What Is the Vascular Endothelial Wall Shear Stress Calculator?
Wall shear stress is the biomechanical frictional force felt by endothelial cells lining blood vessel walls.
How Does the Vascular Endothelial Wall Shear Stress Calculator Work?
In laminar tube flow, the parabolic velocity gradient evaluated at the boundary multiplied by viscosity yields wall shear.
Vascular Endothelial Wall Shear Stress Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
au_w = rac{4 mu Q}{pi R^3} = rac{32 mu Q}{pi D^3}
Hagen-Poiseuille formula for wall shear stress in cylindrical tubes.
How to Use the Vascular Endothelial Wall Shear Stress Calculator
- Input volumetric blood flow in mL/min, internal lumen diameter in mm, and dynamic viscosity in cP.
Step-by-Step Example Calculation
Human Left Anterior Descending (LAD) Coronary Artery
Input Values:
bloodFlowMlMin:85
vesselDiameterMm:3.2
bloodViscosityCp:3.5
Worked Steps: Wall shear stress = 15.1 dyne/cm² (1.51 Pa), Mean velocity = 17.6 cm/s, Reynolds number = 169 (Laminar).
Understanding Your Result
Displays wall shear stress in dynes/cm² and Pascals along with mean velocity and Reynolds number.
Factors That Affect the Result
- Shear stress is inversely proportional to the cube of vessel radius; minor vasoconstriction strongly elevates WSS.
When Should You Use This Calculator?
- Atherosclerosis risk assessment, vascular stent hemodynamic design, and arterial remodeling studies.
Assumptions & Limitations
- Assumes steady, laminar, Newtonian flow in rigid straight cylindrical tubes.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard Hagen-Poiseuille biomechanical model.