Standardized Kt/V 2588457 174350751 2007-11-28T11:51:32Z SmackBot 433328 Standard headings &/or gen fixes. using [[Project:AutoWikiBrowser|AWB]] '''Standardized Kt/V''', also '''std Kt/V''', is a way of measuring ([[renal]]) [[dialysis adequacy]]. It was developed by [[Frank Gotch (MD)|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 (medicine)|clearance]]. :<math>V \frac{dC}{dt} = -K \cdot C + \dot{m} \qquad(1)</math> where *<math>\dot{m}</math> 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<sup>3</sup>] *K is the clearance [mL/min] or [m<sup>3</sup>/s] *C is the concentration [mmol/L] or [mol/m<sup>3</sup>] (in the [[USA]] often [mg/mL]) From the above definitions it follows that <math>\frac{dC}{dt}</math> 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 :<math>C = \frac{\dot{m}}{K} + \left(C_{o}-\frac{\dot{m}}{K}\right) e^{-\frac{K \cdot t}{V}} \qquad(2)</math> where *C<sub>o</sub> is the concentration at the beginning of dialysis [mmol/L] or [mol/m<sup>3</sup>] *[[E (mathematical constant)|e]] is the base of the [[natural logarithm]] The steady state solution is :<math> C_{\infty} = \frac {\dot{m}}{K} \qquad(3a)</math> This can be written as :<math> K = \frac {\dot{m}}{C_{\infty}} \qquad(3b)</math> Equation ''3b'' is the equation that defines [[clearance (medicine)|clearance]]. It is the motivation for K' (the equivalent clearance): :<math> {K'} = \frac {\dot{m}}{C_o} \qquad(4)</math> where *K' is the equivalent clearance [mL/min] or [m<sup>3</sup>/s] *<math>\dot{m}</math> 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<sub>o</sub> is the concentration at the beginning of dialysis [mmol/L] or [mol/m<sup>3</sup>] Equation ''4'' is normalized by the volume of distribution to form equation ''5'': :<math> \frac {K'}{V} = \frac {\dot{m}}{C_o \cdot V} \qquad(5)</math> Equation ''5'' is multiplied by an arbitrary constant to form equation ''6'': :<math> \mbox{const} \cdot \frac {K'}{V} = \mbox{const} \cdot \frac {\dot{m}}{C_o \cdot V} \qquad(6)</math> Equation ''6'' is then defined as standardized Kt/V (std Kt/V): :<math>\mbox{std} \frac{K \cdot t}{V} \ \stackrel{\mathrm{def}}{=}\ \mbox{const} \cdot \frac {\dot{m}}{C_o \cdot V} \qquad(7)</math><ref>Gotch FA. The current place of urea kinetic modelling with respect to different dialysis modalities. Nephrol Dial Transplant. 1998;13 Suppl 6:10-4. PMID 9719197. [http://ndt.oxfordjournals.org/cgi/reprint/13/suppl_6/10 Full Text].</ref><ref name=gotch_10936795>Gotch FA, Sargent JA, Keen ML. Whither goest Kt/V? Kidney Int Suppl. 2000 Aug;76:S3-18. PMID 10936795.</ref> where * ''const'' is 7×24×60×60 seconds, the number of [[second]]s 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: :<math>\mbox{std} \frac{K \cdot t}{V} \ \stackrel{\mathrm{def}}{=}\mbox{ const} \cdot \frac {\dot{m}}{V} \frac{1}{C_o} \qquad(8)</math> 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''. :<math>\left[ std \frac{K \cdot t}{V} \right]^{-1} \propto \frac{C_o}{\dot{m}/V} \qquad(9)</math> ==Comparison to Kt/V== [[Kt/V]] and ''standardized Kt/V'' are 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 equation ''8'' and equation ''10''). Kt/V is defined as (see article on [[Kt/V]] for derivation): :<math> \frac{K \cdot t}{V} = \ln \frac{C_o}{C} \qquad(10)</math><ref>Gotch FA, Sargent JA. A mechanistic analysis of the National Cooperative Dialysis Study (NCDS). Kidney Int. 1985 Sep;28(3):526-34. PMID 3934452.</ref> 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<sub>o</sub> 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, <math>\dot{m}</math>, are known.<ref name=gotch_10936795/> ==Criticism/disadvantages of std Kt/V== * It is complex and tedious to calculate, although [http://www.hdcn.com/calcf/ley.htm web-based calculators] are available to do this fairly easily. * Many nephrologists have difficulty understanding it. * [[Urea]] is not associated with toxicity.<ref>Johnson WJ, Hagge WW, Wagoner RD, Dinapoli RP, Rosevear JW. Effects of urea loading in patients with far-advanced renal failure. Mayo Clin Proc. 1972 Jan;47(1):21-9. PMID 5008253.</ref> * 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 [[diffusion|diffusion-limited]] 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 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 <ref>Gotch FA. The current place of urea kinetic modelling with respect to different dialysis modalities. Nephrol Dial Transplant. 1998;13 Suppl 6:10-4. Review. PMID 9719197</ref>, Leypoldt <ref>Leypoldt JK, Jaber BL, Zimmerman DL. Predicting treatment dose for novel therapies using urea standard Kt/V. Semin Dial. 2004 Mar-Apr;17(2):142-5. PMID 15043617</ref>, and the FHN trial network <ref>Suri RS, Garg AX, Chertow GM, Levin NW, Rocco MV, Greene T, Beck GJ, Gassman JJ, Eggers PW, Star RA, Ornt DB, Kliger AS. Frequent Hemodialysis Network (FHN) randomized trials: Study design. Kidney Int. 2007 Feb;71(4):349-59. Epub 2006 Dec 13. PMID 17164834</ref> 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 <ref>Diaz-Buxo JA, Loredo JP. Standard Kt/V: comparison of calculation methods. Artif Organs. 2006 Mar;30(3):178-85. Erratum in: Artif Organs. 2006 Jun;30(6):490. PMID: 16480392 </ref>. One equation, proposed by Leypoldt and modified by Depner that is cited in the [http://www.kidney.org/professionals/kdoqi/guideline_upHD_PD_VA/hd_rec2.htm KDOQI 2006 Hemodialysis Adequacy Guidelines] and which is the basis for a [http://www.hdcn.com/calcf/ley.htm web calculator for stdKt/V] is as follows: <BR/><BR/> <math>stdKt/V = \frac { \frac {10080 \cdot (1 - e^{-eKt/V})}{t} }{ \frac {1 - e^{-eKtV}}{spKt/V} + \frac{10080}{N \cdot t} - 1} </math> <BR/><BR/> where ''stdKt/V'' is the standardized Kt/V <BR/> ''spKt/V'' is the single-pool Kt/V, computed as described in [[Kt/V]] section using a simplified equation or ideally, using urea modeling, and <BR> ''eKt/V'' is the equilibrated Kt/V, computed from the single-pool Kt/V (spKt/V) and session length (t) using, for example, the Tattersall equation <ref>Tattersall JE, DeTakats D, Chamney P, Greenwood RN, Farrington K. The post-hemodialysis rebound: predicting and quantifying its effect on Kt/V. Kidney Int. 1996 Dec;50(6):2094-102. PMID 8943495</ref>: <math>ekt/V = spKt/V \cdot \frac {t}{t+C}</math> 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" <ref>Daugirdas JT, Greene T, Depner TA, Leypoldt J, Gotch F, Schulman G, Star R; Hemodialysis Study Group. Factors that affect postdialysis rebound in serum urea concentration, including the rate of dialysis: results from the HEMO Study. J Am Soc Nephrol. 2004 Jan;15(1):194-203. PMID 14694173 </ref> also can be used to determine equilibrated Kt/V from the spKt/V, as long as session length is 120 min or longer. ==Plot relating different treatment regimens ("Kt/V nomogram")== [[Image:Std ktv.svg#file|200 px|thumb|right|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. Incorrectly, this plot is frequency referred to as a "[[nomogram]]."<ref>Kt/V calculator. UpToDate.com. URL: [http://patients.uptodate.com/topic.asp?file=calculat/6479 http://patients.uptodate.com/topic.asp?file=calculat/6479]. Accessed on: November 25, 2007.</ref><ref>Nomogram. dictionary.com. URL: [http://dictionary.reference.com/browse/nomogram http://dictionary.reference.com/browse/nomogram]. Accessed on: November 25, 2007.</ref> 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== {{reflist}} {{Renal physiology}} ==External links== *[http://www.hdcn.com/calcf/ley.htm Standardized Kt/V calculator] - HDCN [[Category:Renal dialysis]]