Fetal cortical surface atlas parcellation based on growth patterns

Abstract

Defining anatomically and functionally meaningful parcellation maps on cortical surface atlases is of great importance in surface‐based neuroimaging analysis. The conventional cortical parcellation maps are typically defined based on anatomical cortical folding landmarks in adult surface atlases. However, they are not suitable for fetal brain studies, due to dramatic differences in brain size, shape, and properties between adults and fetuses. To address this issue, we propose a novel data‐driven method for parcellation of fetal cortical surface atlases into distinct regions based on the dynamic “growth patterns” of cortical properties (e.g., surface area) from a population of fetuses. Our motivation is that the growth patterns of cortical properties indicate the underlying rapid changes of microstructures, which determine the molecular and functional principles of the cortex. Thus, growth patterns are well suitable for defining distinct cortical regions in development, structure, and function. To comprehensively capture the similarities of cortical growth patterns among vertices, we construct two complementary similarity matrices. One is directly based on the growth trajectories of vertices, and the other is based on the correlation profiles of vertices' growth trajectories in relation to a set of reference points. Then, we nonlinearly fuse these two similarity matrices into a single one, which can better capture both their common and complementary information than by simply averaging them. Finally, based on this fused similarity matrix, we perform spectral clustering to divide the fetal cortical surface atlases into distinct regions. By applying our method on 25 normal fetuses from 26 to 29 gestational weeks, we construct age‐specific fetal cortical surface atlases equipped with biologically meaningful parcellation maps based on cortical growth patterns. Importantly, our generated parcellation maps reveal spatially contiguous, hierarchical and bilaterally relatively symmetric patterns of fetal cortical surface development.

1. INTRODUCTION

Cortical surface atlases represent anatomical structures and other reference information in a spatial framework, thus playing a fundamental role for spatial normalization, analysis, visualization, and comparison of results across individuals or studies (Li et al., 2018; Van Essen & Dierker, 2007). Cortical surface atlases are usually equipped with parcellation maps featuring mosaic of subdivisions that are distinct in structure, function, or connectivity, thereby illuminating the structural and functional organizations of the cortex. These parcellation maps are essential for many neuroimaging studies for providing common cortical basic parcels in both region‐based and network‐based analyses, thus allowing efficient comparison of results across subjects and studies, and communication among researchers (Glasser et al., 2016). As each cortical parcel is relatively uniform in terms of cortical properties, parcellation maps also allow considerable reduction of the feature dimensionality in describing cortical properties for better prediction of cognitive outcomes and diagnosis of brain disorders.

Available cortical parcellation maps have been defined according to many different cortical properties in adult brains, such as anatomical sulcal–gyral foldings (Desikan et al., 2006), cytoarchitecture (Brodmann, 1909; Zilles & Amunts, 2009), myelin architecture (Glasser et al., 2016; Nieuwenhuys, Broere, & Cerliani, 2015), functional connectivity (Wang et al., 2015; Yeo et al., 2011), or a combination of multimodal information (Glasser et al., 2016). Among them, the AAL (Tzourio‐Mazoyer et al., 2002) and FreeSurfer Desikan (Desikan et al., 2006) parcellation maps based on cortical sulcal–gyral folding patterns have been extensively used in neuroimaging studies, since cortical folding can be relatively easily observed and reconstructed from structural MR images, in comparison with other cortical properties. However, to define fetal cortical parcellation maps, sulcal–gyral folding patterns are not very suitable, due to the following reasons. First, the cortical folding patterns are actually highly variable across individuals (Duan et al., 2017; Meng et al., 2018) and poorly match with the boundaries defined by microstructure, function, and development (Zilles & Amunts, 2010). Second, primary and secondary cortical folds are not well established and are still developing rapidly in the fetal brain (Benkarim et al., 2017; Studholme, 2011), which makes the sulcal–gyral landmarks unstable. As shown in Figure 1, which illustrates the typical development of the fetal cortical surfaces, many sulcal–gyral folds do not exist in early gestation and are gradually emerging when growth proceeds. Specifically, the central sulcus appears at 25 gestational weeks (GW) (Habas et al., 2011) and develops during 26–29 GW (Rajagopalan et al., 2011); the superior temporal sulcus appears between 25 and 27 GW, and forms between 28 and 29 GW (Clouchoux, Du Plessis, et al., 2012). Overall, during the latter half of gestation, the complexity of the cortical plate increases following a highly orchestrated sequence of sulcal–gyral formation (Clouchoux, Kudelski, et al., 2012; Rajagopalan et al., 2011; Wright et al., 2014). In particular, this sequence occurs in a hierarchical manner, in which primary and secondary sulci form in a consistent spatiotemporal pattern (Dubois et al., 2018; Wright et al., 2015), followed by tertiary folds that show increasing variability across individuals (Bendersky et al., 2006; Studholme, 2011).

Figure 1.

Dynamic development of fetal cortical surfaces, color‐coded by sulcal depth (mm) [Color figure can be viewed at http://wileyonlinelibrary.com]

In contrast, it is more appropriate to leverage the informative dynamic “growth patterns” of cortical properties (e.g., surface area, cortical thickness, and myelin content) for fetal cortical parcellation. This is because growth patterns of cortical properties in the fetus brain indirectly reflect the underlying rapid changes of cortical microstructures and their connections (e.g., increase in dendritic arborization, axonal elongation, and thickening, synaptogenesis (Kostović & Jovanov‐Milošević, 2006) and glial proliferation (Chan, Lorke, Tiu, & Yew, 2002; Dobbing & Sands, 1973). These microstructures essentially determine the molecular organization and functional principles of the cerebral cortex (Zilles & Amunts, 2010). Therefore, growth patterns of cortical properties provide a comprehensive view in defining parcellation maps that indicate distinct and meaningful regions in development, microstructure, and function.

In this article, we construct a set of spatiotemporal fetal cortical surface atlases and equip them with the first parcellation maps based on fetal cortical growth patterns. To this end, we propose a novel cortical parcellation method based on growth patterns of cortical properties, as shown in Figure 2. Specifically, to comprehensively capture both the low‐order (linear) and high‐order (nonlinear) similarities of growth patterns of vertices, we first construct two complementary similarity matrices of cortical vertices on the surface atlas. Then, we adopt a nonlinear network fusion method (Wang et al., 2014) to adaptively integrate these two similarity matrices together to capture both their common and complementary information. Finally, we perform spectral clustering on the fused similarity matrix to divide the spatiotemporal fetal cortical surface atlases into distinct regions. By applying our method on 25 normal fetuses from 26 to 29 GW, we create biologically meaningful parcellation maps based on fetal cortical growth patterns.

Figure 2.

Flowchart of fetal cortical parcellation based on growth patterns [Color figure can be viewed at http://wileyonlinelibrary.com]

2. MATERIALS AND METHODS

2.1. Subjects and MR image acquisition

In this study, we included 25 healthy fetuses (11 females) from singleton pregnancies with normal growth, without structural malformations or perinatal infections. Pregnancies were dated according to the first‐trimester crown‐rump length measurements (Robinson & Fleming, 1975). Fetal MRI was performed between 26 and 29 GW without sedation following the American College of Radiology Guidelines for Pregnancy and Lactation. Approval was obtained for the study protocol from the Ethics Committee of the Hospital Clínic in Barcelona, Spain (HCB/2014/0484) and all patients gave written informed consent.

T2‐weighted MR images were acquired on a 1.5 T scanner (Siemens Magnetom Aera syngo MR D13; Munich, Germany) with an eight‐channel body coil. Half Fourier acquisition single‐shot turbo spin echo (HASTE) sequences were used with the following parameters: Echo time = 82 ms, repetition time = 1,500 ms, slice thickness = 2.5 mm, field of view = 280 × 280 mm², and voxel size = 0.5 × 0.5 × 2.5 mm³. For each subject, multiple orthogonal two‐dimensional (2D) scans were collected, including 4 axial, 2 coronal, and 2 sagittal stacks. Final 3D motion‐corrected reconstructions were obtained from these eight stacks of thick 2D scans. Brain localization and extraction from 2D scans were carried out in an automatic manner using the approach proposed by (Keraudren et. al., 2014), followed by high‐quality 3D volume reconstruction using the method presented in (Kuklisova‐Murgasova et al., 2012).

2.2. Image processing and cortical surface atlas construction

All 3D MR images were processed using the following procedures. First, for each subject, we segmented the reconstructed high‐quality 3D MR image into white matter, gray matter, cerebrospinal fluid, ventricles, cerebellum, and brainstem using the method proposed in (Sanroma et al., 2016), which is an ensemble method learning the optimal spatial combination of a set of base methods. Second, we masked and filled noncortical structures, and also separated the left and right hemispheres. Third, based on the segmentation of each hemisphere, we corrected topological errors (Hao et al., 2016) and reconstructed inner, middle, and outer cortical surfaces, by using a topology‐preserving deformable surface method (Li, Nie, et al., 2014; Li, Nie, Wu, et al., 2012; Nie et al., 2011). Fourth, we mapped each cortical surface onto a standard spherical surface using FreeSurfer and then group‐wisely coregistered spherical surfaces across all subjects for each hemisphere using Spherical Demons (Yeo et al., 2010). Fifth, based on registration results, we resampled each cortical surface to a standard mesh tessellation, thus establishing intersubject vertex‐to‐vertex cortical correspondences. Finally, for each vertex, we computed its multiple cortical properties, for example, surface area, sulcal depth, average convexity, and mean curvature (Li et al., 2015). Herein, the sulcal depth of each vertex was defined as the distance to its nearest corresponding vertex on the cerebral hull surface, which is a surface running along the margins of gyri without dipping into sulci (Li et al., 2013; Van Essen, 2005). The vertex‐wise surface area was computed as one‐third the sum of the areas of all triangles associated with this vertex on the resampled middle surface (Li, Nie, Wang, et al., 2012). For cortical parcellation, each cortical surface initially in high resolution was downsampled to have 2,562 vertices.

To characterize the dynamic spatiotemporal fetal cortical changes, we divided all subjects into four age groups with balanced subject numbers, that is, 26.3–26.7 (6 subjects), 26.8–27.3 (6 subjects), 27.4–28.4 (7 subjects), and 28.5–28.9 GW (6 subjects), and constructed a cortical surface atlas for each age group. Specifically, a cortical surface atlas consists of the mean and variance of geometric features of cortical folding, for example, mean curvature, sulcal depth, average convexity of the original surface, and mean curvature of inflated surface, across all subjects at this age group on the spherical surface, as in (Li et al. 2015). In this way, the constructed fetal cortical surface atlases were temporally consistent and also unbiased to any individual and any age. Figure 3 shows the constructed fetal cortical surface atlases at four time points.

Figure 3.

The constructed fetal cortical surface atlases. Panels (a–c) are the mean curvature, average convexity, and sulcal depth (mm) in the spherical space. Panels (d–f) are the mean curvature, average convexity, and sulcal depth (mm) on age‐specific, population‐averaging inner surfaces, respectively. Numbers on the left denote the average gestational weeks of each group [Color figure can be viewed at http://wileyonlinelibrary.com]

2.3. Computing similarity matrices of cortical growth patterns

To define the growth patterns of the fetal cerebral cortex, ideally, we should use longitudinal fetal MRI data. This is, however, very difficult to obtain due to both ethical and practical issues. Therefore, as an alternative, we leveraged healthy fetuses in a cross‐sectional study, with each fetal subject only having one time point, to perform growth‐pattern‐based cortical parcellation. Specifically, we sorted all fetal cortical surfaces by incremental gestational age and then constructed the growth trajectories of cortical properties for each vertex. Herein, we adopted the surface area, as the convoluted cerebral cortex is achieved predominately by an increase in the surface area of a smooth sheet rather than its thickness, or other cortical properties (Rakic, 1988; Rakic et al., 2009). However, our method is generic and can also work on other cortical properties, for example, cortical thickness and local gyrification index, as long as their computation is reliable. Thus, our goal is to create a population‐level cortical parcellation map, which will be used to equip our constructed fetal cortical atlases, based on the growth patterns of surface area in the fetal brain. To this end, we first computed the similarities of growth patterns between each pair of vertices on the cortical surface. To comprehensively capture the similarities of growth patterns, we constructed two complementary similarity matrices S₁ and S₂, based on (a) growth trajectories of surface area and (b) growth correlation profiles of surface area, respectively.

Specifically, we defined the first similarity matrix S₁ by considering the growth trajectory of surface area at each surface vertex as a feature vector F₁. Between each pair of vertices i and j, we computed the Pearson's correlation coefficient p of their growth trajectories and obtained their similarity as follows.

$${\mathbf{S}}_1\left(i,j\right)=\frac{1+p\left({\mathbf{F}}_1\left(i\right),{\mathbf{F}}_1\left(j\right)\right)}{2},i,j\in 1,\dots ,N.$$ (1)

Here, N is the total number of vertices on the cortical surface (N = 2562 × 2, considering both hemispheres in our case), and vectors F₁(i) and F₁(j) are the growth trajectories of surface area of vertex i and j, respectively. S₁ ranges from 0 to 1. Intuitively, high correlations between two vertices indicate high similarities of growth patterns. However, this similarity definition is inherently linear (low‐order), thus ignoring the complex and high‐order similarity of growth patterns.

To address this issue, we defined the second similarity matrix S₂ to capture the complex similarity of cortical growth patterns among vertices. First, we uniformly sampled 320 vertices from both cortical hemispheres as reference points, marked by the small yellow balls in Figure 2a. Then, for each vertex, we calculated the Pearson's correlation coefficient between its growth trajectory of surface area and that of each reference point. In this way, for each vertex, we constructed a growth correlation profile as a new feature vector F₂(i), representing the correlation of growth trajectories between this vertex and each reference point. We then computed the similarity matrix S₂ based on the growth correlation profiles of vertices as:

$${\mathbf{S}}_2\left(i,j\right)=\frac{1+p\left({\mathbf{F}}_2\left(i\right),{\mathbf{F}}_2\left(j\right)\right)}{2},i,j\in 1,\dots ,N.$$ (2)

Intuitively, two vertices with a high correlation of their growth correlation profiles indicate a high similarity of their growth patterns. Thus, S₂, based on “correlations of correlations”, captures more complex and high‐order nonlinear similarity in growth patterns.

2.4. Fusing similarity matrices of cortical growth patterns for parcellation

To parcellate the fetal cortical surfaces into a set of regions based on these two complementary similarity matrices S₁ and S₂, one intuitive method is to simply average them after normalization and then perform clustering based on this averaged matrix. However, simple averaging cannot fully capitalize on both common and complementary information across the two matrices, thus leading to biased and less meaningful parcellations. To address this issue, we nonlinearly fused the two similarity matrices, that is, S₁ and S₂, into a single matrix S in order to capture the full spectrum of underlying low‐order and high‐order data similarities, by using a similarity network fusion (SNF) (Wang et al., 2014) and then performed spectral clustering (Ng, Jordan, & Weiss, 2002) based on the fused matrix. Specifically, to fuse these two similarity matrices, for each S_m, m ∈ {1, 2}, we first computed a full kernel matrix P_m as:

$${\mathbf{P}}_{\mathrm{m}}\left(i,j\right)=\left\{\begin{array}{c}\frac{{\mathbf{S}}_{\mathrm{m}}\left(i,j\right)}{2{\sum }_{k\ne i}{\mathbf{S}}_{\mathrm{m}}\left(i,k\right)},j\ne i\\ \frac{1}{2},j=i\end{array}\right.,m\in \left\{1,2\right\}.$$ (3)

The full kernel matrix P_m is a normalized weight matrix, where the normalization not only ensured ∑_jP_m(i, j) = 1 but also guaranteed that P_m is free of the scale of self‐similarity in the diagonal entries. Then, we also computed a sparse kernel matrix Q_m as:

$${\mathbf{Q}}_{\mathrm{m}}\left(i,j\right)=\left\{\begin{array}{c}\frac{{\mathbf{S}}_{\mathrm{m}}\left(i,j\right)}{{\sum }_{k\in {\mathcal{N}}_i}{\mathbf{S}}_{\mathrm{m}}\left(i,k\right)},j\in {\mathcal{N}}_i\\ 0,\text{otherwise}\end{array}\right.,m\in \left\{1,2\right\},$$ (4)

where the neighborhood ${\mathcal{N}}_i$ denotes the K most similar neighbors of vertex i, based on high correlation coefficients. In the sparse kernel matrix Q_m, the similarity between nonneighboring vertices (in terms of the pairwise similarity values) is set as zero, based on the basic assumption that neighboring high similarities are more reliable than remote ones. As a result, P₁ and P₂ carry full information about the similarity of each vertex to all others in terms of growth patterns, whereas Q₁ and Q₂ only encode the similarities to the K most similar vertices for each vertex. To fuse the two similarities, for iteration t, ${\mathbf{P}}_1^t$ and ${\mathbf{P}}_2^t$ were updated as:

$${\mathbf{P}}_1^t={\mathbf{Q}}_1\times {\mathbf{P}}_2^{t-1}\times {\left({\mathbf{Q}}_1\right)}^{\mathrm{T}},$$ (5)

$${\mathbf{P}}_2^t={\mathbf{Q}}_2\times {\mathbf{P}}_1^{t-1}\times {\left({\mathbf{Q}}_2\right)}^{\mathrm{T}},$$ (6)

where (·)^T indicates matrix transpose. Essentially, in Equations 5, 6, the two matrices P₁ and P₂ were fused based on a message‐passing method, where these two matrices were updated iteratively to become more similar to each other with each iteration. The advantage of this procedure is that weak similarities (low‐weight edges/connections) gradually disappear, thus helping reduce the noise, and strong similarities (high‐weight edges/connections) present in one or more matrices are added to others. After t^* iterations, the fused matrix S was computed as the average of ${\mathbf{P}}_1^{t^{*}}$ and ${\mathbf{P}}_2^{t^{*}}$.

Another way to interpret the updating rule (5) is:

$${\mathbf{P}}_1^t\left(i,j\right)={\sum }_{k\in {\mathcal{N}}_i}{\sum }_{l\in {\mathcal{N}}_j}{\mathbf{Q}}_1\left(i,k\right)\times {\mathbf{Q}}_1\left(j,l\right)\times {\mathbf{P}}_2^{t-1}\left(k,l\right);$$ (7)

(similar for ${\mathbf{P}}_2^t\left(i,j\right)$). Here, ${\mathcal{N}}_j$ denotes the K nearest neighbors of vertex j in terms of similarity values. We can see the similarity information is only propagated through the common neighbors. If vertices i and j have common neighbors in both similarity matrices P₁ and P₂, it is highly possible that they belong to the same cluster. Moreover, even if vertices i and j are not very similar in one matrix, their similarity can be expressed in the other matrix and this similarity information can be propagated through the fusion process.

Based on the fused similarity matrix S, the parcellation was performed by using spectral clustering (Ng et al., 2002). In spectral clustering, the data are represented in an eigenspace of the similarity matrix using only its top eigenvectors, which can better capture the distributions of the original data points. As spectral clustering requires a predefined number of clusters, we determined an adequate number using both existing neuroscience knowledge and the widely used silhouette coefficient (Chen et al., 2013; Zilles & Amunts, 2012).

3. RESULTS

3.1. Visual inspection of parcellation results

We performed the cortical surface parcellations based on the growth patterns of surface area, by utilizing 25 normal fetuses. The parameter K was defined empirically through visual inspection of the results, which was subsequently set as 200 in the current work. In Section 3.1.1, to illustrate the effectiveness of the nonlinear fusion in our method, we compared the parcellation results using our fusion‐based method with the parcellation results using the average‐based method (which simply averages the two similarity metrices after normalization) and the parcellation results using only each of the two similarity matrices separately. Moreover, in Section 3.1.2, we also compared with results by using Spearman's rank coefficient (Jessica et al., 2012), which can measure nonlinear correlations, instead of Pearson's correlation in our method. In all results, we empirically set K (the number of nearest neighbors) to 200. Of note, this study mainly focused on parcellations with relatively large‐scale, primary structures, as in (Chen et al. 2013).

3.1.1. Effectiveness of nonlinear fusion

Figure 4 shows the parcellation results on both the left and right hemispheres jointly by increasing the numbers of clusters from 2 to 10. Four panels of a–d in Figure 4 show the parcellation results obtained by using (a) our fusion‐based method, (b) the average‐based method, (c) the similarity matrix based on the growth trajectory, and (d) the similarity matrix based on the growth correlation profile, respectively.

Figure 4.

Fetal cortical surface parcellations based on the growth patterns of surface area, with different numbers of clusters from 2 to 10 on the left and right hemispheres, by (a) our proposed fusion of the two similarity matrices, (b) simply averaging of the two similarity matrices, (c) using the similarity matrix based on the growth trajectory, and (d) using the similarity matrix based on the growth correlation profile [Color figure can be viewed at http://wileyonlinelibrary.com]

It is worth to note that our method outperforms the other three methods in terms of both boundary stability and hemispheric symmetry. First, as shown in Figure 4a, when the number of clusters increased, new emerging clusters identified by our proposed approach tended to respect the boundaries of preceding clusters, thus forming a meaningful hierarchical organization of the growth patterning of surface area. Specifically, in the parcellation with 2 clusters, the proposed method identified a dorsal–ventral (D–V) division. The division separated the motor, premotor, and parietal regions (the dorsal cluster) from the prefrontal, temporal, occipital, and precuneus regions (the ventral cluster). This boundary (as indicated by black arrows) was continuously well‐preserved in our proposed method from 2 clusters till 10 clusters. Also, the boundary between the medial frontal cortex and the lateral frontal cortex (as indicated by red arrows) appeared in 4 clusters and was well‐preserved to 10 clusters by our method. In contrast, the boundaries identified by the other three methods were not well respected across different numbers of clusters. Therefore, these comparisons indicate that the parcellation boundaries discovered by our proposed method are more meaningful, in comparison with other three methods.

Second, the parcellations produced by our method presented relatively symmetric patterns on the left and right hemispheres. Of note, the clustering was performed on both hemispheres simultaneously with no constraint for hemispheric symmetry. In contrast, the parcellation results obtained by the other three methods showed relatively inconsistent left–right patterns, especially from 8 clusters to 10 clusters, as indicated by blue, gray, orange, and dark green arrows in Figure 4b–d. For example, in Figure 4b, the cluster of the anterior insula and ventrolateral prefrontal regions, as indicated by gray arrows, only appeared in the right hemisphere from 8 clusters to 10 clusters. In Figure 4b–d, the dark pink clusters at the left orbitofrontal region, as indicated by dark green arrows, had meaningless corresponding regions at the right temporal pole from 8 clusters to 10 clusters. The boundaries indicated by light green arrows crosscut the central sulcus in the left hemisphere, but the corresponding boundaries on the right hemisphere aligned with the precentral sulcus. The light blue clusters at the right medial occipital cortex in Figure 4b,d, and the dark green cluster at the right medial occipital cortex in Figure 4c, as indicated by the orange arrows, had meaningless corresponding regions at the left medial occipital cortex. All these results suggested that the proposed method led to more meaningful parcellations with more hierarchical and symmetric organizations.

3.1.2. Comparison with using nonlinear similarity metric

Figure 5 shows the parcellations with different numbers of clusters, from 2 to 10, jointly on the left and right hemispheres, by using our fusion‐based method based on the Spearman's rank correlation coefficient, instead of the Pearson's correlation coefficient. Compared with the parcellations using the Pearson's correlation coefficient in Figure 4a, the boundaries of parcellations in Figure 5 were not well respected across different numbers of clusters. For example, the boundary between the superior frontal gyrus and the middle frontal cortex (as indicated by red arrows in Figure 5) appeared at 4 clusters but was not well preserved from 6 clusters. The boundary between parietal and temporal cortices (as indicated by blue arrows in Figure 5) was not well preserved at 10 clusters. Moreover, compared with Figure 4a, the parcellations in Figure 5 showed less symmetric patterns. For instance, the light green cluster at the left sensorimotor region, as indicated by the light green arrow, had larger and meaningless corresponding regions at the right parietal cortex at 10 clusters. The dark green cluster at the left pericalcarine region, as indicated by orange arrows, had meaningless corresponding regions in the right hemisphere at 10 clusters. These parcellation results suggest that it is more suitable to use the Pearson's correlation coefficient to measure the similarity of growth patterns during 26–29 GW.

Figure 5.

Fetal cortical surface parcellations based on the growth patterns of surface area, with different numbers of clusters from 2 to 10 on the left and right hemispheres, by our proposed fusion‐based method based on the Spearman's rank correlation coefficient [Color figure can be viewed at http://wileyonlinelibrary.com]

3.2. Evaluation of parcellation quality using silhouette coefficient

Evaluation of the parcellation results is important, as any clustering method can find clusters in the data, even if the data may not have natural cluster structures. There are two important cluster properties typically evaluated: Intraclass dissimilarity and interclass dissimilarity. The first one determines how distinct the objects in the same cluster are, and the second one determines how distinct a cluster is from other clusters. Ideally, the best cluster number shows small intraclass dissimilarity and large interclass dissimilarity. As employed by many cortical parcellation studies (Chen et al., 2013), the silhouette coefficient combining these two criteria is commonly used to evaluate the clustering, computed as:

$$\mathit{sc}\left(i\right)=\frac{b\left(i\right)-a\left(i\right)}{\max \left(a\left(i\right),b\left(i\right)\right)},$$ (8)

where sc(i) is the silhouette coefficient for the vertex i, a(i) is the average dissimilarity between the vertex i and all other vertices in the same cluster; b(i) is the minimum average dissimilarity of vertex i to any other clusters that vertex i does not belong to. The dissimilarity between two vertices i and j is computed as 1 − S(i, j). High sc means small intraclass dissimilarity and large interclass dissimilarity, while low sc means large intraclass dissimilarity and small interclass dissimilarity.

Figure 6 shows the average silhouette coefficients of parcellations by using the single similarity matrix based on the growth trajectories, the single similarity matrix based on the growth correlation profile, the average‐based and fusion‐based methods for cluster numbers from 2 to 20. To compare the silhouette coefficients clearly, we connected the points at different clusters for each method by imaginary lines. From 5 clusters to 17 clusters, the parcellations by using fusion‐based method (as indicated by the red line) consistently achieve higher silhouette coefficient values than using any single matrix, indicating that our method leads to smaller intraclass dissimilarity and larger interclass dissimilarity. In the following, we will further determine the appropriate number of clusters and analyze this parcellation obtained by using the fusion‐based method.

Figure 6.

Average silhouette coefficients of the parcellations by different methods using different numbers of clusters [Color figure can be viewed at http://wileyonlinelibrary.com]

3.3. Determining region numbers in parcellation maps

According to the silhouette coefficient, we determined the appropriate number of clusters by looking for the numbers of clusters with high values, while their neighboring numbers also show stable values without steep jumps. The highest silhouette coefficient corresponds to 5 clusters. After that, the silhouette coefficient reaches a relatively stable plateau from 6 clusters to 10 clusters and then decreases significantly after 10 clusters. Accordingly, we showed our final parcellation results at two resolution levels with 5 clusters (for relatively coarse parcellation) and 10 clusters (for relatively fine parcellation; Figure 7a,b). It is worth mentioning that all clusters largely correspond to anatomically meaningful specializations, with their approximated names shown in columns below the parcellation results. In 10 clusters parcellation results, subdivisions of the frontal cortex roughly include the dorsolateral prefrontal cortex, cingulate and medial frontal cortex, ventrolateral prefrontal, as well as orbitofrontal and anterior cingulate cortex (Figure 7b, Clusters 3–6). The sensorimotor region includes the precentral gyrus in the frontal cortex and the postcentral gyrus in the parietal cortex (Figure 7b, Cluster 1). The posterior parietal cortex constitutes a single cluster (Figure 7b, Cluster 2). The temporal cortex includes the medial temporal, anterior temporal and posterior insula, as well as posterior temporal regions (Figure 7b, Clusters 7–9). The occipital cortex and precuneus constitute one cluster (Figure 7b, Cluster 10).

Figure 7.

Parcellation results with 5 clusters and 10 clusters, respectively [Color figure can be viewed at http://wileyonlinelibrary.com]

3.4. Seed‐based analysis of parcellation map

To further verify our parcellation at 10 clusters, we performed seed‐based correlation analysis as employed in adult cortical parcellations by (Chen et al. 2013). Specifically, we showed the correlation patterns of 25 uniformly sampled seeds on each hemisphere with all vertices across the hemisphere (Figure 8). As can be observed, on both hemispheres, the seeds are strongly correlated with other vertices in the same cluster, while seeds have low correlations with those vertices in other different clusters. Moreover, seeds in the same cluster yielded similar correlation patterns, while seeds across the boundaries of clusters led to quite different patterns, indicating the meaningfulness of our parcellation.

Figure 8.

Seed‐based correlation analysis of growth patterns of surface area. For each of the 25 seeds on each hemisphere, its correlation with all other vertices in terms of growth patterns is shown as a small respective color‐coded surface map [Color figure can be viewed at http://wileyonlinelibrary.com]

3.5. Comparison with FreeSurfer Desikan parcellation

To quantitively analyze our parcellation map at 10 clusters, we evaluated the overlap between our parcellation and the FreeSurfer Desikan parcellation (Desikan et al., 2006) in our atlas space by using Dice coefficient, as in (Lefèvre et al., 2018). Of note, the FreeSurfer Desikan parcellation in our atlas space was generated by mapping all individual's Desikan parcellation maps onto the atlas space and then performing majority voting. Since the number of regions in our parcellations is different from that of the FreeSurfer parcellation with 34 cortical regions, we accordingly merged the corresponding FreeSurfer regions in the atlas space to match our parcellation. The region correspondences were shown in Table 1, and the merged FreeSurfer parcellations were shown in Figure 9. Dice coefficients between each cluster obtained by our method and the merged FreeSurfer parcellations in both atlas space and the individual surfaces were summarized in Tables 2 and 3, respectively. We found that some clusters on the left hemisphere in our parcellation have relatively high Dice values with the merged FreeSurfer parcellation, especially in clusters 2, 7, and 10. However, we should note that our parcellation is generated based on growth patterns of fetal cortical surface area, thus indicating developmentally distinct regions, while FreeSurfer parcellation is based on sulcal–gyral patterns.

Table 1.

Our parcellation with 10 clusters and the corresponding merged FreeSurfer parcellation

Cluster in our parcellation	Merged clusters in FreeSurfer Desikan parcellation
Sensorimotor	Postcentral and precentral gyri
Posterior parietal	Supramarginal gyrus, inferior parietal, and superior parietal cortices
Dorsolateral prefrontal	Caudal middle frontal gyrus, rostral middle frontal gyrus, and pars opercularis
Cingulate and media frontal	Superior frontal gyrus, paracentral lobule, posterior‐cingulate, and caudal anterior‐cingulate cortices
Ventrolateral prefrontal and anterior insula	Pars triangularis, pars orbitalis, lateral orbital frontal, and insula cortices
Orbitofrontal and anterior cingulate	Medial orbital frontal cortex, rostral anterior cingulate, and frontal pole
Medial temporal	Temporal pole, entorhinal cortex, parahippocampal gyrus, and fusiform gyrus
Posterior temporal	Banks of the superior temporal sulcus
Anterior temporal and posterior insula	Superior temporal gyrus, middle temporal gyrus, inferior temporal gyrus, and transverse temporal cortex
Occipital and precuneus	Lingual gyrus, pericalcarine cortex, cuneus cortex, isthmus‐cingulate cortex, and precuneus cortex

Figure 9.

Our parcellations with 10 clusters and the merged FreeSurfer parcellation [Color figure can be viewed at http://wileyonlinelibrary.com]

Table 2.

Dice coefficients between the merged FreeSurfer parcellation and each of the 10 clusters in the atlas space obtained by our proposed method

Clusters	1	2	3	4	5	6	7	8	9	10
LH (left hemisphere)	0.68	0.80	0.46	0.72	0.63	0.53	0.81	0.57	0.72	0.79
RH (right hemisphere)	0.68	0.63	0.43	0.81	0.51	0.57	0.69	0.32	0.54	0.71

Table 3.

Dice coefficients between individual's merged FreeSurfer parcellation and each of the 10 clusters obtained by our method

Clusters	1	2	3	4	5	6	7	8	9	10
LH	0.64 ± 0.040	0.75 ± 0.027	0.42 ± 0.040	0.72 ± 0.022	0.61 ± 0.022	0.64 ± 0.057	0.81 ± 0.023	0.53 ± 0.072	0.71 ± 0.025	0.71 ± 0.052
RH	0.60 ± 0.059	0.62 ± 0.042	0.32 ± 0.136	0.73 ± 0.060	0.48 ± 0.062	0.53 ± 0.103	0.67 ± 0.052	0.29 ± 0.062	0.54 ± 0.029	0.66 ± 0.036

3.6. Tree diagram of region hierarchy

We next examined the region‐level relations of the 10 identified clusters, which forms a tree diagram showing the hierarchy of the regional organization. Specifically, the similarity between each pair of clusters was defined as the average similarity between any pair of vertices in these two clusters. By analyzing the relatedness between regions, a tree diagram can be specified, summarizing the relationship of the organization of regions as shown in Figure 10. We found that the clusters within the same lobe are generally more correlated than clusters in different lobes. As reflected in the tree diagram, where the functionally specialized subdivisions are generally nested within lobes. The frontal cortex which includes the dorsolateral prefrontal cortex, cingulate and medial frontal cortex, ventrolateral prefrontal, as well as orbitofrontal and anterior cingulate cortex (Clusters 3–6) share the similar color in Figure 10, marked by a pink rectangle. Of note, there is a high correlation with the sensorimotor (Cluster 1) and posterior parietal cluster (Cluster 2), marked by a black rectangle. The temporal cortex includes the medial temporal, anterior temporal and posterior insula, as well as posterior temporal regions (Figure 7b, Clusters 7–9), share the similar color in Figure 10, marked by a green rectangle. An exception is the posterior temporal cluster (Cluster 8), which also showed high correlations with two clusters, that is, the sensorimotor and the posterior parietal clusters (Clusters 1 and 2), even though they are in different lobes.

Figure 10.

The similarity matrix and the dendrogram of parcellation regions. The color scale represents the mean growth pattern correlations within and between clusters. The parietal cortex is marked by black rectangle, the frontal cortex is marked by pink rectangle, and the temporal cortex is marked by green rectangle [Color figure can be viewed at http://wileyonlinelibrary.com]

This tree diagram suggests that successive clusters tend to be subdivisions of previous clusters, which implies the hierarchical structure of the parcellation results. This observation is also consistent with the hierarchical progression of cluster solutions from 2 to 10 clusters as shown in Figure 11. Of note, no hierarchical constraint has been imposed in our approach, where each cluster was derived independently. Yet, the sequentially nonoverlapping patterns reveal that the emerging clusters tended to respect the boundaries of preceding clusters and appeared to be nested subdivisions. Some examples of nested subdivisions, consistent with hierarchical organization, are as follows: At 3 clusters, the occipital and precuneus regions are separated from the ventral cluster; at 5 clusters, the prefrontal, cingulate, medial frontal, and temporal regions are additionally subdivided from the ventral cluster. Further subdivisions of the basic structure continue in the successive cluster solutions. For example, the posterior parietal, sensorimotor, and dorsolateral prefrontal regions are all subdivisions of the dorsal cluster in the 2 clusters parcellation. Also, in the 10 clusters solution, the anterior temporal and posterior temporal regions are all the subdivisions of the temporal cluster in the 5 clusters solution. The convergence of results of this analysis and the dendrogram thus provide further evidence for a hierarchical structure of growth patterning that is intrinsic to the data.

Figure 11.

The newly emerged regions with increasing the number of clusters, shown on gray cortical surfaces (lh: left hemisphere, rh: right hemisphere) [Color figure can be viewed at http://wileyonlinelibrary.com]

3.7. Growth pattern of surface area in each cluster

Based on our parcellation with 10 clusters, we investigated the growth pattern of surface area of each cluster, as shown in Figures 12 and 13. For each cluster on both hemispheres, we showed its growth trend and growth rate (per week) of surface area. To determine which function can more accurately model the growth trends that reflect the relationship between surface area and gestational weeks, we have used three previously‐adopted models, that is, a quadratic function (Clouchoux, Du Plessis, et al., 2012), a Gompertz function (Dubois et al., 2018; Wright et al., 2014), and a linear function (Garcia et al., 2018), to fit the growth trend in each cluster. From Table 4, we found that overall the quadratic function was best to fit the growth trends (with highest R² values) during 26–29 GW. Therefore, we finally selected the quadratic function to fit the growth trend of surface area, which also has been used in (Clouchoux, Kudelski, et al., 2012). In Figures 12 and 13, as we can see, each cluster exhibited region‐specific dynamic growth patterns, with the clusters on the dorsal lateral surface generally exhibiting higher growth rates than other clusters on ventral and medial surfaces.

Figure 12.

The growth trajectory of surface area for each cluster on the left hemisphere, with second‐order polynomial fitting. The percentages shown on the top surfaces are the growth rate of the surface area for all the clusters [Color figure can be viewed at http://wileyonlinelibrary.com]

Figure 13.

The growth trajectory of surface area for each cluster on the right hemisphere, with second‐order polynomial fitting. The percentages shown in the top surfaces are the growth rate of the total surface area for all the clusters [Color figure can be viewed at http://wileyonlinelibrary.com]

Table 4.

R² of fitted models in each cluster on the left and right hemispheres

Clusters	Left hemisphere			Right hemisphere
	Quadratic	Gompertz	Linear	Quadratic	Gompertz	Linear
Sensorimotor	0.8018	0.8015	0.7998	0.7903	0.7904	0.7662
Posterior parietal	0.6815	0.6810	0.6814	0.7308	0.7300	0.7305
Dorsolateral prefrontal	0.7755	0.7752	0.7726	0.6755	0.6751	0.6727
Cingulate and media frontal	0.6275	0.6191	0.6180	0.6375	0.6375	0.6375
Ventrolateral prefrontal and anterior insula	0.6146	0.6071	0.5976	0.7241	0.6551	0.6214
Orbitofrontal and anterior cingulate	0.6425	0.6085	0.5308	0.6057	0.6002	0.5918
Medial temporal	0.5398	0.5317	0.5068	0.6181	0.6062	0.5759
Posterior temporal	0.6850	0.6833	0.6820	0.6286	0.6011	0.5981
Anterior temporal and posterior insula	0.6565	0.6548	0.6516	0.6822	0.6819	0.6643
Occipital and precuneus	0.7352	0.6655	0.7321	0.7282	0.6344	0.7226

On the left hemisphere, the sensorimotor exhibited the highest growth rate of 26.75% per week, and the posterior parietal, posterior temporal, and dorsolateral prefrontal regions also exhibited relatively high growth rate, that is, 22.60, 25.64, and 21.35% per week, respectively. While the medial temporal cortex presented the lowest growth rate of 11.96% per week, and the orbitofrontal and anterior cingulate regions presented relatively low growth rate of 13.72% per week. On the right hemisphere, the growth pattern of each cluster is generally similar to that of its corresponding cluster on the left hemisphere. Especially, the posterior temporal region presented the highest growth rate of 31.34% per week, which is even higher than the growth rates of the corresponding regions on the left hemisphere. The posterior parietal, sensorimotor, and dorsolateral prefrontal regions presented relatively high growth rates, that is, 30.25, 22.89, and 21.19% per week, respectively. The medial temporal cortex still showed the lowest growth rate of 12.30% per week, and the orbitofrontal and anterior cingulate cluster showed relatively low growth rate of 12.94% per week.

3.8. Hemispheric asymmetries of clusters

In Figures 12 and 13, most clusters on the left and right hemispheres are relatively symmetric, but there are still a few asymmetric clusters, such as the posterior temporal cluster, medial occipital and precuneus cluster, medial temporal cluster as well as anterior temporal and posterior insula cluster. The mean area in each cluster of all subjects on the left and right hemispheres is shown in Table 5. To identify the hemispheric differences of surface area, for the surface area in each cluster, left and right hemispheres were statistically compared by using paired t‐test. To correct for multiple comparisons, an adaptive false discovery rate (FDR) method (Benjamini & Hochberg, 1995) was used. The t‐value and p‐value of the mean area in each cluster were shown in Table 5, and the significantly (p < .001) asymmetric clusters of area are marked by “*”. Moreover, for the surface area in each cluster, its asymmetry index (AI) was computed as AI = (left − right)/(0.5 (left + right) (Li et al., 2013), shown in Table 5. Herein, a positive AI indicates leftward hemispheric asymmetry (with the left side larger than the right side), and a negative AI indicates rightward asymmetry. As we can see, the right posterior temporal cluster (Cluster 8) and the right occipital and precuneus cluster (Cluster 10) are significantly larger, compared to that of the corresponding left clusters. Oppositely, the left medial temporal cluster (Cluster 7) and the left anterior temporal and posterior insula cluster (Cluster 9) are significantly larger compared to that of the corresponding right clusters.

Table 5.

Distribution of surface area and its hemispheric asymmetry of each cluster

Clusters	Left (mm2)	Right (mm2)	AI	t‐value	p‐value
Sensorimotor	647.26	637.99	0.014	1.05	0.152
Posterior parietal	854.02	837.87	0.019	1.46	0.078
Dorsolateral prefrontal	890.90	863.88	0.031	2.95	0.047
Cingulate and medial frontal	648.81	665.07	−0.025	−2.57	0.083
Ventrolateral prefrontal and anterior insula	1,015.07	1,042.27	−0.026	−2.68	0.065
Orbitofrontal and anterior cingulate	633.98	632.72	0.002	0.32	0.623
Medial temporal	1,056.17	982.15	0.073	8.42	0.00005*
Posterior temporal	286.23	317.65	−0.104	−4.93	0.0005*
Anterior temporal and posterior insula	675.94	640.48	0.054	5.54	0.0001*
Occipital and precuneus	1,279.46	1,361.95	−0.063	−6.83	0.00009*

Significantly (p < .001) asymmetric clusters of area are marked by “*”.

4. DISCUSSION AND CONCLUSIONS

Several fetal cortical parcellation maps have been defined based on geometrical features using the spectral clustering method (Dahdouh & Limperopoulos, 2016; Lefèvre et al., 2018; Pepe et al., 2015). However, these studies did not leverage the rich dynamic growth information in fetal brains. In this article, we proposed a novel approach to unprecedentedly parcellate the fetal cortical surface atlases into distinct regions based on the dynamic growth patterns of cortical properties. Since the shape, size, and properties (e.g., surface area, cortical thickness, and myelination) of the fetal cerebral cortex change rapidly and complicatedly (Benkarim et al., 2017), utilizing the similarity of dynamic growth patterns of cortical properties to partition fetal cortical surface can better capture the developmental information of the fetal cerebral cortex, and reflect the underlying microstructural boundaries. To comprehensively capture both the linear (low order) and nonlinear (high order) similarities of growth patterns of vertices, we constructed two similarity matrices. The first similarity matrix was defined based on Pearson's correlation of the growth trajectories between each pair of vertices on the cortical surface. The second similarity matrix was defined based on the correlation of the “growth correlation profiles” between each pair of vertices on the cortical surface. For each vertex, its growth correlation profile was defined as the Pearson's correlation coefficient between its growth trajectory of surface area and that of each reference point (uniformly sampled from both hemispheres). To effectively leverage the information of the two similarity matrices, we used a nonlinear fusion method (Wang et al., 2014) to fuse these two similarity matrices together for parcellation by using the spectral clustering (Ng et al., 2002), thus better capturing both their common and complementary information. Experimental results indicated the proposed fusion‐based method leads to biologically more meaningful results with spatially contiguous, hierarchical and more symmetric patterns, in comparison to the conventional methods.

Note that several methods can be used to compute the local surface area, such as the method in (Winkler et al. 2012). They raised the question that surface area computed at the level of the original individual meshes cannot be directly interpolated, and proposed an effective interpolation method to interpolate the surface areal features for better preserving the native geometric information. Herein, we adopt another widely used method to compute the local surface area (Garcia et al., 2018; Hill, Dierker, et al., 2010; Hill, Inder, et al., 2010; Li, Nie, Wang, et al., 2012; Li, Wang, et al., 2014), which can be easily comparable across subjects at each vertex. Specifically, we first resampled all coregistered cortical surfaces using the same number of vertices and then computed the surface area at each vertex in the resampled cortical surfaces in the native space. All these registered cortical surfaces have been visually checked to ensure accurate alignment. The resampling procedure preserved the geometric information of the original individual cortical surfaces and led to vertex‐to‐vertex cortical correspondences, thus allowing meaningful measure and comparison of the local surface area.

For large temporal intervals during fetal brain development with potential nonlinear growth patterns (Clouchoux, Du Plessis, et al., 2012; Dubois et al., 2018), the Pearson's correlation coefficient might not be the best method for measuring similarity, although some researchers have used the linear function to model the development trajectories of fetal cortical surface (Garcia et al., 2018). In this case, researchers can instead use other measures, for example, the Spearman's rank correlation coefficient, which can measure nonlinear correlations. It should be noted that our method is flexible to adopt either linear or nonlinear similarity measures. In the results, we exhibited the parcellation results using both Pearson's correlation coefficient and Spearman's rank correlation coefficient as similarity measures. Our parcellation results showed that it might be more suitable to use the Pearson's correlation coefficient to measure the similarity of growth patterns during 26–29 GW. A possible reason could be the relatively small range of age and accelerative development patterns during this stage, which renders the development patterns of surface area close to linear (Clouchoux, Kudelski, et al., 2012; Dubois et al., 2018).

The most prominent growth pattern partition of surface area corresponds to a D–V division. Although there are no formed cortical folding patterns that match this D–V division, it did correspond to the emergence and development of sulci and gyri in these regions. The dorsal cluster subdivides the extra rapidly developing regions such as the sensorimotor, posterior parietal and dorsolateral prefrontal regions. In the dorsolateral prefrontal region, the superior frontal sulcus appears between 22 and 25 GW (Chi, Dooling, & Gilles, 1977; Hansen et al., 1993), and develops rapidly from 27 to 30 GW (Dubois et al., 2007). Also, the inferior frontal sulcus appears around 26 GW and develops rapidly from 27 GW (Clouchoux, Du Plessis, et al., 2012). In the sensorimotor region, the central sulcus appears at 25 GW and grows at an accelerated rate during 26–29 GW (Habas et al., 2011; Rajagopalan et al., 2011). The postcentral sulcus appears at 27 GW and the precentral sulcus appears around 28 GW (Dubois et al., 2007), which also lead the high development speed of surface area in the sensorimotor region. In the posterior parietal region, the intra‐parietal fissure appears very early from 27 GW and expands rapidly until 30 GW (Clouchoux, Kudelski, et al., 2012). Oppositely, the ventral cluster subdivides the relatively slowly developing regions, such as the temporal and insula regions. Note that there is one exception region in the ventral cluster, that is, the superior temporal sulcus (STS), which locates in the temporal lobe but also presents rapid growth. The STS appears between 25 and 27 GW and develops between 28 and 29 GW (Clouchoux, Du Plessis, et al., 2012). Our parcellation maps are based on the growth patterns of local surface area, which can be caused by multiple complicated changing patterns of surface area, for example, the emerging of new folds, growth along the length of existing folds, and growth along the depth of existing folds (Xia et al., 2018). Hence, the growth patterns of local surface area are related to the gross shapes of cortical anatomical structures. Therefore, the differences in gross shapes between regions can also contribute to our parcellation clusters. For example, at 2 clusters, the D–V division not only corresponds to the emergence and development of sulci and gyri, but also is related to the existed shape differences of the anatomic structures, for example, the smooth cap of the superior frontal, central, and parietal cortex and the more curved inferior occipital and temporal regions.

The growth pattern D–V division of surface area may also be related to the border characterized by cytoarchitectonic features (Kandel et al., 2000). The border separates the granular and agranular cortex in the frontal lobe. The granular cortex is defined by the presence of a granule cell layer IV (Kandel et al., 2000). The agranular cortex is a cytoarchitecturally defined term denoting the type of heterotypic cortex that is distinguished by its relative thickness and lack of granule cells. The prefrontal region is classified as the granular cortex. Meanwhile, the motor–premotor region is classified as the agranular cortex, primarily in the precentral gyrus, caudal portions of the superior frontal gyrus, and middle frontal gyrus. Thus, differences in cytoarchitecture might also reflect the D‐V growth pattern of the surface area. In addition, this D–V pattern is also largely similar to the genetically determined D–V division (Chen et al., 2013). Most subdivisions in our D–V growth pattern are generally nested within lobes, except the posterior temporal cluster (Cluster 8), which also showed high correlations with the sensorimotor and the posterior parietal clusters (Clusters 1 and 2) in different lobes. Cross‐lobe clustering in these regions is generally consistent with the fetal brain development subdivision specialized for the high growth rates in the central sulcus, posterior parietal region, and superior temporal sulcus from 26 GW to 29 GW (Clouchoux, Kudelski, et al., 2012; Habas et al., 2011; Rajagopalan et al., 2011).

Most clusters on the left and right hemispheres in the parcellation results based on the growth pattern of surface area are symmetric, except a few clusters, such as the posterior temporal cluster, the occipital and precuneus cluster, and the medial temporal cluster. This result corresponds well to the asymmetric development of the fetal cortical surface. Several studies have reported the area of the right STS is larger and deeper than the left STS from 26 GW to 30 GW (Benkarim et al., 2017; Clouchoux, Du Plessis, et al., 2012; Dubois et al., 2007; Dubois & Dehaene‐Lambertz, 2015; Habas et al., 2011; Kasprian et al., 2010), and even in term‐born infants (Li et al., 2013). These results are in line with our findings where the region around the right STS is larger than the region around the left STS, and the growth rate of the right posterior temporal region is higher than the left posterior temporal region. Moreover, the medial occipital region of the fetal brain also exhibits an early asymmetry. Beginning at 24 GW, the parieto‐occipital sulcus is more concave on the right than the left hemisphere, and the difference becomes statistically significant after 26 GW (Benkarim et al., 2017; Habas et al., 2011). This is consistent with our finding that the right occipital and precuneus cluster is larger than the left occipital and precuneus cluster, and presents larger growth percentage than that on the left hemisphere. Furthermore, the medial temporal region of the fetal brain presents an early asymmetry. A small area of the left parahippocampal gyrus, a cortical ridge in the left medial temporal cluster, was larger than that of the right parahippocampal gyrus from 20 to 28 GW (Rajagopalan et al., 2011). Our result of the cluster around the left parahippocampal gyrus being larger than the corresponding cluster in the right hemisphere is likely associated with this asymmetric cortical ridge.

Although the proposed approach showed to be able to generate biologically meaningful parcellations of the fetal cortical atlases, there are some limitations. First, the lack of longitudinal fetal scans precluded our approach from using the true cortical growth trajectories. Nonetheless, the ethical and practical issues posed by longitudinal imaging of fetuses renders its appropriateness to rely on cross‐sectional fetal brain scans. In fact, existing spatiotemporal atlases of the fetal brain have also used cross‐sectional data to analyze in utero neurodevelopment (Gholipour et al., 2017; Wright et al., 2015). Second, our parcellations were obtained using growth patterns based on a single cortical attribute (i.e., surface area), which might not be able to fully characterize the cortical development. Other cortical properties, such as cortical thickness, cortical folding, and myelin content, can also be used. In fact, the fetal cortical development is jointly driven by several different biological mechanisms that lead to differential and regionally variable increase in surface area, cortical thickness, myelin content, and cortical folding. Each of these cortical properties may be associated with distinct genetic underpinnings, cellular mechanisms, and present different developmental trajectories. As a result, these distinct cortical features likely lead to different parcellation maps that show distinct aspects of fetal brain development. Of note, we cannot directly use curvature as a measure of cortical folding in our method, since both negative and positive curvatures indicate cortical folding. To address this issue, one could use other curvature‐derived nonnegative features, such as curvedness, or other measures of cortical folding, for example, local gyrification index, for performing parcellation. In the future, these distinct cortical properties can be jointly used to characterize the growth patterns and create our cortical parcellations. However, we should note that, due to the low contrast, poor imaging resolution, and strong partial volume effects, especially considering the small fetal brain, the cortical thickness, and myelin measurements during this stage are less reliable, compared to surface area. Third, our sample size is still limited in both size and age range. In the future, it would be better to leverage a large‐scale dataset covering a wide range of developmental stages for parcellation.

In summary, this article has two main contributions. First, we proposed a novel method for fetal cortical surface atlas parcellation based on the growth patterns of cortical properties. We constructed two complementary similarity matrices to comprehensively capture both the low‐order and high‐order similarities of growth patterns of vertices. To effectively leverage their information, we nonlinearly fused these two similarity matrices as a single one for clustering, thus better capturing both their common and complementary information. Second, by applying our method, we derived the first set of fetal cortical surface atlas parcellation maps based solely on dynamic growth patterns of surface area, and also applied the parcellations maps to study fetal cortical development. We will release these fetal cortical surface atlases, including both our generated parcellation maps and some representative cortical attributes of the cortex, for example, the mean curvature, average convexity, and sulcal depth, as shown in Figure 3. We will also add more cortical attributes, such as the local gyrification index, sharpness, and curvedness, onto our fetal cortical surface atlases. Thus, our atlases will provide a more accurate reference for aligning individual fetal brains onto a common space. With public access of such cortical atlases with diverse cortical attributes, researchers will be able to align their data onto our atlas space, comparing cortical attributes of different gestational ages or different fetal cohorts, as well as project our parcellation maps onto their own data and perform region‐based analysis.

Xia J, Wang F, Benkarim OM, et al. Fetal cortical surface atlas parcellation based on growth patterns. Hum Brain Mapp. 2019;40:3881–3899. 10.1002/hbm.24637

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.