CT quantification of the heterogeneity of fibrosis boundaries in idiopathic pulmonary fibrosis

Abstract

Objectives: To quantify the heterogeneity of fibrosis boundaries in idiopathic pulmonary fibrosis (IPF) using the Gaussian curvature analysis for evaluating disease severity and predicting survival.

Methods: We retrospectively included 104 IPF patients and 52 controls who underwent baseline chest CT scans. Normal lungs below - 500 HU were segmented, and the boundary was three-dimensionally reconstructed using in-house software. Gaussian curvature analysis provided histogram features on the heterogeneity of the fibrosis boundary. We analyzed the correlations between histogram features and the gender-age-physiology (GAP) and CT fibrosis scores. We built a regression model to predict diffusing capacity of carbon monoxide (DLCO) using the histogram features and calculated the modified GAP (mGAP) score by replacing DLCO with the predicted DLCO. The performances of the GAP, CT-GAP, and mGAP scores were compared using 100 repeated random-split sets.

Results: Patients with moderate-to-severe IPF had more numerous Gaussian curvatures at the fibrosis boundary, lower uniformity, and lower 10th to 30th percentiles of Gaussian curvature than controls or patients with mild IPF (all p < 0.0033). The 20th percentile was most significantly correlated with the GAP score (r = - 0.357; p < 0.001) and the CT fibrosis score (r = - 0.343; p = 0.001). More numerous Gaussian curvatures, higher entropy, lower uniformity, and 10th to 30th percentiles (p < 0.001-0.041) were associated with mortality. The mGAP score was comparable to the GAP and CT-GAP scores for survival prediction (mean C-indices, 0.76 vs. 0.79 vs. 0.77, respectively).

Conclusions: Gaussian curvatures of fibrosis boundaries became more heterogeneous as the disease progressed, and heterogeneity was negatively associated with survival in IPF.

Key points: • Gaussian curvature of the fibrotic lung boundary was more heterogeneous in patients with moderate-to-severe IPF than those with mild IPF or normal controls. • The 20th percentile of the Gaussian curvature of the fibrosis boundary was linearly correlated with the GAP score and the CT fibrosis score. • A modified GAP score that replaced the diffusing capacity of carbon monoxide with a composite measure using histogram features of the Gaussian curvature of the fibrosis boundary showed a comparable ability to predict survival to both the GAP and the CT-GAP score.

Keywords: Idiopathic pulmonary fibrosis; Lung; Quantitative evaluation; Tomography, X-ray computed.

Fig. 1

Schematic diagram of (a) Gaussian curvature of the fibrosis boundaries of (b) the normal lung and (c) the fibrotic lung. a Gaussian curvature is defined as the product of two principal curvatures which are the maximum (κ₁) and minimum (κ₂) of curvatures that intersect the normal plane—a plane containing the normal vector of the surface at a certain point (P). b In the normal lung, fibrotic areas do not exist; therefore, the boundary (colored in yellow) of non-fibrotic areas (below − 500 HU is colored in red) corresponds to pleural surfaces, which are smoothly elliptic and have a radius of the tangent sphere (R) that is mostly larger than 1 mm. c In IPF, the fibrosis boundary (colored in yellow) is irregular and the radius of the tangent sphere (r) is much smaller. Thus, the frequency of either positive or negative Gaussian curvature (according to the direction of the boundary curvature) is higher, although overall concavity of the boundary is maintained along pleural surfaces

Fig. 2

Study diagram for the inclusion of patients and controls

Fig. 3

Representative images of extracting the boundaries between fibrotic and non-fibrotic lung areas. a, d Baseline chest CT images of patients with (a) mild IPF (GAP stage I) and (d) severe IPF (GAP stage III). b, e After segmenting into fibrotic and non-fibrotic areas using a threshold value of − 500 HU, the fibrosis boundary was automatically extracted and reconstructed three-dimensionally by applying marching cube. c, f The Gaussian curvature analysis was performed at the fibrosis boundary. The Gaussian curvature value at each point of the boundary was coded into red (negative), green (near-zero), and blue (positive). Note that the fibrosis boundary in severe IPF is more irregular than in mild IPF

Fig. 4

Summary histogram of the Gaussian curvature of the fibrosis boundaries in healthy controls and patients with mild and moderate-to-severe IPF. a, b The general shape of the histogram of the Gaussian curvature of the fibrosis boundaries is similar across groups, as the overall concavity of the boundaries is maintained along pleural surfaces, resulting in a dominant peak of Gaussian curvature at 0. c When the upper bound of the relative frequency on the Y-axis is adjusted in the same graph, it becomes clear that positively or negatively skewed Gaussian curvatures with a smaller radius exist primarily in IPF patients

Fig. 5

Representative images of (a, b) mild and (c, d) severe IPF. a Baseline chest CT image of a 50-year-old man with mild IPF (GAP stage I). b The histogram of the Gaussian curvature of the subpleural fibrosis boundary is shown: entropy, 1.141; uniformity, 0.664; 10th to 30th percentiles, − 0.696, − 0.316, and 0.000, respectively (data with Gaussian curvature < − 10.5 or > 10.5 are cropped for visibility). c Baseline chest CT image of a 66-year-old man with severe IPF (GAP stage III). d The histogram of the Gaussian curvature of the subpleural fibrosis boundary is shown: entropy, 2.231; uniformity, 0.400; 10th to 30th percentiles, − 2.152, − 1.134, and − 0.565, respectively (data with Gaussian curvature < − 10.5 or > 10.5 are cropped for visibility)