A 63-year-old man with long-standing hypertension has undergone multiple changes in his antihypertensive regimen over the years with only minimal improvement in his blood pressure. A CT study of his thoracolumbar spine is performed for evaluation of chronic back pain, and the study incidentally reveals a small right kidney. Angiography demonstrates atherosclerotic narrowing of the right renal artery. The left renal artery is intact. You conclude that the flow in the right-sided artery is decreased by a factor of 16 compared to the left. By what percentage has the radius of the lumen been reduced?

Question

A 63-year-old man with long-standing hypertension has undergone multiple changes in his antihypertensive regimen over the years with only minimal improvement in his blood pressure.  A CT study of his thoracolumbar spine is performed for evaluation of chronic back pain, and the study incidentally reveals a small right kidney.  Angiography demonstrates atherosclerotic narrowing of the right renal artery.  The left renal artery is intact.  You conclude that the flow in the right-sided artery is decreased by a factor of 16 compared to the left.  By what percentage has the radius of the lumen been reduced?

Quizplus · Accepted Answer

11ec160b_3ca3_c635_9249_97f469db717c_MD0001_00 The flow of blood through a vessel can be calculated by dividing the pressure gradient between two points in the vessel by the resistance to flow in that vessel. The resistance in a blood vessel can be calculated using Poiseuille's equation as follows: Resistance (R) = ηL /r⁴ η = viscosity of blood L = length of the blood vessel r = radius of the blood vessel (note: raised to the 4^th power) Combining these equations illustrates the profound effect that a small change in blood vessel radius can have on the flow through a vessel. This is due to the fact that the resistance to flow in a blood vessel is inversely proportional to the radius raised to the fourth power. In the patient described above, flow through the right renal artery has been decreased by a factor of 16 compared to the left renal artery. It can be assumed that the pressure gradient, blood viscosity, and blood vessel lengths are equivalent bilaterally, leaving the blood vessel radius as the only variable. Using the above equation, it can be determined that decreasing the radius by a factor of 2 decreases the flow by a factor of 16. FLOW = (P₁-P₂) / ηL * r⁴ = CONSTANT * r⁴, which can be simplified to: FLOW = r⁴, and: (FLOW / 16) = (r⁴ / 16) = (r/2)⁴ Thus, when flow is reduced by a factor of 16, the radius of the lumen is decreased to r/2 (50% of the original radius). Educational objective: Blood flow is directly proportional to the vessel radius raised to the fourth power. Resistance to blood flow is inversely proportional to the vessel radius raised to the fourth power.

A 63-Year-Old Man with Long-Standing Hypertension Has Undergone Multiple Changes