Transcatheter aortic valve replacement $($TAVR$)$ is a valve replacement procedure during

which a new valve is inserted inside the diseased aortic valve. Generally, a replacement

valve consists of a metallic frame with valve leaflets made from cow or pig heart tissue $($see

figure below$).$ These valves can last many years, but they are associated with an increased

risk of developing blood clots. As a result, people after TAVR must take antiplatelet drugs

$($e$.$g$.,$ aspirin$)$ that prevent blood clot formation for the rest of their lives.

You propose an alternative, where you infuse the surface of the valve leaflets with aspirin.

You hypothesize that a small amount of aspirin will be convected into the blood as it flows

over the leaflets of the heart valve, and that this will be sufficient to stop blood clot formation

for the lifespan of the replacement valve.

Given:

You can model the valve leaflets as a pipe with the inside diameter of $20mm,$ length

of $17mm,$ and leaflet thickness of $0\mathrm{.}25mm.$

Since the length of the valve is less than the diameter, flow across the valve is

underdeveloped.

You estimate that the required rate at which aspirin must be released into the blood

is $0\mathrm{.}095\frac{g}{sec}.$

The maximum amount of aspirin you can add on the surface of the leaflets cannot

exceed $50\%$ of total leaflet mass.

The cardiac output is $5\frac{L}{m}in,$ but the valve is opened and the flow occurs only

during systole, which lasts $30\%$ of cardiac cycle time.

The diffusivity of aspirin in blood is $7{10}^{-6}c\frac{m^2}{sec}.$

The density of valve leaflets is $1080k\frac{g}{m^3}.$

Blood density and viscosity are $1080k\frac{g}{m^3}$ and $8\mathrm{.}5cP,$ respectively.

a$.[0\mathrm{.}5$ points