Dialysis Kt/V Calculator
Work out the dialysis dose from the urea before and after a session, with the reduction ratio and the Kt/V values.
What it does
Dialysis is measured by how much urea it removes from the blood, and the number that carries this is called Kt/V. It is the clearance of urea times the length of the session, divided by the volume that the urea is spread through, so it ends up as a plain number with no units. The KDOQI guideline for haemodialysis says the delivered dose should be measured at least monthly and that the frequency of the treatments should be part of that dose.
The urea in the blood falls as the session runs, and the drop gives a first estimate of the dose. The simplest form, called the log ratio, is the natural log of the before value over the after value. The UK Kidney Association explains that this simple form comes from the fact that the rate of removal of urea is proportional to its concentration, so the concentration after a session is the concentration before multiplied by the exponential of minus Kt/V.
Two refinements follow. The single pool Kt/V, in the form proposed by Daugirdas, also takes into account the fluid removed during the session and the size of the patient, and it is the value most units aim at. The equilibrated Kt/V then corrects for urea rebound, the rise in urea during roughly the hour after the machine stops, because dialysis pulls urea out of the blood faster than it can leave the tissues.
This page runs the chain from a pre dialysis and a post dialysis urea value. Give it those two numbers, the length of the session, the fluid removed and the target weight, and it returns the reduction ratio, the log ratio, the single pool value and the equilibrated value, with a plain comparison against the guideline targets.
The limits are important. The urea values have to come from a properly timed sample, taken at the end of the session rather than after the patient has been sitting for a while, and the formulae are approximations of the full kinetic model that uses three measurements. Most importantly, no number on this page decides whether a treatment is right for one person. That decision belongs to the treating team.
How to use
- Enter the urea value from before the session, in milligrams per decilitre.
- Enter the urea value from the end of the session, taken as soon as the blood is returned.
- Enter the length of the session on the machine.
- Enter the fluid removed during the session and the patient's target weight, which together give the ultrafiltration term used in the single pool value.
- Read the reduction ratio and the log ratio first, since they need nothing but the two urea values.
- Read the single pool and the equilibrated values, then check the comparison with the guideline targets. Take the whole set to your dialysis team.
Formula
- URR
- Urea reduction ratio, the share of the urea removed during the session, in percent.
- Kt/V
- Dialysis dose, the clearance of urea times the time divided by the volume of urea distribution.
- R
- Ratio of the post dialysis urea to the pre dialysis urea.
- UF
- Volume of fluid removed during the session, in litres.
- W
- Target weight of the patient, in kilograms.
The equilibrated value uses the Tattersall version of the rebound correction, which is the single pool value times the time in minutes, divided by the time in minutes plus 35. The 35 is replaced by 22 for a patient dialysing through a catheter, because the rebound is then smaller. The UK Kidney Association also notes that for a four hour session with fluid removal of 2 percent of the target weight in a fistula patient, the log ratio is almost the same as the equilibrated value, and that a reduction ratio of 70 percent corresponds to an equilibrated Kt/V of 1.2.
Worked example
Example: a four hour session with urea 60 before and 18 after
Defaults: urea 60 mg per dL before and 18 mg per dL after, a 4 hour session, 2 L of fluid removed and a target weight of 70 kg.
- The reduction ratio is 100 x (60 - 18) / 60 = 70.00 %.
- The log ratio is the natural log of 60 over 18, which is ln(3.3333) = 1.2040.
- The ratio R is 18 / 60 = 0.3, and the fluid term is 2 / 70 = 0.028571.
- Single pool: -ln(0.3 - 0.008) + (4 - 3.5 x 0.3) x 0.028571 = 1.2311 + 0.0843 = 1.3153.
- For the equilibrated value the session is 240 minutes, so eKt/V = 1.3153 x 240 / (240 + 35) = 1.1479.
- The single pool value of 1.3153 sits between the 1.2 minimum and the 1.4 target for a thrice weekly schedule.
- The tool shows 70.00 %, 1.2040, 1.3153, 1.1479 and that the dose is between the 1.2 minimum and the 1.4 target.
Reference table
| Urea after | Reduction ratio | Log ratio | Single pool Kt/V | Equilibrated Kt/V |
|---|---|---|---|---|
| 24 mg per dL | 60.00 % | 0.9163 | 0.9885 | 0.8627 |
| 21 mg per dL | 65.00 % | 1.0498 | 1.1284 | 0.9848 |
| 18 mg per dL | 70.00 % | 1.2040 | 1.2900 | 1.1258 |
| 15 mg per dL | 75.00 % | 1.3863 | 1.4813 | 1.2928 |
| 12 mg per dL | 80.00 % | 1.6094 | 1.7163 | 1.4978 |
Limits
- The formulae are approximations. The full urea kinetic model uses three urea measurements and fits the clearance and the urea generation, and that is the reference method.
- The post dialysis sample has to be taken at the end of the session. A sample taken later shows a higher urea because of rebound.
- The log ratio ignores fluid removal, urea generation and rebound, so it can overstate the dose in short sessions and understate it in long ones.
- The target numbers apply to thrice weekly haemodialysis. Other schedules, and patients with some residual kidney function, have different goals.
Common mistakes
- Taking the post dialysis urea sample too late. Rebound raises the value, and the calculated dose comes out lower than it really was.
- Using the log ratio and treating it as the delivered dose. It ignores the fluid removed and the rebound, and the guideline targets are set on the single pool and the equilibrated values.
- Forgetting that the fluid term needs the target weight, and using the current weight instead.
- Comparing a Kt/V from a once weekly or home schedule against the thrice weekly targets.
- Reading a number on this page as a verdict on a treatment. The dose is one part of a decision that also covers blood pressure, fluid removal, nutrition and the other blood tests.
Try it yourself
Quick checks. Answers sit tucked under each question.
A session takes urea from 70 down to 25 over 4 hours with 2 L removed on a 70 kg patient. What is the dose?
A reduction ratio of 64.29 %, a log ratio of 1.0296, a single pool Kt/V of 1.1308 and an equilibrated value of 0.9869. The single pool value sits below the 1.2 minimum the guideline asks for, which is the kind of finding the dialysis team would want to look at.
What happens with a 3 hour session that takes urea from 50 to 15 with 1.5 L removed on a 62 kg patient?
A reduction ratio of 70.00 %, a log ratio of 1.2040, a single pool Kt/V of 1.3024 and an equilibrated value of 1.0904. The same reduction ratio in a shorter session gives a lower equilibrated dose, because there is less time for rebound to matter.
What does the log ratio assume?
That urea is spread evenly through the body water, that no urea is generated during the session and that no fluid is removed. It is the simplest version and the easiest to check by hand.
Questions
What does Kt/V mean?
K is the clearance of urea, t is the time of the session and V is the volume that urea is distributed through. The guideline puts it as the delivered dose of haemodialysis, and it is measured at least monthly.
What is the guideline target?
The KDOQI clinical practice guideline for haemodialysis recommends a target single pool Kt/V of 1.4 per session for a patient treated thrice weekly, with a minimum delivered value of 1.2.
What is the difference between the single pool and the equilibrated value?
The single pool value treats the body as one pool of water, while the equilibrated value corrects for the fact that urea comes back from the tissues during and after the session. For short treatments the difference matters more.
Why is the reduction ratio on its own not enough?
The UK Kidney Association points out that it ignores clearance by ultrafiltration, urea generation and urea rebound, so it tends to overestimate the dose in shorter sessions and underestimate it in sessions longer than four hours.
What is urea rebound?
The rise in blood urea during roughly the hour after dialysis finishes. Dialysis clears urea from the blood faster than it can leave the cells, so urea flows back into the blood and the post dialysis value understates the real effect.
Does the frequency of the treatments matter to the dose?
Yes. The guideline says the frequency of the treatments should be included in the expression of the dose, so the same session length means a different weekly dose on a twice weekly schedule than on a thrice weekly one.
Sources
- UK Kidney Association, appendix A: simplified mathematics of urea clearance
- National Kidney Foundation: KDOQI clinical practice guideline for haemodialysis adequacy