Biomedical Engineering Reference
In-Depth Information
Blood
Concentration
(mg/dL)
Solute
MW
K
i
(cm/min)
Urea
60
200
0.001
Creatinine
113
6
0.0005
β
2
-globulin 12,000
0.8
0.00004
10.14 The concentration of a urea leaving the dialyzer
C
UM
is related to the con-
centration of urea in the body (
C
UB
), and the reservoir by the equation
⎛
⎞
CC
CC
−
UM
UR
ln
=−
0.874
. At the start of the dialysis process, the urea concen-
⎜
⎟
−
⎝
⎠
UB
UR
tration in the blood within the body
C
UB
is 1.0 g/L. The volume of blood
V
B
is 6.0L, the blood flow rate
Q
b
is 5.94 L/hr, and
C
UR
is constant at 0.05 g/L.
Determine the time required for the urea concentration in the body (
C
UB
) to
drop to 0.2 g/L.
10.15 Consider the filtration of the urea from blood using a countercurrent flow, a
dialysate exchanger with an area of 210 cm
2
. The mass transfer coefficient
K
for the exchanger is 0.2 cm/min. If the dialysate flow rate is 400 mL/min, the
blood flow rate is 200 mL/min and the urea concentration in the blood at the
start of dialysis is 150 mg/cm
3
; then:
(a) After a short transient during which the dialyzer reaches steady state,
what are the concentration of the urea in the dialysate outlet and in the
blood outlet?
(b) At the start of dialysis, what is the clearance?
(c) How long will it take to bring the urea concentration in the blood to 10%
of its initial value if the body fluid volume is 10L?
10.16 Assume that a drug overdose is taken, is rapidly absorbed into the body, and
distributes into the extracellular fluids (13L) only. If the drug is neither se-
creted nor reabsorbed by the kidneys, how long will it take for 90% of the
drug to be eliminated in the urine? Model the extracellular fluid pool as a well-
mixed compartment, neglect drug metabolism (not a good assumption for
most drugs), use a GFR of 125 ml/min, and assume a blood flow of 1,200 ml/
min to the kidneys. This example will show you why
forced dieresis
(stimula-
tion of high rates of urine formation by the use of certain agents) is a common
technique for treating drug overdose.
10.17 Derive the governing equation for the alveolar partial pressure in the control
volume as a function of time. Assume that it has a solubility of
β
b
in the blood
and an apparent solubility
β
a
is a convention that
merely allows one to talk about the relative solubility of a gas between air and
blood.) Further assume that the inhaled concentration and volumetric flow
rate are constant with respect to time and that
C
v
(
t
)
β
a
in the air. (Note that
0. This is a flow-through
model (i.e., the ventilation does not change the volume of the alveolus). As-
sume that the inhaled tracer is not soluble in the tissue volume.
=
(a) Once you have found the differential equation describing this system, solve
it for
P
A
(
t
).
