Diameters and cross‐sectional areas of branches in the human pulmonary arterial tree
The mean value of the exponent z in the equation flow = k (diameterz) was found to be 2.3 ± 0.1, which is equal to the optimal value for minimizing power and metabolic costs for fully developed turbulent flow.
Tree asymmetry--a sensitive and practical measure for binary topological trees.
Hydraulic geometry and minimum rate of energy dissipation
The theory of minimum rate of energy dissipation states that a system is in an equilibrium condition when its rate of energy dissipation is at its minimum value. This minimum value depends on the…
Finding the optimal lengths for three branches at a junction.
Branching and Self‐Organization in Marine Modular Colonial Organisms: A Model
- J. A. Sánchez, H. Lasker, E. Nepomuceno, J. Sánchez, M. Woldenberg
- Environmental ScienceAmerican Naturalist
- 17 February 2004
A model of branching and colony growth in Caribbean gorgonian corals using parameters and variables related to actual modular structures and a scaling power law suggesting self‐organized criticality is developed.
Relation of branching angles to optimality for four cost principles.
Models for growth, decline and regrowth of the dendrites of rat Purkinje cells induced from magnitude and link-length analysis.
- M. Woldenberg, M. O'Neill, L. J. Quackenbush, R. Pentney
- BiologyJournal of Theoretical Biology
- 21 June 1993
Analysis of Purkinje neurons of rats aged 1, 10, 18 and 28 months to investigate growth and decline in the magnitude of the dendritic tree finds that exterior links are longer than interior links (non-terminal or intermediate segments), which indicates that they follow a Fibonacci series of link lengths.
HORTON'S LAWS JUSTIFIED IN TERMS OF ALLOMETRIC GROWTH AND STEADY STATE IN OPEN SYSTEMS
- M. Woldenberg
- 1 April 1966
Rivers are open systems and achieve a steady state or grow allometrically, according to the general equation y = ax b . This equation yields a straight line on double logarithmic paper and reflects a…
A generalization of the optimal models of arterial branching
Optimal models of arterial branching angles are usually based on the assumption that the equation relating flow and radius is given byf=kr3, but theoretical considerations coupled with empirical evidence suggest that the cubic flow equation may not be appropriate to describe the branching pattern of the arterial tree.