Download Hemodialysis and the Artificial Kidney

Hemodialysis and the
Artificial Kidney
• Kidney failure - affects 200 000
patients worldwide
– 15 000 in Canada
– Hamilton?
Arterial blood
Venous blood
Waste
• What sort of things are excreted?
– Urea - 30 g/day
– Creatinine - 2 g/day
– Salt - 15 g/day
– Uric Acid - 0.7 g/day
– Water - 1500 mL/day
– Unknown
• Kidney failure
– accumulation of waste
– acidosis, edema, hypertension, coma
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
•
•
•
•
•
•
•
•
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
L/day
mL/min
170
120
Resorption
168.5
119
Urine
Excretion
1.5
1
Filtration
What does this mean in
terms of dialysis?
• 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
• 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
• Membrane Material
– Permeable to waste products
– Impermeable to essential blood
components
– Sufficiently strong
– Compatible with blood
Mechanisms of Transport
through the Membrane
• Diffusion (true dialysis)
– 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
– Slow
– If dialysate concentration is higher, the flow
goes toward the blood
• Convection
– Massive movement of fluid across
membrane
– Fluid carries dissolved or suspended
species that can pass through the
membrane
– Usually as a result of fluid pressure
(both positive and suction pressure)
– Principal means of water and electrolyte
removal (ultrafiltration)
– Can also remove water by adding
glucose to dialysate (osmotic gradient)
Membrane Materials
• Wettability - usually hydrophilic for
transport of dissolved materials
• Permeability
• Mechanical strength
• Blood compatibility
• Recall from mass transfer:
J s  PM c  c 1   s J v
dc
 D  c 1   s J v
dx
Js = solute flux
PM = diffusive permeability
c = concentration difference
c = average membrane conc
s = reflection coefficient
Jv = volume flux
Design Considerations
• Should be:
– Efficient in removing toxic wastes
– Efficient in removing water
(ultrafiltration or osmosis)
– Small priming volume (<500 mL)
– Low flow resistance on blood side
– Convenient, disposable, reliable, cheap
Performance - Engineering
Approach
• Use of film theory model
– resistance to mass transfer in fluids is
in thin stagnant films at solid surfaces
– Leads to concept of mass transfer
coefficients
Blood
Dialysate
db dm
dd
• Assume linear profiles in the films
and in the membrane
• Define a partition coefficient a


CM
CM
a



CB
CD
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  DB
CB  CB
dB

 DD

CD  CD
dD
 DM
N - weight of solute removed /time area
D’s are diffusion coefficients

CM  CM
dM

• 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 CB and CD
Overall concentration difference




CB  CD   CB  CB    CB  CD    CD  CD 

 
 

Also
 C  C    d BN
B
 B
 DB
 C   C   d D N
D
D

 DD
And using the definition of a
DM  
  DM a  

N
 CM  CM  
 CB  CD 
 dM 

dM 

  Nd M

  CB  CD  

 DM a
dBN
dM N dDN
 CB  CD 


DB DM a DD
N  K o CB  C D 
dM
dD
K 


DB DM a DD
1
o
dB
Ko is the overall mass transfer coefficient
It includes two fluid films and the membrane
• Note also that Ko can be defined in terms
of resistances to mass transfer
1
 R  RB  RM  RD
Ko
Analogous to electricity (and like heat transfer),
resistances in series are additive
RB represents limitation for small molecules
RM represents limitation for large molecules
RD can be neglected when high flowrate on dialysate
side is used
• 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
• Consider a differential element of the
dialyzer
QD,CD
CB+dCB
dW
dx
(dA)
dW  K o CB  CD dA
and
dW  QD dCD  QB dCB
CD+dCD
QB,CB
 QB 
 QB 
dW  
QD dC D  QB dC D
 
 QD 
 QD 
&
 QB 
dW  QB dC B  QB dC D
dW  
 QD 
 QB 
  QB dC B  dC D   QB d C B  C D 
dW 1 
 QD 
d C B  C D 
 dW  QB
QB
1
QD
Equating the dW’s
d C B  C D 
QB
 K o C B  C D dA
QB
1
QD
 1
d C B  C D 
1 
dA
 K o 

CB  CD 
 QB QD 
Integrate assuming constant Ko
 C B i  C Do 
 1
1 
 A
ln 

  K o 
 QB QD 
 C Bo  C Di  
C Bi  C Bo C Do  C Di
1
1
Since



QB QD
W
W





C Bi  C Do   C Bo  C Di  

W  Ko A


 C Bi  C Do 

ln 




 C Bo  C Di 
W  K o AC logmean
• Ko describes performance of dialyzer
• Combines
– diffusivity of molecule
– permeability of membrane
– effects of flow (convection etc)
• Similar model to that obtained in heat
transfer
Performance -Clinical
Approach
• Clearance / dialysance - more clinical
than fundamental
QB, CBi
CBo
CDo
QD, CDi
Clearance defined as:
C Bi  C Bo W
C  QB

C Bi
C Bi
*
W- weight of solute removed/time
• C* is volume of blood completely
“cleared” of solute per unit time
• Maximum value of QB
Dialysance
• Defined by:
 CBi  CBo 
W
D  QB 

 CBi  CDi  CBi  CDi
*
Allows for possible presence of solute in inlet dialysate
• Extraction ratio
– Measurement of efficiency
C Bi  C Bo
E
C Bi  C Di
Can show
1  exp NT 1  z 
E
z  exp NT 1  z 
Ko A
NT 
QB
QB
z
QD
• If z is small (QB<QD)
E  1  exp  N T 
 Ko A 
C Bi  C Bo

 1  exp  
C Bi
 QB 
C Bo
 Ko A 

 C Bi exp  
 QB 

 K o A 

C  QB 1  exp  
 QB 

*
Assuming Cdi = 0
• Analysis for countercurrent flow
• Similar analysis for cocurrent flow
with slightly different results
• Countercurrent flow more commonly
used
• Assume
– QB = 200 mL/minute
– QD = high
– A = 1.0 m2
– urea Ko = 0.017 cm/minute
Ko A
 0.833
QB
C  200  1  exp  0.833
*
 113 ml / min
• Time required for treatment
– Model patient as CSTR (exit conc. =
conc. in tank - well mixed)
– Mass balance on patient – can show
CBo
CBi
dC Bi
VB
 QB C Bo  C Bi 
dt
and know that
C Bo
 Ko A 

 C Bi exp  
 QB 
• Integrate to yield
C Bo
C Bi
   Ko A   
  1t 
 QB exp  
 QB   


 exp 

VB




C Bi  C Bi at t  0
0
• Consider:
– Curea0 = 150 mg/dL
– Require Curea = 50 mg/dL
– Using previous data we find that
required t is approximately 8 h
Hemofiltration
• Cleansing by ultrafiltration
• Materials removed from the blood by
convection
• Analogous to glomerulus of natural
kidney
• Features
– Same equipment as hemodialysis
– Leaky membrane required
– Water lost is replaced either before or
after filter (physiologic solution)
– No dialysate needed
– Clearance less dependent on molecular
weight - better for middle molecules
– Generally faster than hemodialysis
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