Mathematical Representation of Standard Kt/V Including Ultrafiltration and Residual Renal Function

A new formula for calculating standard Kt/V from clinical data has been derived mathematically. It is based on using the relation between eKt/V and the pre- and postdialysis concentrations in order to find the steady state concentrations. The resulting expression for standard Kt/V depends on the treatment schedule (number, length, and spacing of treatments), residual renal function, and eKt/V and relative ultrafiltration volume of each individual treatment. These results include the effects of ultrafiltration and residual renal function also in the case with unequal treatments that may be arbitrarily distributed over the week. The new formula is found to agree, within small fractions of a percentage, with standard Kt/V from simulations of 3 and 5 days per week schedules. Several approximations are also suggested and their accuracies analyzed. It is shown that the use of the midweek eKt/V and ultrafiltration for all treatments of the week is an acceptable approximation. In the presence of residual renal function, the timing of the treatments is an important factor, and particularly in this case, the new formula shows improved accuracy over previously published formulas.