Abstract
Purpose
Computed tomography (CT) image is promising for diagnosing of interstitial idiopathic pneumonias (IIPs); however, quantification of IIPs lesions in CT images is required. This study aimed to quantitatively evaluate fibrotic lesions in CT images using homology-based image analysis.
Methods
We collected publicly available CT images comprising 47 fibrotic images and 36 non-fibrotic images. The homology-profile (HP) image analysis method provides b0 and b1 profiles, indicating the number of isolated components and holes in a binary image. We locally applied the HP method to the CT image and generated homology-based feature (HF) maps as resultant images. The collected images were randomly divided into the tuning dataset and the testing dataset. The cut-off value for classifying the HF map for fibrotic or non-fibrotic images was defined using receiver operating characteristic (ROC) analysis with the tuning dataset. This cut-off value was evaluated using the testing dataset with accuracy, sensitivity, specificity, and precision.
Results
We successfully visualized the quantification of fibrotic lesions in the HF map. The b0 HF map was more suitable for quantifying fibrotic lesions than b1. The mean cut-off value of the b0 HF map was 199, with all performances achieved at 1.0. Furthermore, the classification of the b0 HF map for fibrotic or lung cancer images achieved all maximum performances at 1.0.
Conclusion
This study demonstrated the feasibility of using the HF in quantitatively evaluating fibrotic lesions in CT images. Our proposed HP-based method can also be promising in quantifying the fibrotic lesions of patients with IIPs, which can be applicable to assist the diagnosis of IIPs.
Supplementary Information
The online version contains supplementary material available at 10.1007/s11548-025-03428-8.
Keywords: Idiopathic interstitial pneumonias, Quantitative image analysis, Homology, CT image, Computer-aided diagnosis
Introduction
Idiopathic interstitial pneumonia (IIP) is a fatal disease with no clear cause known and no cure. There are various categories, namely, mainly idiopathic pulmonary fibrosis (IPF), idiopathic nonspecific interstitial pneumonia, cryptogenic organizing pneumonia, respiratory bronchiolitis-associated interstitial lung disease (RB-ILD), desquamative interstitial pneumonia, and acute interstitial pneumonia [1]. As for the treatment, there is a large difference of strategies, and the prognosis depends on the category. The prognosis of the patients with IPF is significantly poorer than that with non-IPF IIPs. In addition, the acute exacerbation of IPF is associated with a high mortality rate [2, 3].
High-resolution computed tomography (HRCT) images are commonly used to diagnose IIPs definitively, and the HRCT image provides the typical findings (e.g., extensive traction bronchiectasis or honeycomb lung) which indicate the IPF [4–7]. Those typical findings can be able to aid diagnosis in the HRCT image; however, it is challenging to classify the category from the HRCT image accurately even though the radiological experts exert their skill. Moreover, an inter-observer variability can lead to diagnostic limitations [4]. Therefore, a valid quantification method for fibrosis findings in the HRCT image could be a useful to assist the deciding the category and diagnosis for IIPs.
Homology-based image analysis has been reported to be effective to detect the certain features of medical images such as pathological and radiological images [8–10]. Nakane et al. proposed a homology-profile (HP) method to detect the tumor cell in the hematoxylin–eosin-stained pathological image [8]. It has been demonstrated that the homology-based feature (HF) is effective in capturing the CT imaging feature and can improve the performance of radiomic analyses [9]. Betti numbers composed of b0 and b1 are obtained by using the HP method, namely, HFs. These Betti numbers indicate the number of isolated components and the number of holes in a binary image, respectively (Fig. 1a). This calculation is performed by changing the threshold value applied to the image binarization. As a result of the calculation, the connectivity of objects in an image is quantified. Ninomiya and Arimura showed that the HFs from CT images are an effective feature in the prognostic prediction of lung cancer patients [10]. They demonstrated that the HFs are helpful in extracting the topologically invariant morphological features of lung cancers in CT images, which could be included in patterns of tumor inhomogeneity. Therefore, the HFs may extract the practical features in quantifying fibrotic lesions in CT images from the pattern of fibrosis homogeneity.
Fig. 1.
A concept of the HP method in this study. a counting Betti numbers composed of b0 and b1 in a binary image processed with a threshold value. b the extracted lung field image and the HP method that continuously counts the Betti numbers in binary images by changing the threshold value along with the HU value. Red circles indicate fibrotic lesions. The red rectangle in the lung field image is an example of a tile cropped for analysis using the HP method. Each red rectangle in the binary images indicates each hole, and the number of the holes is annotated. c the procedure of tile-shifted HP method. Abbreviations: HP, homology-profile; CT, computed tomography; HU, Hounsfield unit; and HF, homology-based feature
Hereby, we have hypothesized that the HFs may be promising in quantification of the fibrotic lesion of IIPs in the HRCT image. CT images of the COVID-19 case also display fibrotic lesions as a typical finding which is similar to fibrotic lesions of IIPs. This study shows a proof of concept for quantifying the fibrotic lesion of IIPs in the HRCT image by applying the HP method to CT images of the COVID-19 cases.
Materials and methods
Data collecting
Eighteen CT image datasets of patients with COVID-19 and 20 radiotherapy datasets for lung cancer consisting of CT images and radiotherapy structures were obtained from the Cancer Image Archive [11, 12]. We selected CT datasets of COVID-19 according to the following criteria: the patients underwent a non-contrast-enhanced CT examination; the manufacturer of the CT equipment was GE Health Care LTD.; and the CT images did not display pleural fluid in the lung field. From the COVID-19 cases, we selected forty-seven CT images that show obvious fibrotic lesions and used them for classification in this study. The association between the cause of lung cancer and interstitial lung abnormalities (ILAs), such as ground-glass opacity, has been reported, the ILAs can be observed in the CT images of patients with lung cancer [13]. These ILAs lesions can be a noise for quantitatively evaluating the fibrotic lesions. As lung cancer lesions and/or obvious lung abnormalities were observed in the whole lung of two patients with lung cancer, these cases were excluded when classifying fibrotic and non-fibrotic cases. The excluded cases were used to classify fibrotic and lung cancer cases. A total of thirty-six CT images were acquired by selecting two CT images from each lung cancer case, these images did not include lung cancer lesions defined by radiologists and/or any lung abnormalities. The data collection scheme is illustrated in Fig. 2. The patient demographic data are presented in Table 1.
Fig. 2.
A scheme of data collecting and a concept for this study. a and b indicate the classification between fibrotic cases and non-fibrotic cases and fibrotic cases and lung cancer cases, respectively. Abbreviations: ROC, receiver operative characteristics
Table 1.
Patient demographic data
| Characteristic | COVID-19 (n = 18) | Lung cancer (n = 20) | Overall (n = 38) |
|---|---|---|---|
| Age (median [25th–75th percentile]) | 60 (46.5–69) | NA | NA |
| Sex (male/female) | 10/8 | 12/8 | 22/16 |
| Fibrosis vs non-fibrosis | 10/8 | 10*/8 | 20/16 |
| Fibrosis vs lung cancer | 10/8 | 12/8 | 22/16 |
The age of patients with lung cancer was not described in this dataset. *Two cases were excluded because lung cancer lesions and/or obvious abnormalities were confirmed in the whole lung
Abbreviation: NA, not applicable
Preprocessing
These collected CT images underwent the following preprocessing. First, the mask image covering the lung field was created from the CT image with numpy, scipy, and scikit-image. Second, the lung field image was extracted by using the mask image, as shown in Fig. 1b.
Obtaining HF map
The HFs are composed of b0 and b1 indicating the connectivity of isolated components and connectivity of holes in a binary image, as shown in Fig. 1a. These indices are calculated by using the HP method, in which changing the threshold value is applied to the image binarization (Fig. 1b). The HP calculation was executed with the in-house HP software. The calculation region of interest was set to a 32 × 32 matrix, named a tile. The tile was shifted every eight pixels on the CT image through the entire 512 × 512 matrix, and the maximum value of HP derived from each tile was assigned to corresponded region in the output image. Here, the matrix size of tile and the shifting size were validated (Online Resource 1), and they have been decided. When pixels on the calculation tiles were overlapped, the assigned maximum values were summed. This output image is called HF map in this study. Each HP was standardized by dividing it by its own pixel size. The range of threshold values was set from − 700 to − 400 Hounsfield unit (HU) because the range has been reported to be a representative range of the fibrotic lesion of IPF [14]. When the ratio of pixels contained in the calculation tile was over 95%, the calculation was systematically skipped. This tile-shifted HP method is detailed in Fig. 1c.
Cut-off value for classification of fibrosis or non-fibrosis
We conducted slice-wise classification of a CT image as a fibrosis or non-fibrosis based on the maximum value of b0 HF map. First, the collected dataset was randomly patient-wise split into two datasets for tuning the cut-off value (12/18: 67%) and testing (6/18: 33%), as shown in Fig. 2a. Second, the cut-off value was defined with the slice-wise receiver operating characteristic (ROC) analysis by using tuning dataset and Youden Index. Third, the cut-off value was slice-wise tested and evaluated using the testing dataset for the accuracy, sensitivity, specificity, and precision score. The above procedures were repeated 5 times, and these cut-off value and these performances were averaged. In addition, the slice-wise classification of a CT image as fibrosis or lung cancer was conducted using the same procedure as the above. Two excluded cases in the former classification were also included in the latter classification, as shown in Fig. 2b. It validated the feasibility of the b0 HF map in quantitatively classifying even if CT images including lung cancer lesions and those abnormalities.
Development environment
This methodology was implemented by Python version 3.11.7, numpy version 1.26.4, pydicom version 2.4.4, scipy version 1.11.4, skimage 0.22.0, and opencv version 4.9.0. This calculation was executed on the CPU of 13th Gen Intel (R) Core (TM) i9-13900H 2.6 GHz and the super-computing resource provided by Human Genome Center, the Univ. of Tokyo (http://sc.hgc.jp/shirokane.html).
Results
HF map
HF maps were acquired by the tile-shifted HP method, as shown in Fig. 3. According to the HF maps (Fig. 3), the b0 HF has the highest association with the fibrotic lesions. The b0 HF map more specifically detected fibrotic lesions than the b1 HF maps, and the value covering the fibrotic lesion depends on the density of the fibrosis, the fibrotic type, or surrounding lung nodules (e.g., vessels). In contrast, almost whole lung field was enhanced even though the area included the nodules in the b1 HF map. Thus, we validated the conditions for obtaining HF maps that can detect fibrotic lesions in CT images and qualitatively confirmed that b0 could clearly detect fibrotic lesions more than b1. Furthermore, we also validated a method that applied the argmax value, but not the maximum value, of the HP; however, we confirmed that it was not suitable for detecting fibrotic lesions (Online Resource 2). For these reasons, we decided to use b0 to generate HF maps in this study.
Fig. 3.
Examples of the HF maps. a, b and c show the CT image, b0 HF map, and b1 HF map, respectively. The area annotated with the red line in the CT images indicates fibrotic lesions. The colorbar presents the absolute HF map value. Here, the HF map value is adjusted from 0 to 1000 to compare the b0 HF and b1 HF maps with the same scale. The HF maps show that b0 is superior to b1 in quantifying fibrotic lesions in the CT images. Red line indicates lung cancer lesions defined by radiologists. Abbreviations: CT, computed tomography; HF, homology-based feature
Cut-off value for slice-wise classification of fibrosis or non-fibrosis
According to the ROC analysis using the tuning datasets, the mean ± standard deviation (SD) of the cut-off value and area under the ROC curve (AUROC) were 199 ± 0 and 1.00 ± 0, respectively. Figure 4a depicts the ROC curves. As a result of the slice-wise classification using the testing datasets based on a cut-off value in each experiment, the mean ± SD of accuracy, sensitivity, specificity, and precision were 1.00 ± 0, 1.00 ± 0, 1.00 ± 0, and 1.00 ± 0, respectively. These results have shown the feasibility of b0 HF map applying to classify the CT image for fibrosis or non-fibrosis.
Fig. 4.
ROC curves for defining the cut-off value. a the ROC curves for classifying fibrotic and non-fibrotic cases. b the ROC curves for classifying fibrotic and lung cancer cases. Abbreviations: ROC, receiver operative characteristics; AUC, area under the ROC curve
Cut-off value for slice-wise classification of fibrosis or lung cancer
The mean ± SD of the cut-off value and AUROC were 191.4 ± 5.32 and 0.992 ± 0.008, respectively, based on the result of the ROC analysis for the tuning dataset (Fig. 4b). Thus, there were no substantial differences in the b0 HF map cut-off values used to classify fibrotic or non-fibrotic lung lesions and those used to differentiate lung cancer from fibrotic lesions. According to the slice-wise classification using the testing dataset, the mean ± SD of accuracy, sensitivity, specificity, and precision were 0.892 ± 0.059, 1.00 ± 0, 0.721 ± 0.158, and 0.854 ± 0.068, respectively. These maximum performances have achieved an accuracy of 0.966, sensitivity of 1.00, specificity of 0.917, and precision of 0.944 (Table 2). These findings indicate that the b0 HF map value could also be applied to discriminate between fibrotic and lung cancer lesions.
Table 2.
Comparison between previous studies and our proposed methodology
| Ref. No | Accuracy (%) | Sensitivity (%) | Specificity (%) | Precision (%) |
|---|---|---|---|---|
| 24 | 99.5 | 100 | 99.0 | NA |
| 25 | 98.9 | 99.0 | 98.9 | 98.9 |
| 26 | 99.4 | 99.6 | 99.2 | NA |
| Ours (vs non-fibrosis) | 100 | 100 | 100 | 100 |
| Ours (vs lung cancer) | 96.6 | 100 | 91.7 | 94.4 |
Abbreviation: Ref., reference; NA, not applicable
Discussion
We have successfully quantified the fibrotic lesion of the COVID-19 case displayed on the CT image by using the HF in this study. The association between the HF and the fibrotic lesion in the CT image has been demonstrated. The HFs are composed of the b0 and b1, which equal the number of isolated components (black pixels) and the number of holes (white pixels) in a binary image. These indices represent the connectivity of object in an image. Our developed b0 HF map visualizes the fibrotic lesion with a higher value than that of the non-fibrotic lung field and lung cancer nodule. This demonstrated that the feasibility of the b0 HF map value in classifying CT images into fibrosis or non-fibrosis and lung cancer case. Hence, we found that b0 HF, the connective caused by the number of isolated components, could capture the topological features that lead to the quantification of inhomogeneity differences between fibrotic and non-fibrotic lung fields. On the other hand, our proposed method misclassified the lung cancer cases (slices 9 and 10 in Fig. 3) complicated with fibrotic lesions. It has probably been caused by the ILAs related to lung cancer, as Hata et al. mentioned [13], and the similarity of the fibrotic lesions and the ILAs has been shown based on the HF map value in this study. To address the complicated case, the ILA lesions may be discriminated from lung cancer lesions by pixel-wise applying the cut-off value to the b0 HF map. Thus, this study has demonstrated the feasibility of homology-based image analysis in quantitatively evaluating fibrotic lesions in the CT image.
There have been many studies that can quantitatively evaluate the fibrotic lesions in the CT images. These methods have been based on histogram features and/or texture features of the CT image and have been frequently applied to many studies to quantify the fibrotic lesion in the CT images [15–19]. While the methods are promising in quantifying the fibrotic lesion, those performances are influenced by CT imaging conditions (e.g., KVp and slice thickness) [20]. It may be more challenging to correctly regulate the histogram-based features than that of the HF since the feature of the histogram is simply derived from the histogram of CT images. These CT imaging conditions could also influence the performance of our proposed method. However, the HP method can quantify the connectivity of objects in the image, and the effect can be flexibly reduced by optimizing the calculation parameters (e.g., the range of the HP calculation). Therefore, our proposed methodology is probably more robust than the past reported studies based on the histogram and/or texture analysis. Moreover, machine learning (ML)-based methods have also been proposed [4, 21–26]. Regarding the classification of CT images as fibrotic or non-fibrotic, previous supervised ML-based studies have shown an accuracy of approximately 0.99 [24–26]. Thus, ML-based techniques show excellent performances, but the performance using supervised ML depends on the quantity of training datasets. Our proposed methodology provides the excellent performances comparable to these ML-based studies, as shown in Table 2; however, a larger cohort size is required to accurately compare the performances in this study. While ML-based classification and segmentation for fibrotic lesions in the CT image are less challenging than other strategies, it may be challenging to develop the absolute quantification of the fibrotic lesions with only CT image features, like the HF map. Our proposed method is thought to reflect the actual types, densities, and morphologies of cells, so it is possible that they can be used to find fibrotic lesions without relying on prior knowledge, along with values (b0) that indicate their characteristics. Thus, it has been shown that it is possible to create features based on cell biology and mathematics, even without a large number of images or annotations by experts.
The current study has a few limitations. First, our proposed method is influenced by the pixel size of the CT image while a standardization based on the pixel size was implemented to overcome it in this study. In the future, this standardization method will be completely developed. However, the standardization must not be considered if the analysis is specified to IIPs in the HRCT image. Second, the analysis resolution of the proposed method is not high. This issue happens due to setting the shift parameter in the tile-shifted HP calculation to 8 pixels. If the shift size of the tile is smaller, a higher resolution analysis result can be obtained. Although the high-resolution result is acquired due to the optimization of this calculation, then time consumption can also be an issue, which our future study can dissolve. Third, these cases are COVID-19, which we used in this study, but not the cases of IIPs. There has a difference in detailed characteristics of the fibrotic lesion between the COVID-19 case and IIPs, so we must validate the feasibility of this methodology in quantitative evaluation for the fibrotic lesions in IIPs patient in the near future.
CALIPER (Computer-Aided Lung Informatics for Pathology Evaluation and Rating) is the representative model that quantifies fibrotic lesions in the CT image. This model visualizes typical findings in the HRCT image (e.g., reticular or honeycombing) by using each color [19]. While CALIPER is considered one of the state-of-the-art models for quantifying fibrotic lesions in CT images, CALIPER quantifies fibrotic lesions based on the histogram information of CT images. The histogram information is directly affected by imaging conditions; however, HF maps are assumed to be less affected because the HF map is based on homological features that are not directly related to imaging conditions. Thereby, it is possible that the quantification by the HF map is superior to CALIPER in terms of quantifying fibrotic lesions in CT images. Although the HF map is thought to be a promising method for quantitatively evaluating fibrotic lesions in CT images, the HF map value also needs to clarify the correlation with the typical HRCT image findings and clinical examination values (e.g., forced vital capacity), like CALIPER. It is expected that diffusion equation quantification (DEQ) model [27] could also improve our proposed HF maps with contrast enhancement in lung lesions. In the future, we will improve the proposed HF map by using the DEQ model and HRCT images of IIPs, which are pathologically confirmed, to quantify fibrotic lesions of each IIP type and typical findings in HRCT images. Furthermore, we eventually aim to visualize the gene expression information relating to IIPs on the HRCT image by quantitatively associating the HF map value and the local gene expression information obtained by using the bulk RNA-seq analysis.
Conclusions
This study has demonstrated the feasibility of the homology-based feature in the quantitative evaluation of the fibrotic lesions in the CT image. This quantification of the fibrotic lesion may be promising in establishing a quantitative relationship between the HF map value and the local gene expression in the CT image. It can assist in diagnostic imaging for fibrotic lesions without extra examination and reduce the burden on patients and clinicians. We will validate the feasibility of the HF map in quantitatively evaluating the fibrotic lesion of IIPs cases that have already been collected in our institute.
Supplementary Information
Below is the link to the electronic supplementary material.
Acknowledgements
This work was supported by JSPS KAKENHI [grant number 24K23909].
Declarations
Conflict of interests
The authors declare that they have no conflict of interest.
Footnotes
Publisher's Note
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