# Calculation of Dialysis Clearance

Currently, the efficiency of hemodialysis is expressed in terms of dialysis clearance. Dialysis clearance (CLd) is usually estimated from the Fick equation as follows:

where A is the solute concentration entering (arterial) and V is the solute concentration leaving (venous) the dialyzer. The terms in brackets collectively describe what is termed the extraction ratio (E). As a general principle, clearance from an eliminating organ can be thought of as the product of organ blood flow and extraction ratio.

Single-pass dialyzers are now standard for patient care and clearance calculations suffice for characterizing their performance. However, recirculating dia-lyzers were used in the early days of hemodialysis.

Dialysis bath solute concentration (Bath) had to be considered in describing the performance of recirculating dialyzers and was included in the equation for calculating dialysance (D), as shown in the following equation (7):

Considerable confusion surrounds the proper use of Equation 6.2 to calculate dialysis clearance. There is general agreement that blood clearance is calculated when Q is set equal to blood flow and A and V are expressed as blood concentrations. In conventional practice, plasma clearance is obtained by setting Q equal to plasma flow and expressing A and V as plasma concentrations. In fact, this estimate of plasma clearance is only the same as plasma clearance calculated by standard pharmacokinetic techniques when the solute is totally excluded from red blood cells.

This dilemma is best avoided by calculating dialysis clearance using an equation that is analogous to the equation used to determine renal clearance:

where the amount of drug recovered by dialysis is calculated as the product of the drug concentration in dialysate (Cd) and total volume of dialysate (VoId) collected during the dialysis time (t), and P is the average concentration of drug in plasma entering the dialyzer. The term recovery clearance has been coined for this clearance estimate, and it is regarded as the "gold standard" of dialysis clearance estimates (11).

Equation 6.3 provides an estimate of dialysis plasma clearance (CLp) that is pharmacokinetically consistent with estimates of elimination and intercompartmen-tal clearance that are based on plasma concentration measurements. On the other hand, if the average drug concentration in blood entering the dialyzer (B) is substituted for P, a valid estimate of blood clearance (CLb) is obtained:

We can use these recovery clearances to examine the effective flow of plasma (Qeff) that is needed if Equation 6.2 is to yield an estimate of dialysis clearance that is consistent with the corresponding recovery clearance value. Since CLb = QbE, it follows from Equation 6.4 that:

Rearranging,

But from Equation 6.3,

3-Compartment Model

Dialysis Machine

Therefore,

However,

Therefore,

For drugs like NAPA that partition preferentially into red blood cells and are fully accessible to the dialyzer from both plasma and erythrocytes, the effective plasma flow will not be less than but will exceed measured blood flow (12).

Some authorities argue that it is improper to combine organ blood flow and plasma concentrations in Equation 6.2 (7,11). However, in many cases the ratio of red cell/plasma drug concentrations remains constant over a wide concentration range so the same estimate of extraction ratio is obtained regardless of whether plasma concentrations or blood concentrations are measured.

As shown in Figure 6.2, pharmacokinetic models can be constructed that incorporate all the measurements made during hemodialysis (12). For this purpose it is convenient to rearrange Equation 6.2 to the form

where Qpk is the pharmacokinetically calculated flow of blood or plasma through the dialysis machine. Since CLd is calculated from the recovery of drug in dialysis bath fluid, an estimate of Qpk can be obtained from the observed ratio of V/A (Equation 6.5 and Figure 6.2).

In a study of NAPA hemodialysis kinetics, blood flow measured through the dialyzer averaged 195 mL/min (12). When evaluated by paired t test this was significantly less than Qpk, which averaged 223 mL/min. However, Qpk was similar to estimates of Qeff, which averaged 217 mL/min. In this case

3-Compartment Model

Dialysis Machine FIGURE 6.2 Multicompartmental system for modeling pharmacokinetics during hemodialysis. Drug is delivered to the dialysis machine from the central compartment (VC) and represents A in the Fick equation. The dialysis machine is modeled by a compartment representing drug recovery in dialysis bath fluid and a proportionality (triangle) representing the drug concentration in blood returning to the patient.

FIGURE 6.2 Multicompartmental system for modeling pharmacokinetics during hemodialysis. Drug is delivered to the dialysis machine from the central compartment (VC) and represents A in the Fick equation. The dialysis machine is modeled by a compartment representing drug recovery in dialysis bath fluid and a proportionality (triangle) representing the drug concentration in blood returning to the patient.

NAPA concentrations in erythrocytes were 1.5 times as high as in plasma, and this preferential distribution of drug into red blood cells enhanced drug removal by hemodialysis. Unfortunately, most hemodialysis studies have not incorporated the full range of readily available measurements in an integrated pharmacoki-netic analysis.

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