Predicting infant cortical surface development using a 4D varifold-based learning framework and local topography-based shape morphing

Highlights

• Topography-based cortical shape evolution prediction model.

• Cortical growth prediction in the first year of life solely from baseline shape.

• 4D varifold-based shape evolution learning framework.

Abstract

Longitudinal neuroimaging analysis methods have remarkably advanced our understanding of early postnatal brain development. However, learning predictive models to trace forth the evolution trajectories of both normal and abnormal cortical shapes remains broadly absent. To fill this critical gap, we pioneered the first prediction model for longitudinal developing cortical surfaces in infants using a spatiotemporal current-based learning framework solely from the baseline cortical surface. In this paper, we detail this prediction model and even further improve its performance by introducing two key variants. First, we use the varifold metric to overcome the limitations of the current metric for surface registration that was used in our preliminary study. We also extend the conventional varifold-based surface registration model for pairwise registration to a spatiotemporal surface regression model. Second, we propose a morphing process of the baseline surface using its topographic attributes such as normal direction and principal curvature sign. Specifically, our method learns from longitudinal data both the geometric (vertices positions) and dynamic (temporal evolution trajectories) features of the infant cortical surface, comprising a training stage and a prediction stage. In the training stage, we use the proposed varifold-based shape regression model to estimate geodesic cortical shape evolution trajectories for each training subject. We then build an empirical mean spatiotemporal surface atlas. In the prediction stage, given an infant, we select the best learnt features from training subjects to simultaneously predict the cortical surface shapes at all later timepoints, based on similarity metrics between this baseline surface and the learnt baseline population average surface atlas. We used a leave-one-out cross validation method to predict the inner cortical surface shape at 3, 6, 9 and 12 months of age from the baseline cortical surface shape at birth. Our method attained a higher prediction accuracy and better captured the spatiotemporal dynamic change of the highly folded cortical surface than the previous proposed prediction method.

Introduction

Quantifying cortical morphological dynamics at an early postnatal stage of brain growth will help neuroscientists identify and characterize early neurodevelopmental disorders (Narr, Bilder, Luders, Thompson, Woods, Robinson, Szeszko, Dimtcheva, Gurbani, Toga, 2007, Shaw, Eckstrand, Sharp, Blumenthal, Lerch, Greenstein, Clasen, Evans, Giedd, Rapoport, 2007, Lyall, Shi, Geng, Woolson, Li, Wang, Hamer, Shen, Gilmore, 2015). More importantly, if one could learn to predict the normal cortical shape evolution for healthy infants, as well as for infant groups with specific brain disorders, one could learn to predict and distinguish normal from abnormal cortical development. However, prior to reaching this goal, a robust prediction model of cortical surface growth needs to be devised. Furthermore, noting that the cortex represents the abode of vital cognitive and decision-making brain functions as well as health-related behaviors, examining neurodiversity in both health and disease can be further propelled through developing efficient infant brain growth models that may help predict later changes in normal behavior, reasoning or learning abilities (Gabrieli et al., 2015).

On the other hand, modeling approaches for predicting the early postnatal human brain morphometry changes using longitudinal neuroimaging data are scarce – particularly for cortical dynamics prediction. Herein, we imply by cortical dynamics prediction the estimation of the spatiotemporal cortex shape deformation in the future (i.e., the evolution trajectories of the shape) using a set of available observations and measurements. Nie et al. developed the first mechanical cortical growth model (Nie et al., 2012) to simulate the dynamics of cortical folding from longitudinal MRI data in the first postnatal year, during which the cortical surface area increases by 76% (Lyall et al., 2015) and the gray matter volume increases by 149% (Gilmore et al., 2007). Although promising, this method requires the use of cortical surfaces at later timepoints of the same infant to guide the growth model and also gradually loses its accuracy as the number of data acquisition timepoints decreases. Ideally, one would expect to use the least number of input surfaces to accurately predict the development of the highly convoluted shape of the cortical surface.

Recently developed methods (Fletcher, 2013, Niethammer, Huang, Vialard, 2011, Singh, Hinkle, Joshi, Fletcher, 2013a, Singh, Hinkle, Joshi, Fletcher, 2013b) proposed various geodesic shape regression models to estimate diffeomorphic (i.e., smooth and invertible) evolution trajectories; however, they were implemented for image time-series change tracking. A richer variant of these geodesic image regression methods was proposed in Fishbaugh et al. (2014), where the regression scheme integrated surface shape information to improve 4D image deformation trajectories estimation. This method estimates both baseline image and surface through finding the optimal points and initial momenta that guide the image-surface deformation. One of its applications included the estimation of joint white matter surface and image deformation backwards in time from 20 months to 6 months. Although this model was able to extrapolate the future image-surface deformation, it required at least two observations for prediction. A geodesic shape regression in the framework of currents was developed in Fishbaugh et al. (2013) to estimate subcortical structures at 6 months of age based on shapes from 9 to 24 months – which also requires more than one timepoint for what we refer to as backward-in-time prediction. A non-linear mixed effect dynamic prediction model was proposed in Sadeghi et al. (2014)) to estimate temporal change trajectories of radial diffusivity images derived from diffusion tensor imaging (DTI) of early brain development. However, it was limited to estimating region-level changes in 3D scalar fields (images) and required a predefined complex parametric form of the development trajectory.

Very recently, we proposed the first learning-based framework that predicts the dynamic postnatal cortical shape from a single baseline cortical surface at birth using a 4D diffeomorphic surface growth model rooted in the theory of currents (Rekik et al., 2015a). The developed prediction framework includes a training stage and a prediction stage. In the training stage, the proposed framework learns both geometric (vertices positions) and dynamic (diffeomorphic evolution trajectories) features of cortical surface growth for each infant using the available acquisition timepoints. We then estimate the mean empirical spatiotemporal atlas at the most commonly shared timepoints among the training subjects to simultaneously initialize the cortical surface shapes at all later timepoints for prediction. In the prediction stage, for each new subject, we refine this initialization by simultaneously moving vertices in the shapes to predict, based on how close the baseline cortical shape to the baseline cortical atlas. Once the positions of the baseline vertices are updated, they form together a virtual baseline shape, which is spatially close to the ground truth baseline cortical shape. Finally, retrieving the corresponding learnt smooth deformation trajectory for every vertex belonging to the constructed virtual shape predicts the cortical shape up to the last timepoint in the training dataset.

In this paper, we further improve the performance of the described framework by proposing two important variants. First, we use the varifold metric, which was demonstrated to perform better than the current metric in registering a pair of surfaces (Durrleman et al., 2014). We also extend the conventional varifold-based surface registration model into a spatiotemporal surface regression model to estimate the diffeomorphic temporal evolution trajectories of the baseline cortical surface shape. Second, we locally morph the baseline surface based on its topographic attributes, such as normal orientation or principal curvature sign, instead of solely relying on the most ‘similar’ vertices in only spatial closeness. Of note, the proposed method requires neither predefined parametric forms of the cortical developmental trajectories nor the guidance from the later time points of the same subject, in comparison with existing methods.