Kinetics of ultrafiltration hemodialysis

Abstract

The expressions of Wolfet al. (1951) and Renkin (1956) for the kinetics of artificial kidneys are generalized to include the effects of filtration. IfB is the bath volume,b the relevant volume of distribution,f the filtration rate,t the time, andA ₀,B ₀,b ₀ representA, B, andb at timet=0, then the plasma concentrationA is given by

$$\frac{A}{{A_0 }} = \frac{{B_0 }}{{B_0 + b_0 }}e^{ - \frac{{\left( {B_0 + b_0 } \right)}}{{B_0 }}\frac{{D_f }}{{b_0 }}K\left( {ft} \right)t} + \frac{{b_0 }}{{B_0 + b_0 }}$$

whereD _f is a rate constant, andK(ft) is given by

$$K\left( {ft} \right) = \frac{1}{{B_0 + b_0 }}\sum\limits_{M = 0}^\infty {\frac{{B_0 ^{M + 1} + \left( { - 1} \right)^M b_0 ^{M + 1} }}{{\left( {M + 1} \right)B_0 ^M b_0 ^M }}} \left( {ft} \right)^M = 1 + \frac{{B_0 - b_0 }}{{2B_0 b_0 }}ft + \ldots $$

Lettinga ₀ denote the flow rate at the entrane to the dialysis tubing,f the net rate of filtration,P the permeability,S the surface area,V the volume of fluid in the dialysis tubing, andt _c the circulation time of the fluid through the dialysis tubing, thenD _f is given by

$$D_f = \left( {a_0 - f} \right)\left( {1 - e^{ - \frac{{PS}}{V}t_c } } \right)$$

Whenf=0,D _f reduces to the ordinary dialysance constant.

These corrections to the filtration-free case are small when considering an adult male body volume together with the parameters of present day artificial kidneys.