1. Wall Stress (σ)
Definition:
Internal force per unit area within the vessel wall (response to blood pressure).
Formula:
σ = (P × r) / h
P: Intraluminal pressure, r: radius, h: wall thickness.
Direction:
Acts circumferentially (hoop stress) and longitudinally.
Key Points:
- ↑ in hypertension (↑ pressure) or aneurysms (↑ radius, ↓ thickness).
- Causes wall fatigue → rupture risk (e.g., aortic dissection).
2. Shear Stress (τ)
Definition:
Frictional force per unit area exerted by blood flow parallel to the vessel wall.
Formula:
τ = 4μQ / πr³
μ: Blood viscosity, Q: flow rate, r: radius.
Direction:
Acts parallel to the endothelial surface.
Key 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).
Formula:
T = P × r (Laplace's Law for thin-walled cylinders)
Units:
Force per unit length (e.g., N/m).
Key Points:
- Explains why larger vessels (↑ r) rupture at lower pressures (e.g., aortic aneurysms).
- Clinically used to estimate rupture risk (e.g., abdominal aortic aneurysm >5 cm).
Comparison Table
| 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 |
Clinical Examples
Wall Stress:
Aortic dissection: ↑σ from hypertension thins the media → tear.
Shear Stress:
Plaque formation: Low τ at carotid bifurcation → endothelial dysfunction.
Wall Tension:
AAA rupture risk: T > 120 N/m → emergency repair.
Visual Aid for PowerPoint
Graphic Suggestion:
Artery cross-section with arrows showing:
- Wall stress (outward arrows).
- Shear stress (parallel arrows at lumen).
- Wall tension (circumferential force ring).
Equation Highlight:
Animate Laplace's Law (T = P × r) for aneurysm rupture risk.
Key Takeaway
- Wall stress = Internal wall load → rupture.
- Shear stress = Blood flow effects → atherosclerosis.
- Wall tension = Net force → surgical planning.