• Ei tuloksia

Substantial differences between 2D and 3D morphological analyses

5.5 Experimental results

5.5.2 White matter morphology analysis

5.5.2.1 Substantial differences between 2D and 3D morphological analyses

of myelinated axons in a high-resolution sham-operated dataset. Figure 11 shows that when the axonal skeleton is not parallel to any of the three principal axes, the relative difference increases between the 2D and 3D quantifications. Comparing 2D and 3D measurements for all myelinated axons in one dataset showed that the median of the relative difference was 16.23% for the equivalent diameter and 11.34% for the eccentricity, which was substantial. In addition, as 2D

measurements are usually carried on a single 2D image, such analysis cannot capture the morphological variations along the axons.

Figure 11. Comparison of the traditional 2D and proposed 3D morphology analysis of myelinated axons. The measurements showed that the median of the relative difference was 16.23% for the equivalent diameter and 11.34% for the eccentricity, indicating substantial differences between the 2D and 3D-based measurements.

5.5.2.2 Ultrastructural analysis of white matter in traumatic brain injury In the morphological analysis, we excluded myelinated axons whose length was shorter than 5 µm. In the statistical hypothesis testing, we used the median of equivalent diameters, the median of eccentricities, and the mean of

inter-mitochondrial distances for each myelinated axon. We subjected these quantities to the nested 1-way ANOVA separately for each hemisphere and set the alpha-threshold defining the statistical significance as 0.05 for all analyses.

In studies I and II, for both corpus callosum and cingulum, we found that the diameter of myelinated axons varies substantially along their length. The

distribution of axonal diameters was bimodal, which can partially be related to the location of mitochondria (Wang et al., 2003). The cross-sections of myelinated axons were elliptic rather than circular. The central axis of myelinated axons was approximately straight, and the inter-mitochondrial distance distribution along a myelinated axon was bimodal as mitochondria were either accumulated or appeared distant from each other.

In study I, we compared the morphology of myelinated axons (axonal diameter and eccentricity) in sham-operated and TBI rats. We presented our results in Figure 12 and summarized the statistics in Table 2.

Figure 12. ACSON morphometry of the high-resolution SBEM datasets of white matter. On each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the 'o' symbol. Nested ANOVA showed a significant reduction in the diameter of myelinated axons in the ipsilateral corpus callosum of rats after TBI.

Table 2. Comparison of the axonal diameter and eccentricity of myelinated axons in the corpus callosum in sham-operated and TBI rats.

In study II, we compared the morphology of myelinated axons (axonal

diameter, eccentricity, and tortuosity) and inter-mitochondrial distances in sham-operated and TBI rats. We presented our results in Figure 13 and summarized the statistics in

Table 3 and Table 4. We also found that defining the inter-mitochondrial distance as the distance between centroids of mitochondria was highly correlated with defining the inter-mitochondrial distance as the shortest distance between consecutive mitochondria; the Pearson correlation coefficient was 0.99. When quantifying the volumetric aspects of the ultrastructures, we did not directly compare the volume of the myelin and myelinated axons among datasets. Instead, we calculated the density of myelinated axons as the ratio of the volume of

myelinated axons to the myelin volume plus the volume of myelinated axons. We also calculated the cell density as the number of cell nuclei over the volume of the corresponding dataset, presented in Figure 13 and summarized in

Table 5.

Table 3. Comparison of the morphology of myelinated axons in the corpus callosum and cingulum of sham-operated and TBI rats.

Tissue Hemisphere Axonal diameter Axonal eccentricity

Corpus callosum

Ipsilateral Significantly smaller in TBI F = 14.392, p = 0.03

Tissue Hemisphere Axonal diameter Axonal eccentricity Axonal tortuosity

Corpus callosum

Ipsilateral Significantly smaller in TBI F = 15.75, p = 0.047

Ipsilateral Significantly smaller in TBI F = 16.27, p = 0.027

No difference F = 3.33, p = 0.165

Significantly bigger in TBI F = 25.23, p = 0.018 Contralateral Significantly smaller in TBI

F = 29.28, p = 0.011

No difference F = 1.57, p = 0.299

No difference F = 3.20, p = 0.134

Table 4. Comparison of the inter-mitochondrial distances in the corpus callosum and cingulum of sham-operated and TBI rats. The distance between centroids of mitochondria is defined as (1) and as the shortest distance between consecutive mitochondria as (2).

Tissue Hemisphere Mitochondrial distance (1) Mitochondrial distance (2) Corpus

callosum

Ipsilateral No difference (F = 1.04, p = 0.414

No difference F = 0.43, p = 0.577 Contralateral No difference

F = 0.07, p = 0.812

No difference F = 0.05, p = 0.830

Cingulum

Ipsilateral No difference F = 6.27, p = 0.086

No difference F = 7.10, p = 0.073 Contralateral No difference

F = 0.33, p = 0.603

No difference F = 0.28, p = 0.630

Table 5. Comparison of the density of myelinated axons and cell nuclei in the corpus callosum and cingulum of sham-operated and TBI rats.

Tissue Hemisphere Density of myelinated axons Density of cell nuclei

Corpus callosum

Ipsilateral No difference F = 3.42, p = 0.162

No difference 1.02, p = 0.419 Contralateral No difference

F = 2.13, p = 0.282

No difference F = 0.48, p = 0.540

Cingulum

Ipsilateral Significantly smaller in TBI F = 13.03, p = 0.037

No difference F = 1.79, p = 0.273 Contralateral No difference

F = 4.29, p = 0.130

No difference F = 0.16, p = 0.717

5.5.3 Evaluations

In study I, we evaluated ACSON segmentation against manual segmentation, where an expert segmented three 2D images from the contralateral corpus callosum of a sham-operated dataset. We evaluated the ACSON segmentation using the precision and recall in the tissue-type and weighted Jaccard index and weighted Dice coefficients at the region level. The results showed an excellent agreement between the automated and manual segmentations for myelin (precision ≥ 0.86, recall ≥ 0.88, weighted Jaccard index ≥ 0.78, and weighted Dice coefficients ≥ 0.87) and myelinated axons (precision ≥ 0.84, recall ≥ 0.88, weighted Jaccard index ≥ 0.80, and weighted Dice coefficients ≥ 0.88). For unmyelinated Figure 13. (a) Using DeepACSON, we quantified the axonal diameter, eccentricity, and tortuosity of about 288,000 myelinated axons and the inter-mitochondrial distance of about 1,800,000 mitochondria. On each bean plot, the central mark indicates the median, and the left and right edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers. The colors correspond with the animal ID. (b) The comparison of the density of myelinated axons, as the ratio of the volume of myelinated axons to the myelin volume plus the volume of myelinated axons. (c) The comparison of the density of cells, as the number of cell nuclei over the dataset volume. DeepACSON segmented about 2,600 cell nuclei in the ten large field-of-view datasets. The color of the indicators corresponds with the animal ID.

Jaccard index and weighted Dice coefficients of unmyelinated axons showed approximately 0.37 and 0.50 agreement, respectively, which indicated geometrical and topological errors in the automated segmentation of unmyelinated axons.

In study II, we tested DeepACSON using two test sets: 1) a test set consisting of six high-resolution SBEM volumes (each volume had approximately 300 axons) that were down-sampled to the resolution of low-resolution images. We used this test set to compare DeepACSON to DeepEM2D and DeepEM3D (Zeng, Wu and Ji, 2017) and FFN (Januszewski et al., 2018) and conducted an ablation analysis on DeepACSON. Labels for this test set were generated automatically using ACSON; 2) a test set comprising 50 patches of size 300×300 voxels for expert evaluations. We randomly sampled every low-resolution dataset for five non-overlapping windows of size 300×300 voxels (10 datasets, 50 samples). Each patch, on average, had approximately 130 axonal cross-sections and 30 mitochondria. Therefore, the expert has evaluated approximately 6,500 axonal cross-sections and 1,500

mitochondria in total. The dataset ID and sampling location were both unknown to the expert. The expert evaluated the sampled images of the final segmentation by counting the number of true-positives, false-positives, and false-negatives.

To compare DeepACSON to DeepEM2D/3D and FFN, we trained DeepACSON and DeepEM2D/3D for one day and FFN for one week on a single NVIDIA Tesla V100-32 GB GPU. Figure 14 shows that DeepACSON outperformed DeepEM2D/3D and FFN as it generated the smallest VOI and ARE and the greatest Wallace

measures. We also evaluated the DeepACSON semantic segmentation of myelin and myelinated axons (including mitochondria) on the six SBEM volumes. We reported the average precision, recall, and F1 scores of our evaluations in Table 6.

In addition, we evaluated the performance of the two SVMs by the leave-one-Figure 14. We compared DeepACSON against DeepEM2D, DeepEM3D, and FFN using (a) VOI (split and merge contribution, lower value is better), (b) Wallace indices (split and merge contribution, higher value is better), and (c) ARE (lower value is better) and the sum of VOI split and VOI merge (VOI sum, lower value is better). DeepACSON outperformed other techniques as it produced the smallest VOI split, VOI merge, VOI sum, and ARE, and the biggest Wallace split and merge values.

group-out (LOGO) cross-validation approach: the classifier was trained excluding the data from one group of animals (sham-operated or TBI) and evaluated against the excluded data. As reported in Table 6, the LOGO cross-validation showed that the performance of the SVMs was equally robust in all datasets, regardless of the condition (sham-operated or TBI). Finally, an expert evaluated the DeepACSON segmentation of myelinated axons and mitochondria at the object level. The expert’s evaluation is shown in Table 6.

Table 6. Evaluation of DeepACSON semantic segmentation of myelin and

myelinated axons. We evaluated the performance of SVMs using leave-one-group-out (LOGO) cross-validation (CV). An expert evaluated the final segmentation of myelinated axons and mitochondria.

Model Tissue Precision Recall F1 score

CNN Myelin 0.902±0.078 0.873±0.024 0.886±0.049

Myelinated axons 0.918±0.023 0.813±0.0728 0.861±0.037

SVM (LOGO CV)

Myelinated axons sham 0.988 0.988 0.988

TBI 0.920 0.991 0.955

Cell nuclei sham 0.961 0.977 0.969

TBI 0.964 1 0.981

Final segmentation

(expert) Myelinated axons 0.965±0.027 0.877±0.061 0.918±0.038) Final segmentation

(expert) Mitochondria 0.856±0.100 0.804±0.091 0.823±0.067

In study III, we examined how the proposed CSD method handled synthetic voxelized objects from the Princeton segmentation benchmark database (Chen, Golovinskiy and Funkhouser, 2009). Figure 15 shows a gallery of decomposition on a mixture of objects with high, moderate, and small articulation. We compared ACD (Kaick et al., 2015), GCD (Zhou et al., 2015), and CSD to the human

decomposition over objects acquired from the Princeton database for the quantitative analysis. We selected two objects per category from the Princeton database, excluding categories containing objects with a genus greater than zero, such as cups or vases, and categories containing an ambiguous skeleton, such as

busts or mechs. We converted the objects and their corresponding human

segmentations from mesh to voxel-based representation. To aggregate evaluation metrics over multiple human segmentations for the same model and multiple models for the same object category, we reported averages per category (averages are computed first within each model, then the results are averaged within each object category). We reported the Rand error (Rand, 1971) and boundary error (Martin et al., 2001) and proposed using VOI. Table 7 shows that the proposed CSD algorithm outperformed both ACD and GCD methods in decomposing voxel-based objects.

Table 7. Comparison of decomposition techniques using Rand error (RE), the variance of information (VOI), and boundary error (BE) to human shape decomposition. The smallest value in each row is bolded; smaller values are better.

Input model Evaluation ACD GCD Proposed

RE 0.2421 0.2897 0.2029

Human VOI 3.0345 1.7049 1.7360

BE 0.4002 0.4145 0.1703

RE 0.2402 0.1650 0.2394

Glasses VOI 1.7264 0.7111 0.8842

BE 0.0654 0.0506 0.0088

RE 0.2588 0.1450 0.1868

Airplane VOI 1.9981 0.9944 1.4765

BE 0.1066 0.0678 0.0677

RE 0.2284 0.0699 0.0842

Ant VOI 2.4227 1.0315 0.5978

BE 0.4930 0.1573 0.0281

RE 0.3135 0.1657 0.0215

Octopus VOI 3.0222 0.9684 0.2418

BE 0.5433 0.1736 0.0223

RE 0.0353 0.0444 0.0109

Table VOI 0.4656 0.2476 0.1082

Figure 15. A gallery of CSD decomposition of synthetic objects.

BE 0.1530 0.0305 0.0051

RE 0.3721 0.3530 0.0621

Teddy VOI 3.2006 1.1708 0.5542

BE 1.5860 0.2210 0.1851

RE 0.3625 0.3400 0.2201

Hand VOI 2.7837 1.6841 1.1728

BE 0.5442 0.2967 0.1739

RE 0.2399 0.0830 0.0656

Pliers VOI 2.7210 0.6070 0.5419

BE 0.2736 0.0936 0.0386

RE 0.5879 0.5140 0.2232

Fish VOI 2.6352 1.7495 0.8839

BE 1.1104 0.4107 0.1337

RE 0.1764 0.2309 0.2208

Bird VOI 1.6971 1.2629 1.3959

BE 1.0669 0.1431 0.0901

RE 0.2312 0.1897 0.1870

Armadillo VOI 2.9909 1.3408 1.5887

BE 0.8717 0.3583 0.3407

RE 0.4082 0.3667 0.1868

Four-leg VOI 2.9593 1.9207 1.0821

BE 0.6796 0.3486 0.1738