representaciones juveniles para las OSJ

3.2.2.1 Reference Tracings

R1 contains one dendrite and 106 spines, either attached or in close proximity of the dendritic stem, which resembles the reference number of true objects. In addition to these referential true objects, six false objects and 20 loops were also generated. In comparison, the stricter reference dataset R2 provides one dendrite, 105 spines, one false object and 15 loops. Comparing the volumes of both datasets, R1 (4,994,244 voxels/ 93.64 µm³) is 5.2% larger than R2 (4,734,906 voxels / 88.78µm³). Data and findings are summarized in Table 3.4.

3.2.2.2 Comparison of the Computational Tracing (NSt) and the Manual Tracings (MTs) to Reference Tracings R1 and R2

3.2.2.2.1 3D Object Space Analysis

Table 3.5 summarizes the results of the quantitative analysis for both the manual and NSt 3D reconstructions using R1 as a reference: NSt, M1, M3 and M4 found all true objects - M2 and M5 missed one and three spines, respectively. Large deviations are observed in the number of false objects discovered by the MTs. The NSt traced zero R1 positive and five R1 negative false objects. One of these false R1 negative objects is M1 positive. All tracings present a number between 12 and 18 loops. Remarkably, M3 did not trace any R1 negative loops. Table 3.6 summarizes the results in the object space using R2 as a reference. R2 missed one Table 3.4: Quantitative findings for R1 and R2 datasets at the object and image space.

true object due to the stricter foreground pixel selection rule. The statistical weight of tracings M2 and M5, which are missing one and three true objects respectively, dominates this dataset.

3.2.2.2.2 Image Space Analysis

At the image (voxel) space, the manual tracings calculate the R1 false positive volume (1.1% V(R1) as 7.4% V(R1)), and the R1 false negative volume (1.3% V(R1) as 7.9% V(R1)) to the same extent. The NSt’s volumes are comparable to these values (2.3% V(R1) R1 positive voxels and 7.9% V(R1) R1 negative) (Table 3.7). MTs show a mean value of false R1 positive voxel deficit (3.6±1.0)% V(R1), that is balanced by a (4.1±1.1)% V(R1) false R1 negative surplus. The voxel volumes of the computed tracing (NSt) show a minimal deviation from the Table 3.5: Quantitative validation results of NSt in comparison to the MTs with respect to R 1 (weak majority) regarding the object space .

Table 3.6: Quantitative validation results of NSt in comparison to the MTs with respect to R2 (strong majority) regarding the object space.

Table 3.7: Quantitative validation results of NSt in comparison to the MTs with respect to R 1 (weak majority) at the image space. All values are given as %V(R1).

predicted statistical error of the M̅(R1) positive volume (M̅+(R1)) of just 0.3% V(R1) and 2.7% V(R1) as predicted by the statistical error of the M̅ R1) negative volume M̅-(R1)). Furthermore, we estimate the volume deviations of the false objects of the datasets M1, M3 and M4 on the total volume of the segmented structure by rejecting all objects that are not within a certain distance R from the dendritic stem and that possess a volume larger than V. For R = 60 and V = 600 the volume differences between reference data and filtered manual data are very small (0.2%) (Table 3.7, last column). This result supports the observation that the voxel volume variability is contributed mainly by the dendritic stem, as has already been shown from the embracing voxel surplus in Figure 3.28(b.) and (d.). Table 3.8 shows the quantitative analysis of the image space using R2. The mean false positive volume (M̅+(R2)) of all manual tracings converges to a difference of (1.5±0.5)% V(R1), which is half (M̅+(R1). This results from the stricter selection criteria, which led to less variation in the shape of the foreground structure. As a consequence, the deviation of the volume M̅-(R2) is with (7.2±1.6)% V(R1) almost twice the value of M̅-(R1). The volume deviations for each tracing, however, do not significantly differ from the analysis of R1.

Table 3.8: Quantitative validation results of NSt in comparison to the MTs with respect to R2 (strong majority) at the image space. All values are given as %V(R 2).

Figure 3.29: Ranking of the M1-M5 and NSt tracings with respect to R1 (a.) and R2 (b.) tracings in the object, image and combined (both) image and object space. The bars are slightly shifted in order to be visually distinguished.

3.2.2.3 Quantification of the Tracing’s Accuracy

To obtain a clearer perspective of the quality of the tracings, we quantified the results of all tracings in both the object and the image space and validated them against both R1 and R2. For this purpose, the relative error of each tracing’s finding (manual and computed) was calculated in regards to the reference. In the object space we used five categories: true objects, false positive, false negative, loops positive and loops negative. Especially for the categories of the negative artifacts (false objects and loops), which by definition was zero items for RT, we defined the relative error with respect to M3 (MT with the most negative objects) and M1 (MT with the most loops). At the image space, the false positive and false negative volume deviations were used as a metric. Taking all seven categories (total object and image space categories) into account resulted in a ranking for all tracings, shown in Figure 3.29(a.) and (b.) for R1 and R2 as a reference, respectively. In all three spaces (object, image and combination of both) the relative errors of all tracings cluster and no large deviations are observed. We conclude that our computational approach (NSt) provides a reliable and high quality reconstruction, which matches and in some parameters even outperforms the quality of the manual reconstructions.

Figure 3.30: GLT-L5B Neuron TK100909A1: (a.): Slice overview with patch pipette; (b.): overlay of DIC- and GFP-Channel identifying the patched neuron as GLT; (c.) DAB stained neuron.