AXCEND Axon Centerline Detection using Topologically-aware 3D U-Nets

AXCEND: Axon Centerline Detection using Topologically-aware 3D U-Nets Introduction Goal: Improve automated tracing of axons in light sheet microscopy data  Ability to analyze neural circuits will help us understand the relationship between healthy brain structure and function  Manual segmentation of microscopy volumes is slow and labor-intensive, will not scale to the billions of neurons that comprise a human brain Approach: Focus on axon centerlines  Morphological skeleton of a segmentation mask can distill down information about topology, length, trajectory, and connectivity  Implemented three recently-proposed deep learning approaches to centerline Maximum intensity projection of a mouse brain detection and evaluated on a mouse imaged using light sheet microscopy (left) and the brain dataset labeled subvolume used for experiments (right). Results Experiments:  Trained each model 10 times via stochastic gradient descent with the Adam optimizer and early stopping, using the same hyperparameters for each trial  Evaluated performance of predicted segmentations and centerlines on held out test set using Dice, clDice, and ρ-Dice (similarity between predicted and ground truth centerlines with radial ρ-voxel buffer) Dice clDice a) b) c) d) ρ-Dice (ρ=3) Model Mean Std. Mean Std. Mean Std. Baseline 0.543 0.021 0.687 0.021 0.703 0.024 CasNet 0.545 0.024 0.683 0.028 0.701 0.031 clDiceNet 0.564 0.033 0.715 0.032 0.710 0.025 Similarity metrics for ten trials evaluated WITH test-time augmentation. Dice clDice ρ-Dice (ρ=3) Model Mean Std. Mean Std. Mean Std. Baseline 0.580 0.027 0.720 0.020 0.761 0.015 CasNet 0.598 0.002 0.763 0.010 0.750 0.004 clDiceNet 0.628 0.018 0.785 0.018 0.787 0.021 a) b) c) d) e) Residual 3D U-Net architecture. Alternatives explored: a. CasNet consists of a segmentation network cascading into a centerline detection network2 b. An auxiliary path classifier is trained to predict whether paths extracted from a predicted segmentation lie within the ground truth mask3 c. clDiceNet replaces cross entropy with a topology-preserving loss function4: 𝑇𝑝𝑟𝑒𝑐  clDiceNet outperforms Baseline and CasNet models across every metric, and achieves better Dice score than previously reported on same dataset5  Auxiliary path classification results omitted because the classifier was unable to learn--perhaps because positive and negative path examples were too similar Similarity metrics for ten trials evaluated WITHOUT test-time augmentation. Methods Baseline: A residual 3D U-Net1 was trained to perform voxel-wise classification using binary cross entropy loss between the output and training images, followed by binary thresholding and morphological thinning to yield a voxel-wide skeleton. Discussion (𝑇𝑝𝑟𝑒𝑐 ∗ 𝑇𝑠𝑒𝑛𝑠 ) 𝑆𝑃 ∩ 𝑉𝐿 𝑆𝐿 ∩ 𝑉𝑃 = ; 𝑇𝑠𝑒𝑛𝑠 = ; 𝑐𝑙𝐷𝑖𝑐𝑒 = 2 ∗ 𝑆𝑃 𝑆𝐿 (𝑇𝑝𝑟𝑒𝑐 + 𝑇𝑠𝑒𝑛𝑠 ) 𝐿 = 𝛼 1 − 𝑐𝑙𝐷𝑖𝑐𝑒 + (1 − 𝛼) 1 − 𝐷𝑖𝑐𝑒 Flow of test pipeline: (a) maximum intensity projection of test volume; (b) example prediction of clDiceNet model; (c) binarized prediction with colors representing different connected components; (d) skeletonized prediction showing true positive centerline detections (green), false negatives (blue), and false positives (red); and (e) ground truth segmentation mask with colors representing connected components. © 2021 Massachusetts Institute of Technology. MIP of test volume (a), with true positive (green), false negative (blue), and false positive (red) example centerline predictions of Baseline (b), CasNet (c), and clDiceNet (d). Greater connectivity can be seen in (d). MIP of training volume with extracted nodes, positive path examples (blue) and negative path examples (red)  There are similarities between clDiceNet and CasNet: both incorporate centerline predictions into the loss function, but the former uses “softskeletonization” by iterative max- and min-pooling, while the latter uses a downstream U-Net which greatly increases its parameter count  clDiceNet still requires morphological thinning as a post-processing step  Will explore an analogous loss function using the ρ-Dice formulation that directly predicts centerlines in future work  Previous work on the same dataset demonstrated a benefit to pretraining models on a self-supervised learning (SSL) task with unlabeled data5  Next step is to combine SSL approach with clDiceNet, which could yield incrementally better results