# Vascular resistance

As vascular resistance refers to the resistance to flow that a blood vessel the blood stream opposes. The vessel resistance is defined analogously to the ohmic resistance as the quotient of the pressure difference between the ends of the vessel and the volume flow rate:

${\ displaystyle R = {\ frac {\ Delta p} {\ dot {V}}}}$

If you replace a vessel with a rigid tube with the radius r and the length l , the vessel resistance results according to the Hagen-Poiseuille law :

${\ displaystyle R = {\ frac {8 \ cdot \ eta \ cdot l} {\ pi \ cdot r ^ {4}}}}$

It shows that the vascular resistance depends not only on the properties of the vessel, but also on the viscosity η of the blood (which, however, is not a constant, but depends on the vessel diameter and the flow rate). Nonetheless, it can be stated that the vascular resistance increases with the length of the vessel and reacts very sensitively to changes in the vascular radius (halving the radius sixteen times the resistance in the model). Stenoses (e.g. of the coronary arteries in coronary artery disease ) increase the vascular resistance and thus reduce the blood flow; however, they often only affect short vessel sections, which is why only high-grade stenoses become symptomatic.

By analogously applying the rules for adding electrical resistances in series and parallel connection , resistances for entire circulatory sections can be calculated from individual vessel resistances. A basic distinction is the total vascular resistance (TPR, of English resistance total peripheral , equivalent resistance of the systemic circulation ) and the pulmonary vascular resistance (PVR, from English resistance pulmonary vascular , equivalent resistance of the pulmonary circulation ). In addition, the vascular resistance of individual organs (e.g. the cerebral vascular resistance in the brain ) can also be specified.

## literature

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