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Updated: Mar 13 2018

# Resistance, Pressure, and Flow

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• 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
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