Rationale For Kt/V As A Marker of Dialysis Adequacy
K (clearance) multiplied by t (time) is a volume (since mL/min x min = mL, or L/hr x hr = L), and (K x t) can be thought of as the mL or L of fluid (blood in this case) cleared of urea (or any other solute) during the course of a single treatment. V also is a volume, expressed in mL or L. So the ratio of K x t / V is a so-called "dimensionless ratio" and can be thought of as a multiple of the volume of plasma cleared of urea divided by the distribution volume of urea. When Kt/V = 1.0, a volume of blood equal to the distribution volume of urea has been completely cleared of urea.
The relationship between Kt/V and the concentration of urea C at the end of dialysis can be derived from the first-order differential equation that describes exponential decay and models the clearance of any substance from the body where the concentration of that substance decreases in an exponential fashion:
where
- C is the concentration
- t is the time
- K is the clearance
- V is the volume of distribution
From the above definitions it follows that is the first derivative of concentration with respect to time, i.e. the change in concentration with time.
This equation is separable and can be integrated as follows:
After integration,
where
- const is the constant of integration
If one takes the antilog of Equation 2b the result is:
where
- e is the base of the natural logarithm
By integer exponentiation this can be written as:
where
- C0 is the concentration at the beginning of dialysis or .
The above equation can also be written as
Normally we measure postdialysis serum urea nitrogen concentration C and compare this with the initial or predialysis level C0. The session length or time is t and this is measured by the clock. The dialyzer clearance K is usually estimated, based on the urea transfer ability of the dialyzer (a function of its size and membrane permeability), the blood flow rate, and the dialysate flow rate. In some dialysis machines, the urea clearance during dialysis is estimated by testing the ability of the dialyzer to remove a small salt load that is added to the dialysate during dialysis.
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