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The Pharmacokinetics series - Non-linear Kinetics
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Quite simply, non-linearity usually happens as a consequence of the saturation of some process involved in drug disposition. Saturability is normal in every biological process as long as you can keep increasing the concentration of the substrate.
The biological processes that concern us here are those in involved in drug disposition. Commonly, these are drug transporters, enzymes and binding proteins. For the sake of this discussion, we will just concentrate on enzymes involved in drug metabolism.
The reason for our concern is that the saturability of enzymes causes therapeutic difficulties. In a linear system, there is a constant and direct relationship between dose and steady state concentrations of a drug. But with saturation of the drug metabolism enzymes, drug concentrations rise disproportionately with any increase in dose
Let me explain. You’ve seen this graph before. In a linear pharmacokinetic model, the elimination rate is concentration dependent. And clearance is a constant. On a semi-log plot, you get a straight line where the slope is the elimination rate constant. Under these circumstance, there is a direct relationship between the dose and the area under the curve. As you increase the dose, the area under the curve increases proportionately. Dosage adjustments are a relatively easy task.
Under non-linear kinetics, the rate of elimination is not concentration dependent, but is a constant. Here clearance is inversely related to the concentration. The semi-log plot here is a convex. Because the clearance is inversely related to the concentrations, as you increase the dose, the clearance decreases, and the area under the curve show disprortionately large increases.
In most textbooks, linear and non-linear pharmacokinetics are presented as if they are alternate realities, not unlike what I have just shown you. Unfortunately this is a gross over-simplification, and a false dichotomy. In reality, linear and non-linear models are merely extremes of the same continuum.
You see, the elimination rate of any drug is actually described by a function that is similar to the Michaelis – Menten expression for enzyme kinetics – (Vmax * Concentration) divided by (Km+ concentration). The full elimination profile looks something like this. This is in fact a simulation of a large single dose profile for phenytoin.
If concentrations are very much lower compared to the Km of the elimination process, Km + C simplifies to Km, and the equation approximates a first order model. In this case, because for phenytoin, the Km is about 0.09 mg/mL, the truly linear part of the profile is best seen at the curved lower right extreme of the plot, a bit beyond the range shown.
By contrast, if concentrations are much higher compared to Km, The concentration term may be eliminated from the equation. Here it approximates a zero order model. You can see this best at the extreme top left of the plot, where the elimination profile approximates a straight line.
This is the line of identity with the max rate of elimination. You can see that the true zero order occurs only at the extreme upper end of the plot. For the most part, the curve deviates from the maximum rate until it approaches first order at the other extreme end of the graph.
Note also that the therapeutic range is midway between these two extremes, where it is neither completely zero order or first order. Under such conditions, you need to be careful about dosage adjustments. Most drugs probably operate somewhere between the extremes, perhaps more of one than the other, but not being completely first or zero order.
Here is a series of plots showing the changes in steady state concentrations following increasing doses of phenytoin. You can see how easy, the concentrations move out of the therapeutic range, with relatively minor changes to the dose. Note also how the time to reach steady state changes. At the highest dose, steady state hasn’t even been established after 2 weeks.
I hope you can now better understand and appreciate the complexities introduced by non-linearity in elimination kinetics.
Here are some tips for you. If you have to make dosage adjustments, do so cautiously. Check plasma concentrations regularly. If you are dosing with phenytoin, a loading dose may be necessary.
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The biological processes that concern us here are those in involved in drug disposition. Commonly, these are drug transporters, enzymes and binding proteins. For the sake of this discussion, we will just concentrate on enzymes involved in drug metabolism.
The reason for our concern is that the saturability of enzymes causes therapeutic difficulties. In a linear system, there is a constant and direct relationship between dose and steady state concentrations of a drug. But with saturation of the drug metabolism enzymes, drug concentrations rise disproportionately with any increase in dose
Let me explain. You’ve seen this graph before. In a linear pharmacokinetic model, the elimination rate is concentration dependent. And clearance is a constant. On a semi-log plot, you get a straight line where the slope is the elimination rate constant. Under these circumstance, there is a direct relationship between the dose and the area under the curve. As you increase the dose, the area under the curve increases proportionately. Dosage adjustments are a relatively easy task.
Under non-linear kinetics, the rate of elimination is not concentration dependent, but is a constant. Here clearance is inversely related to the concentration. The semi-log plot here is a convex. Because the clearance is inversely related to the concentrations, as you increase the dose, the clearance decreases, and the area under the curve show disprortionately large increases.
In most textbooks, linear and non-linear pharmacokinetics are presented as if they are alternate realities, not unlike what I have just shown you. Unfortunately this is a gross over-simplification, and a false dichotomy. In reality, linear and non-linear models are merely extremes of the same continuum.
You see, the elimination rate of any drug is actually described by a function that is similar to the Michaelis – Menten expression for enzyme kinetics – (Vmax * Concentration) divided by (Km+ concentration). The full elimination profile looks something like this. This is in fact a simulation of a large single dose profile for phenytoin.
If concentrations are very much lower compared to the Km of the elimination process, Km + C simplifies to Km, and the equation approximates a first order model. In this case, because for phenytoin, the Km is about 0.09 mg/mL, the truly linear part of the profile is best seen at the curved lower right extreme of the plot, a bit beyond the range shown.
By contrast, if concentrations are much higher compared to Km, The concentration term may be eliminated from the equation. Here it approximates a zero order model. You can see this best at the extreme top left of the plot, where the elimination profile approximates a straight line.
This is the line of identity with the max rate of elimination. You can see that the true zero order occurs only at the extreme upper end of the plot. For the most part, the curve deviates from the maximum rate until it approaches first order at the other extreme end of the graph.
Note also that the therapeutic range is midway between these two extremes, where it is neither completely zero order or first order. Under such conditions, you need to be careful about dosage adjustments. Most drugs probably operate somewhere between the extremes, perhaps more of one than the other, but not being completely first or zero order.
Here is a series of plots showing the changes in steady state concentrations following increasing doses of phenytoin. You can see how easy, the concentrations move out of the therapeutic range, with relatively minor changes to the dose. Note also how the time to reach steady state changes. At the highest dose, steady state hasn’t even been established after 2 weeks.
I hope you can now better understand and appreciate the complexities introduced by non-linearity in elimination kinetics.
Here are some tips for you. If you have to make dosage adjustments, do so cautiously. Check plasma concentrations regularly. If you are dosing with phenytoin, a loading dose may be necessary.
Feel free to use, share and subscribe!
and at our Facebook page:
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