Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits
Introduction
Relating cortical structure to functional organization remains a major challenge in neuroimaging and the definition of the best set of morphological descriptors is still a matter of controversy (Van Essen and Dierker, 2007, Van Essen and Glasser, 2014). For instance, the points of maximum depth within folds have been proposed as reliable cortical landmarks (Im et al., 2010, Lohmann et al., 2008, Régis et al., 2005). However, a clear definition of these remarkable cortical points is still lacking, as illustrated by the fact that they have been successively named sulcal roots and sulcal pits in the literature. Regis and co-workers were the first to propose the concept of “sulcal roots” that refers to indivisible atomic folding entities located in the deeper parts of sulci and stable across subjects (Regis et al., 1995, Régis et al., 2005). This model establishes a link between the morphology of the cortical surface, its principal landmarks (sulci, gyri) and their development during ontogeny (Lefèvre et al., 2009, Régis et al., 2005, Van Essen, 1997). This idea was subsequently implemented as usable measures that can be extracted from anatomical MRI using a scale-space of the cortex mean curvature, applied for instance to the Central Sulcus (Cachia et al., 2003). In Li et al. (2009), Lohmann and von Cramon (2000) and Yang and Kruggel (2008), the authors proposed a framework to decompose each cortical fold into several substructures called “sulcal basins” using a watershed approach. Lohmann et al. then introduced in Lohmann et al. (2008) the “sulcal pits”, defined as the deepest points of each sulcal basin, and that are a concrete representation of the abstract concept of sulcal roots. The distinction between sulcal roots and sulcal pits thus lies in the fact that sulcal roots are conceptual entities while sulcal pits are defined algorithmically as the outcome of an automatic extraction procedure. Recently, Im et al. (2010) proposed a surface-based approach for the extraction of sulcal pits from a reconstructed cortical surface tessellation. Based on this method, several studies provided evidence of the interest of sulcal pits as remarkable macro-anatomical features. For instance, Im et al. (2010) quantified hemispheric asymmetries in the frequency and distribution of pits in cortical language areas. In Im et al. (2011b) the sulcal pits were used to analyze sulcal pattern variations across twins. The relationship between the presence of sulcal pits and intelligence was assessed in Im et al. (2011a). Recently, sulcal pits were used in a longitudinal study in order to quantify the development of cortical folds after birth (Meng et al., 2014).
Despite these very encouraging findings, the influence of several crucial parameters of the method used in these works for the extraction of sulcal pits (Im et al., 2010) has not been evaluated extensively, and no optimization procedure has been proposed so far. Designing an appropriate optimization framework for these parameters is mandatory to guarantee the reproducibility of results across studies and ensure the feasibility of sulcal pit extraction and analysis on large cohorts.
The algorithm proposed in Im et al. (2010) is intended to extract sulcal pits from an individual cortical surface and consists of two main steps: the estimation of a sulcal depth map, and the extraction of pits using a watershed by flooding algorithm (Rettmann et al., 2002). In order to filter noisy sulcal pits, the watershed is applied on a smoothed depth map until the water reaches a depth threshold value, and neighboring basins are merged when necessary. In Im et al. (2010), the merging decision is based on the following features when two basins meet at a ridge (see Fig. 1 for illustration):
- 1)
the ridge height (R) is the height difference between the shallowest pit and the ridge point (mm).
- 2)
the basin area (A) is calculated by summing the Voronoi region areas of the vertices (mm2)
- 3)
the distance between the two pits (D) is the geodesic distance between the pits (mm).
During the flooding, the shallowest basin is merged with the deepest one if: R < ThR and (D < ThD or A < ThA), where ThR, ThD and ThA are three threshold values set empirically to [ThR = 2.5 mm, ThD = 15 mm, ThA = 30 mm2] respectively. This filtering strategy aims at eliminating spurious extrema related to anatomically irrelevant variations in the depth map.
It is intuitive that the parameters [ThR, ThD, ThA], as well as the size of the smoothing applied to the depth map have a direct influence on the resulting sulcal basins and pits. More specifically, setting these parameters to arbitrary values could potentially induce an uncontrolled bias in the occurrence and spatial distribution of sulcal pits across the cortical surface, and artificially reduce their reproducibility across individuals. A strategy for defining optimal value for these parameters is crucial to ensure reproducible results across studies, and the use of different values of ThA in different studies shows that these parameters are essential: ThA = 30 mm2 in Im et al., 2010, Im et al., 2011a, Im et al., 2013 while ThA = 20 mm2 in Im et al. (2011b).
The present work aims at proposing a more robust and objective approach for the automatic extraction of sulcal pits. In order to reach this goal, we propose a framework specifically dedicated to optimizing the parameters of the method. This optimization framework relies on new measures for a better quantification of the reproducibility of the number of sulcal pits per region across individuals, in line with the assumptions of one-to-one correspondence of sulcal roots across individuals which is an explicit aspect of the sulcal roots model (Régis et al., 2005). We also propose several algorithmic improvements, including the use of a convenient sulcus depth estimation. Throughout this paper, we detail step-by-step each improvement. Our experiments on two different groups of subjects, with a total of 137 individuals, provide evidence of the good reliability of our sulcal pit extraction procedure across populations.
In addition to the above-mentioned improvements, we also demonstrate that the concept of sulcal pits can be extended to shallower and more superficial folds. This is a significant advance compared to previous work, where the authors considered deeper folds only. We further show the interest of extracting superficial pits by measuring the local asymmetry in the frequency of pits within all cortical regions, and by quantifying the relationship between the reproducibility of the number of sulcal pits per region across individuals and their respective depth.
Including superficial sulcal pits in further studies might provide additional insights e.g. concerning the anatomical and functional development of the brain.
Section snippets
Methods
In the following, we present a combination of improvements to the former method for the automatic extraction of sulcal pits (Im et al., 2010). Fig. 2 illustrates each of these improvements.
Data and preprocessing
137 right-handed subjects were selected from the Open Access Series of Imaging Studies (OASIS) database (www.oasis-brains.org) (Marcus et al., 2007). The OASIS cross-sectional dataset has a collection of 416 subjects aged from 18 to 96, including older adults with dementia. For each subject, three to four individual T1-weighted magnetization-prepared rapid gradient echo (MP-RAGE) scans were obtained on a 1.5 T Vision system (Siemens, Erlangen, Germany) with the following protocol: in-plane
Discussion
In this work, we presented a series of improvements to the method proposed in Im et al. (2010) for the automatic extraction of sulcal pits. These include 1) a notable modification of the watershed algorithm, 2) the use of a convenient depth estimation method, 3) an original subject-specific normalization procedure of the parameters and 4) a procedure for optimizing the parameters of the method in order to maximize inter-subject reproducibility, based on three new dedicated measures. Our
Conclusion
In this work, we presented a combination of improvements to the former method for the automatic extraction of sulcal pits. It has several major outcomes: 1) a more objective definition of pits through data-driven optimization of the parameters, 2) an increased reproducibility of the number of sulcal pits across individuals in deep sulcal pits clusters as compared to previous approach and 3) the extraction of pits is extended to shallow and variable folds and covers the entire cortical surface.
Acknowledgments
We are very grateful to Guillaume Masson for his helpful comments and careful reading of this manuscript. This research was supported through a Fondation de France (OTP 38872) and Fondation Orange (S1 2013-050) to G. Auzias and C. Deruelle. We also thank the reviewers of the paper for their valuable comments and the improvements they brought to the paper.
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