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.
Gillett et al., in a prospective evaluation of carotid bruit as a predictor of first stroke in patients with type 2 diabetes, found that patients with incidental carotid bruits have >6 times the risk of first stroke in the first 2 years than patients without a bruit and concluded that these patients should receive intensified management of vascular risk factors.
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.
Answers 1-3, 5: None of these answers accurately reflect the relationship between the radius of a vessel and flow through that vessel.
Gillett M, Davis WA, Jackson D, Bruce DG, Davis TM; Fremantle Diabetes Study. Prospective evaluation of carotid bruit as a predictor of first stroke in type 2 diabetes: the Fremantle Diabetes Study. Stroke. 2003 Sep;34(9):2145-51. Epub 2003 Aug 7. PubMed PMID: 12907819.
PMID:12907819 (Link to Abstract)
U.S. Preventive Services Task Force. Screening for carotid artery stenosis: recommendation statement. Am Fam Physician. 2008 Apr 1;77(7):1006-10. PubMed PMID: 18441867.
Lee BK, Lim HS, Fearon WF, Yong AS, Yamada R, Tanaka S, Lee DP, Yeung AC, Tremmel JA. Invasive evaluation of patients with angina in the absence of obstructive coronary artery disease. Circulation. 2015 Mar 24;131(12):1054-60.
PMID:25712205 (Link to Abstract)