Transcript
0:00Linear pharmacokinetics
Lesson 6.5 of our pharmacokinetic models module: nonlinear pharmacokinetics. Plasma is the liquid part of the blood. The rate of elimination is the amount of drug removed per unit of time. Clearance is the rate of elimination divided by the plasma concentration. Exposure is the area under the plasma concentration-time curve, the AUC. Parameters are the values of a pharmacokinetic model, such as clearance. In linear pharmacokinetics, the parameters stay the same at every dose. Exposure then rises in proportion to the dose. This property is dose proportionality.
0:53Nonlinear pharmacokinetics and saturation
In nonlinear pharmacokinetics, at least one parameter changes with the dose. Exposure can then rise more, or less, than in proportion to the dose. Enzymes, the proteins that make chemical reactions faster, and transport proteins, which carry drugs across cell membranes, have a limited number of binding sites. Saturation is the condition in which most of these sites are occupied, so the rate rises little when the concentration rises. It is a common cause of nonlinear pharmacokinetics, although few drugs show nonlinear behavior with clinical effects.
1:41The Michaelis-Menten equation
The Michaelis-Menten equation gives the rate as Vmax times C, divided by the sum of Km and C. C is the drug concentration, Vmax is the maximum rate, and Km is the concentration that gives half of Vmax. When C is much lower than Km, the rate is nearly proportional to C. When C is much higher, the rate stays close to Vmax. For saturable elimination, clearance is therefore Vmax divided by the sum of Km and C. It is nearly constant at low concentrations and falls as the concentration approaches and exceeds Km.
2:30Three causes of nonlinear pharmacokinetics
Three common causes of nonlinear pharmacokinetics are saturable metabolism, saturable absorption and saturable binding to plasma proteins.
2:43Saturable metabolism
The first is saturable metabolism. Metabolism is the chemical change of a drug by enzymes, mainly in the liver. At steady state, the dose rate, the dose per unit of time, equals the rate of elimination when the whole dose reaches the systemic circulation. When the concentration is near or above Km, clearance falls as the dose rate rises. The steady-state concentration then rises more than in proportion to the dose rate. When saturable metabolism is the only route of elimination, the concentration rises without a steady state at any dose rate above Vmax.
3:31Saturable absorption
The second is saturable absorption. Bioavailability is the fraction of an oral dose that reaches the systemic circulation unchanged. Gabapentin, a drug for seizures and nerve pain, crosses the gut wall by a saturable transport process. Its bioavailability fell from 60 to 33 percent as the daily dose rose from 900 to 3,600 milligrams. Its exposure therefore rises less than in proportion to the dose.
4:11Saturable binding to plasma proteins
The third is saturable binding to plasma proteins. The unbound fraction is the fraction of drug in plasma not bound to proteins. When most binding sites on the plasma proteins are occupied, the unbound fraction rises with the concentration. The total concentration then rises less than in proportion to the unbound concentration. In six healthy subjects, the unbound fraction of valproic acid, a drug for epilepsy, rose from 7 to 10 percent when the dose doubled.
4:52Phenytoin
Phenytoin, a drug for epilepsy, shows how saturable metabolism makes a small dose increase give a large rise in concentration. The liver enzymes CYP2C9 and CYP2C19 convert up to 90 percent of a phenytoin dose to one inactive metabolite. The usual target range of the total plasma concentration is 10 to 20 milligrams per liter, and higher concentrations raise the risk of side effects.
5:29Phenytoin: Vmax and Km
A population analysis used data from 322 patients. For a typical 70-kilogram European adult, Vmax was 415 milligrams per day, and Km was 5.7 milligrams per liter. This Km is below the target range. With these values, the Michaelis-Menten equation gives a steady-state concentration of 10 milligrams per liter at 264 milligrams per day, and 20 at 323. A dose increase of about 22 percent thus doubles the concentration.
6:14Phenytoin: dose increments
In each of 12 patients with epilepsy, the concentration rose more than in proportion to the dose above 6 to 9 milligrams per liter. In one patient, the rate of metabolite excretion in urine did not rise while the concentration rose steeply. The authors explained this as the limit of the body's capacity to metabolize phenytoin. A second study reported that, in most patients, an extra 50 to 100 milligrams per day raises the concentration across the whole target range. Vmax and Km also differ between patients, so doctors adjust the phenytoin dose of each patient to the measured plasma concentration.
7:08Summary
In summary, in linear pharmacokinetics, exposure rises in proportion to the dose. Saturable metabolism lowers clearance at concentrations near and above Km, so the steady-state concentration rises more than in proportion to the dose rate. Saturable absorption lowers the bioavailability of gabapentin at higher doses, so its exposure rises less than in proportion to the dose. Saturable binding raises the unbound fraction, as for valproic acid. In a typical 70-kilogram European adult, the Km of phenytoin is below its target range. A second study reported that, in most patients, an extra 50 to 100 milligrams per day raises the concentration across the whole range. This concludes lesson 6.5 on nonlinear pharmacokinetics.
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