Introduction

Diffusion magnetic resonance imaging (dMRI)¹ allows the analysis of brain white matter connections via a computational process called tractography². White matter parcellation classifies tractography streamlines into clusters or anatomically meaningful tracts to enable quantification and visualization. Most parcellation methods focus on the deep white matter (DWM) that traverses the depth of the white matter and connects remote cortical areas^3–7, while few methods can parcellate the superficial white matter (SWM) that covers short-range association connections (u-fibers) connecting adjacent gyri^8–11 due to its complexity. SWM tractography parcellation methods currently employ either ROI-based selection or streamline clustering. However, ROI-based methods^8,12 highly depend on ROI parcellation schemes, and there are still challenges for clustering methods in achieving consistent parcellation and reducing runtime^9,11,13. Recently, deep-learning-based methods^5–7,14,15 have achieved promising results in tractography parcellation, but none have been developed for SWM parcellation.

We propose a novel deep learning framework, Superficial White Matter Analysis (SupWMA), for SWM parcellation from whole-brain tractography. SupWMA is designed based on a point-cloud-based network¹⁶ with supervised contrastive learning¹⁷ to classify streamlines into SWM clusters and remove outliers. Our point-cloud-based network can have the same global representation for streamlines with equivalent forward and reverse point orders (e.g., from cortex to subcortical structures or vice versa). Supervised contrastive learning enables more discriminative representations between plausible streamlines and outliers. SupWMA obtains fast and consistent results on testing datasets across populations and dMRI acquisitions.

Methods

Our network (Figure 1 (a)) is based on PointNet¹⁶ and it can be divided into two parts: the encoder Enc(·) that extracts the global feature for each streamline and the classifier Cla(·) that predicts the streamline label. We remove transformation nets from PointNet to preserve spatial position of streamlines and improve the computational speed. For our Enc(·), the input is the Right-Anterior-Superior (RAS) coordinates of streamline points. A shared MLP of three layers individually encodes each point on a streamline. Then, a symmetric function (max-pooling¹⁶) aggregates the encoded features into a global shape feature (g) of the streamline. Because g is invariant to the order of points along a streamline, streamlines with equivalent forward and reverse point orderings will have the same global shape feature. Finally, Cla(·), consisting of three FC layers, is used for streamline class prediction.

Supervised contrastive learning (SCL)¹⁷ is an extension of self-supervised contrastive learning¹⁹. In our task, streamlines in SWM outliers can be geometrically similar to those in SWM clusters, SCL assists Enc(·) in extracting more discriminative features between plausible streamlines and outliers. In SCL training (Figure 1 (b)), a projector head Proj(·)^17,19 with two additional FC layers is added on Enc(·). Proj(·) may retain more instance-specific streamline information in the global feature, benefiting downstream tasks¹⁹. The supervised contrastive loss is as follows:
$$\mathcal{L}^{sup}_{out}=\sum_{i \in I}\mathcal{L}^{sup}_{out,i}=\sum_{i \in I} \frac{-1}{|P(i)|} \sum_{p \in P(i)} \log \frac{\exp ( z_{i} \cdot z_{p} / \tau )}{\sum_{a \in A(i)} \exp ( z_{i} \cdot z_{a} / \tau )}$$
where I is the streamline set in a training batch (i ∈ I ≡ {1, …, M}); P(i) is the streamline set that has the same class label as streamline i (p ∈ P(i)); A(i) is the set of all other streamlines in I except for streamline i (a ∈ A(i) ≡ I \ {i}); z_i, z_p and z_a are contrastive features from Proj(·) for streamlines i, p and a; τ (temperature) is a pre-defined hyperparameter.

The training procedure has two phases^17,19 (Figure 1 (b)). In the SCL phase, Enc(·) and Proj(·) are trained with supervised contrastive loss. In the downstream learning phase, Enc(·)’s parameters are frozen¹⁷, and Proj(·) is unused. Cla(·) is trained with cross-entropy loss for streamline classification. A high-quality large-scale dataset with 1 million labeled streamlines (198 SWM clusters and one “non-SWM cluster") was used for model training and validation. This dataset was derived from an anatomically curated white matter tractography atlas¹¹ (Figure 2).

Figure 1 (c) demonstrates parcellation of unlabeled tractography data (i.e., the testing data). We tested SupWMA using publicly available data (150 subjects) from three independently acquired datasets^20–22 (Figure 2).

Results

Compared to two SOTA methods (Figure 3), SupWMA achieves the highest mean accuracy and macro F1-score with the lowest standard deviation. Also, FLOPs of SupWMA are much lower than other SOTA methods. Figure 4 gives the comparison results using the cluster identification rate (CIR)^6,11 that measures the success of white matter cluster identification. Our method performs the best on all three testing datasets compared to three SOTA methods. Figure 5 shows visualization results of example clusters for each testing dataset and each method. All methods perform relatively well on clusters shown in magenta and cyan (except DeepWMA on HCP). However, SupWMA identifies more anatomically reasonable streamlines (yellow clusters) than other methods on the HCP and ABCD datasets.

Discussion

The quantitative results demonstrate that our proposed method has good performance on datasets with ground truth (atlas) and can generalize well to obtain highly consistent SWM parcellation results for subjects across populations. The cluster visualization results show visually successful identification of SWM clusters across datasets.

Conclusion

We proposed SupWMA, a novel deep learning framework for SWM parcellation, with successful application on datasets across ages and health conditions. SupWMA enables consistent and efficient SWM parcellation.

Acknowledgements

R01MH125860, R01MH119222, R01MH074794, and P41EB015902

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