Kt / V

Kt / V is a parameter to determine the dialysis effectiveness and an essential component for the assessment of the dialysis efficiency. Another parameter for this assessment is URR ( Urea Reduction Ratio ).

The value can be given by the simplified formula

${\displaystyle {\frac {K\cdot t}{V}}}$

be determined.

It is

• K clearance , is determined from the urea content of the blood before and after dialysis.
• t effective dialysis time in minutes
• V 60% of the body mass (weight) in which the blood can circulate (body water content)

The reading was developed by Frank Gotch and John Sargent as a way to measure the dose of dialysis and assess its efficiency. The minimum value for hemodialysis is aimed at a Kt / V of ≥ 1.3; in peritoneal dialysis , the goal is ≥ 1.7 per week.

Derivation of the Kt / V as a parameter for measuring the dialysis effectiveness

K (renal clearance) multiplied by t (dialysis time) results in a volume (because ml / min × min = ml, or l / h × h = l), and the product ( K × t ) can be imagined as milliliters or liters Fluid (in this case blood) that is purged of urea during a treatment session. The V in the denominator is also a volume, measured in milliliters or liters. The fraction K × t / V is therefore dimensionless (i.e. without a physical unit). This fraction relates the volume of purified blood to the volume of urea distribution. In the case of Kt / V = ​​1.0, urea was removed from an amount of blood which is equal to the urea distribution volume.

The physical relationship between Kt / V and the urea concentration C at the end of dialysis can be derived from an ordinary first-order differential equation as follows . This models the clearance of any substance from the body, provided that the concentration of this substance in the body decreases exponentially over time ( exponential decay ):

${\displaystyle V{\frac {dC}{dt}}=-K\cdot C.\qquad (1)}$

It is

• C is the concentration of the substance, here urea [mol / m ³ ]
• t the time [s]
• K is the clearance [m ³ / s]
• V is the volume of distribution [m ³ ]

From the above equation it follows that the first derivative of the concentration is with respect to time, that is, the change in the urea concentration over time. This differential equation is separable and can be integrated as follows : ${\displaystyle {\frac {dC}{dt}}}$

${\displaystyle \int {\frac {dC}{C}}=\int -{\frac {K}{V}}\,dt.\qquad (2a)}$

Integration gives the equation

${\displaystyle \ln(C)=-{\frac {K\cdot t}{V}}+{\text{const}},\qquad (2b)}$

in which

• ln ( C ) is the natural logarithm of C
• const is the constant of integration

designated. Applying the natural exponential function to both sides of equation (2b), one obtains:

${\displaystyle C=e^{-{\frac {K\cdot t}{V}}+{\text{const}}},\qquad (2c)}$

wherein e the Euler's number , respectively. Basic rules of calculation in algebra allow this equation to be rewritten as:

${\displaystyle C=C_{0}\cdot e^{-{\frac {K\cdot t}{V}}},\qquad (3)}$

where C ₀ denotes the concentration at the start of dialysis (in [mmol / l] or [mol / m ³ ]). This equation can alternatively be written as

${\displaystyle {\frac {K\cdot t}{V}}=\ln {\frac {C_{0}}{C}}.\qquad (4)}$

Using the calculation rules for logarithms, the formula (4) can also be written as

${\displaystyle {\frac {K\cdot t}{V}}=-\ln R,\qquad (4a)}$

where is. ${\displaystyle R={\frac {C}{C_{0}}}}$

Relationship to Urea Reduction Ratio

The Urea Reduction Ratio (URR) is simply the relative reduction of urea during dialysis. According to the definition, URR = 1 - C / C ₀ . This results in 1-URR = C / C ₀ . By algebraic transformation, namely by substituting in the above equation (4a), one thus obtains:

${\displaystyle {\frac {K\cdot t}{V}}=-\ln(1-URR).\qquad (5)}$

Calculation according to the formula of Daugirdas

Formula (4) neglects the following two facts: on the one hand, the body produces new urea during dialysis, and on the other hand, urea is removed by ultrafiltration (which contributes to clearance K, but does not affect reduction ). Daugirdas has therefore proposed a modified formula for calculating the Kt / V in order to take these influencing factors into account: ${\displaystyle R={\frac {C}{C_{0}}}}$

${\displaystyle {\frac {K\cdot t}{V}}=-\ln(R-0{,}008\cdot T)+(4-3{,}5\cdot R)\cdot {\frac {UF}{KG}}.\qquad (6)}$

It is

• T is the effective dialysis time in h;
• R is the post-dialytic urea content divided by the predialytic urea content ; ${\displaystyle C}$ ${\displaystyle C_{0}}$
• KG is the dry weight (in kg), d. H. the body weight after dialysis treatment;
• UF is the ultrafiltration volume of the same date (in liters); the ultrafiltration volume (in liters) is calculated as the difference between body weight before dialysis and body weight after dialysis treatment (each in kg).

According to the guidelines for ensuring the quality of dialysis treatments, the Kt / V is calculated according to formula (6).

Rebound after dialysis

The physical model explained above assumes that the urea diffuses evenly throughout the body, as if the entire volume in which the urea is distributed consisted only of liquid (single pool model). A more precise model uses the division of the human body into several compartments , in particular the extracellular space , in which z. B. the blood vessels are included, and the intracellular space . Observations have shown that urea migrates from the intracellular space into the bloodstream about 30 to 60 minutes after the end of hemodialysis. Because more urea was briefly withdrawn from the bloodstream than from the intracellular space, the urea concentration levels out again so that the concentration in both compartments is ultimately the same again - this is referred to as urea rebound . There are other formulas for calculating the kt / V based on the double pool model, which takes the various compartments into account.

Web links

• Kt / V - Calculator Labor Limbach
• Hemodialysis Dose and Adequacy - US Department of Health and Human Services (English; PDF file; 94 kB)

Individual evidence

1. ↑ Gotch FA, Sargent JA: A mechanistic analysis of the National Cooperative Dialysis Study (NCDS) . In: Kidney Int . tape 28 , no. 3 , September 1985, pp. 526-534 , doi : 10.1038 / ki.1985.160 , PMID 3934452 .
2. ^ John T. Daugirdas: Second generation logarithmic estimates of single-pool variable volume Kt / V: an analysis of error . In: Journal of the American Society of Nephrology . tape 4 , no. 5 , November 1993, pp. 1205–1213 ( online PDF [accessed February 5, 2014]).
3. ↑ Kt / V (single pool) for hemodialysis according to Daugirdas. Limbach Laboratory. Retrieved February 17, 2014 . 
4. ↑ Quality assurance guideline for dialysis (Sections 136 and 136a of the fifth book of the Social Code Book V), Annexes 1 - 4: Description of the data set and SOPs. August 19, 2010, accessed February 5, 2014 .  , Appendix 2, No. 1.6: "Kt / V (single pool)"
5. ^ I. NKF-K / DOQI Clinical Practice Guidelines for Hemodialysis Adequacy: Update 2000 . In: National Kidney Foundation (Ed.): American Journal of Kidney Diseases . 37 issue 1, 2000, pp. 7-64 ( online ).

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