Pulsatile blood flow, shear force, energy dissipation and Murray's Law

Area of Science:

• Physiology
• Biophysics
• Fluid Dynamics

Background:

• Murray's Law posits a relationship between parent and daughter blood vessel radii, derived from energy minimization principles.
• Previous derivations assumed constant blood flow, limiting their applicability to the pulsatile arterial system.
• Alternative derivations suggest a constant shear force hypothesis, also under the assumption of steady flow.

Purpose of the Study:

• To investigate the implications of the constant shear force hypothesis in pulsatile flow.
• To extend Murray's energy cost minimization to the dynamic arterial system.
• To derive an exact solution for pulsatile flow characteristics and shear force.

Main Methods:

• Analysis of a mathematical model for pulsatile flow in an elastic tube.
• Derivation of exact solutions for flow velocity, blood flow rate, and shear force.
• Evaluation of Murray's Law under pulsatile flow conditions.

Main Results:

• Murray's Law holds true for medium and small arteries experiencing pulsatile flow.
• The constant maximum shear force hypothesis approximates Murray's Law for most of the arterial system.
• Deviations from Murray's Law are noted primarily in the largest vessels like the aorta.

Conclusions:

• Cellular mechanisms sensing and responding to shear force can explain Murray's Law.
• Shear force thresholds trigger vessel wall remodeling, influencing vascular radii.
• This provides a cellular basis for the observed scaling laws in the vascular system.