Video 2 - Hemodynamics: Resistance, Cross-Sectional Area & Velocity

Physiological Need for Slow Capillary Flow

• Fundamental purpose: allow adequate time for diffusion of O$2$, CO$2$, glucose, hormones, wastes, etc.
• Structural prerequisites
  • Capillary wall = one thin endothelial cell → maintains a minimal diffusion barrier.
  • Red blood cells (RBCs) forced into single-file orientation → maximizes membrane contact.
  • Therefore velocity must decrease as blood enters capillary beds.

Determinants of Tissue Blood Flow

• Two broad categories
  • Driving force (∆P)
  • Generated by cardiac output & arterial blood pressure (BP).
  • Blood moves high → low pressure analogous to diffusion.
  • Resistance (R)
  • Frictional drag as blood rubs against the vessel wall.
  • Governs how easily flow occurs through a given segment.

Resistance: The Friction Story

• In any vessel, cells adjacent to the wall experience maximal shear → slowest velocity.
• RBCs in the axial (centerline) stream encounter less wall contact → faster.
• The narrower the vessel the higher the proportion of blood near the wall → overall velocity drops.

Variables that Alter Resistance (Poiseuille-like logic)

1. Length (L) – essentially fixed once growth completed.
2. Viscosity (η) – regulated within narrow physiologic limits ("not too watery, not too thick").
3. Radius (r) – primary adjustable parameter via vasoconstriction/vasodilation.
   • Small radius → R \uparrow dramatically (remember R \propto \frac{1}{r^4}).
   • Large radius → R \downarrow.

Visual Comparison – Small vs. Large Vessel Cross-Section

• Small vessel: every RBC touches wall → universal friction.
• Large vessel: only peripheral ring touches wall; core RBCs interact mostly with other cells → faster axial flow.

Total Cross-Sectional Area (Aₜ) Concept

• Individual capillary = tiny, high-resistance tube.
• Capillary bed = thousands of parallel tubes.
  • When bundled ("ponytail" thought experiment) → aggregate lumen area often exceeds that of the supplying arteriole.
• Consequence: even though each capillary has high R, the enormous collective area slows bulk velocity.

Velocity (v) vs. Total Cross-Sectional Area Relationship

• At constant flow (Q):
  Q = v \times At → v \propto \frac{1}{At} (inverse proportionality).

Garden-Hose Thumb Analogy

• Thumb over hose = small outlet (Aₜ ↓) → stream accelerates (v ↑) to reach distant flowers.
• Thumb removed = outlet widens (Aₜ ↑) → stream slows (v ↓) → water "blooms" out.
• Applies directly to arteries vs. capillary networks.

Sample Calculations (Q kept at 100 arbitrary units)

Branching Pattern & Velocity Profile in the Vascular Tree

• Diagram logic:
  1. Large artery → moderate Aₜ.
  2. Multiple branches → total Aₜ skyrockets in capillary zone.
  3. Venules/veins converge → Aₜ falls again.
• Therefore velocity pattern = high → low → modest uptick.
  • Counter-intuitive bump in venules because reduction in Aₜ acts like replacing thumb on hose.
• Important distinction: Pressure continuously falls along the system; velocity does not mirror pressure.

Flow, Pressure, and Resistance—Clinical Framing

• Basic hemodynamic identity: Q = \frac{\Delta P}{R}.
• For blood to move, \Delta P must exceed resistive forces.
• Types of pressure cited
  • Arterial (systemic) – what we measure as BP.
  • Capillary pressure – drives filtration/reabsorption.
  • Venous pressure – lowest, aided by valves & muscle pump.

Arterial Blood Pressure Numbers

• Traditional "normal": 120/70\ \text{mmHg} (systolic/diastolic).
• Clinical nuance
  • Elevation of diastolic (lower number) often considered more worrisome because vessel wall never fully relaxes.
  • Example: 140/70 > transient systolic surge but diastole normal – less concerning than 120/90.

Practical & Conceptual Take-aways

• Slowed capillary transit time is engineered by two synergistic mechanisms:
  1. Micro-radius → intrinsic high resistance.
  2. Massive total cross-sectional area → velocity suppression.
• Inverse v–Aₜ principle explains garden-hose behavior, blood velocity dip in capillaries, and modest venous speed increase.
• Never confuse velocity with pressure; pressure gradient keeps dropping, while velocity can rise or fall depending on area changes.
• Clinically, blood pressure must be adequate to overcome microvascular resistance; chronic elevation (hypertension) largely reflects maladaptive changes in radius & wall tension.