Standardized Kt/V

Standardized Kt/V,alsostd Kt/V,is a way of measuring (renal)dialysis adequacy.It was developed byFrank Gotchand is used in the United States to measuredialysis.Despite the name, it is quite different fromKt/V.In theory, bothperitoneal dialysisandhemodialysiscan be quantified with std Kt/V.

Derivation

Standardized Kt/V is motivated by the steady state solution of the mass transfer equation often used to approximate kidney function (equation1), which is also used to defineclearance.

$V{\frac {dC}{dt}}=-K\cdot C+{\dot {m}}\qquad (1)$

where

• ${\dot {m}}$is the mass generation rate of the substance - assumed to be a constant, i.e. not a function of time (equal to zero for foreign substances/drugs) [mmol/min] or [mol/s]
• t is dialysis time [min] or [s]
• V is thevolume of distribution(totalbody water) [L] or [m³]
• K is the clearance [mL/min] or [m³/s]
• C is the concentration [mmol/L] or [mol/m³] (in the United States often [mg/mL])

From the above definitions it follows that${\frac {dC}{dt}}$is the firstderivativeof concentration with respect to time, i.e. the change in concentration with time.

Derivation equation1is described in the articleclearance (medicine).

The solution of the above differential equation (equation 1) is

$C={\frac {\dot {m}}{K}}+\left(C_{o}-{\frac {\dot {m}}{K}}\right)e^{-{\frac {K\cdot t}{V}}}\qquad (2)$

where

• C_ois the concentration at the beginning of dialysis [mmol/L] or [mol/m³]
• eis the base of thenatural logarithm

The steady state solution is

$C_{\infty }={\frac {\dot {m}}{K}}\qquad (3a)$

This can be written as

$K={\frac {\dot {m}}{C_{\infty }}}\qquad (3b)$

Equation3bis the equation that definesclearance.It is the motivation for K' (the equivalent clearance):

${K'}={\frac {\dot {m}}{C_{o}}}\qquad (4)$

where

• K' is the equivalent clearance [mL/min] or [m³/s]
• ${\dot {m}}$is the mass generation rate of the substance - assumed to be a constant, i.e. not a function of time [mmol/min] or [mol/s]
• C_ois the concentration at the beginning of dialysis [mmol/L] or [mol/m³]

Equation4is normalized by the volume of distribution to form equation5:

${\frac {K'}{V}}={\frac {\dot {m}}{C_{o}\cdot V}}\qquad (5)$

Equation5is multiplied by an arbitrary constant to form equation6:

${\mbox{const}}\cdot {\frac {K'}{V}}={\mbox{const}}\cdot {\frac {\dot {m}}{C_{o}\cdot V}}\qquad (6)$

Equation6is then defined as standardized Kt/V (std Kt/V):

${\mbox{std}}{\frac {K\cdot t}{V}}\ {\stackrel {\mathrm {def} }{=}}\ {\mbox{const}}\cdot {\frac {\dot {m}}{C_{o}\cdot V}}\qquad (7)$

where

• constis 7×24×60×60 seconds, the number ofsecondsin a week.

Interpretation of std Kt/V

Standardized Kt/V can be interpreted as a concentration normalized by the mass generation per unit volume of body water.

Equation7can be written in the following way:

${\mbox{std}}{\frac {K\cdot t}{V}}\ {\stackrel {\mathrm {def} }{=}}{\mbox{ const}}\cdot {\frac {\dot {m}}{V}}{\frac {1}{C_{o}}}\qquad (8)$

If one takes the inverse of Equation8it can be observed that theinverse of std Kt/Vis proportional to theconcentration of urea(in the body) divided by theproduction of urea per timeperunit volume of body water.

$\left[std{\frac {K\cdot t}{V}}\right]^{-1}\propto {\frac {C_{o}}{{\dot {m}}/V}}\qquad (9)$

Comparison to Kt/V

Kt/Vandstandardized Kt/Vare not the same. Kt/V is a ratio of the pre- and post-dialysis urea concentrations. Standardized Kt/V is an equivalent clearance defined by the initial urea concentration (compare equation8and equation10).

Kt/V is defined as (see article onKt/Vfor derivation):

${\frac {K\cdot t}{V}}=\ln {\frac {C_{o}}{C}}\qquad (10)$

Since Kt/V and std Kt/V are defined differently, Kt/V and std Kt/V values cannot be compared.

Advantages of std Kt/V

• Can be used to compare any dialysis schedule (i.e.nocturnal home hemodialysisvs. daily hemodialysis vs. conventional hemodialysis)
• Applicable toperitoneal dialysis.
• Can be applied to patients with residual renal function; it is possible to demonstrate that C_ois a function of the residual kidney functionandthe "cleaning" provided by dialysis.
• The model can be applied to substances other than urea, if the clearance,K,and generation rate of the substance,${\dot {m}}$,are known.

Criticism/disadvantages of std Kt/V

• It is complex and tedious to calculate, althoughweb-based calculatorsare available to do this fairly easily.
• Many nephrologists have difficulty understanding it.
• Ureais not associated with toxicity.
• Standardized Kt/V only models the clearance of urea and thus implicitly assumes the clearance of urea is comparable to other toxins. It ignores molecules that (relative to urea) havediffusion-limitedtransport - so calledmiddle molecules.
• It ignores themass transferbetween body compartments and across theplasma membrane(i.e.intracellulartoextracellulartransport), which has been shown to be important for the clearance of molecules such asphosphate.
• The Standardized Kt/V is based on body water volume (V). TheGlomerular filtration rate,an estimate of normal kidney function, is usually normalized to body surface area (S). S and V differ markedly between small vs. large people and between men and women. A man and a woman of the same S will have similar levels of GFR, but their values for V may differ by 15-20%. Because standardized Kt/V incorporates residual renal function into the calculations, it makes the assumption that kidney function should scale by V. This may disadvantage women and smaller patients of either sex, in whom V is decreased to a greater extent than S.

Calculating stdKt/V from treatment Kt/V and number of sessions per week

The various ways of computing standardized Kt/V by Gotch,Leypoldt,and the FHN trial networkare all a bit different, as assumptions differ on equal spacing of treatments, use of a fixed or variable volume model, and whether or not urea rebound is taken into effect.One equation, proposed by Leypoldt and modified by Depner that is cited in theKDOQI 2006 Hemodialysis Adequacy Guidelinesand which is the basis for aweb calculator for stdKt/Vis as follows:

$stdKt/V={\frac {\frac {10080\cdot (1-e^{-eKt/V})}{t}}{{\frac {1-e^{-eKtV}}{spKt/V}}+{\frac {10080}{N\cdot t}}-1}}$

wherestdKt/Vis the standardized Kt/V
spKt/Vis the single-pool Kt/V, computed as described inKt/Vsection using a simplified equation or ideally, using urea modeling, and
eKt/Vis the equilibrated Kt/V, computed from the single-pool Kt/V (spKt/V) and session length (t) using, for example, the Tattersall equation:

$ekt/V=spKt/V\cdot {\frac {t}{t+C}}$

wheretis session duration in minutes, andCis a time constant, which is specific for type of access and type solute being removed. For urea,Cshould be 35 minutes for arterial access and 22 min for a venous access.

The regular "rate equation"also can be used to determine equilibrated Kt/V from the spKt/V, as long as session length is 120 min or longer.

Plot showing std Kt/V depending on regular Kt/V for different treatment regimens

Plot relating standardized Kt/V, Kt/V and treatment frequency per week.

One can create a plot to relate the three grouping (standardized Kt/V, Kt/V, treatment frequency per week), sufficient to define a dialysis schedule. The equations are strongly dependent on session length; the numbers will change substantially between two sessions given at the same schedule, but with different session lengths.

For the present plot, a session length of 0.4 Kt/V units per hour was assumed, with a minimum dialysis session length of 2.0 hours.

External links

• Standardized Kt/V, HDP(HemoDialysis Product calculation- hdtool.net
• Standardized Kt/V using formal 2-pool kinetics- Ureakinetics.org
• Standardized Kt/V calculator- HDCN