hemodialysis modeling
Hemodialysis is a process that is used to purify the blood of patients with malfunctioning
kidneys. In conventional hemodialysis patients are hooked up to a dialysis machine that uses a
peristaltic pump to push uncleaned blood from their body through a bundle of thousands of hollow-
ber membranes in a unit called the dialyzer. A counter-current
ow of clean
uid exists outside of
these tubules. While passing through the membranes, toxins diuse out of the blood while water
and electrolytes diuse in, eectively replacing the lost mass and creating a steady-state
ow. After
passing through the hollow-ber membranes, the clean blood is rejoined into a single, large tubule
that re-enters the patients body, creating a closed cycle. In one session, patients have their entire
volume of blood cycled numerous times through the dialysis machine in a period of around 3 to 4
hours. For those with chronic kidney problems, this is usually performed three times each week.
Your task is to model the dialysis process using your current knowledge of
uid mechanics and
some background research on the conventional dialysis process. Specically, you are to determine:
The total pressure drop across the hollow-ber dialyzer
The power required to drive the pump
Many necessary parameters for this calculation are not given here (e.g. viscosity of blood, average
blood
ow rate, number of tubules, diameter and length of tubules, etc…) but will require some
preliminary research and estimation. You may make the following assumptions in your model:
The entire process is steady-state (i.e. you may neglect the eects of pulsatile blood
ow)
The toxin/electrolyte exchange through the membrane has a negligible eect on the
ow
throughout each tubule
Pay specic attention to the estimated Reynold’s numbers through each of the small tubules and
the corresponding
uid regime.
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