Hemodialysis and the Hemodialysis and the Artificial KidneyArtificial Kidney

Hemodialysis and the Hemodialysis and the Artificial KidneyArtificial Kidney

• Kidney failure - affects 200 000 Kidney failure - affects 200 000 patients worldwidepatients worldwide– 15 000 in Canada15 000 in Canada– Hamilton?Hamilton?

• Kidney failure - affects 200 000 Kidney failure - affects 200 000 patients worldwidepatients worldwide– 15 000 in Canada15 000 in Canada– Hamilton?Hamilton?

Arterial blood Venous blood

Waste

• What sort of things are excreted?What sort of things are excreted?– Urea - 30 g/dayUrea - 30 g/day– Creatinine - 2 g/dayCreatinine - 2 g/day– Salt - 15 g/daySalt - 15 g/day– Uric Acid - 0.7 g/dayUric Acid - 0.7 g/day– Water - 1500 mL/dayWater - 1500 mL/day– UnknownUnknown

• Kidney failureKidney failure– accumulation of wasteaccumulation of waste– acidosis, edema, hypertension, comaacidosis, edema, hypertension, coma

• What sort of things are excreted?What sort of things are excreted?– Urea - 30 g/dayUrea - 30 g/day– Creatinine - 2 g/dayCreatinine - 2 g/day– Salt - 15 g/daySalt - 15 g/day– Uric Acid - 0.7 g/dayUric Acid - 0.7 g/day– Water - 1500 mL/dayWater - 1500 mL/day– UnknownUnknown

• Kidney failureKidney failure– accumulation of wasteaccumulation of waste– acidosis, edema, hypertension, comaacidosis, edema, hypertension, coma

Kidney Structure and Function: Kidney Structure and Function: NephronsNephrons

Kidney Structure and Function: Kidney Structure and Function: NephronsNephrons

• Functional units of the kidneyFunctional units of the kidney• 1.2 million per kidney1.2 million per kidney• Filtration and removal of wastesFiltration and removal of wastes• Reabsorption of water, proteins, other essentials into the bloodReabsorption of water, proteins, other essentials into the blood

• Functional units of the kidneyFunctional units of the kidney• 1.2 million per kidney1.2 million per kidney• Filtration and removal of wastesFiltration and removal of wastes• Reabsorption of water, proteins, other essentials into the bloodReabsorption of water, proteins, other essentials into the blood

Actively Secreted SubstancesActively Secreted SubstancesActively Secreted SubstancesActively Secreted Substances

• HydroxybenzoatesHydroxybenzoates• HippuratesHippurates• Neutrotransmitters (dopamine)Neutrotransmitters (dopamine)• Bile pigmentsBile pigments• Uric acidUric acid• AntibioticsAntibiotics• MorphineMorphine• SaccharinSaccharin

• HydroxybenzoatesHydroxybenzoates• HippuratesHippurates• Neutrotransmitters (dopamine)Neutrotransmitters (dopamine)• Bile pigmentsBile pigments• Uric acidUric acid• AntibioticsAntibiotics• MorphineMorphine• SaccharinSaccharin

Reabsorbed SubstancesReabsorbed SubstancesReabsorbed SubstancesReabsorbed Substances

• GlucoseGlucose• Amino acidsAmino acids• PhosphatePhosphate• SulfateSulfate• LactateLactate• SuccinateSuccinate• CitrateCitrate

• GlucoseGlucose• Amino acidsAmino acids• PhosphatePhosphate• SulfateSulfate• LactateLactate• SuccinateSuccinate• CitrateCitrate

Filtration and Reabsorption Filtration and Reabsorption of Water by the Kidneysof Water by the Kidneys

Filtration and Reabsorption Filtration and Reabsorption of Water by the Kidneysof Water by the Kidneys

L/day mL/min

Filtration 170 120

Resorption 168.5 119

UrineExcretion

1.5 1

L/day mL/min

Filtration 170 120

Resorption 168.5 119

UrineExcretion

1.5 1

What does this mean in What does this mean in terms of dialysis?terms of dialysis?

What does this mean in What does this mean in terms of dialysis?terms of dialysis?

• Purpose - removal of wastes from the Purpose - removal of wastes from the bodybody

• Kidney should be the ideal model for Kidney should be the ideal model for hemodialysishemodialysis

• Water retention / removalWater retention / removal• Salt retention / removalSalt retention / removal• Protein retentionProtein retention

• Purpose - removal of wastes from the Purpose - removal of wastes from the bodybody

• Kidney should be the ideal model for Kidney should be the ideal model for hemodialysishemodialysis

• Water retention / removalWater retention / removal• Salt retention / removalSalt retention / removal• Protein retentionProtein retention

Artificial KidneyArtificial KidneyArtificial KidneyArtificial Kidney

• Removes waste products from the Removes waste products from the blood by the use of an extracorporeal blood by the use of an extracorporeal membrane processmembrane process

• Waste products pass from the blood Waste products pass from the blood through the membrane into the through the membrane into the dialysatedialysate

• Removes waste products from the Removes waste products from the blood by the use of an extracorporeal blood by the use of an extracorporeal membrane processmembrane process

• Waste products pass from the blood Waste products pass from the blood through the membrane into the through the membrane into the dialysatedialysate

• Membrane MaterialMembrane Material– Permeable to waste productsPermeable to waste products– Impermeable to essential blood Impermeable to essential blood

componentscomponents– Sufficiently strongSufficiently strong– Compatible with bloodCompatible with blood

• Membrane MaterialMembrane Material– Permeable to waste productsPermeable to waste products– Impermeable to essential blood Impermeable to essential blood

componentscomponents– Sufficiently strongSufficiently strong– Compatible with bloodCompatible with blood

Mechanisms of Transport Mechanisms of Transport through the Membranethrough the Membrane

Mechanisms of Transport Mechanisms of Transport through the Membranethrough the Membrane

• Diffusion (true dialysis)Diffusion (true dialysis)– movement due to concentration gradientmovement due to concentration gradient– If concentration is higher in the blood and the If concentration is higher in the blood and the

species can pass through the membrane, species can pass through the membrane, transport occurs until the concentrations are transport occurs until the concentrations are equalequal

– SlowSlow– If dialysate concentration is higher, the flow If dialysate concentration is higher, the flow

goes toward the bloodgoes toward the blood

• Diffusion (true dialysis)Diffusion (true dialysis)– movement due to concentration gradientmovement due to concentration gradient– If concentration is higher in the blood and the If concentration is higher in the blood and the

species can pass through the membrane, species can pass through the membrane, transport occurs until the concentrations are transport occurs until the concentrations are equalequal

– SlowSlow– If dialysate concentration is higher, the flow If dialysate concentration is higher, the flow

goes toward the bloodgoes toward the blood

• ConvectionConvection– Massive movement of fluid across Massive movement of fluid across

membranemembrane– Fluid carries dissolved or suspended Fluid carries dissolved or suspended

species that can pass through the species that can pass through the membranemembrane

– Usually as a result of fluid pressure Usually as a result of fluid pressure (both positive and suction pressure)(both positive and suction pressure)

– Principal means of water and electrolyte Principal means of water and electrolyte removal (ultrafiltration)removal (ultrafiltration)

– Can also remove water by adding Can also remove water by adding glucose to dialysate (osmotic gradient)glucose to dialysate (osmotic gradient)

• ConvectionConvection– Massive movement of fluid across Massive movement of fluid across

membranemembrane– Fluid carries dissolved or suspended Fluid carries dissolved or suspended

species that can pass through the species that can pass through the membranemembrane

– Usually as a result of fluid pressure Usually as a result of fluid pressure (both positive and suction pressure)(both positive and suction pressure)

– Principal means of water and electrolyte Principal means of water and electrolyte removal (ultrafiltration)removal (ultrafiltration)

– Can also remove water by adding Can also remove water by adding glucose to dialysate (osmotic gradient)glucose to dialysate (osmotic gradient)

Membrane MaterialsMembrane MaterialsMembrane MaterialsMembrane Materials

• Wettability - usually hydrophilic for Wettability - usually hydrophilic for transport of dissolved materialstransport of dissolved materials

• PermeabilityPermeability

• Mechanical strengthMechanical strength

• Blood compatibilityBlood compatibility

• Wettability - usually hydrophilic for Wettability - usually hydrophilic for transport of dissolved materialstransport of dissolved materials

• PermeabilityPermeability

• Mechanical strengthMechanical strength

• Blood compatibilityBlood compatibility

• Recall from mass transfer:Recall from mass transfer:• Recall from mass transfer:Recall from mass transfer:

vs

vsMs

Jcdx

dcD

JccPJ

1

1

Js = solute fluxPM = diffusive permeabilityc = concentration differencec = average membrane concs = reflection coefficientJv = volume flux

Design ConsiderationsDesign ConsiderationsDesign ConsiderationsDesign Considerations

• Should be:Should be:– Efficient in removing toxic wastesEfficient in removing toxic wastes– Efficient in removing water Efficient in removing water

(ultrafiltration or osmosis)(ultrafiltration or osmosis)– Small priming volume (<500 mL)Small priming volume (<500 mL)– Low flow resistance on blood sideLow flow resistance on blood side– Convenient, disposable, reliable, cheapConvenient, disposable, reliable, cheap

• Should be:Should be:– Efficient in removing toxic wastesEfficient in removing toxic wastes– Efficient in removing water Efficient in removing water

(ultrafiltration or osmosis)(ultrafiltration or osmosis)– Small priming volume (<500 mL)Small priming volume (<500 mL)– Low flow resistance on blood sideLow flow resistance on blood side– Convenient, disposable, reliable, cheapConvenient, disposable, reliable, cheap

Performance - Engineering Performance - Engineering ApproachApproach

Performance - Engineering Performance - Engineering ApproachApproach

• Use of film theory modelUse of film theory model– resistance to mass transfer in fluids is resistance to mass transfer in fluids is

in thin stagnant films at solid surfacesin thin stagnant films at solid surfaces– Leads to concept of mass transfer Leads to concept of mass transfer

coefficientscoefficients

• Use of film theory modelUse of film theory model– resistance to mass transfer in fluids is resistance to mass transfer in fluids is

in thin stagnant films at solid surfacesin thin stagnant films at solid surfaces– Leads to concept of mass transfer Leads to concept of mass transfer

coefficientscoefficients

Blood Dialysate

mb d

• Assume linear profiles in the films Assume linear profiles in the films and in the membraneand in the membrane

• Define a partition coefficient Define a partition coefficient

• Assume linear profiles in the films Assume linear profiles in the films and in the membraneand in the membrane

• Define a partition coefficient Define a partition coefficient

D

M

B

M

C

C

C

C

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

M

MMM

D

DDD

B

BBB

CCD

CCD

CCDN

N - weight of solute removed /time areaD’s are diffusion coefficients

• Recall from mass transfer that Recall from mass transfer that concentrations in the membrane and in concentrations in the membrane and in the films are difficult to measurethe films are difficult to measure

• When the system is at steady state we When the system is at steady state we can manipulate this equation along with can manipulate this equation along with the partition coefficient to give an the partition coefficient to give an equation that is based on the easily equation that is based on the easily measurable concentrations Cmeasurable concentrations CB B and Cand CDD

• Recall from mass transfer that Recall from mass transfer that concentrations in the membrane and in concentrations in the membrane and in the films are difficult to measurethe films are difficult to measure

• When the system is at steady state we When the system is at steady state we can manipulate this equation along with can manipulate this equation along with the partition coefficient to give an the partition coefficient to give an equation that is based on the easily equation that is based on the easily measurable concentrations Cmeasurable concentrations CB B and Cand CDD

Overall concentration difference

DDDBBBDB CCCCCCCC

Also

D

DDD

B

BBB

D

NCC

D

NCC

And using the definition of

DB

M

MMM

M

M CCD

CCD

N

D

D

M

M

B

Bo

DBo

D

D

M

M

B

BDB

M

MDB

DDDK

CCKN

D

N

D

N

D

NCC

D

NCC

1

Ko is the overall mass transfer coefficientIt includes two fluid films and the membrane

• Note also that KNote also that Koo can be defined in terms can be defined in terms

of resistances to mass transferof resistances to mass transfer• Note also that KNote also that Koo can be defined in terms can be defined in terms

of resistances to mass transferof resistances to mass transfer

DMBo

RRRRK

1

Analogous to electricity (and like heat transfer), resistances in series are additiveRB represents limitation for small moleculesRM represents limitation for large moleculesRD can be neglected when high flowrate on dialysate side is used

• This is a model based on molecular This is a model based on molecular mass transfermass transfer

• Gives concentrations and fluxGives concentrations and flux

• We are interested in the amount of We are interested in the amount of waste that can be removed in a waste that can be removed in a period of time (efficiency of the period of time (efficiency of the system)system)

• To do this we need to do an overall To do this we need to do an overall balance on the dialyzerbalance on the dialyzer

• This is a model based on molecular This is a model based on molecular mass transfermass transfer

• Gives concentrations and fluxGives concentrations and flux

• We are interested in the amount of We are interested in the amount of waste that can be removed in a waste that can be removed in a period of time (efficiency of the period of time (efficiency of the system)system)

• To do this we need to do an overall To do this we need to do an overall balance on the dialyzerbalance on the dialyzer

• Consider a differential element of the Consider a differential element of the dialyzerdialyzer

• Consider a differential element of the Consider a differential element of the dialyzerdialyzer

QB,CBCB+dCB dx

(dA)

dWQD,CD CD+dCD

BBDD

DBo

dCQdCQdW

dACCKdW

and

D

B

DBB

DBBDBBD

B

DBBBD

B

DBDDD

B

D

B

QQCCd

QdW

CCdQdCdCQQ

QdW

dCQdCQdWQ

QdW

dCQdCQQ

QdW

Q

Q

1

1

&

Equating the dW’s

dA

QQK

CC

CCd

dACCK

QQCCd

Q

DBo

DB

DB

DBo

D

B

DBB

11

1

Integrate assuming constant Ko

meano

DiBo

DoBi

DiBoDoBio

DiDoBoBi

DB

DBo

DiBo

DoiB

CAKW

CCCC

CCCCAKW

W

CC

W

CC

QQSince

AQQ

KCC

CC

log

ln

11

11ln

• KKoo describes performance of dialyzer describes performance of dialyzer

• CombinesCombines– diffusivity of moleculediffusivity of molecule– permeability of membranepermeability of membrane– effects of flow (convection etc)effects of flow (convection etc)

• Similar model to that obtained in heat Similar model to that obtained in heat transfertransfer

• KKoo describes performance of dialyzer describes performance of dialyzer

• CombinesCombines– diffusivity of moleculediffusivity of molecule– permeability of membranepermeability of membrane– effects of flow (convection etc)effects of flow (convection etc)

• Similar model to that obtained in heat Similar model to that obtained in heat transfertransfer

Performance -Clinical Performance -Clinical ApproachApproach

Performance -Clinical Performance -Clinical ApproachApproach

• Clearance / dialysance - more clinical Clearance / dialysance - more clinical than fundamentalthan fundamental

• Clearance / dialysance - more clinical Clearance / dialysance - more clinical than fundamentalthan fundamental

QB, CBi CBo

QD, CDiCDo

Clearance defined as:

BiBi

BoBiB C

W

C

CCQC

*

W- weight of solute removed/time

• CC** is volume of blood completely is volume of blood completely “cleared” of solute per unit time“cleared” of solute per unit time

• Maximum value of QMaximum value of QBB

• CC** is volume of blood completely is volume of blood completely “cleared” of solute per unit time“cleared” of solute per unit time

• Maximum value of QMaximum value of QBB

DialysanceDialysanceDialysanceDialysance

• Defined by:Defined by:• Defined by:Defined by:

DiBiDiBi

BoBiB CC

W

CC

CCQD

*

Allows for possible presence of solute in inlet dialysate

• Extraction ratioExtraction ratio– Measurement of efficiencyMeasurement of efficiency

• Extraction ratioExtraction ratio– Measurement of efficiencyMeasurement of efficiency

DiBi

BoBi

CC

CCE

Can show

D

B

B

oT

T

T

Q

Qz

Q

AKN

zNz

zNE

1exp

1exp1

• If z is small (QIf z is small (QBB<Q<QDD))• If z is small (QIf z is small (QBB<Q<QDD))

B

oB

B

oBiBo

B

o

Bi

BoBi

T

Q

AKQC

Q

AKCC

Q

AK

C

CC

NE

exp1

exp

exp1

exp1

*

Assuming Cdi = 0

• Analysis for countercurrent flowAnalysis for countercurrent flow

• Similar analysis for cocurrent flow Similar analysis for cocurrent flow with slightly different resultswith slightly different results

• Countercurrent flow more commonly Countercurrent flow more commonly usedused

• Analysis for countercurrent flowAnalysis for countercurrent flow

• Similar analysis for cocurrent flow Similar analysis for cocurrent flow with slightly different resultswith slightly different results

• Countercurrent flow more commonly Countercurrent flow more commonly usedused

• Assume Assume – QQBB = 200 mL/minute = 200 mL/minute

– QQDD = high = high

– A = 1.0 mA = 1.0 m22

– urea Kurea Koo = 0.017 cm/minute = 0.017 cm/minute

• Assume Assume – QQBB = 200 mL/minute = 200 mL/minute

– QQDD = high = high

– A = 1.0 mA = 1.0 m22

– urea Kurea Koo = 0.017 cm/minute = 0.017 cm/minute

min/ml113

833.0exp1200

833.0

*

C

Q

AK

B

o

• Time required for treatmentTime required for treatment– Model patient as CSTR (exit conc. = Model patient as CSTR (exit conc. =

conc. in tank - well mixed)conc. in tank - well mixed)– Mass balance on patient – can showMass balance on patient – can show

• Time required for treatmentTime required for treatment– Model patient as CSTR (exit conc. = Model patient as CSTR (exit conc. =

conc. in tank - well mixed)conc. in tank - well mixed)– Mass balance on patient – can showMass balance on patient – can show

CBi

CBo

B

oBiBo

BiBoBBi

B

Q

AKCC

thatknowand

CCQdt

dCV

exp

• Integrate to yieldIntegrate to yield• Integrate to yieldIntegrate to yield

0at

1exp

exp

0

tCC

V

tQAK

Q

C

C

BiBi

B

B

oB

Bi

Bo

• Consider:Consider:– CCureaurea

00 = 150 mg/dL = 150 mg/dL

– Require CRequire Cureaurea = 50 mg/dL = 50 mg/dL

– Using previous data we find that Using previous data we find that required t is approximately 8 hrequired t is approximately 8 h

• Consider:Consider:– CCureaurea

00 = 150 mg/dL = 150 mg/dL

– Require CRequire Cureaurea = 50 mg/dL = 50 mg/dL

– Using previous data we find that Using previous data we find that required t is approximately 8 hrequired t is approximately 8 h

HemofiltrationHemofiltrationHemofiltrationHemofiltration

• Cleansing by ultrafiltrationCleansing by ultrafiltration

• Materials removed from the blood by Materials removed from the blood by convectionconvection

• Analogous to glomerulus of natural Analogous to glomerulus of natural kidneykidney

• Cleansing by ultrafiltrationCleansing by ultrafiltration

• Materials removed from the blood by Materials removed from the blood by convectionconvection

• Analogous to glomerulus of natural Analogous to glomerulus of natural kidneykidney

• FeaturesFeatures– Same equipment as hemodialysisSame equipment as hemodialysis– Leaky membrane requiredLeaky membrane required– Water lost is replaced either before or Water lost is replaced either before or

after filter (physiologic solution)after filter (physiologic solution)– No dialysate neededNo dialysate needed– Clearance less dependent on molecular Clearance less dependent on molecular

weight - better for middle moleculesweight - better for middle molecules– Generally faster than hemodialysisGenerally faster than hemodialysis

• FeaturesFeatures– Same equipment as hemodialysisSame equipment as hemodialysis– Leaky membrane requiredLeaky membrane required– Water lost is replaced either before or Water lost is replaced either before or

after filter (physiologic solution)after filter (physiologic solution)– No dialysate neededNo dialysate needed– Clearance less dependent on molecular Clearance less dependent on molecular

weight - better for middle moleculesweight - better for middle molecules– Generally faster than hemodialysisGenerally faster than hemodialysis

Hemoperfusion / Hemoperfusion / HemoadsorptionHemoadsorptionHemoperfusion / Hemoperfusion / HemoadsorptionHemoadsorption

• Blood passed over bed of activated Blood passed over bed of activated charcoalcharcoal

• Waste materials adsorbed on charcoalWaste materials adsorbed on charcoal• No dialysateNo dialysate• Relatively simpleRelatively simple• Little urea removal, no water removalLittle urea removal, no water removal• Used in combination with hemodialysis / Used in combination with hemodialysis /

hemoperfusionhemoperfusion

• Blood passed over bed of activated Blood passed over bed of activated charcoalcharcoal

• Waste materials adsorbed on charcoalWaste materials adsorbed on charcoal• No dialysateNo dialysate• Relatively simpleRelatively simple• Little urea removal, no water removalLittle urea removal, no water removal• Used in combination with hemodialysis / Used in combination with hemodialysis /

hemoperfusionhemoperfusion