FASSt : Filtering via Symmetric Autoencoder for Spherical Superficial White Matter Tractography

Abstract

Superficial white matter (SWM) plays an important role in functioning of the human brain, and it contains a large amount of cortico-cortical connections. However, the difficulties of generating complete and reliable U-fibers make SWM-related analysis lag behind relatively matured Deep white matter (DWM) analysis. With the aid of some newly proposed surface-based SWM tractography algorithms, we have developed a specialized SWM filtering method based on a symmetric variational autoencoder (VAE). In this work, we first demonstrate the advantage of the spherical representation and generate these spherical tracts using the triangular mesh and the registered spherical surface. We then introduce the Filtering via symmetric Autoencoder for Spherical Superficial White Matter tractography (FASSt) framework with a novel symmetric weights module to perform the filtering task in a latent space. We evaluate and compare our method with the state-of-the-art clustering-based method on diffusion MRI data from Human Connectome Project (HCP). The results show that our proposed method outperform these clustering methods and achieves excellent performance in groupwise consistency and topographic regularity.

Keywords: Autoencoder; Spherical representation; Superficial white matter; Tractography filtering.

Fig. 1.

3D volume-based motor-sensory U-fibers (a,b) and its 2D spherical representation (c) for subject 101006 in HCP dataset. (e) is the spherical representation of the frontal lobe U-fibers (d) for the same subject.

Fig. 2.

FASSt has two compotents: (a) the scheme of a symmetric variational autoencoder, (b) filtering procedure for learned latent representation.

Fig. 3.

Illustration of fiber orientation and symmetric weights module: (a) the same streamline is represent very differently when the orientation is not fixed, (b) symmetric weights module for 1D convolution kernel. We set kernel size to be 3 with initial weights = (w_i1, w_i2, w_i3) and after (j + 1)th epoch (assume j is even number) we got the final weights = (w_f1, w_f2, w_f3).

Fig. 4.

Filtering results for subject 101006 and 114318 in HCP dataset. Subject 101006: unfiltered U-fibers for frontal lobe (a,b), filtering results for frontal lobe (c,d); Subject 114318: unfiltered U-fibers for frontal lobe (e,f), filtering results for frontal lobe (g,h), where (a,c,e,g) are the volume-based U-fibers and (b,d,f,h) are the converted spherical representation of the corresponding U-fibers.

Fig. 5.

Effectiveness demonstration of the symmetric weight module for test set in HCP dataset: the mean Euclidean distance calculated using the proposed symmetric weights module and without using symmetric weights module for frontal lobe U-fibers (a) and motor-sensory U-fibers (b).

Fig. 6.

Groupwise consistency comparison results: (a,b) show the box plots of groupwise consistency before any filtering, using FASSt and using FASSt but without symmetric module for frontal lobe U-fibers and motor-sensory U-fibers.

Fig. 7.

Topographic regularity and groupwise consistency comparison results: this figure shows the box plot of topographic regularity of group A (blue: before any filtering), group B (orange: filtering using 3D volume-based data and FASSt), group C (green: filtering using 2D spherical representation and FASSt but without symmetric weights module), group D (red: filtering using 2D spherical representation and FASSt), group E (purple: same as C with flipped U-fibers), group F (brown: filtering using QuickBundles), group G (pink: filtering using minimum fiber length).