Understanding Murray's Law in Pulsatile Blood Flow
Author Information
Author(s): Painter Page R, Edén Patrik, Bengtsson Hans-Uno
Primary Institution: Office of Environmental Health Hazard Assessment, California Environmental Protection Agency
Hypothesis
The shear force of moving blood on the inner walls of vessels is constant throughout the vascular system.
Conclusion
A mechanism that senses shear force at the inner wall of a blood vessel can explain the scaling of vessel radii described by Murray's Law.
Supporting Evidence
- Murray's Law states that the cube of the radius of the parent vessel equals the sum of the cubes of the daughter vessels' radii.
- The hypothesis that maximum shear force is constant throughout the arterial system supports the approximation of Murray's Law.
- Experimental observations support the role of shear stress in determining artery radius.
Takeaway
When blood vessels branch, the size of the parent vessel relates to the sizes of the daughter vessels, and this relationship helps explain how blood flows through our bodies.
Methodology
A model of pulsatile flow in an elastic tube was analyzed to derive solutions for flow velocity, blood flow rate, and shear force.
Limitations
The model may not accurately predict behavior in the largest vessels like the aorta.
Digital Object Identifier (DOI)
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