Artificial kidney device is a device that removes water and waste metabolism products from the blood. In the hollow fiber hemodialyzer, which is such a device, the blood coming out of the artery is filled with hollow cellulose acetate fibers It flows through the fiber bundle, and the dialysis fluid, consisting of water and various dissolved salts, flows outside the fiber bundle. Water and waste metabolism products $-$ mainly urea, creatinine, uric acid and phosphate ions $-$ pass through the fiber walls into the dialysis fluid and the cleaned blood returns to the vessel. Assume that the blood conditions in the arteries and veins during a certain dialysis period are as follows.

The arterial and vein blood conditions during dialysis are as follows:

Flow Rate

Urea $(N{H}_{2}CON{H}_2)$ concentration

Arterial $($entering$)$ blood venous $($outgoing$)$ blood

blood from

arteries

Calculate the rates at which urea and water are removed from the blood.

$($b$)$ If the dialysis fluid enters at a rate of $1500m\frac{l}{m}in$ and the exiting solution $($dialysis products$)$ exits at approximately the same rate, what will be the concentration of urea in the dialysis products?

$($c$)$ Assume that we want to reduce the patient's urea level from an initial value of $2\mathrm{.}7m\frac{g}{m}L$ to a final value of $1\mathrm{.}1m\frac{g}{m}L.$ If the total blood volume is $5\mathrm{.}0$ liters and the average urea removal rate is the value calculated in $($a$),$ how long should the patient remain on dialysis? $($Ignore the loss in total blood volume due to water removed in the dialyzer.$)$

Research Exercises $-$ Research and Finding

$($d$)$ The device described in this problem is outside the body and the patient must go to the dialysis center several times a week. What kind of difficulties would be encountered if the artificial kidney were placed inside the patient's body?

$($e$)$ Briefly describe the current state$-$of$-$the$-$art designs in artificial kidney design.