Intraspecific scaling laws of vascular trees

Abstract

A fundamental physics-based derivation of intraspecific scaling laws of vascular trees has not been previously realized. Here, we provide such a theoretical derivation for the volumediameter and flow-length scaling laws of intraspecific vascular trees. In conjunction with the minimum energy hypothesis, this formulation also results in diameter -length, flow -diameter and flow-volume scaling laws. The intraspecific scaling predicts the volume -diameter power relation with a theoretical exponent of 3, which is validated by the experimental measurements for the three major coronary arterial trees in swine (where a least-squares fit of these measurements has exponents of 2.96, 3 and 2.98 for the left anterior descending artery, left circumflex artery and right coronary artery trees, respectively). This scaling law as well as others agrees very well with the measured morphometric data of vascular trees in various other organs and species. This study is fundamental to the understanding of morphological and haemodynamic features in a biological vascular tree and has implications for vascular disease.

Computed tomography-based diagnosis of diffuse compensatory enlargement of coronary arteries using scaling power laws

“…In addition to the structure-structure scaling power laws, we also verified the function-structure scaling power laws [10,11]. Here, coefficients and exponents between the high-fat diet and control groups showed no significant difference, as illustrated in table 2.…”

“…We derived the theoretical exponent of structure-structure scaling power laws in the stem-crown system of a tree structure, which were validated in vascular trees of various organs, including the heart, lung, mesentery, muscle and eye of different species [10,11]. Here, the length-volume and volume -diameter scaling power laws still hold for the epicardial coronary arterial tree in the control group, as shown in figures 4 and 5.…”

“…Here, coefficients and exponents between the high-fat diet and control groups showed no significant difference, as illustrated in table 2. The function-structure scaling power laws reflect the design of biological trees for flow transport under the principle of minimum energy [11]. The preservation of the scaling power laws suggests that positive remodelling still maintains the same general principle in the early stages of coronary atherosclerosis.…”

“…length-volume) and function-structure (e.g. flow-length) scaling power laws in normal coronary tree structure and validated these laws theoretically and experimentally [10,11]. Here, a deviation from the power law is proposed to be an index for the diagnosis of positive remodelling.…”

“…We have validated several scaling power laws in normal vascular trees for various organs and species [10,11]. To derive the scaling power laws, we first defined a proximal vessel segment as a stem, and the tree distal to the stem as a crown.…”