Urea Kinetic Modelling and Kt/V
In the design of the NCDS study, ‘dose’ of dialysis was defined as a target for time averaged urea (low urea = high dose group). However, urea level in dialysed patients depends as much on protein intake as the amount of dialysis: loss of appetite may lead to low urea, so this cannot be relied on to indicate sufficient dialysis. The concept of Kt/V emerged from this study, where K is dialyser clearance (of urea), t is treatment time and V is volume of distribution (of urea). Despite its appearance, Kt/V is not intended as something to calculate from its constituents K, t and V, since only t is accurately known, but by consideration of the following relationship: the rate of removal of urea is proportional to its concentration. Following this basic rule, the concentration of urea after a dialysis session of duration t, is therefore approximated by:
Upost = Upre x e Kt / V
where Upost = urea post dialysis
Upre = urea pre dialysis
Kt/V is therefore the negative exponent in a numerical model describing the fall in urea during a single dialysis session. Different forms of Kt/V reflect models with differing levels of complexity, which in addition to the concept above, may also take account of other aspects such as: urea removal by convection, urea generation, and separate “pools” within which urea is distributed.
The gold standard Kt/V is derived from ‘Urea Kinetic Modelling’: iterative computation to give the best fitting coefficients for urea clearance and generation, based on three urea measurements (spanning an interdialytic interval and a dialysis session). This approach is broadly accepted, but although online programs are available (e.g. Solute Solver, www.ureakinetics.org) the non formula method hinders widespread use, and a number of simplified approaches are more common three are commonly used and summarised here.
Log Ratio and Urea Reduction Ratio
If the basic model above is used, ignoring other factors, with urea assumed to be distributed evenly in body water, then Kt/V is given by the log ratio:
Kt/V = loge [ Upost / Upre ]
This simple form of Kt/V, sometimes called the “Log Ratio”, is mathematically related to the Urea Reduction Ratio (URR), the reduction in urea as a ratio of the pre dialysis level, often expressed as a percentage:
URR = 100 x (Upre Upost) / Upre
Kt/V = loge [ 100 / (100 URR) ]
A threshold for URR is therefore precisely the same as a threshold for Kt/V calculated by the Log Ratio.
URR is the simplest measure of dialysis dose, and is the current audit measure collected by the Renal Registry. URR has the disadvantage that it does not account for clearance due to ultrafiltration, urea generation or urea rebound. It tends to over estimate dialysis dose in shorter treatments, and under estimate dose in treatments longer than 4 hours. However, it is long established and there is no argument over its calculation.
Single pool Kt/V (spKt/V)
Although the above is technically also a single pool method, the term ‘single pool Kt/V’ usually refers to the method proposed by Daugirdas, which calculates Kt/V by a formula taking account of the effect of ultrafiltration:
spKt/V = loge [ (Upost / Upre) (t / 7500) ] + [ (UF / TW) * (4 (3.5 * (Upost / Upre)) ]
where t = dialysis time (min)
UF = ultrafiltration (litres)
TW = target weight (kg)
This method takes account of more factors but consistently over estimates Kt/V. Targets have therefore often been expressed with an adjustment factor if using spKt/V (eg. “eKt/V = 1.2, or spKt/V = 1.4”).
Equilibrated Kt/V (eKt/V)
The dynamic interaction between urea concentrations in intra and extra cellular pools, results in reduced effectiveness of treatment because dialysis removes urea only from the extracellular pool, which is then refilled from the intracellular pool during and after dialysis. This results in a gradual rebound in urea concentration for approximately one hour after dialysis, so that if post dialysis urea is measured immediately, then the treatment effect is over estimated.
Equilibrated Kt/V attempts to correct for this by using a post rebound urea measurement:
eKt/V = loge [ Upost rebound / Upre ]
Due to the inconvenience of measuring urea post rebound (an hour after dialysis has finished), a formula is used to adjust for this reasonably predictable effect using urea measured immediately. More than one equation has been published but there is very little difference between them. This one is known as the Tattersall version:
eKt/V = (spKt/V * t) / (t + 35)
Apparent urea rebound is dependent on vascular access, so 35 is replaced by 22 in patients dialysing via a catheter. This method is non biased and has most often been used in studies of dialysis dose, such as the HEMO study. Targets given in terms of other measures of dialysis dose such as URR may be useful in comparing units, but are not accurate for individual patients.
All forms of Kt/V (including eKt/V) implicitly use V to normalise for body size, whereas body surface area is conventionally used to normalise renal function. There are theoretical reasons to believe that normalisation of Kt/V to other body size parameters such as body surface area would be more useful, but these concepts have not gained widespread acceptance.
The Log Ratio is a reasonable approximation of eKt/V since…
The Log Ratio is a reasonable approximation of eKt/V since the underestimation (from ignoring ultrafiltration and urea generation) is offset by overestimation (from ignoring urea rebound). In fact, for a 4 hour session, with UF/TW = 0.02, in a fistula patient, the Log Ratio is almost identical to eKt/V, with URR = 70 being equivalent to eKt/V = 1.2. However, in most other settings, Log Ratio will underestimate or overestimate dose, so that the target URR required to achieve eKt/V = 1.2 needs to be varied, as in this table:
