CT-Based Local Distribution Metric Improves Characterization of COPD

Parametric response mapping (PRM) of paired CT lung images has been shown to improve the phenotyping of COPD by allowing for the visualization and quantification of non-emphysematous air trapping component, referred to as functional small airways disease (fSAD). Although promising, large variability in the standard method for analyzing PRMfSAD has been observed. We postulate that representing the 3D PRMfSAD data as a single scalar quantity (relative volume of PRMfSAD) oversimplifies the original 3D data, limiting its potential to detect the subtle progression of COPD as well as varying subtypes. In this study, we propose a new approach to analyze PRM. Based on topological techniques, we generate 3D maps of local topological features from 3D PRMfSAD classification maps. We found that the surface area of fSAD (SfSAD) was the most robust and significant independent indicator of clinically meaningful measures of COPD. We also confirmed by micro-CT of human lung specimens that structural differences are associated with unique SfSAD patterns, and demonstrated longitudinal feature alterations occurred with worsening pulmonary function independent of an increase in disease extent. These findings suggest that our technique captures additional COPD characteristics, which may provide important opportunities for improved diagnosis of COPD patients.

Patient Characteristics Supplementary Table 2 Topological Metric Comparisons between GOLD Supplementary Table 3 Multivariate Regression Supplementary Table 4 Comparison Supplemental Table 1 Supplemental Table 2 Topological Metric Comparisons between GOLD Comparison of mean topological metrics between GOLD status groups was performed using a One-Way ANOVA using Bonferroni post-hoc to control for multiple comparisons. P-values are shown in Supplemental Table 1, with significance determined at the 95% level (highlighted in orange).
Overall between-group significance is also shown for each topological feature of PRM Emph and PRM fSAD in the plot legends of Supplemental Figure 4. Global evaluation of PRM Emph did not reveal significant between-group differences, with the exception of S Emph . Local evaluation of PRM Emph revealed significant trends between groups except for χ Emph . PRM fSAD trends between groups were found significant in S fSAD and χ fSAD for both global and local analysis, while only global a fSAD was significantly different between groups. Table 3 Multivariate Regression Supplemental Table 4 Comparison of Topological Metrics to MicroCT Measurements

Calculation of Morphological Indices
Topological metrics in this study were defined using the 3D Minkowski measures defined in Legland et al. 1  Additional post-processing using the c metric was performed to calculate a condensed descriptor of aggregation (a) 2 . In brief, binary PRM maps were first smoothed using a Gaussian filter with standard deviation of 2 voxels in each direction to generate a density map. The smoothing length determines the scale of interest for groupings. c was then determined at various thresholds (u), between 0 and 1 (101 equally spaced thresholds for the purposes of this study), and averaged using the following equation 2 : The aggregation value is larger with greater heterogeneity in the binary map. The approximation of the c measure, therefore a as well, strongly depends on the choice of adjacency system. The use of 6-connectivity for this study was chosen for simplicity, and exploration of higher connectivity systems could prove beneficial, however such analysis was beyond the scope of this preliminary study.

Simulations
We analyzed random distributions at various volume fractions in order to show typical behavior of each Minkowski measures. Random binary distributions were generated inside a spherical mask with matrix size 256 3 and mask radius of 200 3 . A total of 10 iterations were performed at each volume fraction, with 51 volume fractions spaced evenly between 0 and 1. Aggregation values were determined using 101 equally spaced thresholds (u) from 0 to 1. Local analysis was performed using the same grid spacing that was used in the clinical analysis. Both local and global analyses were performed for each randomized distribution, and local comparisons were evaluated as the mean local measure over the masked volume. Plots of topological feature trends against relative volume are displayed in Supplemental Figure 2 as the mean of measurements. Confidence intervals at the 95% level were determined over the range of volume fractions, however they were too close to the mean to be seen in the plots and are not shown.

Case Study: PRM and Topological Feature Analysis of Lung Cores
Bronchiolitis obliterans syndrome is a chronic lung allograft dysfunction in transplant recipients.
It is known to result in air trapping which is detectable by CT, and is characterized by a spirometric decline and histopathalogical observation of obliterative bronchiolitis (OB) 3,4 . In order to correlate in vivo analysis results with histopathology, we provide a case study with cored lung analysis to serve as a representative sample and provide rationale for further validation studies.
Topological features of individual cores were determined through spatial alignment of the in vivo paired CT scans to a photograph of the explanted cored lung section. The process involves the following 5 steps. First, pre-transplant inspiration CT scan was spatially aligned to the paired expiration CT scans using a deformable registration algorithm as described in the main text. Second, The lung used for the microCT analysis was segmented from the thoracic cavity in the pre-transplant expiration CT scan and spatially aligned to the CT scan of the explanted inflated frozen lung using the same registration algorithm. Third, to register the inflated lung to the uncored section RGB photograph additional post-processing was required. The photograph of the uncored section was converted to gray scale, subsampled by a factor of 10 and a histogram equalization algorithm was applied to improve image contrast. To obtain the 3D PRM fSAD classification map within the core, the image of the uncored lung section was replicated such that a 3D data set was constructed with the same number of slices as the inflated frozen lung 3D CT scan. The explant image on the center slice was then segmented. A similarity transformation, i.e. rotate-translate-isotropic scaling, was performed to spatially align the inflated lung CT scan to the segmented uncored section in the dataset. Fourth, post-processing of the photograph of the uncored lung section and the third step were repeated to register the uncored lung section to the cored lung section. Finally, the transformation matrices from each step were applied to the pre-transplant paired CT scans. PRM classification and resulting topological maps were generated from the paired CT data aligned to the cored section. Mean values for the topological features were calculated for the individual cores. The core volume of interest was determined by contouring the cored volume in the 3D cored lung section dataset. The number of contoured slices was determined by dividing the section thickness by the transformed voxel size (35 slices=20mm section /[0.82 scaling factor*0.7mm slice thickness for inflated lung CT scan]).