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Flow through a vessel is directly proportional to the radius of that vessel to the 4th power. Therefore, flow in this artery would be decreased by a factor of 16. Similar to Ohm's law for electrical current, I =V/R, (where I = current through a conductor, V = voltage difference across a conductor, and R = resistance of a conductor), the flow of blood in an artery is given by Q = P/R, (where Q = flow, P is pressure difference, and R is resistance to flow). Resistance is given by Poiseuille's equation: R = (viscosity of blood)*(length of vessel)/r^4. Therefore, if the radius decreases by a factor of 2, resistance increases by a factor of 16, and flow decreases by a factor of 16. As discussed by the United States Preventative Services Tast Force (USPSTF), the estimated prevalence of severe carotid artery stenosis in the general population 65 years and older is about 1 percent. The USPSTF recommends against screening for asymptomatic carotid artery stenosis in the general adult population. Illustration A shows narrowing of the carotid artery secondary to atherosclerosis. Auscultation of this area can reveal a carotid bruit, a murmur that occurs during systole as a result of turbulent blood flow through an area of stenosis. Incorrect Answers: Answers 1-3, 5: None of these answers accurately reflect the relationship between the radius of a vessel and flow through that vessel.
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