Table 4.

Estimated data of α and Ω in systemic (A) and pulmonary arteries (B) by fractal analysis with published data in the literature.

	References	Range of radius (mm)	α s	Ωs	r
(A) Systemic arteries
Human Ao	Olufsen et al. (2000)	7.2–12.0		3.3 ± 2.51
CCA		2.8–2.9		63.1 ± 5.01
Maj. brs.		1.9–7.0		17.9 ± 7.61
Human mixed	Nakamura et al. (2011)	0.01–0.1	0.782
Dog mixed	Milnor (1982)	0.025–9.5	1.11	70.66	0.99

	References	Whole tree			Proximal (0.1 mm < rp)			Peripheral (0.004 ≤ rp≤ 0.1 mm)
		α p	Ωp	r	α p	Ωp	r	α p	Ωp	r
(B) Pulmonary arteries
Human	Horsfield (1978)	0.85	9.21	0.99	0.97	11.53	0.97	0.83	8.61	0.99
Human lt.	Huang et al. (1996)	0.89	9.38	0.98	0.86	9.69	0.96	0.55	2.61	0.98
Human	Nakamura et al. (2011)							0.712
Human	Singhal et al. (1973)	0.80	8.09	0.99	0.76	8.31	0.97	0.83	8.61	0.99
Dog rt.	Gan and Yen (1994)	0.83	13.13	0.99	0.77	13.30	0.97	0.92	16.51	0.99
Dog	Milnor (1982)	0.68	8.46	0.91
Cat rt.	Zhuang et al. (1983)	1.03	14.11	0.99	0.78	13.01	0.95	1.21	24.77	0.99
Rat lt.	Jiang et al. (1994)	0.72	2.17	0.98	0.83	2.29	0.97	0.93	5.20	0.98

α and Ω represent exponent and proportional coefficients of the relationship between vessel length (l) and radius (r), respectively, defined by equation 17; r, correlation coefficient; s, systemic; p, pulmonary; lt., left; rt., right. Pulmonary arteries were categorized by radius; each range of the radius in subjected data is not indicated but is common to Table 3B. The data included in the present analysis came from table 1 (Gan and Yen 1994), table 6 (Horsfield 1978), table 2 (Huang et al. 1996), table 2 (Jiang et al. 1994), table 2.3 (Milnor 1982), P. 68 (Nakamura et al. 2011), table 1 (Olufsen et al. 2000), table 4 (Singhal et al. 1973), and table 1 (Zhuang et al. 1983). All methods but two (Olufsen et al. 2000; Nakamura et al. 2011) were cast‐morphometry; that of Nakamura et al. (2011), the combination of fractal‐model analysis and catheterization; that of Olufsen et al. (2000), measurement on magnetic resonance images or estimation. Ao stands for aorta, which includes ascending aorta, aortic arch, and abdominal aorta (Olufsen et al. 2000); CCA, common carotid arteries; Maj. brs., major branches, which include superior and inferior mesenteric, renal, internal and external iliac, and superficial and deep femoral arteries (Olufsen et al. 2000). Data of the whole pulmonary arterial tree are indicated with no notation of laterality.

¹indicates estimates under α = 1.0.

²was calculated by equation 25. Data are presented as the mean with one standard deviation.