Scaling laws of vascular trees: of form and function

The branching pattern and vascular geometry of biological tree structure are complex. Here we show that the design of all vascular trees for which there exist morphometric data in the literature (e.g., coronary, pulmonary; vessels of various skeletal muscles, mesentery, omentum, and conjunctiva) obeys a set of scaling laws that are based on the hypothesis that the cost of construction of the tree structure and operation of fluid conduction is minimized. The laws consist of scaling relationships between 1) length and vascular volume of the tree, 2) lumen diameter and blood flow rate in each branch, and 3) diameter and length of vessel branches. The exponent of the diameter-flow rate relation is not necessarily equal to 3.0 as required by Murray's law but depends on the ratio of metabolic to viscous power dissipation of the tree of interest. The major significance of the present analysis is to show that the design of various vascular trees of different organs and species can be deduced on the basis of the minimum energy hypothesis and conservation of energy under steady-state conditions. The present study reveals the similarity of nature's scaling laws that dictate the design of various vascular trees and the underlying physical and physiological principles.

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Intraspecific scaling laws of vascular trees

Journal of The Royal Society Interface ◽

10.1098/rsif.2011.0270 ◽

2011 ◽

Vol 9 (66) ◽

pp. 190-200 ◽

Cited By ~ 82

Author(s):

Yunlong Huo ◽

Ghassan S. Kassab

Keyword(s):

Scaling Laws ◽

Scaling Law ◽

Minimum Energy ◽

Circumflex Artery ◽

Theoretical Derivation ◽

Left Circumflex Artery ◽

Least Squares Fit ◽

Flow Length ◽

Vascular Trees ◽

Length Scaling

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 volume–diameter 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.

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Cerebral blood flow rates in recent great apes are greater than in Australopithecus species that had equal or larger brains

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2019.2208 ◽

2019 ◽

Vol 286 (1915) ◽

pp. 20192208 ◽

Cited By ~ 1

Author(s):

Roger S. Seymour ◽

Vanya Bosiocic ◽

Edward P. Snelling ◽

Prince C. Chikezie ◽

Qiaohui Hu ◽

...

Keyword(s):

Blood Flow ◽

Flow Rate ◽

Homo Sapiens ◽

Brain Size ◽

Blood Flow Rate ◽

Brain Perfusion ◽

Synaptic Activity ◽

Evolutionary Trajectory ◽

Metabolic Intensity ◽

The Cost

Brain metabolic rate (MR) is linked mainly to the cost of synaptic activity, so may be a better correlate of cognitive ability than brain size alone. Among primates, the sizes of arterial foramina in recent and fossil skulls can be used to evaluate brain blood flow rate, which is proportional to brain MR. We use this approach to calculate flow rate in the internal carotid arteries ( Q ˙ ICA ) , which supply most of the primate cerebrum. Q ˙ ICA is up to two times higher in recent gorillas, chimpanzees and orangutans compared with 3-million-year-old australopithecine human relatives, which had equal or larger brains. The scaling relationships between Q ˙ ICA and brain volume ( V br ) show exponents of 1.03 across 44 species of living haplorhine primates and 1.41 across 12 species of fossil hominins. Thus, the evolutionary trajectory for brain perfusion is much steeper among ancestral hominins than would be predicted from living primates. Between 4.4-million-year-old Ardipithecus and Homo sapiens , V br increased 4.7-fold, but Q ˙ ICA increased 9.3-fold, indicating an approximate doubling of metabolic intensity of brain tissue. By contrast, Q ˙ ICA is proportional to V br among haplorhine primates, suggesting a constant volume-specific brain MR.

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Intraspecific scaling laws are preserved in ventricular hypertrophy but not in heart failure

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00084.2016 ◽

2016 ◽

Vol 311 (5) ◽

pp. H1108-H1117 ◽

Cited By ~ 4

Author(s):

Yanjun Gong ◽

Yundi Feng ◽

Xudong Chen ◽

Wenchang Tan ◽

Yunlong Huo ◽

...

Keyword(s):

Heart Failure ◽

Ventricular Hypertrophy ◽

Scaling Laws ◽

Normal Growth ◽

Power Laws ◽

Scaling Analysis ◽

Scaling Exponents ◽

Theoretical Predictions ◽

And Function ◽

Vascular Trees

It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.

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Examination of relationships between building form and function, and the cost of mechanical and electrical services

Construction Management and Economics ◽

10.1080/014461999371402 ◽

1999 ◽

Vol 17 (4) ◽

pp. 483-492 ◽

Cited By ~ 12

Author(s):

L. M. SWAFFIELD ◽

C. L. PASQUIRE

Keyword(s):

Form And Function ◽

And Function ◽

The Cost ◽

Building Form

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Scanning tunneling microscopy (STM) of DNA and RNA

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100152148 ◽

1989 ◽

Vol 47 ◽

pp. 34-35

Author(s):

Patricia G. Arscott ◽

Gil Lee ◽

Victor A. Bloomfield ◽

D. Fennell Evans

Keyword(s):

Molecular Structures ◽

Inorganic Materials ◽

Resolving Power ◽

Scanning Tunneling ◽

Tunneling Microscopy ◽

Form And Function ◽

Dna And Rna ◽

Calf Thymus ◽

And Function ◽

The Relationship

STM is one of the most promising techniques available for visualizing the fine details of biomolecular structure. It has been used to map the surface topography of inorganic materials in atomic dimensions, and thus has the resolving power not only to determine the conformation of small molecules but to distinguish site-specific features within a molecule. That level of detail is of critical importance in understanding the relationship between form and function in biological systems. The size, shape, and accessibility of molecular structures can be determined much more accurately by STM than by electron microscopy since no staining, shadowing or labeling with heavy metals is required, and there is no exposure to damaging radiation by electrons. Crystallography and most other physical techniques do not give information about individual molecules.We have obtained striking images of DNA and RNA, using calf thymus DNA and two synthetic polynucleotides, poly(dG-me5dC)·poly(dG-me5dC) and poly(rA)·poly(rU).

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