Kt/V

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In medicine, Kt/V is a dimensionless number used to quantify hemodialysis and peritoneal dialysis treatment adequacy.

  • K - dialyzer clearance of urea (provided by the manufacturer)
  • t - dialysis time
  • V - patient's total body water

It was developed by Frank Gotch and John Sargent as a way for measuring the dose of dialysis when they analyzed the data from the National Cooperative Dialysis Study.[1] In hemodialysis the US National Kidney Foundation Kt/V target is 1.3, so that one can be sure that the delivered dose is at least 1.2.[2] In peritoneal dialysis the target is 2.0/week.[2]

Despite the name, Kt/V is quite different from standardized Kt/V.

Contents

[edit] Rationale for Kt/V as a marker of dialysis adequacy

Kt/V is derived from the first-order differential equation that describes exponential decay and models clearance of substances from the body by the kidney and hemodialysis machines:

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

where

  • C is the concentration [mol/m3]
  • t is the time [s]
  • K is the clearance [m3/s]
  • V is the body water [m3]

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

This equation is separable and can be integrated as follows:

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

After integration,

\ln(C) = - \frac{K \cdot t}{V} + \mbox{const} \qquad(2b)

where

  • const is the constant of integration

If one takes the antilog of Equation 2b the result is:

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

where

By integer exponentiation this can be written as:

C = C_0 e^{-\frac{K \cdot t}{V}} \qquad(3)

where

  • C0 is the concentration at the beginning of dialysis [mmol/L] or [mol/m3].

The above equation can also be written as

\frac{K \cdot t}{V} = \ln \frac{C_o}{C} \qquad(4)[1]

K - can be shown to depend on the dialysate flow, blood flow, dialyser surface area, recycle flow and mass transfer coefficient.[3] If the recycle flow is assumed to be zero it can be shown that K is the following function (of the blood flood, dialysate flow, dialyser surface area and the mass transfer coefficient):

K = Q_B \left[ \frac{ 1-\exp \left[ \frac{h_0 \cdot A}{Q_B} \left( 1 - \frac{Q_B}{Q_D} \right) \right] } { \frac{Q_B}{Q_D}-\exp \left[ \frac{h_0 \cdot A}{Q_B} \left( 1 - \frac{Q_B}{Q_D} \right) \right] } \right] \qquad(5)

where

  • K is the clearance [m3/s]
  • h0 is the mass transfer coefficient kg/(s·m2)]
  • A is the effective dialyser area [m2]
  • QB is the blood flow [m3/s]
  • QD is the dialysate flow [m3/s]

[edit] Sample calculation

Patient has a mass of 70 kg (154 lb) and gets a hemodialysis treatment that lasts 4 hours where the urea clearance 215 ml/min.

  • K = 215 mL/min
  • t = 4.0 hours = 240 min
  • V = 70 kg × 0.6 L of water/kg of body mass = 42 L = 42,000 mL

Therefore:

Kt/V = 1.23

[edit] Post-dialysis rebound

The above analysis assumes the body can be modeled with a single compartment.

Due to the multiple compartments in the human body, a significant concentration rebound occurs following hemodialysis. This can be characterized if one knows the time constant associated with intra-compartmental transport—the time constant for tranport between the blood plasma and cells.

The single-compartment Kt/V (sKt/V) is an underestimate of the dialysis. To ameliorate for this error several different "corrections" have been devised that are functions of the dialysis time and the temporal concentration gradients.

[edit] Peritoneal dialysis

Kt/V (in the context of peritoneal dialysis) was developed by Michael J. Lysaght in a series of articles on peritoneal dialysis.[4][5]

The steady-state solution of a simplified mass transfer equation that is used to describe the mass exchange over a semi-permeable membrane and models peritoneal dialysis is

C_B=\dot{m}/K. \qquad(6a)

This can also be written as:

K=\dot{m}/C_B. \qquad(6b)

The mass generation (of urea), in steady state, can be expressed as the mass (of urea) in the effluent per time:

\dot m=\frac{C_E \cdot V_E}{t}. \qquad(6c)

Lysaght, motivated by Equations 6b and 6c, defined the value KD:

K_D = \frac{C_E \cdot V_E}{C_B \cdot t} \qquad(6d)

where

  • KD is the clearance [ m3/s ]
  • CE is the concentration of urea in effluent [ mol/m3 ]
  • VE is the volume of effluent [ m3 ]
  • CB is the concentration in the blood [ mol/m3 ]
  • t is the time [ s ]

Lysaght uses "ml/min" for the clearance. In order to convert the above clearance (which is in m3/s) to ml/min one has to multiply by 60 x 1000 x 1000.

Once KD is defined the following equation is used to calculate Kt/V:

\frac{K \cdot t}{V} = \frac{7/3 \cdot K_D}{V_D} \qquad(7a)

where

  • V is the volume of distribution. It has to be in litres (l), as the equation is not really non-dimensional.

The 7/3 is used to adjust the Kt/V value so it can be compared to the Kt/V for hemodialysis, which is typically done thrice weekly in the USA.

[edit] Weekly Kt/V

To calculate the weekly Kt/V (for peritoneal dialysis) KD has to be in litres/day. Weekly Kt/V is defined by the following equation:

\mbox{Weekly } Kt/V = \frac{7 K_D [l/\mbox{day}]}{V [l]}. \qquad(7a)

[edit] Sample calculation

Assume:

  • CB mean = 22.817 mmol/L
  • CD = 17.524 mmol/L
  • VD = 3.75 L per exchange or 15 L/day
  • V_{B}=40.6\ L

Then by Equation 6d KD is: 1.3334e−07 m3/s or 8.00 ml/min or 11.52 l/day.

Kt/V and the weekly Kt/V by Equations 7a and 7b respectively are thus: 0.45978 and 1.9863.

[edit] Reason for adoption

Kt/V has been widely adopted because it was correlated with survival. Before Kt/V nephrologists measured the serum urea concentration (specifically the time-averaged concentration of urea (TAC of urea)), which was found not to be correlated with survival (due to its strong dependence on protein intake) and thus deemed an unreliable marker of dialysis adequacy.

[edit] Relation to URR

The urea reduction ratio (URR) is another measure of dialysis. It is related to Kt/V by the following relationship (if based on Gotch's original definition):


for dialysis treatments where there is little or no fluid removal during the dialysis treatment:

\frac{K \cdot t}{V} = -\ln (1-URR). \qquad(8)

More complicated relationships have been worked-out to account for the fluid removal (ultrafiltration) during dialysis (see urea reduction ratio).

Since the URR and Kt/V are related their predictive power is thought to be similar.

[edit] Criticisms/disadvantages of Kt/V

  • It is complex and tedious to calculate. Many nephrologists have difficulty understanding it.
  • Urea is not associated with toxicity.[6]
  • Kt/V only measures a change in the concentration of urea and implicitly assumes the clearance of urea is comparable to other toxins. (It ignores molecules larger than urea having diffusion-limited transport - so called middle molecules).
  • Kt/V does not take into account the role of ultrafiltration.
  • 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. Practical use of Kt/V requires adjustment for rebound of the urea concentration due to the multi-compartmental nature of the body.
  • Kt/V may disadvantage women and smaller patients in terms of the amount of dialysis received. Normal kidney function is expressed as the Glomerular_filtration_rate or GFR. GFR is usually normalized in people to body surface area. A man and a woman of similar body surface areas will have markedly different levels of total body water (which corresponds to V). Also, smaller people of either sex will have markedly lower levels of V, but only slightly lower levels of body surface area. For this reason, any dialysis dosing system that is based on V may tend to underdose smaller patients and women. Some investigators have proposed dosing based on surface area (S) instead of V, but clinicians usually measure the URR and then calculate Kt/V. One can "adjust" the Kt/V, to calculate a "surface-area-normalized" or "SAN"-Kt/V as well as a "SAN"-standard Kt/V. This puts a wrapper around Kt/V and normalizes it to body surface area. [7]

[edit] Criticism by Scribner

Kt/V has been criticized by Scribner and Oreopoulos[8] as having lead to the short (in-centre) hemodialysis sessions that are typical in the USA. They consider the typical hemodialysis sessions (in the USA) inadequate and are of the opinion that they only appeal to for-profit dialysis centres and uninformed dialysis patients. They have proposed the use of the hemodialysis product (HDP) and advocate long dialysis times.

[edit] References

  1. ^ a b Gotch FA, Sargent JA. A mechanistic analysis of the National Cooperative Dialysis Study (NCDS) Kidney Int. 1985;28(3):526-34. PMID 3934452.
  2. ^ a b (2000) "Clinical practice guidelines for nutrition in chronic renal failure. K/DOQI, National Kidney Foundation.". Am J Kidney Dis 35 (6 Suppl 2): S1-140. PMID 10895784.. Available at: http://www.kidney.org/professionals/KDOQI/guidelines_updates/doqi_uptoc.html
  3. ^ Babb AL, Popovich RP, Christopher TG, Scribner BH. The genesis of the square meter-hour hypothesis. Trans Am Soc Artif Intern Organs. 1971;17:81-91. PMID 5158139.
  4. ^ Lysaght MJ, Farrell PC: Membrane Phenomena and mass transfer kinetics in peritoneal dialysis, J Mem Sci 44: 5-33, 1989.
  5. ^ Lysaght MJ, Pollock CA, Hallet MD, Ibels LS, Farrell PC. The relevance of urea kinetic modeling to CAPD. ASAIO Trans. 1989 Oct-Dec;35(4):784-90. PMID 2611047.
  6. ^ 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.
  7. ^ Daugirdas JT et al. Surface-area-normalized (SAN) adjustment to Kt/V and weekly standard Kt/V. J Am Soc Nephrol (abstract) 2006. and Appendix A. Handbook of Dialysis, 4th Edition. Daugirdas JT, Blake PB, Ing TS, editors. Lippincott Williams and Wilkins, Philadelphia, 2007.
  8. ^ Scribner BH, Oreopoulos DG, The Hemodialysis Product (HDP): A Better Index of Dialysis Adequacy than Kt/V, Dialysis & Transplantation, 2002 Jan;31(1):13-15. Full Text.

[edit] External links

[edit] Hemodialysis

[edit] Peritoneal dialysis

[edit] Calculators

Urinary system - Kidney - edit
Renal fascia | Renal capsule | Renal cortex  (Renal column) | Renal medulla (Renal sinus, Renal pyramids) | Renal lobe | Cortical lobule | Medullary ray | Nephron 
afferent circulation: Renal artery → Interlobar arteries → Arcuate arteries → Cortical radial arteries → Afferent arterioles → Renal corpuscle (Glomerulus, Bowman's capsule)

kidney tubule: Proximal tubule → Loop of Henle (Descending, Thin ascending, Thick ascending)  → Distal convoluted tubule → Connecting tubule → Collecting ducts → Duct of Bellini → Renal papilla → Minor calyx → Major calyx → Renal pelvis → Ureter

efferent circulation: Glomerulus → Efferent arterioles → Peritubular capillaries/Vasa recta → Arcuate vein→ Interlobar veins→ Renal vein

juxtaglomerular apparatus: Macula densa, Juxtaglomerular cells, Extraglomerular mesangial cells
Renal physiology
Filtration - Ultrafiltration | Countercurrent exchange | Glomerular basement membrane | Podocyte | Filtration slits | Intraglomerular mesangial cells

Hormones affecting filtration - Antidiuretic hormone (ADH) | Aldosterone | Atrial natriuretic peptide

Endocrine - Renin | Erythropoietin (EPO) | Calcitriol (Active vitamin D) | Prostaglandins
Assessing Renal function / Measures of dialysis
Glomerular filtration rate | Creatinine clearance | Renal clearance ratio | Urea reduction ratio | Kt/V | Standardized Kt/V | Hemodialysis product
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