32 364 AFIDs defined, 11 (34.4%) were above threshold for the symmetric template and 12 (37.5%) for the 365 asymmetric template. The most prominent misregistrations tended to occur in the posterior brainstem 366 with the infracollicular sulcus (AFID03) and pineal gland (AFID14) quantified as 6.36 mm and 4.42 mm 367 AFRE, respectively. These registration errors can be seen in Fig 7 and are summarized by AFID in Table  368 5. In addition, AFRE up to 2.78 mm were observed for AFIDs placed along the lateral mesencephalic 369 sulcus (AFID06-09) and at the superior interpeduncular fossa (AFID05), which represent features 370 demarcating the lateral and superior bounds of midbrain registration. Registration differences between 371 these templates was also above threshold for the left lateral ventricle at the anterior commissure 372

385
Finally, we explored the differences in correspondence between the MNI2009bSym and MNI2009bAsym. 386 Note that these differences are not registration errors per se, as the two are not meant to be in the exact 387 same coordinate space. The differences were generally more subtle (0.88 +/-0.68 mm) but 4 AFIDs 388 (12.5%) were found to be above threshold. As expected, correspondence differences greater than 2 mm 389 occurred in lateral rather than midline AFIDs, specifically at the left anterolateral temporal horn (AFID22), 390 bilateral origins of the indusium griseum (AFID27-28), and left lateral ventral occipital horn (AFID30). No 391 correlations between correspondence and AFLE were found (tau = 0.210; p-value = 0.09). 392 image contrasts (Xiao et al., 2017) or subcortical tissue priors (Ewert et al., 2019) to drive template 497 registration have been demonstrated using conventional voxel overlap techniques to result in more 498 optimal registrations that can also be tested using the AFIDs framework. 499 Template-to-template registration 500 We recommend that imaging scientists exercise caution when displaying statistical maps using a 501 template other than the one to which the original deformations were performed. For example, it has 502 become increasingly common to project statistical maps and subject data registered to MNI space using 503 BigBrain for visualization purposes. In this study, we identified clear evidence of registration differences 504 between several templates commonly assumed to be in the same coordinate space: BigBrainSym and 505 MNI2009bSym, and even greater between BigBrainSym and MNI2009bAsym because of the differences 506 in AFID locations in MNI2009bSym and MNI2009bAsym. Specifically, misregistrations as high as over 9 507 mm have been identified. Many of these errors occur in the midbrain region (Table 5), which would have 508 implications in particular if using BigBrainSym to project locations of electrode implantations. In support 509 of other recent work (Horn et al., 2017), this study highlights the importance of understanding which 510 exact template one is using for processing and analysis: that multiple "MNI" templates exist (with 511 different version dates, types, and symmetry), as do registration differences between these templates. 512 Teaching neuroanatomy 513 Our AFID32 protocol may also hold particular value for teaching neuroanatomy. In fact, evidence from 514 our study suggests that even relative novices can be trained to place AFIDs accurately, including the AC 515 and PC, with comparable accuracy and variability to trained neurosurgeons (Table 2). By releasing the 516 data acquired in this study, we provide a normative distribution of AFID placements that can be used to 517 quantify how accurately new trainees can place points. These measures can be used to gauge the 518 comprehension of students regarding the specific location of neuroanatomical structures in a quantitative 519 (millimetric) manner and focus efforts on consolidating understanding based on where localization errors 520 28 of 36 were higher. To date, over a series of locally-held workshops and tutorials, over 60 students have been 521 trained to complete the AFID32 protocol. 522 Limitations and future work 523 While we have found the AFIDs proposed to be quite reliable, there is clearly location-related 524 heterogeneity in placement error. We make no claims that this set of anatomical fiducials is optimal and 525 in the future, other locations may prove to be more effective than others. Also, for this first proposed set 526 of AFIDs, we limited our locations to deep structures where less inter-subject variability exists compared 527 to cortical features (Thompson et al., 1996); future extensions could include linking our workflow with 528 neuroimaging modalities such as T2-weighted or diffusion-based contrasts may also be of value. In 531 addition, fiducial localization error may be biased by how the raters were taught to place the fiducials; in 532 our case, we organized an initial interactive tutorial session, and provided text and picture-based 533 resources of how to place the AFIDs. It is also possible that AFLE would be lower if performed by a more 534 experienced group of raters. Also, how AFID placement behaves in the presence of lesional pathology 535 remains an open question. We have made the annotations and images available to allow other groups to 536 propose other AFID locations and descriptions that could be similarly validated. We plan to post any 537 modifications to the protocol as separate versions at the linked repository. 538

539
The AFIDs protocol requires correct placement of the anterior commissure (AFID01) and posterior 540 commissure (AFID02) points. We made this decision as it helps to align the brain images into a more 541 standard orientation for subsequent placement of bilateral fiducials. In particular, 4 of the AFIDs are 542 dependent on AC-PC alignment (the lateral ventricles at AC and PC in the coronal plane). It is possible 543 that error in AFID placements could be compounded by initial error in placement of AC and PC. 544 Fortunately, AC and PC can be placed with high trueness and precision (< 1 mm) (Table 2), consistent  545 with prior studies (Liu & Dawant, 2015). We made the decision to perform AC-PC alignment to permit 546 29 of 36 more accurate placement of lateral AFIDs, which may otherwise have appeared quite oblique from each 547 other if the individual's head was tilted in the scanner. Thus, on balance, AC-PC alignment probably 548 mitigates placement error in lateral AFIDs compared to placing fiducials in the native MRI space. Further 549 research can examine these potential spatial biases more systematically. 550 551 Beyond evaluating correspondence, AFIDs could be used for point-based inter-subject or subject-to-552 template registration. AFIDs used in combination with classic rigid registration algorithms such as 553 Iterative Closest Point (Besl & McKay, 1992) may result in more optimal initial linear registration between 554 images. In addition, point-based deformable registration using (B-splines) may produce more efficient, 555 lower order deformable registrations between two images (Bookstein, 1997). To prevent circular 556 reasoning, we thought this would be best evaluated as independent studies. Finally one compelling 557 extension of this work would be to automate or semi-automate AFID placement, which would enable 558 inclusion of AFID-based metrics in standardized workflows involving template or intersubject registration. 559

Conclusions 560
Our proposed framework consists of the identification of anatomical fiducials, AFIDs, in structural 561 magnetic resonance images of the human brain. Validity has been established using several openly 562 available brain templates and datasets. We found that novice users could be trained to reliably place 563 these points over a series of interactive training sessions to within millimeters of placement accuracy. As 564 an example of different use cases, we examined the utility of our proposed protocol for evaluating 565 subject-to-template and template-to-template registration revealing that AFIDs are sensitive to focal 566 misregistrations that may be missed using other commonly used evaluation methods. This protocol holds 567 value for a broad number of applications including intersubject alignment and teaching neuroanatomy. 568 569