Neonatal Data

Our dataset comprises 17 premature neonates (gestational ages 25–36 weeks, 41.1 ± 5.0 weeks at scan time) with normal MR scans and 19 healthy term born infants (45.1 ± 5.1 weeks at scan time).

MRI scans were acquired using a dedicated neonatal head coil on a 1.5T GE scanner and include a coronal 3D SPGR sequence (TE = 6 ms; TR = 25 ms, FOV = 18 cm; matrix = 256×160), axial and sagittal T1-weighted FLAIR sequences (TE = 7.4, TR = 2100; TI = 750; FOV = 20 cm; Matrix = 256×160) and an axial T2-weighted FSE sequence (TE = 85 ms, TR = 5000 ms, FOV = 20 cm, matrix = 320×160 or 256×128).

Inclusion criteria for our preterm subjects were the following: 1) prematurity, and 2) visually normal scans on conventional MRI. Structural MRI were qualitatively classified as controls by 2 board-certified neonatal neuroradiologists.

This study was approved by the CHLA Committee on Clinical Investigations and the University of Pittsburgh Internal Review Board. Written consents for use of their child’s clinically acquired MRI data and for participation in additional neurodevelopmental and neuroimaging studies were obtained from parents on behalf of the prospectively recruited patients by a research coordinator. The ethics committee approved this consent process. Additionally, as this study involved a retrospective review of all clinically-acquired neonatal data for the period between 2005 and 2011, which included neonates who were not enrolled into prospective studies, approval has also been obtained from the CHLA Committee on Clinical Investigations and the University of Pittsburgh Internal Review Board for the retrospective use of all clinically-acquired neonatal MRI data acquired at CHLA between 2005 and 2011.

We manually segmented the putamen with Insight Toolkit’s SNAP program [18], as shown in Fig. 2. Tracings were performed in the registered template space by an experienced pediatric neuroradiologist, using standard protocols. We consulted neuranatomical references of the human striatum to help guide the placement of the contours [19], [20]. Our segmentation of the putamen did not include the caudate head or the globus pallidus, and was defined laterally by the insular cortex/claustrum/external capsule margin and medially by the anterior limb of the internal capsule and the genu and posterior limb of the internal capsule. We did likely include the nucleus accumbens within the inferior and medial aspect of the contour as this structure is known to be difficult to separate, on MRI, from the adjacent putamen and the basal forebrain region. Our inter-rater average percent volume overlap (intersection of volumes over average of them) for 4 structures segmented twice at a few months interval is 86%.

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Figure 2. Putamen segmentation.

While the caudate head is part of the striatum, we chose not to include this structure because of the poor tissue contrast in the anterior limb of the internal capsule in the neonates, which prevented us from obtaining reliable manual contours in this region in neonates. Additionally, our hypothesis testing for this paper included the ventral striatum, which does not contain the caudate head. Note also that the globes palladius, while not part of the putamen, was still included in our segmentation. It is extremely difficult to accurately segment the globus pallidus from the putamen in neonates due to the lack of tissue contrast on volumetric T1 images. However, since our hypothesis is related to the ventral striatal surface, it is not affected by the inclusion of the globus palladius within our putamen contour.

https://doi.org/10.1371/journal.pone.0066736.g002

Figs. 1 a) shows examples of reconstructed putamen surfaces.

Surface Conformal Grid Generation and Registration

We computed conformal grids on the putamen using holomorphic differentials as described in [14]. Our grid generation method starts with the assumption that some geometrically extreme positions can serve as geometrically valid and consistent landmarks across subjects on the putamen. Hence, we introduce two cuts at the extremities of the putamen. The putamen is consistently bordered by the external capsule laterally, the anterior limb of the internal capsule anteriorly and the posterior limb of the internal capsule posteriorly. We call this step a topology optimization, as it introduces consistent landmarks via a topology change. These landmarks are used to achieve an accurate surface registration (see below), a prerequisite of tensor-based morphometry analyses. This approach was successfully used in several of our prior work with different subcortical structures such as the hippocampus [16], lateral ventricle [17], thalamus [4] and corpus collosum [11].

After the topology optimization is performed, the putamen surface is represented as a genus-zero surface with two open boundaries, i.e. a topological cylinder. We compute its conformal parameterization with a holomorphic 1-form method [14]. Briefly, by solving Laplace equations on the surface, we compute a harmonic 1-form and its conjugate harmonic 1-form and, following Hodge Theorem, we generate the holomorphic 1-form by pairing them. By integrating this holomorphic one-form, a conformal mapping is found from the putamen to a rectangle and introduce a conformal grid on the putamen surface. Examples of grids that we generated are shown in Fig. 1(a).

We then map the surface grids to a common template (i.e., to one of the controls, chosen at random) with a new fluid registration technique that we recently implemented [15]. We use surface features composed of the surface conformal factor and mean curvature to enforce surface correspondence. Similar to prior research [21], [22], a flow computed in the parameter space (a planar domain in our case) of the two surfaces, induces a correspondence field in 3D. To simulate fluid flow on the surfaces, the Navier-Stokes equation is extended into surface space using a manifold version of the Laplacian and divergence operators [23], [24]. With an inverse consistent framework, surface registration is optimized when the sum of squared surface feature intensity differences between the deforming image and template image is minimized [15]. Fig. 1 (b) shows the computed surface feature images and (c) illustrate the inverse consistent fluid registration process on the parameter space.

Since both the conformal mapping and inverse consistent fluid registration generate diffeomorphic mappings, the mapping between the putamen surfaces is diffeomorphic.

To confirm the validity of our analysis, we also compared the fluid registration method to the more usual constrained harmonic map registration [16]. Given two surfaces and , the latter consists of finding a harmonic map between their parameter domains (here a planar surface). Surface matching is achieved by composing the conformal map from to its parameter domain , the harmonic map between and (the parameter domain of ), and the inverse conformal map between and .

Both the constrained harmonic map and the inverse consistent fluid registration methods are valid approaches to subcortical surface registration. In particular, the latter method extends the standard volume-based 3D fluid image registration approach to surfaces by generating a diffeomorphic mapping that minimizes surface features differences. In other words, the surface fluid registration method generates a mapping that enforces key surface features alignment. As a result, we hypothesized here that it would be consistent with but outperform the constrained harmonic mapping by generating more accurate and biologically meaningful surface correspondences.

Surface Multivariate Tensor-based Morphometry

Our ultimate aim is to determine the intrinsic surface morphology of segmented putamens in preterm neonates. We do so by applying a multivariate tensor-based morphometry analysis [16], [17], [25].

In tensor-based morphometry, for each subject in the data set, the registration yields a displacement field between the template and the subject’s images. A Jacobian matrix is computed at each vertex from the registration between template and subjects images, where is the identity matrix. These Jacobian matrices, or a function of their components are used as metrics for group comparisons. For example, the determinant, expresses the ratio of the surface area between the moving and fixed images while in multivariate tensor-based morphometry, we use the deformation tensors (in fact their logarithm [17], [25], [26]). can be represented as a 2D ellipse at the center of each grid cell, whose axes show the direction and size of the change in area between the two surfaces at that location. In general, the multivariate measures yield increased statistical power when compared to the univariate ones (see e.g. [25] for the volume-based multivariate tensor-based morphometry and [4], [17] for the surface-based one).

Medial Axis Method

One of the most commonly used morphometry measure on surface data is the radial distance from a medial axis to a vertex of the surface [27], [28]. We used the medial axis method as a complementary measure to the surface shape analysis from multivariate tensor-based morphometry. Here the medial axis was computed using the center point of the iso-parametric curves, on the conformal grid [16].

Multivariate Statistical Analysis

We used a total of four different statistics: the deformation tensors , the radial distance , the determinant of the Jacobian matrix and a vector containing the elements of and .

To adjust for post-conception age effects, we first covaried the measures at each vertex with this variable. Let A represent one of the four statistic, and Acov is the new adjusted statistic. The Acov were computed by fitting the following general linear model to the data at each image voxel:where the are estimated regression coefficients at that specific vertex. Diagnosis was coded as a binary dummy variable (that is, diagnosis = 0 (term-born) and 1 (preterm)), so that For the multivariate measures, the regression was computed separately for each channel.

For and , a standard voxel-wise -test was used to compare the preterm to the term-born neonates, while for either of the multivariate tests on or , group statistics were computed using the Hotelling’s test [29] - the multivariate extension of the Student’s -test -, as described in [16], [17], [25].

In order not to assume a normal distribution, we ran a vertex-based permutation test on the results [17], [25], [30]. We randomly assigned diagnostic labels (premature or term-born) to each subject, without replacement. A - or -test was performed at each vertex using the new labels. The procedure was repeated 10000 times. We obtained a null distribution of - or -values at each vertex, to which we compared the - or -values from the real data. Fig. 1 (d) shows an example -map in a group difference study where mTBM are adopted as morphometry features.

We also performed a second permutation test for multiple comparison corrections. We again randomly shuffled labels between the two groups, but this time we computed a single value on each image, that is, the number of vertices with -values . This provided us with a null distribution to which we compared from the real data.

We also created cumulative distribution function (CDF) plots of the resulting uncorrected -values (as in a conventional false discovery rate analysis (FDR) [31]). The critical -value [31] is the highest non-zero point at which the CDF plot intersects the line, and represents the highest statistical threshold (if there is one) that can be applied to the data, for which at most false positives are expected in the map. If there is no such intersection point (other than the origin), there is no evidence to reject the null hypothesis.