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 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 • • • • • • • Glucose Amino acids Phosphate Sulfate Lactate Succinate Citrate Filtration and Reabsorption of Water by the Kidneys L/day Filtration Resorption Urine Excretion 170 168.5 1.5 mL/min 120 119 1 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 CM  CM   dM N - weight of solute removed /time area D’s are diffusion coefficients • 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 C  C    C   C    C   C  CB  CD   B B   B D   D D       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   C   C    Nd M  B D    DM a dM N dDN  CB  CD    DB DM a DD N  K o C B  C D  1 o dBN dM dD K    DB DM a DD Ko is the overall mass transfer coefficient It includes two fluid films and the membrane dB • 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 dW CD+dCD CB+dCB dx (dA) QB,CB dW  K o C B  C D dA and dW  QD dC D  QB dC B  QB   QB    Q dW   Q QD dC D  QB dC D     D  D &  QB  dW    Q dW  QB dC B  QB dC D   D  QB  dW 1   Q   QB dC B  dC D   QB d C B  C D   D   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   Ko   Q  Q dA  CB  CD  D   B Integrate assuming constant Ko  CB i  CDo   1 1  A ln    Ko  Q Q  CBo  CDi   D   B  CBi  C Bo C Do  CDi 1 1 Since    QB QD W W      CBi  CDo   CBo  C Di  W  Ko A    CBi  CDo  ln   C C     Di   Bo   W  K o AC lo g mea n • 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 CDo Clearance defined as: CBo QD, CDi CBi  CBo W C  QB  CBi CBi * 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 CBi  CBo E CBi  CDi Can show 1  expN T 1  z  E z  expN T 1  z  Ko A NT  QB QB z QD • If z is small (QB