Arteriography of a patient's left renal artery showsnarrowing of the radius of the artery by 50%. What is theexpected change in blood flow through the stenotic artery?
Question
Arteriography of a patient's left renal artery showsnarrowing of the radius of the artery by 50%. What is theexpected change in blood flow through the stenotic artery?
Solution
The blood flow through a vessel is described by Poiseuille's law, which states that the flow rate (Q) is proportional to the fourth power of the radius (r). Mathematically, this is expressed as Q ∝ r^4.
If the radius of the artery is reduced by 50%, the new radius (r') is 0.5r.
Substituting this into Poiseuille's law gives Q' ∝ (0.5r)^4 = 0.0625r^4.
Therefore, the blood flow through the stenotic artery is expected to decrease to 6.25% of the original flow. This is a significant reduction and could potentially lead to renal ischemia, depending on the extent of the stenosis and the presence of collateral circulation.
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