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Standardized Kt/V, also std
Kt/V, is a way of measuring (renal) dialysis
adequacy. It was developed by Frank Gotch and is used in the USA to measure dialysis. Despite the name,
it is quite different from Kt/V.
In theory, both peritoneal dialysis and hemodialysis can 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 (equation 1), which is also used to define clearance.
where

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 the volume of distribution (total body water) [L] or
[m^{3}]
 K is the clearance [mL/min] or [m^{3}/s]
 C is the concentration [mmol/L] or [mol/m^{3}] (in the
USA often
[mg/mL])
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.
Derivation equation 1 is described in the article clearance
(medicine).
The solution of the above differential equation (equation 1)
is
where
 C_{o} is the concentration at the beginning of dialysis
[mmol/L] or [mol/m^{3}]
 e is the base of the natural
logarithm
The steady state solution is
This can be written as
Equation 3b is the equation that defines clearance. It is the motivation
for K' (the equivalent clearance):
where
 K' is the equivalent clearance [mL/min] or
[m^{3}/s]

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_{o} is the concentration at the beginning of dialysis
[mmol/L] or [mol/m^{3}]
Equation 4 is normalized by the volume of distribution
to form equation 5:
Equation 5 is multiplied by an arbitrary constant to
form equation 6:
Equation 6 is then defined as standardized Kt/V (std
Kt/V):
 ^{[1]}^{[2]}
where
 const is 7×24×60×60 seconds, the number of seconds in 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.
Equation 7 can be written in the following way:
If one takes the inverse of Equation 8 it can be
observed that the inverse of std Kt/V is proportional to
the concentration of urea (in the body) divided by the
production of urea per time per unit volume of body
water.
Comparison
to Kt/V
Kt/V and standardized
Kt/V are not the same. Kt/V is a ratio of the pre and
postdialysis urea concentrations. Standardized Kt/V is an
equivalent clearance defined by the initial urea concentration
(compare equation 8 and equation 10).
Kt/V is defined as (see article on Kt/V for derivation):
 ^{[3]}
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 hemodialysis vs. daily hemodialysis vs. conventional
hemodialysis)
 Applicable to peritoneal dialysis.
 Can be applied to patients with residual renal function; it is
possible to demonstrate that C_{o} is a function of the
residual kidney function and the "cleaning" provided by
dialysis.
 The model can be applied to substances other than urea, if the
clearance, K, and generation rate of the substance, ,
are known.^{[2]}
Criticism/disadvantages
of std Kt/V
 It is complex and tedious to calculate, although webbased calculators are available to do this
fairly easily.
 Many nephrologists have difficulty understanding it.
 Urea is not associated with
toxicity.^{[4]}
 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) have diffusionlimited transport
 so called middle molecules.
 It ignores the mass transfer between body compartments
and across the plasma membrane (i.e. intracellular to extracellular
transport), which has been shown to be important for the clearance
of molecules such as phosphate.
 The Standardized Kt/V is based on body water volume (V). The Glomerular
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 1520%. 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 ^{[5]},
Leypoldt ^{[6]}, and
the FHN trial network ^{[7]} are 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 ^{[8]}. One
equation, proposed by Leypoldt and modified by Depner that is cited
in the KDOQI 2006 Hemodialysis
Adequacy Guidelines and which is the basis for a web calculator for stdKt/V is as follows:
where stdKt/V is the standardized Kt/V
spKt/V is the singlepool Kt/V, computed as described in
Kt/V section using a simplified
equation or ideally, using urea modeling, and
eKt/V is the equilibrated Kt/V, computed from the
singlepool Kt/V (spKt/V) and session length (t) using, for
example, the Tattersall equation ^{[9]}:
where t is session duration in minutes, and C
is a time constant, which is specific for type of access and type
solute being removed. For urea, C should be 35 minutes for
arterial access and 22 min for a venous access.
The regular "rate equation" ^{[10]} 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.
References
 ^
Gotch FA (1998). "The current place of urea
kinetic modelling with respect to different dialysis
modalities". Nephrol Dial Transplant. 13 Suppl
6: 10–4. doi:10.1093/ndt/13.suppl_6.10. PMID 9719197. http://ndt.oxfordjournals.org/cgi/reprint/13/suppl_6/10.
 ^ ^{a}
^{b}
Gotch FA, Sargent JA, Keen ML
(August 2000). "Whither goest Kt/V?". Kidney Int. Suppl.
76: S3–18. doi:10.1046/j.15231755.2000.07602.x. PMID 10936795.
 ^
Gotch FA, Sargent JA (September
1985). "A mechanistic analysis of the National Cooperative Dialysis
Study (NCDS)". Kidney Int. 28 (3):
526–34. doi:10.1038/ki.1985.160. PMID 3934452.
 ^
Johnson WJ, Hagge WW, Wagoner RD,
Dinapoli RP, Rosevear JW (January 1972). "Effects of urea loading
in patients with faradvanced renal failure". Mayo Clinic
Proc. 47 (1): 21–9. PMID 5008253.
 ^
Gotch FA (1998). "The current place of urea
kinetic modelling with respect to different dialysis
modalities". Nephrol Dial Transplant. 13 Suppl
6: 10–4. doi:10.1093/ndt/13.suppl_6.10. PMID 9719197. http://ndt.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=9719197.
 ^
Leypoldt JK, Jaber BL, Zimmerman DL
(2004). "Predicting treatment dose for novel therapies using urea
standard Kt/V". Seminars in Dialysis 17
(2): 142–5. doi:10.1111/j.08940959.2004.17212.x. PMID 15043617.
 ^
Suri RS, Garg AX, Chertow GM, et
al. (February 2007). "Frequent Hemodialysis Network (FHN)
randomized trials: study design". Kidney Int.
71 (4): 349–59. doi:10.1038/sj.ki.5002032. PMID 17164834.
 ^
DiazBuxo JA, Loredo JP (March
2006). "Standard Kt/V: comparison of calculation methods".
Artificial Organs 30 (3): 178–85 Erratum
in 30(6):490. doi:10.1111/j.15251594.2006.00204.x. PMID 16480392.
 ^
Tattersall JE, DeTakats D, Chamney
P, Greenwood RN, Farrington K (December 1996). "The
posthemodialysis rebound: predicting and quantifying its effect on
Kt/V". Kidney Int. 50 (6): 2094–102. doi:10.1038/ki.1996.534. PMID 8943495.
 ^
Daugirdas JT, Greene T, Depner TA,
et al. (January 2004). "Factors that affect
postdialysis rebound in serum urea concentration, including the
rate of dialysis: results from the HEMO Study". J Am Soc
Nephrol. 15 (1): 194–203. doi:10.1097/01.ASN.0000103871.20736.0C. PMID 14694173. http://jasn.asnjournals.org/cgi/pmidlookup?view=long&pmid=14694173.
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