![]() In other words, ΔP is increased by either an increase in flow or resistance.įor example, under laminar flow conditions, doubling the flow across a heart valve or along a length of blood vessel doubles the pressure drop across the valve or along the length of vessel.Ī normal valve, like a normal large artery, has a very small resistance to flow, and therefore the pressure gradient across the valve is very small. In contrast, with vascular or valvular stenosis the pressure gradient is increased because of the increased resistance to flow (e.g., by decreased vessel radius or valve cross-sectional area). The pressure gradient can also be viewed as the pressure drop (i.e., energy loss) that results from a given flow and resistance (i.e., ΔP is the dependent variable), where ΔP=F x R. In this example, ΔP is an independent variable whereas flow is the dependent variable. Flow is decreased, for example, if there is a decrease in ΔP or an increase in R as shown in the figure below. This relationship is based upon Ohm's Law from physics in which current equals the voltage difference divided by the resistance (I= ΔV/R). The pressure gradient can be viewed as the force driving flow (F), where F = ΔP/R. For a heart valve, therefore, the resistance to flow is inversely proportional to A 2. Therefore, the area of the valve orifice is used to compute resistance instead of radius, where area (A) is proportional to the square of the radius (r 2), based upon the equation A = π r 2. For heart valves, it is not possible to use orifice radius because the opening is not circular. Resistance is inversely related to the fourth power of the radius (r 4) of a blood vessel. The most important factor, quantitatively and functionally, is the radius of the vessel, or in the case of a heart valve, the orifice area of the opened valve. The factors determining the resistance are described by the Poiseuille relationship. At any given pressure gradient (ΔP), the flow rate is determined by the resistance (R) to that flow. This force is the difference in blood pressure (i.e., pressure gradient) across the vessel length or across the valve (P 1-P 2 in the figure to the right). In order for blood to flow through a vessel or across a heart valve, there must be a force propelling the blood. ![]()
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