Blood Flow, Pressure & Resistance Vocabulary

Fundamental Flow Equation

• Core relationship revisited (Fick/Poiseuille hybrid form used in class):
  • Q = \frac{\Delta P}{R}
  • Q (or q in shorthand) = rate of blood flow ("cardiac output" at the level of the whole circuit, or regional flow at a specific vessel segment).
  • \Delta P = pressure gradient between two points (always drives flow from high → low).
  • R = resistance (all forces that oppose forward movement of blood).
• Key conceptual cues:
  • If \Delta P \rightarrow 0, flow stops (never occurs in a living person).
  • Variable positions matter: numerator ↑ → flow ↑; denominator ↑ → flow ↓.

What Is Resistance?

• Physiological meaning = "frictional drag" that slows blood.
  • Analogous to water rubbing against pipe walls.
• Three determinants (mnemonic: "LVR" – Length, Viscosity, Radius):
  • L (length of vascular pathway)
  • V (viscosity of blood)
  • r (radius of the vessel lumen)
• Poiseuille‐style proportionality (simplified):
  • R \propto \frac{L\,\cdot V}{r^4}
  • Length and viscosity are directly proportional.
  • Radius sits in the denominator and to the 4th power → tiny radius changes cause huge resistance swings.
• In this course you are not required to solve the full Poiseuille equation numerically—focus on the directional relationships.

Factor-by-Factor Analysis

1. Vessel Length (L)

• Longer pathway ⇒ more cumulative wall contact ⇒ friction ↑ ⇒ R ↑.
• Practical outcome: systemic circuit (long) gradually slows flow as blood travels toward the periphery.
• Length is anatomically fixed after development; the body cannot acutely shorten vessels.

2. Blood Viscosity (V)

• Definition: internal "thickness" of blood relative to water.
• Main influencers:
  • Hydration status (loss of plasma water via dehydration ↑ viscosity).
  • Hematocrit / RBC count (polycythemia ↑; anemia ↓).
• High viscosity blood = “sludgier” → more friction → R ↑ → flow ↓.
• Body cannot sense viscosity directly; adjusts indirectly by changing kidney water handling (urine volume) or altering RBC production over days–weeks.

3. Vessel Radius (r)

• Inverse 4th-power relationship: r↑ \Rightarrow R↓;\; r↓ \Rightarrow R↑.
• Only determinant that can be rapidly and precisely regulated.
• Achieved via smooth-muscle contraction in tunica media:
  • Vasoconstriction (radius ↓).
  • Vasodilation (radius ↑).
• Control signals:
  • Autonomic nerves (sympathetic tone).
  • Circulating hormones (e.g., epinephrine, angiotensin II).
  • Local metabolites, paracrines & autocrines (NO, prostaglandins, etc.).

Vasoconstriction vs. Vasodilation – Hemodynamic Consequences

• Picture the vessel as a pipe with an adjustable nozzle.

Vasoconstriction

1. Smooth muscle contracts → r ↓ → R ↑.
2. According to Q = \frac{\Delta P}{R}, local flow (Q) distal to the constriction ↓.
3. Volume/pressure effects:
   • Proximal (upstream) to the constriction: blood backs up → local pressure ↑.
   • Distal (downstream): less volume delivered → pressure ↓.

Vasodilation (opposite pattern)

1. r ↑ → R ↓.
2. Flow beyond the dilation ↑.
3. Proximal pressure ↓ (less backup); distal pressure ↑ (more volume delivered).

Big-Picture Application: Systemic vs. Pulmonary Circuits

Pressure Profiles (rounded class numbers)

• Therefore:
  • Systemic \Delta P_{sys} \approx 90 - 0 = 90\;\text{mm Hg}.
  • Pulmonary \Delta P_{pul} \approx 15 - 0 = 15\;\text{mm Hg}.

Equality of Flow

• Despite a 6-fold pressure difference, flow rates through both circuits are equal (must match to prevent blood pooling).
• Explanation: R{sys} \gg R{pul} because systemic vessels span the entire body (length ↑↑) whereas pulmonary vessels only traverse the lungs (length ↓).
  • Using Q = \frac{\Delta P}{R}, larger systemic resistance demands a larger pressure gradient to sustain the same Q.
  • Conversely, short low-resistance pulmonary pathways require only a modest \Delta P.

Clinical/Physiological Implications

• Left ventricle must generate much higher pressure than right ventricle (thicker wall) to overcome systemic resistance.
• Pulmonary hypertension (pathological ↑ in pulmonary resistance) forces the right ventricle to pump against higher pressure, leading to right-sided heart strain.

Regulation Hierarchy & Practical Notes

• Acute control lever = radius (smooth muscle tone ⇒ second-to-second adjustments in blood pressure and regional perfusion).
• Chronic/indirect influence = viscosity (hydration status, hematocrit).
• Static influence = vessel length (set anatomically; only changes in growth or disease, e.g., obesity adds capillary beds ↔ slightly ↑ total length/resistance).

Concept Checks & Examples

• Dehydration scenario: plasma water ↓ → viscosity ↑ → R ↑ → blood flow ↓ → potential tissue hypoxia & higher cardiac workload.
• Local metabolic activity (e.g., exercising muscle) releases vasodilators (NO, adenosine) → radius ↑ → R ↓ → flow ↑ to meet oxygen demand.
• Pharmacology tie-ins:
  • Alpha-1 agonists (phenylephrine) → vasoconstrict → ↑ systemic vascular resistance (SVR) → BP ↑.
  • ACE inhibitors → ↓ angiotensin II → vasodilation → ↓ SVR → BP ↓.

Take-Home Equations (memorize relationships, not derivations)

1. Q = \frac{\Delta P}{R} (primary).
2. R \propto \frac{L\,V}{r^4} (determinants and directionality).

Understand how manipulating any numerator or denominator variable will ripple through resistance, pressure, and ultimately blood flow.