Table 2.
The validation of scaling relations in the entire stem-crown system of various – square fits.
| Species and organ | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Asymmetric data | Q ∝ Ncλ | Lc ∝ Ncλ | Vc ∝ Ncλ | Tc*Lc ∝ Vcλ | References | ||||
| Exponent | R2 | Exponent | R2 | Exponent | R2 | Exponent | R2 | ||
| Pig RCA | 1.005 (1.004, 1.005) | 0.9919 | 1.029 (1.029, 1.029) | 0.9992 | 1.481 (1.481, 1.481) | 0.9995 | 0.9814 (0.9814, 0.9814) | 0.9966 | Mittal et al., 2005 |
| Pig LAD | 1.002 (1.002, 1.002) | 0.9937 | 1.031 (1.031, 1.031) | 0.9993 | 1.453 (1.453, 1.453) | 0.9995 | 0.9883 (0.9883, 0.9883) | 0.9973 | Mittal et al., 2005 |
| Pig LCX | 1.005 (1.005, 1.005) | 0.9937 | 1.031 (1.031, 1.031) | 0.9992 | 1.479 (1.479, 1.479) | 0.9995 | 0.9891 (0.9891, 0.9891) | 0.9972 | Mittal et al., 2005 |
| SYMMETRIC DATA | |||||||||
| Hamster Muscle | 1 (1, 1) | 1 | 1.235 (1.063, 1.407) | 0.9943 | 1.622 (1.435, 1.808) | 0.9961 | 0.8052 (0.693, 0.9174) | 0.9093 | Bertuglia et al., 1991 |
| Rat Lungs | 1 (1, 1) | 1 | 1.033 (1.016, 1.05) | 0.998 | 1.441 (1.418, 1.464) | 0.9995 | 1.023 (1.012, 1.035) | 0.9997 | Jiang et al., 1994 |
| Rat Mesentery | 1 (1, 1) | 1 | 1.137 (1.064, 1.211) | 0.9988 | 1.306 (1.221, 1.391) | 0.9987 | 1.106 (1.057, 1.156) | 0.9994 | Ley et al., 1986 |
| Rabbit Omentum | 1 (1, 1) | 1 | 1.179 (1.123, 1.236) | 0.9993 | 1.448 (1.152, 1.745) | 0.9877 | 1.125 (1.11, 1.139) | 0.9999 | Fenton and Zweifach, 1981 |
| Pig RCA | 1 (1, 1) | 1 | 1.021 (1.009, 1.032) | 0.9997 | 1.447 (1.428, 1.467) | 0.9996 | 1.014 (1.006, 1.022) | 0.9999 | Mittal et al., 2005 |
| Pig LAD | 1 (1, 1) | 1 | 1.022 (1.009, 1.034) | 0.9997 | 1.44 (1.408, 1.473) | 0.9999 | 1.015 (1.007, 1.024) | 0.9990 | Mittal et al., 2005 |
| Pig LCX | 1 (1, 1) | 1 | 1.028 (1.013, 1.043) | 0.9996 | 1.506 (1.473, 1.539) | 0.9991 | 1.019 (1.009, 1.029) | 0.9998 | Mittal et al., 2005 |
| Cat Lungs (arterial) | 1 (1, 1) | 1 | 1.03 (1.02, 1.04) | 0.9998 | 1.401 (1.339, 1.463) | 0.9966 | 1.022 (1.016, 1.028) | 0.9999 | Yen et al., 1983 |
| Cat Lungs (venous) | 1 (1, 1) | 1 | 1.029 (1.01, 1.048) | 0.994 | 1.44 (1.414, 1.465) | 0.9994 | 1.021 (1.008, 1.034) | 0.9997 | Yen et al., 1984 |
| Cat Sartorius Muscle | 1 (1, 1) | 1 | 1.092 (1.074, 1.109) | 0.9999 | 1.174 (1.161, 1.187) | 1.0000 | 1.078 (1.063, 1.093) | 0.9999 | Koller et al., 1987 |
| Cat Sartorius Muscle | 1 (1, 1) | 1 | 1.092 (1.074, 1.109) | 0.9999 | 1.196 (1.176, 1.216) | 0.9999 | 1.077 (1.061, 1.092) | 0.9999 | Koller et al., 1987 |
| Human Skeletal Muscle | 1 (1, 1) | 1 | 1.43 (0.9181, 1.943) | 0.9634 | 1.731 (1.087, 2.375) | 0.9607 | 1.27 (1.075, 1.466) | 0.9930 | Ellsworth et al., 1987 |
| Human Conjunctiva (arterial) | 1 (1, 1) | 1 | 1.105 (1.063, 1.146) | 0.9993 | 1.227 (1.181, 1.273) | 0.9993 | 1.086 (1.055, 1.117) | 0.9996 | Fenton and Zweifach, 1981 |
| Human Conjunctiva (venous) | 1 (1, 1) | 1 | 1.113 (1.056, 1.17) | 0.9986 | 1.406 (1.337, 1.476) | 0.9987 | 1.081 (1.043, 1.119) | 0.9994 | Fenton and Zweifach, 1981 |
| Human Lungs I (arterial) | 1 (1, 1) | 1 | 1.006 (1.001, 1.011) | 0.9999 | 1.123 (1.114, 1.132) | 0.9998 | 1.013 (1.009, 1.017) | 0.9999 | Singhal S. S. et al., 1973 |
| Human Lungs II (arterial) | 1.01 (1.003, 1.016) | 0.9999 | 1.01 (1.003, 1.016) | 0.9999 | 1.152 (1.124, 1.18) | 0.9982 | 1.009 (1.004, 1.014) | 0.9999 | Huang et al., 1996 |
| Human Lungs III (arterial) | 1 (1, 1) | 1.0000 | 1.002 (1.001, 1.003) | 1.0000 | 1.197 (1.187, 1.207) | 0.9998 | 1.005 (1.004, 1.005) | 1.0000 | Singhal S. et al., 1973 |
| Human Lungs IV (venous) | 1 (1, 1) | 1 | 1.033 (1.019, 1.046) | 0.9995 | 1.294 (1.24, 1.349) | 0.9947 | 1.026 (1.017, 1.036) | 0.9997 | Huang et al., 1996 |
| Human Lungs V (venous) | 1 (1, 1) | 1 | 1.011 (1.004, 1.019) | 0.9998 | 1.215 (1.204, 1.225) | 0.9998 | 1.01 (1.003, 1.016) | 0.9999 | Horsfield and Gordon, 1981 |
| Mean | 1.0010 | 1.0765 | 1.3723 | 1.0347 | |||||
| SD | 0.0024 | 0.1022 | 0.1659 | 0.0819 | |||||
The morphometric data were obtained from the full asymmetric arterial tree and simplified symmetric trees. The data were normalized using the maximum values in the respective tree. The least-square fit was used to obtain scaling exponent of lambda (Y = Xλ). R2 is correlation coefficient; RCA, right coronary artery; LAD, left anterior descending artery; LCx, left circumflex artery; PA, pulmonary artery; PV, pulmonary vein; SMA, sartorius muscle arteries; MA, mesentery arteries; OV, omentum veins; BCA, bulbar conjunctiva arteries; BCV, bulbar conjunctiva veins; RMA, retractor muscle artery.