Transcript Hemodialysis and the Artificial Kidney
Hemodialysis and the Artificial Kidney
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Kidney failure - affects 200 000 patients worldwide
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15 000 in Canada
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Hamilton?
Arterial blood Venous blood Waste
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What sort of things are excreted?
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Urea - 30 g/day
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Creatinine - 2 g/day
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Salt - 15 g/day
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Uric Acid - 0.7 g/day
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Water - 1500 mL/day
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Unknown
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Kidney failure
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accumulation of waste
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acidosis, edema, hypertension, coma
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Kidney Structure and Function: Nephrons
Functional units of the kidney 1.2 million per kidney Filtration and removal of wastes Reabsorption of water, proteins, other essentials into the blood
Actively Secreted Substances
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Hydroxybenzoates Hippurates Neutrotransmitters (dopamine) Bile pigments Uric acid Antibiotics Morphine Saccharin
Reabsorbed Substances
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Glucose Amino acids Phosphate Sulfate Lactate Succinate Citrate
Filtration and Reabsorption of Water by the Kidneys
Filtration Resorption Urine Excretion L/day 170 168.5
1.5
mL/min 120 119 1
What does this mean in terms of dialysis?
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Purpose - removal of wastes from the body Kidney should be the ideal model for hemodialysis Water retention / removal Salt retention / removal Protein retention
Artificial Kidney
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Removes waste products from the blood by the use of an extracorporeal membrane process Waste products pass from the blood through the membrane into the dialysate
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Membrane Material
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Permeable to waste products
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Impermeable to essential blood components
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Sufficiently strong
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Compatible with blood
Mechanisms of Transport through the Membrane
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Diffusion (true dialysis)
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movement due to concentration gradient If concentration is higher in the blood and the species can pass through the membrane, transport occurs until the concentrations are equal
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Slow If dialysate concentration is higher, the flow goes toward the blood
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Convection
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Massive movement of fluid across membrane
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Fluid carries dissolved or suspended species that can pass through the membrane
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Usually as a result of fluid pressure (both positive and suction pressure)
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Principal means of water and electrolyte removal (ultrafiltration)
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Can also remove water by adding glucose to dialysate (osmotic gradient)
Membrane Materials
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Wettability - usually hydrophilic for transport of dissolved materials Permeability Mechanical strength Blood compatibility
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Recall from mass transfer:
J s
P M
c
c
1
s
J v
D dc dx
c
1
s
J v
J s = solute flux P M = diffusive permeability c = concentration difference c = average membrane conc s = reflection coefficient J v = volume flux
Design Considerations
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Should be:
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Efficient in removing toxic wastes Efficient in removing water (ultrafiltration or osmosis)
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Small priming volume (<500 mL) Low flow resistance on blood side Convenient, disposable, reliable, cheap
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Performance - Engineering Approach
Use of film theory model
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resistance to mass transfer in fluids is in thin stagnant films at solid surfaces
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Leads to concept of mass transfer coefficients Blood Dialysate
d
b
d
m
d
d
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Assume linear profiles in the films and in the membrane Define a partition coefficient
a a
C C M
B
C M C D
At steady state, the fluxes in the membrane and in the films are equal
At steady state, the fluxes in the membrane and in the films are equal
N
D B C B
d
B C B
D D C D
d
D C D
D M C M
d
M C M
N - weight of solute removed /time area D’s are diffusion coefficients
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Recall from mass transfer that concentrations in the membrane and in the films are difficult to measure When the system is at steady state we can manipulate this equation along with the partition coefficient to give an equation that is based on the easily measurable concentrations C B and C D
Overall concentration difference
C B
C D
C B
C B
C B
C D
Also
C B
C B
d
B N C D
C D
D B
d
D N D D
And using the definition of
a
C D
C D N
D M
d
M C M
C M
D M
d
M
a
C B
C D
C B
C B N
K o
C D
C D
C B
d
B
D B C D N N
d
D M M
a d
N M D M
a
K o
1 d
B D B
d
D M M
a d
D D D
d
D N D D
K o is the overall mass transfer coefficient It includes two fluid films and the membrane
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Note also that K o can be defined in terms of resistances to mass transfer
1
K o
R
R B
R M
R D
Analogous to electricity (and like heat transfer), resistances in series are additive R B R M R D represents limitation for small molecules represents limitation for large molecules can be neglected when high flowrate on dialysate side is used
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This is a model based on molecular mass transfer Gives concentrations and flux We are interested in the amount of waste that can be removed in a period of time (efficiency of the system) To do this we need to do an overall balance on the dialyzer
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Consider a differential element of the dialyzer Q D ,C D dW C D +dC D C B +dC B dx (dA)
dW
K o
C B
C D
dA
and
dW
Q D dC D
Q B dC B
Q B ,C B
Q B Q D
dW
Q Q D B
Q D dC D
Q B dC D
&
dW
Q B Q D
dW
Q B dC B
Q B dC D dW
1
Q B Q D
Q B
dC B
dC D
Q B d
C B
dW
Q B d
C
1
B
C D
Q B Q D
C D
Equating the dW’s
Q B d
C B
1
Q B C D Q D d
C C B B
C C D D
K
o
K o
1
Q B
C B
1
Q D C D
dA
dA
Integrate assuming constant K o
ln
C
C B Bo i
C Do C Di
1
Since Q B
1
Q D
K o
1
Q B C Bi
C Bo W
1
Q D
C
Do A
W C Di W W
K o K o A
C Bi A
log ln
C
Do mean C C Bi
Bo C Bo
C Do C Di
C Di
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K o describes performance of dialyzer Combines
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diffusivity of molecule
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permeability of membrane
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effects of flow (convection etc)
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Similar model to that obtained in heat transfer
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Performance -Clinical Approach
Clearance / dialysance - more clinical than fundamental Q B , C Bi C Bo C Do Q D , C Di
Clearance defined as:
C
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Q B C Bi
C Bo C Bi
W C Bi
W- weight of solute removed/time
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C * is volume of blood completely “cleared” of solute per unit time
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Maximum value of Q B
Dialysance
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Defined by:
D
*
Q B
C Bi C Bi
C Bo
C Di
C Bi W
C Di
Allows for possible presence of solute in inlet dialysate
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Extraction ratio
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Measurement of efficiency
E
C Bi C Bi
C Bo
C Di
Can show
E
z
1 exp exp
N N T T
1 1
z z
N T
K o A Q B z
Q B Q D
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If z is small (Q B
E
1 exp
N T
C Bi
C Bo C Bi
1 exp
K o A Q B
C Bo
C Bi
exp
K o Q B A
C
*
Q B
1 exp
K o Q B A
Assuming C di = 0
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Analysis for countercurrent flow Similar analysis for cocurrent flow with slightly different results
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Countercurrent flow more commonly used
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Assume
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Q B
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Q D
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= 200 mL/minute = high A = 1.0 m 2
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urea K o = 0.017 cm/minute
K o A
0 .
833
Q B C
* 200 1 exp 0 .
833 113 ml / min
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Time required for treatment
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Model patient as CSTR (exit conc. = conc. in tank - well mixed) Mass balance on patient – can show C Bo C Bi
V B dC Bi dt
Q B and know that
C Bo
C Bi
C Bo
C Bi
exp
K o Q B A
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Integrate to yield
C C Bo Bi C Bi
0 exp
Q B
exp
V B K o A Q B
1
t
C Bi
at
t
0
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Consider:
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C urea 0
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= 150 mg/dL Require C urea = 50 mg/dL
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Using previous data we find that required t is approximately 8 h
Hemofiltration
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Cleansing by ultrafiltration Materials removed from the blood by convection
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Analogous to glomerulus of natural kidney
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Features
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Same equipment as hemodialysis
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Leaky membrane required
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Water lost is replaced either before or after filter (physiologic solution)
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No dialysate needed
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Clearance less dependent on molecular weight - better for middle molecules
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Generally faster than hemodialysis
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Hemoperfusion / Hemoadsorption
Blood passed over bed of activated charcoal Waste materials adsorbed on charcoal No dialysate Relatively simple Little urea removal, no water removal Used in combination with hemodialysis / hemoperfusion