Revisiting Murray's Law in Pulmonary Arteries: Exploring Branching Patterns and Principles

Area of Science:

• Physiology
• Biophysics
• Comparative Anatomy

Background:

• Murray's Law (1926) describes a cube-law relationship between parent and child vessel diameters, crucial for computational vascular analysis.
• Pulmonary arteries may exhibit unique morphometric and hemodynamic properties not fully explained by classical Murray's Law predictions.

Purpose of the Study:

• To investigate pulmonary arterial network morphometry across different species.
• To examine the relationship between parent and child vessel diameters in pulmonary arteries.
• To compare empirical branching patterns with predictions from Murray's Law and extended models.

Main Methods:

• Analysis of 3D segmentations of pulmonary arterial geometries from human, canine, swine, and murine subjects.
• Quantitative assessment of vessel diameter relationships across species.
• Comparison of observed exponents with theoretical predictions from Murray's Law and pulsatile flow models.

Main Results:

• Empirical exponents for pulmonary artery branching ranged from 2.10 to 2.59 across species, all lower than Murray's Law prediction of 3.0.
• Extended Murray's Law for pulsatile flow indicates mean flow is proportional to radius raised to a power between 2.1 and 3, dependent on the Womersley number.
• Findings suggest pulmonary artery branching adheres to optimization principles influenced by the Womersley number.

Conclusions:

• Pulmonary artery branching patterns deviate from the classical Murray's Law.
• Womersley number-dependent optimization principles appear to govern pulmonary artery structure-function relationships.
• This research enhances understanding of pulmonary vasculature and its implications for modeling vascular diseases.