Resistance, Pressure, and Flow

Vessel Pressure

• Overview   
  • a change in pressure in a vessel is equal to flow times resistance:  ΔP = Q x R
    • this is similar to Ohm’s law where a change in voltage is equal to current times resistance:  ΔV = IR
• a pressure gradient drives flow from high pressure to low

Resistance

• Formula 
  • resistance = (driving pressure ΔP) / (flow Q) = (8η)(viscosity)(length) / (πr⁴)
  • is directly proportional to viscosity and inversely proportional to the radius of a vessel raised to the 4th power 
• Peripheral resistance
  • arterioles account for most of the total peripheral resistance in the cardiovascular system
  • regulates capillary flow
• Total resistance
  • the total resistance of vessels in series is determined by summing the resistance of each vessel:  RTOTAL  = R₁ + R₂ + R₃ + …
  • the total resistance of vessels in parallel is determined by taking the inverse of the sum of the inverses of the resistance of each vessel:  1/RTOTAL= 1/R₁ + 1/R₂ + 1/R₃ + …
• these calculations are done similarly to adding electrical resistors

Viscosity

• Viscosity depends mostly on hematocrit
• Viscosity is increased in several disease states:
  • polycythemia
    • conversely, anemia decreases the viscosity
  • hyperproteinemic states (e.g., multiple myeloma)
  • hereditary spherocytosis