Which equation represents resistance in a blood vessel?

The equation that accurately represents the resistance in a blood vessel is derived from Poiseuille's law, which states that resistance (R) to fluid flow through a cylindrical vessel is determined by several factors, including the viscosity of the fluid, the length of the vessel, and the radius of the vessel. The equation is articulated as R = 8ηL / (πr^4), where η is the dynamic viscosity, L is the length of the vessel, and r is the radius.

This formulation shows that resistance increases with greater viscosity and vessel length, but it dramatically decreases with an increase in the radius. Since blood vessels can change their diameters significantly, this relationship highlights the crucial role of vessel radius in modulating resistance and, consequently, blood flow.

Other equations listed do not relate directly to the resistance of a blood vessel itself. For instance, while driving pressure and flow can be important metrics in cardiovascular physiology, the driving pressure divided by flow gives a different insight into hemodynamics rather than defining resistance itself. Total peripheral resistance to cardiac output and mean arterial pressure to stroke volume also reflect cardiovascular dynamics but do not specify the resistance formula applicable to an individual blood vessel as accurately as the equation derived from Poiseuille's law does.