Question

Describe what happens to vascular resistance during stenosis Where are the radius is reduced by 1/2. Demonstrate this relationship with an equation or ratio. Why, in vivo does this degree of stenosis have a normal affect on the aorta, but little effect is observed in the brain.

vs. Parterial at CO = 5 L/min for Csystolic = 0.1, 0.25, 0.3, 0.4, 0.45, and 0.5 mL/mmHg. 4. Systemic resistance and blood flow partitioning. Describe what happens to vascular resistance during stenosis where the radius is reduced by one-half. Demonstrate this relationship with an equation or ratio. Why, in vivo, does this degree of stenosis have an enormous effect on the flow in the aorta, but little effect if observed in the brain? Please answer in no more than 250 words (hint: think about the relative flow of capillary beds versus larger blood vessels). (12 points)

Answer 1

According to the  Hagen–Poiseuille equation, capillary resistance is given by the following formula

R=8nL/(p.r)

• R = resistance to blood flow
• L = length of the vessel
• η = viscosity of blood
• r = radius of the blood vessel
• pi = 3.14

Resistance is inversely proportional to r⁴ . If radius is reduced by 1/2, the vascular resistance will increase 2⁴ = 16 times.

The aorta is the largest blood vessel in the body. Even a minor change in vessel diameter will increase the vascular resistance tremendously as demonstrated above. The aorta gives off multiple branching arteries which further subdivide into arterioles and capillaries. Since the aorta is distant from capillary beds, the corresponding change in blood flow and tissue prominent is quite prominent.

The capillary bed of the brain is comprised of a dense network of intercommunicating vessels. There is a high degree of collateral circulation due to vascular anastomosis. If there is stenosis in one particular vessel, the blood flow to that region is compensated through the collateral circulation. Hence the effect on tissue perfusion is minimal.