1. Transport phenomena in biological systems
ICCBPE 2015
Transport phenomena in biological systems
Babol University of Technology
«بسمه‌تعالي»
Hemodialysis and the Artificial Kidney
Prof. Ghasem D. Najafpour
Distinguished Scholar from Noshirvani University of Technology
Head of Biotechnology Research Center, Babol, Iran

2. What is the expected job from kidney? Urea: 30 g/day
Creatinine: 2 g/day
Salt: 15 g/day
Uric Acid: 0.7 g/day
Water: 1500 ml/day
Unknowns?
Symptoms of kidney failures
accumulation of waste
acidosis, edema, hypertension, coma
Filtration and removal of wastes
Reabsorption of water, proteins, other essentials into blood 1

3. Reabsorbed Substances
Glucose
Amino acids
Phosphate
Sulfate
Lactate
Succinate
Citrate 1

4. Filtration and Reabsorption of Water by the Kidneys1

5. 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 1

6. 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 1

7. Membrane Material Permeable to waste products
Impermeable to essential blood components
Sufficiently strong
Compatible with blood 1

8. 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 1

9. 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)
How does adding glucose to the dialysate work in terms of water removal? 1

10. Membrane Materials
Wettability - usually hydrophilic for transport of dissolved materials
Permeability
Mechanical strength
Blood compatibility
Discuss wettability - what is wettable? How might this affect the transport properties of the membrane? 1

11. Recall from mass transfer:
Js = solute flux
PM = diffusive permeability
Dc = concentration difference
c = average membrane conc
ss = reflection coefficient
Jv = volume flux
First term represents diffusive mass transfer, second term represents convective mass transfer
What are the units of these terms?
J - g/cm2s
PM - cm/s
Jv - cm3/cm2 s 1

12. 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
Thin, stagnant films are assumed to be adjacent to fully mixed bulk regions. Of course this is not literally true -rather the degree of mixing decreases gradually as we move from bulk towards the surface. Mass transfer near the wall only occurs by diffusion since mixing is minimal and there is no fluid motion perpendicular to the surface
Draw in concentration profiles for each of the different layers - Remember partitioning between different phases
Linear profiles are normal for steady state diffusion across a thin film db dm dd 1

13. Assume linear profiles in the films and in the membrane
Define a partition coefficient a
At steady state, the fluxes in the membrane and in the films are equal
Why would the partition coefficient between the blood and membrane phases and between the membrane and dialysate phases be equal? 1

14. N - weight of solute removed /time area D’s are diffusion coefficients
At steady state, the fluxes in the membrane and in the films are equal
N - weight of solute removed /time area
D’s are diffusion coefficients 1

15. 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 1

16. Overall concentration difference
Also
And using the definition of a 1

17. Ko is the overall mass transfer coefficient
It includes two fluid films and the membrane 1

18. RB represents limitation for small molecules
Note also that Ko can be defined in terms of resistances to mass transfer
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
Also note that CB and CD will vary with position - CB is high at the arterial end and low at the exit. CD will depend on whether using cocurrent or countercurrent flow. 1

19. 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 1

20. Consider a differential element of the dialyzer
QD,CD
CD+dCD dW
CB+dCB
QB,CB dx
(dA)
dW is the mass transferred in a differential element per unit time 1

21. 1

22. Integrate assuming constant Ko
Equating the dW’s
Integrate assuming constant Ko 1

23. W = DCxQ 1

24. 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 1

25. Performance -Clinical Approach
Clearance / dialysance - more clinical than fundamental
QB, CBi
CBo
CDo
QD, CDi
Clearance defined as:
W- weight of solute removed/time 1

26. C* is volume of blood completely “cleared” of solute per unit time
Maximum value of QB 1

27. Dialysance Defined by:
Allows for possible presence of solute in inlet dialysate 1

28. Extraction ratio Measurement of efficiency Can show 1
E is fraction of solute entering which is removed
NT gives measure of mass transfer capabilities of dialyzer 1

29. If z is small (QB<QD)
Assuming Cdi = 0 1

30. Analysis for countercurrent flow
Similar analysis for cocurrent flow with slightly different results
Countercurrent flow more commonly used 1

31. Assume QB = 200 mL/minute QD = high A = 1.0 m2
urea Ko = cm/minute 1

32. Time required for treatment
Model patient as CSTR (exit conc. = conc. in tank - well mixed)
Mass balance on patient – can show
CBo
CBi 1

33. Integrate to yield 1

34. Consider: Curea0 = 150 mg/dL Require Curea = 50 mg/dL
Using previous data we find that required t is approximately 8 h
Expect to know and to be able to use these relationships 1

35. Hemofiltration Cleansing by ultrafiltration
Materials removed from the blood by convection
Analogous to glomerulus of natural kidney 1

36. 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 1

37. 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
Why do we need a small priming volume?
Why do we want a low flow resistance on the blood side? 1

38. Artificial kidney (hollow fiber hemodiafilter)1

39. 1