Derivation and Application of K Ratio

So the question becomes how to derive the K ratio. Now we know for uremic patient k here the K is the overall elimination rate constant is equal to Knr plus kr. If we assume that we know excretion of the drug is proportionate to creatinine clearance which is truth for drugs that are extensively excreted by the kidneys. Then the top equation can be rewritten to the second one which says overall K is equal to Knr plus alpha times creatinine clearance. Don’t worry about too much about alpha is simply a proportionality constant. So it will rewrite the previous equation and then divide both sides of the equation by Kn that is by the elimination rate constant of the normal patient.

Then this is what we get the second equation at the bottom. Now the same equation this is the expression for K ratio. Now this equation appears to be complicated but in fact it is not. It is equivalent to y equals mx plus b where Y is the K ratio and creatinine clearance is the X and the B is the Y-intercept, which is the Knr to Kn ratio. Now when the ratio is equal to 1 indicate the kidney function is normal If the ratio is zero It indicates ESRD.

So here remember we make one assumption that is the Knr to kn ratio is a true constant That is to say that non renal excretion rate is the same for both the uremic and the normal patient. So based on that k ratio we can construct a graph such as this The k ratio on the y-axis. Creatinine clearance on the x-axis. And here you have drug categories A B C and the D. Now in terms of increasing order of necessity for dosing adjustment in renal failure, D is greater than C is greater than B and is greater than A. And in fact drug A does not need dosing adjustment in renal failure.

This is another graph based on K ratio on the left y-axis and a half-life ratio on the right y-axis. Likewise, creatinine clearance on the x-axis. Here the drugs are divided into A through L categories. And again in the order of increasing necessity for dosing adjustment in renal failure L requires the adjustment the most and A or even B really do not need adjustment.