# An Automatic Approach for Individual HU-Based Characterization of Lungs in COVID-19 Patients
## 3 Results
### HI-Density Histogram Parameters--Extraction and Analysis of 166 COVID-19 Patients
Of note, the approach of using a plot that follows the trend of real data, rather than a fit made on these data, removes the intrinsic uncertainty linked to the fit, obtaining values that better represent the true condition of the lungs. Consequently, in the remaining part of this work, sub-segmentation will always refer to this method. After identifying the threshold values that separate the components of the lungs in COVID-19 patients, information characterizing each of the regions of the lungs was extracted from the histograms. The first relevant parameter extracted was the volume (in cc) of the aerated, intermediate, and consolidation regions. To calculate the volume in cc starting from the CT images, the area under the curve of the HU-density histograms was considered. Each voxel had a known size of 1.5 \(\times\) 1.5 \(\times\) 1.5 mm\({}^{3}\); thus the area under the \begin{table}
\begin{tabular}{c|c c c c c} \hline \hline
**Method** & **Threshold** & **Minimum** & **Maximum** & **Median** & **Standard Deviation** \\ \hline \multirow{2}{*}{_Gaussian_} & Th1 & \(-870\) & \(-386\) & \(-768\) & \(73\) \\  & Th2 & \(-232\) & \(32\) & \(-114\) & \(41\) \\  & Th1 & \(-927\) & \(-322\) & \(-780\) & \(77\) \\  & Th2 & \(-706\) & \(10\) & \(-87\) & \(61\) \\  & Th1 & \(-900\) & \(-430\) & \(-798\) & \(71\) \\  & Th2 & \(-271\) & \(64\) & \(-34\) & \(41\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary table of the threshold values found with the methods used. Figure 6: Boxplot of the distributions of threshold values Th1 and Th2 according to method used: Gaussian, maximum gradient on the fit (Max grad fit) and maximum gradient on the data (Max grad data). curve was linked to the volume of the lung considered with a normalization factor taking voxel size into account. Figure 7 shows the histogram of the volume distributions of the lung components within the entire patient population. The bin size used was 150 cc. It can be seen that the consolidated component had the smallest volume, with a median value of 126 cc \(\pm\) 111 cc. The intermediate component had a median volume of 914 cc with a standard deviation of 291 cc, while the aerated component had a median volume of 793 \(\pm\) 499 cc. In addition to the volumes of the lung regions, their ratio was also calculated. The absolute measurement of volumes, in fact, may not provide full information on the residual functionality of the lung. The values found for the consolidated over aerated component ratio and the ratio between intermediate and aerated components are shown in Figure 8 and were 0.16 \(\pm\) 0.89 and 1.09 \(\pm\) 2.56, respectively. Other extracted features that characterized the HU-density histogram were:  
1. HU value corresponding to the peak of the curve for the aerated regions;
2. Shift with respect to \(-\)1000 HU, a characteristic value of the aerated component under normal conditions;
3. Width in HU of the intermediate region. The median of the values of the peak position of the aerated region curve was \(-\)853 \(\pm\) 56 HU in a range of \(-\)1000 to \(-\)583 HU. Consequently, the median value of the  
Figure 8: Boxplot of the volume ratios of the consolidated component compared to the aerated component and of the intermediate component compared to the aerated one. Figure 7: Histogram of the volume distributions of the aerated, intermediate, and consolidated components. The bin size used was 150 cc. The number on the y-axis represents the number of patients per bin. peak shift of the aerated region with respect to \(-\)1000 HU was 147 HU. The width of the intermediate region was calculated as the difference between the th2-th1 threshold values. The width values found were in the range of 282 to 878 HU, with a median and standard deviation of 754 and 88 HU, respectively. As shown in Figure 9, the inter-patient distribution of these values was very large and did not follow a Gaussian shape.