Vascular Biomechanics & Stress
Wall Stress, Shear Stress, and Wall Tension Analysis
1. Wall Stress (σ)
Definition: Internal force per unit area within the vessel wall (response to blood pressure).
σ = (P × r) / h
P: Intraluminal pressure • r: radius • h: wall thickness
Key Clinical Points:
- ↑ in hypertension (↑ pressure) or aneurysms (↑ radius, ↓ thickness)
- Causes wall fatigue → rupture risk (e.g., aortic dissection)
- Acts circumferentially (hoop stress) and longitudinally
2. Shear Stress (τ)
Definition: Frictional force per unit area exerted by blood flow parallel to the vessel wall.
τ = 4μQ / πr³
μ: Blood viscosity • Q: flow rate • r: radius
Key Clinical Points:
- High shear (laminar flow): Protective (↑ eNOS, anti-inflammatory)
- Low shear (disturbed flow): Atherogenic (↑ LDL retention, inflammation)
- Measured via 4D flow MRI or computational models
3. Wall Tension (T)
Definition: Total force acting along the length of the vessel wall (integrates stress over thickness).
T = P × r
Laplace's Law for thin-walled cylinders • Units: Force per unit length (N/m)
Key Clinical Points:
- Explains why larger vessels (↑ r) rupture at lower pressures
- Clinically used to estimate rupture risk (AAA >5 cm)
- Critical for surgical graft design
Comprehensive Comparison
| Parameter | Wall Stress (σ) | Shear Stress (τ) | Wall Tension (T) |
|---|---|---|---|
| Definition | Force/area in wall | Flow-induced drag on wall | Total force/length |
| Direction | Circumferential/longitudinal | Parallel to lumen | Circumferential |
| Depends on | Pressure, radius, thickness | Viscosity, flow rate | Pressure, radius |
| Clinical Impact | Aneurysm rupture | Atherosclerosis location | Surgical graft design |
Essential Clinical Concepts
- Wall stress = Internal wall loading → drives rupture pathophysiology
- Shear stress = Hemodynamic flow effects → determines atherosclerosis patterns
- Wall tension = Integrated mechanical force → guides surgical planning