Application of the homology method for quantification of low-attenuation lung region inpatients with and without COPD

Figures & data

Figure 1 Representative images of the binarized images at the percentage of low-attenuation lung area =30% obtained in the simulation study.

Notes: (A and B) correspond to the results of simulations A and B, respectively. R of (A and B) is 0.103 and 0.380, respectively.

Figure 2 Representative images of computed tomography (CT) image and results of preprocessing.

Notes: (A) CT image of the lower lung field. (B–D) Binarized images after lung segmentation, after deletion of small pulmonary vessels, and after all preprocessing, respectively. (D) Used for evaluation of the homology-based emphysema quantification.

Table 1 Results of the homology-based emphysema quantification for different values of LAA% in the simulation study

LAA%	Simulation A			Simulation B
	b0	b1	R	b0	b1	R
10	4,325	7	0.00162	1,109	125	0.113
15	5,049	31	0.00614	1,513	203	0.134
20	5,116	94	0.0184	1,657	305	0.184
25	4,670	183	0.0392	1,700	443	0.261
30	3,867	400	0.103	1,669	634	0.380
35	2,941	798	0.271	1,603	782	0.488
40	1,958	1,287	0.657	1,433	1,091	0.761
45	1,192	2,087	1.751	1,244	1,306	1.050
50	675	3,180	4.711	969	1,638	1.690

Notes: b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; R, b₁/b₀.

Abbreviation: LAA%, percentage of low-attenuation lung area.

Figure 3 R and the percentage of low-attenuation lung area (LAA%) in the simulation study.

Notes: (A and B) correspond to the results of simulations A and B, respectively. The relationships between R and LAA% are represented as R = 0.000307 × e^{0.193 × LAA%} in (A) and R = 0.0496 × e^{0.0682 × LAA%} in (B). The determinants of the coefficients were 0.997 and 0.993 in (A and B), respectively.

Table 2 Summary of patient characteristics, PFT results, and emphysema quantification

Variables	Mean	SD
Age (years)	67.8	11.0
Sex (M:F)	84:28
Smoking history (pack year)	44.7	36.8
FVC (%)	89.6	23.8
FEV1/FVC (%)	68.1	16.8
FEV1 (%)	73.0	26.2
VC (%)	95.4	23.8
LAA%	10.7	14.1
b0	902	490
b1	114	159
nb0	0.00580	0.00258
nb1	0.000665	0.000870
R	0.880	0.115

Notes: The PFT results are expressed as percentages of the standard predicted values except for those of FEV₁/FVC. b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; nb₀, b₀ normalized to the total number of lung pixels; nb₁, b₁ normalized to the total number of lung pixels; R, b₁/b₀.

Abbreviations: PFT, pulmonary function test; FEV₁, forced expiratory volume in 1 second; FEV₁/FVC, ratio of forced expiratory volume in 1 second to forced vital capacity; FVC, forced vital capacity; VC, vital capacity; LAA%, percentage of low-attenuation lung area; SD, standard deviation.

Table 3 Pearson’s correlation coefficients for homology-based emphysema quantification, PFT results, and LAA%

Variables	FEV1		FEV1/FVC		LAA%
	Coefficient	P-value	Coefficient	P-value	Coefficient	P-value
b0	−0.173	0.0677	−0.460	3.34×10^−7	0.597	<1.0×10^−10
b1	−0.314	0.000726	−0.500	1.97×10^−8	0.868	<1.0×10^−10
nb0	−0.191	0.04338	−0.449	6.96×10^−7	0.53	1.8×10^−9
nb1	−0.329	0.000393	−0.524	3.11×10^−9	0.88	<1.0×10^−10
R	−0.409	7.70×10^−6	−0.574	<1.0×10^−10	0.932	<1.0×10^−10

Notes: b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; nb₀, b₀, normalized to the total number of lung pixels; nb₁, b₁ normalized to the total number of lung pixels; R, b₁/b₀.

Abbreviations: PFT, pulmonary function test; FEV₁, forced expiratory volume in 1 second; FEV₁/FVC, ratio of forced expiratory volume in 1 second to forced vital capacity; LAA%, percentage of low-attenuation lung area.

Table 4 Statistical tests of emphysema quantification among the three groups

	Group A vs Group B	Group B vs Group C	Group A vs Group C
LAA%	0.274	0.000265*	0.000102*
b0	0.0237	0.0100*	0.000168*
b1	0.139	0.000950*	0.000146*
nb0	0.00858*	0.0579	0.000343*
nb1	0.0777	0.000683*	0.0000578*
R	0.162	0.000792*	0.000182*

Notes: The numbers in the table are P-values.

* Indicates a P-value <0.0167. Group A, nonsmokers; Group B, smokers without COPD, mild COPD, moderate COPD; Group C, smokers with severe COPD and very severe COPD; b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; nb₀, b₀ normalized to the total number of lung pixels; nb₁, b₁ normalized to the total number of lung pixels; R, b₁/b₀.

Abbreviation: LAA%, percentage of low-attenuation lung area.

Table 5 Results of the linear model predicting PFT results using the homology-based emphysema quantification

Model	Predictive variable	Coefficient	SE of coefficient	P-value	AIC	Adjusted R squared
For FEV1					1,025.84	0.239
	R	−288	74.3	0.000182
	nb0	−2,327	1,337	0.0846
	Nb1	31,646	11,231	0.00576
	Smoking history	−0.142	0.0599	0.0200
For FEV1/FVC					892.00	0.440
	R	−201	40.9	3.11×10^−6
	Nb0	−3,148	735	4.07×10^−5
	Nb1	21,877	6,179	0.000593
	Smoking history	−0.0826	0.0330	0.0137

Notes: b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; nb₀, b₀ normalized to the total number of lung pixels; nb₁, b₁ normalized to the total number of lung pixels; R, b₁/b₀.

Abbreviations: AIC, Akaike information criterion; PFT, pulmonary function test; FEV₁, forced expiratory volume in 1 second; FEV₁/FVC, ratio of forced expiratory volume in 1 second to forced vital capacity; SE, standard error.

Figure S1 All binarized images used in the simulation study.

Notes: Left: the binarized images obtained from simulation A. Right: the binarized images obtained from simulation B. LAA% of the two images in the same row was identical. For each row, LAA% increases by 5%.

Abbreviation: LAA%, percentage of low-attenuation lung area.

Figure S2 Representative computed tomography (CT) images and results of preprocessing of the upper, middle, and lower lung fields in a 64-year-old man with COPD.

Notes: Forced expiratory volume in 1 second (FEV₁)/forced vital capacity; FEV₁; b₀, b₁, R; and the percentage of low-attenuation lung area were 67.4%; 61.4%; 944, 39, 0.0413; and 5.13%, respectively (b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; R, b₁/b₀). The CT images and the binarized images are shown in (A–C) and (D–F), respectively.

Figure S3 Representative computed tomography (CT) images and results of preprocessing of the upper, middle, and lower lung fields in a 77-year-old man with COPD.

Notes: Forced expiratory volume in 1 second (FEV₁)/forced vital capacity; FEV₁; b₀, b₁, R; and the percentage of low-attenuation lung area were 42.8%; 50.2%; 1,420, 321, 0.226; and 26.5%, respectively (b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; R, b₁/b₀). The CT images and the binarized images are shown in (A–C) and (D–F), respectively.

Figure S4 Representative computed tomography (CT) images and results of preprocessing of the upper, middle, and lower lung fields in a 75-year-old man with COPD.

Notes: Forced expiratory volume in 1 second (FEV₁)/forced vital capacity; FEV₁; b₀, b₁, R; and the percentage of low-attenuation lung area were 28.1%; 27.5%; 977, 443, 0.453; and 56.6%, respectively (b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; R, b₁/b₀). The CT images and the binarized images are shown in (A–C) and (D–F), respectively.

Table S1 Results of emphysema quantification in the three groups

Variables	Group A		Group B		Group C
	Mean	SD	Mean	SD	Mean	SD
LAA%	4.54	9.83	7.66	9.66	26.26	19.13
b0	617.8	366.8	884.3	500.4	1,169.4	404.5
b1	42.73	96.71	87.51	133.51	259.00	198.01
nb0	0.00429	0.00168	0.00579	0.00266	0.00694	0.00231
nb1	0.000239	0.000517	0.000529	0.000742	0.001461	0.001036
R	0.0358	0.0697	0.0650	0.0786	0.2086	0.1648

Notes: Group A, nonsmoker; Group B, smokers without COPD, mild COPD, and moderate COPD; Group C, severe COPD and very severe COPD; b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; nb₀, b₀ normalized to the total number of lung pixels; nb₁, b₁ normalized to the total number of lung pixels; R, b₁/b₀.

Abbreviations: LAA%, percentage of low-attenuation lung area; SD, standard deviation.

Table S2 Summary of the emphysema quantification in all the patients, nonsmokers, smokers without COPD, and COPD patients

Variables	All patients		Nonsmokers		Smokers		COPD
	Mean	SD	Mean	SD	Mean	SD	Mean	SD
LAA%	10.73	14.08	4.54	9.83	4.69	6.89	18.53	16.54
b0	902.1	490.2	617.8	366.8	780.0	514.2	1,108.7	417.0
b1	113.7	159.5	42.7	96.7	66.4	139.0	181.7	169.2
nb0	0.00580	0.00258	0.00429	0.00168	0.00522	0.00278	0.00684	0.00220
nb1	0.000665	0.000870	0.000239	0.000517	0.000401	0.000769	0.001054	0.000900
R	0.0880	0.1147	0.0358	0.0697	0.0456	0.0726	0.1455	0.1335
Variables	Mild COPD		Moderate COPD		Severe COPD		Very severe COPD
	Mean	SD	Mean	SD	Mean	SD	Mean	SD
LAA%	12.91	7.51	12.72	12.09	20.66	16.77	35.35	20.26
b0	926.3	393.6	1,079.5	436.2	1,096.5	447.0	1,287.9	314.7
b1	94.0	77.5	127.3	121.8	207.2	171.5	343.1	220.3
nb0	0.00615	0.00237	0.00683	0.00218	0.00670	0.00250	0.00733	0.00206
nb1	0.000614	0.000490	0.000765	0.000671	0.001234	0.000992	0.001830	0.001064
R	0.0941	0.0551	0.0987	0.0817	0.1587	0.1269	0.2896	0.1946

Notes: b₀, the zero-dimensional Betti number; b₁, the one-dimensional Betti number; nb₀, b₀ normalized to the total number of lung pixels; nb₁, b₁ normalized to the total number of lung pixels; R, b₁/b₀.

Abbreviations: LAA%, percentage of low-attenuation lung area; SD, standard deviation.