Hemodynamics and Blood Flow

Basic Hemodynamics - Flow's ABCs

• Blood Flow (Q): Volume/time (L/min). $Q \propto \Delta P$, $Q \propto 1/R$.
• Pressure Gradient ($\Delta P$): Pressure difference driving flow (High P → Low P).
• Resistance (R): Opposition to flow.
• Ohm's Law for Flow: $Q = \Delta P / R$.
  • ↑ $\Delta P$ or ↓ R → ↑ Q.
• Poiseuille's Law for Resistance: $R = (8 \eta L) / (\pi r^4)$
  • $\eta$: Viscosity (↑ $\eta$ → ↑ R).
  • L: Vessel Length (↑ L → ↑ R).
  • r: Vessel Radius (most critical; $R \propto 1/r^4$).

⭐ Vessel radius ($r$) is paramount: halving $r$ increases resistance 16x and reduces flow 16x (if $\Delta P$ constant), due to the $r^4$ factor in Poiseuille's law.

Vascular Resistance - Poiseuille's Power Play

• Poiseuille's Law quantifies vascular resistance: $R = \frac{8 \eta L}{\pi r^4}$.
  • $R$: Resistance
  • $\eta$: Blood viscosity (e.g., polycythemia $\uparrow \eta \uparrow R$)
  • $L$: Vessel length (relatively constant)
  • $r$: Vessel radius (paramount factor)
• Resistance dynamics:
  • Directly proportional to viscosity ($\eta$) and length ($L$).
  • Inversely proportional to radius to the fourth power ($r^4$).
    • 📌 $r^4$ Dominance: Small radius change $\rightarrow$ massive resistance change. E.g., halving radius $\uparrow$ resistance 16x.
• Arterioles are the principal sites of systemic vascular resistance (SVR) regulation. ⭐ > Arterioles, through vasodilation and vasoconstriction, exert the most significant control over Total Peripheral Resistance (TPR), directly impacting blood pressure.

Blood Flow Patterns - Smooth or Shaky Show

• Laminar Flow:
  • Smooth, silent, layered (parabolic velocity profile: fastest at center).
  • Normal physiological flow; energy efficient.
• Turbulent Flow:
  • Disordered, noisy (e.g., murmurs, bruits).
  • Causes: High velocity (stenosis, high output states), ↓ blood viscosity (anemia), large vessel diameter, vessel branching.
  • Energy inefficient; ↑ endothelial stress.
• Reynolds Number ($Re$):
  • Predicts flow pattern: $Re = \frac{\rho v D}{\eta}$ (where $\rho$=density, $v$=velocity, $D$=diameter, $\eta$=viscosity).
  • Laminar flow: $Re < \textbf{2000}$.
  • Turbulent flow: $Re > \textbf{3000}$.

⭐ Audible bruits often indicate turbulent flow, which can predispose to endothelial damage and atheroma formation, particularly at vessel bifurcations.

Vessel Dynamics & Control - Stretch, Squeeze, Survive

• Vascular Properties:
  • Compliance ($C = \Delta V / \Delta P$): Ability to distend. Veins (high capacitance) > Arteries.
  • Elasticity: Ability to recoil. Arteries (maintain diastolic pressure) > Veins.
  • Stress-relaxation & Reverse stress-relaxation: Gradual adaptation to changes in blood volume/pressure.
• Blood Flow Regulation:
  • Local (Autoregulation):
    • Myogenic: Stretch (↑pressure) → Vascular Smooth Muscle (VSM) contraction (Bayliss effect).
    • Metabolic: Vasodilators (e.g., ↓O₂, ↑CO₂, ↑H⁺, ↑K⁺, adenosine).
    • Endothelial: Nitric Oxide (NO) (potent vasodilator); Endothelin-1 (potent vasoconstrictor).
  • Neural:
    • Sympathetic α₁ receptors: Vasoconstriction (most arterioles).
    • Sympathetic β₂ receptors: Vasodilation (skeletal muscle, coronary arteries).
  • Hormonal:
    • Vasoconstrictors: Angiotensin II, Vasopressin (ADH).
    • Vasodilators: Atrial Natriuretic Peptide (ANP), Bradykinin.
    • Adrenaline: Dual effect (α₁ constrict, β₂ dilate).

⭐ Flow-mediated vasodilation, primarily via Nitric Oxide (NO) release from endothelium in response to shear stress, is a critical physiological mechanism.

High‑Yield Points - ⚡ Biggest Takeaways

• Poiseuille's Law: Resistance is dominated by vessel radius (to the 4th power); radius ↓ by half, resistance ↑ 16 times.
• Ohm's Law for flow: Blood Flow equals Pressure Gradient divided by Resistance.
• Velocity is slowest in capillaries (largest total cross-sectional area), aiding exchange.
• Reynolds number predicts turbulent flow, which ↑ resistance and cardiac work.
• Veins show high compliance (volume/pressure change), acting as blood reservoirs.
• Mean Arterial Pressure (MAP approximately Diastolic + one-third Pulse Pressure) is key for tissue perfusion.