**2. Theoretical principles**

The connection between the dialyser's technical parameters and the flow rates involved (QB, QD in the counter current flow) is based on the following relationship [1]:

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1 / ln <sup>a</sup> (1 / ) 1 / b (1 / ) *B D O B D B O B Q KQ K A Q Q KQ <sup>K</sup> K A K Q* é ù - <sup>=</sup> ê ú - - ë û <sup>=</sup> - (1)

For QB=QD the following applies: *KO <sup>A</sup>*<sup>=</sup> *<sup>K</sup>* 1 − *K* / *QB*

where *Ko* is the "overall mass transfer coefficient" and *A* is the dialyser membrane surface area.

In dialysis log sheets, the *KoA*-value is usually recorded for urea, thus allowing the calculation of urea-clearance in relation to blood and dialysate flow rates.

**Figure 1.** Dependence of clearance K on the flow rates of blood QB and dialysate QD (KoA=1000 ml/min)

Fig. 1 shows how clearance rate K, derived from the KoA value for a low molecular substance (urea), changes in relation to blood flow rates, with the relationship demonstrated at different dialysate flow rates, and for a high-flux dialyser. At low dialysate flow rates, the dialysate compartment soon becomes saturated, leading to a large reduction in the concentration gradient. This in turn means that an increase in blood flow will no longer produce a substantial improvement in the rate of clearance. It is only when the dialysate flow rate is high enough for the substance in question to be removed quickly from the dialysate chamber that a higher blood flow rate can produce substantial improvements in the rate of clearance. This is effectively only ever the case when the dialysate flow rate QD is at least 1.5…2.0 times as high as the blood flow rate, QB.

This theoretical relationship requires the KoA value to be constant for all dialysate and blood flow rates. This does of course not apply in practice in cases where the total surface area of the dialyser's fibre bundle is not completely bathed in dialysate. This may happen when low dialysate flow rates lead to preferential channels being formed (please also refer to Sections 3 and 4). In the presence of relatively low dialysate flow rates, therefore, clearance values which may seem possible in theory are in fact unachievable in practice.

It must be emphasised, however, that these observations only apply to transport by diffusion, the most important transport mechanism for low molecular weight substances such as urea, creatinine and phosphate. As far as larger molecules are concerned, it is convective solute transport that becomes increasingly important as the molecular weight of the solute increases. With regard to the manner in which the overall clearance KT depends on both of these mechanisms, only an incomplete explanation can be provided. Werynski's equation [2] offers a reasonable approach:

$$K\_T = K\_{diff} + TrQ\_F \text{ where } Tr = \text{S(1 - K\_{diff} / Q\_{Bl})} \tag{2}$$

Tr: transmittance coefficient; S: sieving coefficient; QF: ultrafiltration rate

As the value for clearance by diffusion, Kdiff in relation to blood flow rate, QB, decreases, the transmittance coefficient approaches the sieving coefficient, and the overall clearance KT is effectively determined by the ultrafiltration rate QF. It follows that the dialysate flow rate QD has less significance with regard to larger molecules than it does with regard to smaller ones.
