🧠 Poiseuille’s Law for USMLE Step 1: Blood Flow, Resistance, and Vessel Radius
Poiseuille’s Law helps explain why small changes in vessel radius cause big changes in blood flow. It’s a classic Step 1 crossover between physiology and physics, frequently tested in questions on:
Blood flow
Pressure gradients
Arteriolar regulation
Resistance-driven pathology
🧮 The Formula
Poiseuille’s Law:
Where:
Q = Flow
ΔP = Pressure gradient
r = Radius of vessel
η = Viscosity
L = Length of vessel
📊 Key Takeaways
| Variable | Relationship with Flow (Q) |
|---|---|
| Radius (r) | ∝ r⁴ → MOST significant factor |
| Pressure (ΔP) | Directly proportional |
| Viscosity (η) | Inversely proportional |
| Length (L) | Inversely proportional |
🧠 Step 1 Insight:
Radius affects flow exponentially. If radius is halved, resistance increases 16x, and flow drops 16x.
💡 Clinical Examples on Step 1
1. Aortic stenosis
↓ radius → ↓ flow
Pressure builds up proximal to obstruction
2. Polycythemia vera
↑ viscosity (η) → ↓ flow
Patient may have sluggish circulation and clot risk
3. Anaphylaxis or exercise
Arteriolar vasodilation → ↑ r → ↑ flow
Useful for explaining shock or thermoregulation
🧠 Mnemonic to Remember
“R to the Fourth is a Big Deal”
Flow is exponentially dependent on radius
Double the radius = 16x more flow
“High Viscosity, Low Velocity”
↑ Viscosity (η) = ↓ Flow
📚 High-Yield Step 1 Questions Look Like:
A patient with anemia has reduced blood viscosity. According to Poiseuille’s Law, how will this affect tissue perfusion?
✅ Answer: Decreased viscosity → increased flow
🧪 Practice Table: Vascular Flow Changes
| Change | Impact on Q (Flow) |
|---|---|
| Radius doubles | ↑↑↑↑ (16× increase) |
| Viscosity increases | ↓ Flow |
| Pressure gradient increases | ↑ Flow |
| Length increases | ↓ Flow |
🎯 Call-To-Action
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