Hemodialysis Home End Stage Renal Disease
(ESRD) Principles
Dialyzers Modeling
Hemodialysis Therapy Demonstration History
Derivation of
Rate Equations Properties of
Rate Equations Example of Rate
Equation Derivation
Modeling
Hemodialysis Therapy
Kidney function in patients with
partial or complete kidney (renal) failure is insufficient to adequately remove
fluid (water) intake, resulting in the retention of fluids that is
characterized as edema. Kidney function
is also insufficient to adequately remove excess electrolytes (salts) and waste
metabolites generated through ordinary digestive and metabolic processes. As a result, the concentrations of such
metabolites will increase to toxic levels unless something is done to help
remove them.
The major source of waste metabolites
is the liver since this is where most of the energy conversion processes in the
body take place. The end products of
carbohydrate and fat metabolism tend to be water and carbon dioxide, both of
which can be lost from the body through respiratory processes (breathing). The end products of protein metabolism,
however, are generally eliminated through the kidneys. Urea is the largest mass of waste metabolite
produced in the liver from protein metabolism.
Because it is present in such large quantities in the blood and is
easily measured, urea is generally used as a marker of renal function.
Hemodialysis, the first and most
successful artificial organ technology, is a life-saving breakthrough for
people with renal failure. Hemodialysis
is based upon the thermodynamic principle that a difference in concentration
(potential) can drive a flux that moves a substance from a region of high
concentration to a region of low concentration. During hemodialysis blood is removed from the body and passed
through a filter called a dialyzer before returning to the body. The dialyzer is made from thousands of
hollow plastic fibers contained in a plastic shell. Unlike the plastic shell, which is made of impermeable material,
the hollow fibers are permeable to the passage of low molecular weight
molecules across the fiber. Blood flows
through the center (lumen side) of the fibers.
A fluid, called dialysate, flows on the exterior of the fibers (shell
side). Dialysate is a “physiologic”
fluid that contains electrolyte (salt) concentrations similar to that found in
a healthy person’s blood. The difference
in waste metabolite concentration in the blood and the dialysate creates a flux
of the metabolite from the blood to the dialysate. Electrolytes are not removed because the dialysate and blood have
similar electrolyte concentrations.
The schematic diagram at the right
depicts the simplest model for generation and elimination of urea in the
body. Urea is generated in the liver
and passed into the blood stream. The
blood stream is considered a single “compartment” in the body that acts as a
reservoir for urea. Urea can be removed
from the body by the kidney, eliminated with urine. If the kidneys are not functioning, urea can be eliminated by
hemodialysis. The symbols associated
with the diagram are:
C :
blood urea concentration, mg/mL
t : time, min
G : urea generation rate, mg/min
V : blood volume, mL
Kr :
renal (kidney) mass transfer
coefficient, mL/min
Kd : dialyzer mass transfer
coefficient, mL/min
Model
building
a) Use
conservation of
mass, i.e., the change in mass
of urea in the body (blood) over a period of time is equal to the mass produced
by the liver less the loss through kidney elimination and dialysis over that
period of time, to derive
a first order rate equation
that describes the concentration of urea in the body as a function of
time. You may have to use dimensional
analysis to find the appropriate groupings of variables to represent the
generation and removal rates.
b) What is an appropriate initial condition?
c) What is the steady-state
solution to your differential
equation?
d) When
Kr is zero (no renal function) and G is much, much less than the
dialysis removal rate, what is the time constant for your differential equation? What is the physical meaning of this time
constant?
e) What is the analytical solution for your
equation?
f) For
Kr = 0 and dialysis treatment for 6 hours every 48 hours (Kd
= 0 when dialysis is not taking place), sketch a graph of urea concentration
(relative to an initial urea concentration) for 120 hours. How does the magnitude of G impact your
sketch? How does the magnitude of Kd
impact your sketch?
Hemodialysis Home End Stage Renal Disease
(ESRD) Principles
Dialyzers Modeling
Hemodialysis Therapy Demonstration History
Derivation of
Rate Equations Properties of
Rate Equations Example of Rate
Equation Derivation
Copyright ©
2001, John F Patzer II
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