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Sorption kinetics in haemoperfusion columns. Part 2: modelling column performance

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Abstract

The relative influences of the normalised adsorption, mass transfer and hydrodynamic parameters on the performance of haemoperfusion columns are quantified using a lumped parameter, mass transfer model, validatedin vitro. The effects of patient pharmacokinetics and protein binding are then investigated using the model. In addition, the solution of the distributed parameter model of an adsorber column, at small times, is used to emphasise the role of the external diffusion resistance in determining column performance for both free and protein bound toxins. This rationale facilitates a logical comparison between haemoperfusion and haemodialysis on the basis of the controlling mass transfer mechanisms in each technique.

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Abbreviations

A m :

Membrane area of haemodialyser

a p :

Specific surface area of sorbent

Cl :

Clearance=Q b(1−C out/Cin)

c n :

Bulk concentration in fluid phase ofnth cell

c *n :

Fluid phase concentration at sorbent surface

c 0 :

Normalising fluid phase concentration

D a :

Axial dispersion coefficient

D s :

Solid diffusivity in sorbent

d p :

Diameter of sorbent particle

K :

Protein binding coefficient

K 1 :

Affinity constant in Langmuir isotherm

k :

Mass transfer coefficient

l :

Length of column

M :

Mass of sorbent

N e :

Number of external mass transfer units=(k eap(l−ε)nv/Qb)

N o :

Number of mass transfer units in haemodialyser=(k tAm/Qb)

N s :

Number of intraparticle mass transfer units=(60D sΛnv/d 2p Qb

n :

Number of cells in lumped-parameter model

Pe l :

Longitudinal Pectlet number=U sl/Da

Q :

Volumetric flow rate

q m :

Maximum solid-phase concentration in Langmuir isotherm

q n :

Bulk solid-phase concentration

q *n :

Solid phase concentration at sorbent surface

q o :

Normalising solid phase concentration=q m(K1 c 0/(1+K lc0))

R :

Isotherm shape parameter=1/(1+K lco)

Re :

Reynolds number=U sdp/v

RR :

Recircular ratio =ρ bnqO/VpcO

Sc :

Schmidt number=v/D

Sh :

Sherwood number=kd p/D

T :

Throughput (normalised time) parameter=(Q bt/nvΛ)

t :

Real time

U s :

Superficial velocity

V p :

Volume of single-pool patient model

v :

Total volume ofnth cell

X n :

Normalised fluid phase concentration=(c n/co)

X p :

Normalised toxin concentration in patient

Y n :

Normalised solid phase concentration=(q n/qo)

Z :

Qb/Qd

ε:

Bed porosity

Λ:

Adsorption coefficient=ρ bqo/co

μ* :

Volume fraction water in blood

v :

Kinematic viscosity

ρ:

Density

ρ * :

Protein binding coefficient

ψ q :

Correction factor (Hall et al., 1996)

b :

Blood or bulk

d :

Dialysate

e :

External

in :

Inlet concentration to column

m :

Membrane

o :

Standard value

out :

Outlet concentration from column

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Authors and Affiliations

  1. Bioengineering Unit, University of Strathclyde, Glasgow, Scotland

    D. F. Radcliffe & J. D. S. Gaylor

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  1. D. F. Radcliffe
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  2. J. D. S. Gaylor
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Radcliffe, D.F., Gaylor, J.D.S. Sorption kinetics in haemoperfusion columns. Part 2: modelling column performance. Med. Biol. Eng. Comput. 19, 627–637 (1981). https://doi.org/10.1007/BF02442778

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  • DOI: https://doi.org/10.1007/BF02442778

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