## Kt/V – Wikipedia

In drugs, Kt/V is a quantity used to quantify hemodialysis and peritoneal dialysis therapy adequacy.

• Okay – dialyzer clearance of urea
• t – dialysis time
• V – quantity of distribution of urea, roughly equal to affected person’s complete physique water

Within the context of hemodialysis, Kt/V is a pseudo-dimensionless quantity; it’s depending on the pre- and post-dialysis focus (see under). It’s not the product of Okay and t divided by V, as can be the case in a real dimensionless quantity.[1] In peritoneal dialysis, it is not dimensionless in any respect.

It was developed by Frank Gotch and John Sargent as a manner for measuring the dose of dialysis after they analyzed the information from the Nationwide Cooperative Dialysis Examine.[2] In hemodialysis the US Nationwide Kidney Basis Kt/V goal is ≥ 1.3, in order that one can ensure that the delivered dose is no less than 1.2.[3] In peritoneal dialysis the goal is ≥ 1.7/week.[3]

Regardless of the title, Kt/V is kind of completely different from standardized Kt/V.

## Rationale for Kt/V as a marker of dialysis adequacy

Okay (clearance) multiplied by t (time) is a quantity (since mL/min × min = mL, or L/h × h = L), and (Okay × t) will be regarded as the mL or L of fluid (blood on this case) cleared of urea (or some other solute) through the course of a single therapy. V is also a quantity, expressed in mL or L. So the ratio of Okay × t / V is a so-called “dimensionless ratio” and will be regarded as a a number of of the quantity of plasma cleared of urea divided by the distribution quantity of urea. When Kt/V = 1.0, a quantity of blood equal to the distribution quantity of urea has been fully cleared of urea.

The connection between Kt/V and the focus of urea C on the finish of dialysis will be derived from the first-order differential equation that describes exponential decay and fashions the clearance of any substance from the physique the place the focus of that substance decreases in an exponential style:

${displaystyle V{frac {dC}{dt}}=-Kcdot Cqquad (1)}$

the place

• C is the focus [mol/m3]
• t is the time [s]
• Okay is the clearance [m3/s]
• V is the quantity of distribution [m3]

From the above definitions it follows that

${displaystyle {frac {dC}{dt}}}$

is the primary spinoff of focus with respect to time, i.e. the change in focus with time.

This equation is separable and will be built-in (assuming Okay and V are fixed) as follows:

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

After integration,

${displaystyle ln(C)=-{frac {Kcdot t}{V}}+{mbox{const}}qquad (2b)}$

the place

• const is the fixed of integration

If one takes the antilog of Equation 2b the result’s:

${displaystyle C=e^{-{frac {Kcdot t}{V}}+const}qquad (2c)}$

the place

By integer exponentiation this may be written as:

${displaystyle C=C_{0}e^{-{frac {Kcdot t}{V}}}qquad (3)}$

the place

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

The above equation can be written as

${displaystyle {frac {Kcdot t}{V}}=ln {frac {C_{o}}{C}}qquad (4)}$

[2]

Usually we measure postdialysis serum urea nitrogen focus C and evaluate this with the preliminary or predialysis stage C0. The session size or time is t and that is measured by the clock. The dialyzer clearance Okay is normally estimated, based mostly on the urea switch means of the dialyzer (a operate of its dimension and membrane permeability), the blood movement price, and the dialysate movement price.[4] In some dialysis machines, the urea clearance throughout dialysis is estimated by testing the power of the dialyzer to take away a small salt load that’s added to the dialysate throughout dialysis.

## Relation to URR

The URR or Urea discount ratio is solely the fractional discount of urea throughout dialysis. So by definition, URR = 1 –C/C0. So 1-URR = C/C0. So by algebra, substituting into equation (4) above, since ln C/C0 = – ln C0/C, we get:

${displaystyle {frac {Kcdot t}{V}}=-ln(1-URR).qquad (8)}$

### Pattern calculation

Affected person has a mass of 70 kg (154 lb) and will get a hemodialysis therapy that lasts 4 hours the place the urea clearance is 215 mL/min.

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

Subsequently:

Kt/V = 1.23

Because of this if you happen to dialyze a affected person to a Kt/V of 1.23, and measure the postdialysis and predialysis urea nitrogen ranges within the blood, then calculate the URR, then -ln (1-URR) ought to be about 1.23.

The maths doesn’t fairly work out, and extra difficult relationships have been worked-out to account for the fluid removing (ultrafiltration) throughout dialysis in addition to urea era (see urea discount ratio). Nonetheless, the URR and Kt/V are so intently associated mathematically, that their predictive energy has been proven to be no completely different when it comes to prediction of affected person outcomes in observational research.

### Publish-dialysis rebound

The above evaluation assumes that urea is faraway from a single compartment throughout dialysis. The truth is, this Kt/V is normally known as the “single-pool” Kt/V. Because of the a number of compartments within the human physique, a big focus rebound happens following hemodialysis.
Often rebound lowers the Kt/V by about 15%. The quantity of rebound is dependent upon the speed of dialysis (Okay) in relation to the dimensions of the affected person (V). Equations have been devised to foretell the quantity of rebound based mostly on the ratio of Okay/V, however normally this isn’t mandatory in medical apply. One can use such equations to calculate an “equilibrated Kt/V” or a “double-pool Kt/V”, and a few suppose that this ought to be used as a measure of dialysis adequacy, however this isn’t broadly executed in america, and the KDOQI pointers (see under) suggest utilizing the common single pool Kt/V for simplicity.

## Peritoneal dialysis

Kt/V (within the context of peritoneal dialysis) was developed by Michael J. Lysaght in a sequence of articles on peritoneal dialysis.[5][6]

The steady-state resolution of a simplified mass switch equation that’s used to explain the mass change over a semi-permeable membrane and fashions peritoneal dialysis is

${displaystyle C_{B}={dot {m}}/Okay.qquad (6a)}$

the place

• CB is the focus within the blood [ mol/m3 ]
• OkayD is the clearance [ m3/s ]

• ${displaystyle {dot {m}}}$

is the urea mass era [ mol/s ]

This can be written as:

${displaystyle Okay={dot {m}}/C_{B}.qquad (6b)}$

The mass era (of urea), in regular state, will be expressed because the mass (of urea) within the effluent per time:

${displaystyle {dot {m}}={frac {C_{E}cdot V_{E}}{t}}.qquad (6c)}$

the place

• CE is the focus of urea in effluent [ mol/m3 ]
• VE is the quantity of effluent [ m3 ]
• t is the time [ s ]

Lysaght, motivated by Equations 6b and 6c, outlined the worth OkayD:

${displaystyle K_{D}={frac {C_{E}cdot V_{E}}{C_{B}cdot t}}qquad (6d)}$

Lysaght makes use of “ml/min” for the clearance. As a way to convert the above clearance (which is in m3/s) to ml/min one has to multiply by 60 × 1000 × 1000.

As soon as OkayD is outlined the next equation is used to calculate Kt/V:

${displaystyle {frac {Kcdot t}{V}}={frac {7/3cdot K_{D}}{V_{D}}}qquad (7a)}$

the place

• V is the quantity of distribution. It must be in litres (l), because the equation will not be actually non-dimensional.

The 7/3 is used to regulate the Kt/V worth so it may be in comparison with the Kt/V for hemodialysis, which is often executed thrice weekly within the USA.

### Weekly Kt/V

To calculate the weekly Kt/V (for peritoneal dialysis) OkayD must be in litres/day.
Weekly Kt/V is outlined by the next equation:

${displaystyle {mbox{Weekly }}Kt/V={frac {7K_{D}[l/{mbox{day}}]}{V[l]}}.qquad (7b)}$

### Pattern calculation

Assume:

• ${displaystyle C_{B{mbox{ imply}}}=22.817{mbox{ mmol/L}}}$

• ${displaystyle C_{D}=17.524{mbox{ mmol/L}}}$

• ${displaystyle V_{D}=3.75{mbox{ L per change or }}15{mbox{ L/day}}}$

• ${displaystyle V_{B}=40.6 L}$

Then by Equation 6d OkayD is: 1.3334e−07 m3/s or 8.00 mL/min or 11.52 L/d.

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

### A simplified evaluation of Kt/V in PD

On a sensible stage, in peritoneal dialysis the calculation of Kt/V is commonly comparatively straightforward as a result of the fluid drained is normally near 100% saturated with urea,[citation needed] i.e. the dialysate has equilibriated with the physique. Subsequently, the day by day quantity of plasma cleared is solely the drain quantity divided by an estimate of the affected person’s quantity of distribution.

For example, if somebody is infusing 4 2 liter exchanges a day, and drains out a complete of 9 liters per day, then they drain 9 × 7 = 63 liters per week. If the affected person has an estimated complete physique water quantity V of about 35 liters, then the weekly Kt/V can be 63/35, or about 1.8.

The above calculation is restricted by the truth that the serum focus of urea is altering throughout dialysis.
In automated PD this transformation can’t be ignored; thus, blood samples are normally measured at a while level within the day and assumed to be consultant of a median worth. The clearance is then calculated utilizing this measurement.

Kt/V has been broadly adopted as a result of it was correlated with survival. Earlier than Kt/V nephrologists measured the serum urea focus (particularly the
time-averaged focus of urea (TAC of urea)), which was discovered to not be correlated with survival (because of its robust dependence on protein consumption) and thus deemed an unreliable marker of dialysis adequacy.

• It’s complicated and tedious to calculate. Many nephrologists have problem understanding it.
• Urea will not be related to toxicity.[7]
• Kt/V solely measures a change within the focus of urea and implicitly assumes the clearance of urea is similar to different toxins. (It ignores molecules bigger than urea having diffusion-limited transport – so known as center molecules).
• Kt/V doesn’t take note of the position of ultrafiltration.
• It ignores the mass switch between physique compartments and throughout the plasma membrane (i.e. intracellular to extracellular transport), which has been proven to be essential for the clearance of molecules similar to phosphate. Sensible use of Kt/V requires adjustment for rebound of the urea focus as a result of multi-compartmental nature of the physique.
• Kt/V might drawback girls and smaller sufferers when it comes to the quantity of dialysis obtained. Regular kidney operate could also be modeled as optimum Glomerular filtration price or GFR. GFR is normally normalized in individuals to physique floor space. A person and a lady of comparable physique floor areas may have markedly completely different ranges of complete physique water (which corresponds to V). Additionally, smaller individuals of both intercourse may have markedly decrease ranges of V, however solely barely decrease ranges of physique floor space. Because of this, any dialysis dosing system that’s based mostly on V might are inclined to underdose smaller sufferers and ladies. Some investigators have proposed dosing based mostly on floor space (S) as an alternative of V, however clinicians normally measure the URR after which calculate Kt/V. One can “modify” the Kt/V, to calculate a “surface-area-normalized” or “SAN”-Kt/V in addition to a “SAN”-standard Kt/V. This places a wrapper round Kt/V and normalizes it to physique floor space.[8]

### Significance of complete weekly dialysis time and frequency

Kt/V has been criticized as a result of fairly excessive ranges will be achieved, significantly in smaller sufferers, throughout comparatively brief dialysis periods. That is very true for small individuals, the place “satisfactory” ranges of Kt/V usually will be achieved over 2 to 2.5 hours. One essential a part of dialysis adequacy has to do with satisfactory removing of salt and water, and likewise of solutes apart from urea, particularly bigger molecular weight substances and phosphorus. Phosphorus and related molecular weights stay elusive to filtration of any diploma. Quite a lot of research recommend {that a} longer period of time on dialysis, or extra frequent dialysis periods, result in higher outcomes. There have been varied different strategies of measuring dialysis adequacy, most of which have proposed some quantity based mostly on Kt/V and variety of dialysis periods per week, e.g., the standardized Kt/V, or just variety of dialysis periods per week squared multiplied by the hours on dialysis per session; e.g. the hemodialysis product by Scribner and Oreopoulos[9] It isn’t sensible to present lengthy dialysis periods (better than 4.5 hours) 3x/week in a dialysis heart through the day. Longer periods will be virtually delivered if dialysis is completed at dwelling. Most expertise has been gained with such lengthy dialysis periods given at night time. Some facilities are providing every-other-night or 3x/week nocturnal dialysis. The advantages of giving extra frequent dialysis periods can be an space of energetic research, and new easy-to-use machines are allowing simpler use of dwelling dialysis, the place 2–3+ hour periods will be given 4–7 days per week.

### Kt/V minimums and targets for hemodialysis

One query when it comes to Kt/V is, how a lot is sufficient? The reply has been based mostly on observational research, and the NIH-funded HEMO trial executed in america, and likewise, on kinetic evaluation.
For a US perspective, see the[10] and for a United Kingdom perspective see:[11] In keeping with the US pointers, for 3x/week dialysis a Kt/V (with out rebound) ought to be 1.2 at a minimal with a goal worth of 1.4 (15% above the minimal values). Nonetheless, there may be suggestive proof that bigger quantities might should be given to girls, smaller sufferers, malnourished sufferers, and sufferers with medical issues. The advisable minimal Kt/V worth modifications relying on what number of periods per week are given, and is diminished for sufferers who’ve a considerable diploma of residual renal operate.

### Kt/V minimums and targets for peritoneal dialysis

For a US perspective, see:[12] For america, the minimal weekly Kt/V goal was 2.0. This was lowered to 1.7 in view of the outcomes of a big randomized trial executed in Mexico, the ADEMEX trial,[13] and likewise from reanalysis of earlier observational research outcomes from the angle of residual kidney operate.

For a United Kingdom perspective see:[14] That is nonetheless in draft kind.

## References

1. ^ Bonert, M.; Saville, BA. (2010). “A non-dimensional evaluation of hemodialysis”. Open Biomed Eng J. 4: 138–55. doi:10.2174/1874120701004010138. PMC 3111706. PMID 21673980.
2. ^ a b Gotch FA, Sargent JA (September 1985). “A mechanistic evaluation of the Nationwide Cooperative Dialysis Examine (NCDS)”. Kidney Int. 28 (3): 526–34. doi:10.1038/ki.1985.160. PMID 3934452.
3. ^ a b “Scientific apply pointers for diet in continual renal failure. Okay/DOQI, Nationwide Kidney Basis”. Am J Kidney Dis. 35 (6 Suppl 2): S1–140. 2000. PMID 10895784. Archived from the unique on 2006-09-03.
4. ^ Babb AL, Popovich RP, Christopher TG, Scribner BH (1971). “The genesis of the sq. meter-hour speculation”. Trans Am Soc Artif Intern Organs. 17: 81–91. PMID 5158139.
5. ^ Lysaght MJ, Farrell PC (1989). “Membrane Phenomena and mass switch kinetics in peritoneal dialysis”. Journal of Membrane Science. 44 (1): 5–33. doi:10.1016/S0376-7388(00)82339-X.
6. ^ Lysaght MJ, Pollock CA, Hallet MD, Ibels LS, Farrell PC (1989). “The relevance of urea kinetic modeling to CAPD”. ASAIO Trans. 35 (4): 784–90. PMID 2611047.
7. ^ Johnson WJ, Hagge WW, Wagoner RD, Dinapoli RP, Rosevear JW (January 1972). “Results of urea loading in sufferers with far-advanced renal failure”. Mayo Clinic Proceedings. 47 (1): 21–9. PMID 5008253.
8. ^ Daugirdas JT et al. Floor-area-normalized (SAN) adjustment to Kt/V and weekly customary Kt/V. J Am Soc Nephrol (summary) 2006. and Appendix A. Handbook of Dialysis, 4th Version. Daugirdas JT, Blake PB, Ing TS, editors. Lippincott Williams and Wilkins, Philadelphia, 2007.
9. ^ Scribner BH, Oreopoulos DG (January 2002). “The Hemodialysis Product (HDP): A Higher Index of Dialysis Adequacy than Kt/V” (PDF). Dialysis & Transplantation. 31 (1): 13–5. Archived from the unique (mirrored PDF) on 2016-03-03. Retrieved 2007-02-07.
10. ^ KDOQI Hemodialysis Adequacy Archived 2007-02-11 on the Wayback Machine Replace 2006.
11. ^ U.Okay. Renal Affiliation Scientific Follow Tips, 2006 Replace. Archived 2007-02-09 on the Wayback Machine
12. ^ KDOQI Peritoneal Adequacy Archived 2007-07-11 on the Wayback Machine Replace 2006.
13. ^ Paniagua R, Amato D, Vonesh E, et al. (Could 2002). “Results of elevated peritoneal clearances on mortality charges in peritoneal dialysis: ADEMEX, a potential, randomized, managed trial”. J Am Soc Nephrol. 13 (5): 1307–20. PMID 11961019.
14. ^ U.Okay. Renal Affiliation Scientific Follow Tips, Peritoneal Dialysis. Archived 2007-02-10 on the Wayback Machine 2006 Replace.