Zero-order Input Research Articles

Computation of the explicit solution to the Michaelis-Menten equation.

An explicit solution to the Michaelis-Menten differential equation with bolus and zero-order input is presented. This solution involves certain simple functions whose values are not readily available. Efficient algorithms for computing values of these functions to any desired degree of accuracy and FORTRAN codes for implementing them are also given.

The Wagner‐Nelson method applied to a multicompartment model with zero order input

It is shown that the Wagner-Nelson absorption method provides zero-order input rate constants exactly, or with small error, in a large number of cases where the two-compartment open disposition model applies. Factors affecting the accuracy of the method were studied with error-free simulated data. The method was applied to real data for three drugs. With ethanol infused over 2 h in eight human trials the estimated rate constant averaged 99.6 per cent of the known rate constant with a coefficient of variation of 6.86 per cent. With pindolol infused over 3 h five human subjects the estimated rate constant averaged 98.7 per cent of the known rate constant with a coefficient of variation of 22.5 per cent. With theophylline administered orally in a sustained-release form to seven human subjects the Wagner-Nelson method provided estimated zero-order rate constants which averaged 95.8 per cent of those estimated by an exact two-compartment absorption equation with a coefficient of variation of 38.1 per cent (in this case bolus intravenous data were available for the same subjects).

Pharmacokinetics of acyclovir in humans following intravenous administration: A model for the development of parenteral antivirals

Data are reported from three step-wise pharmacokinetic studies in 43 patients who received acyclovir. Dosage regimens began at 0.5 mg/kg administered as a single dose intravenously and were increased to 15 mg/kg per dose given three times dairy for five days. All patients evaluated were immunocompromised by underlying disease or received cytolytic and/or cytotoxic therapy. Patients with virologically confirmed herpes simplex or zoster infections were assessed in the multiday, multidose pharmacokinetic trial. Postinfusion plasma concentrations of acyclovir declined in a biphasic manner such that the plasma-concentration time data were fitted by a two-compartment, open-model with zero-order input. The drug's half-life showed little variation with a mean of 3.16 ± 0.20 hours. In both single-dose and multiple-dose studies there was dose proportionality with peak plasma levels and area under the plasma concentration-time curve indicating dose-independent pharmacokinetics. The kidney was the principal route of drug clearance with a mean recovery of 60 ± 12 percent. Renal clearance exceeded creatinine clearance indicating renal tubular secretion of drug. No significant clinical or laboratory evidence of toxicity appeared. These studies provide a foundation for the evaluation of acyclovir in controlled trials.

Nonlinear pharmacokinetics of ethanol: the disproportionate AUC-dose relationship.

Whole venous blood concentrations of ethyl alcohol were measured following the constant rate intravenous infusion of ethanol to four Beagle dogs. Five different doses (0.1-0.8 g ethanol/kg body weight) were administered at scheduled intervals. The area under the blood ethanol concentration-time curves (AUC) was found to demonstrate a markedly nonlinear relationship with the administered dose. Simulations of one and two compartment open models with Michaelis-Menten elimination kinetics and zero-order input are presented with their theoretical AUC-dose relationships.

Integrated equation to evaluate accumulation profiles of drugs eliminated by Michaelis-Menten kinetics

Using an equation for the calculation of plasma profiles of drug based on the zero-order input and Michaelis-Menten kinetic output in a one-compartment open model system, the times required to reach various degrees of several steady-state plasma concentrations of phenytoin are calculated. The effect of the apparent volume of distribution (due to intersubject variation or change in protein and/or tissue binding, etc.) on the time required to reach various fractions of steady-state plasma concentrations is discussed.

Pharmacokinetic Description of Drug Interactions by Enzyme Induction: Carbamazepine-Clonazepam in Monkeys

The applicability of a pharmacokinetic model for drug interactions by enzyme induction was tested in rhesus monkeys using a design in which both the inducer (carbamazepine) and the induced agent (clonazepam) were infused chronically. Two types of studies were conducted. Studies 1 and II examined the kinetic behavior of plasma clonazepam levels during induction and postinduction, respectively. The addition of carbamazepine (Study I) caused the preinduction clonazepam steady-state level to decrease exponentially to a lower (induced) steady state after lag times of 14.0–60.5hr, and the removal of carbamazepine (Study II) caused induced clonazepam steady-state levels to climb exponentially to a higher steady state after lag times of 34.0–81.0hr. The extent of induction ranged between 23 and 54%. The time course of clonazepam levels was described in terms of a one-compartment induction model with zero-order input and a metabolic clearance that increased (Study I) or decreased (Study II) exponentially with time. In both studies, induced clonazepam half-lives (3.7–7.7hr) were significantly shorter (p<0.0005) than control values (5.2–12.2hr). Apparent enzyme turnover half-lives were shorter in Study II (2.7–19.3hr) than in Study I (6.9–66.4hr). A two- to threefold increase in urinary excretion of D-glucaric acid during carbamazepine administration provided additional evidence that the present interaction was due to enzyme induction.

Rate of phenytoin accumulation in man: a simulation study.

Computer simulations were performed using a one-compartment open model with either first-order or zero-order input and either Michaelis-Menten or Michaelis-Menten and first-order elimination. Twelve theoretical cases constructed from various combinations of typical and atypical values for phenytoin pharmacokinetic parameters, Vmax and Km, were examined. In many cases, at least 90% of the eventual steady-state serum level would be achieved within 4 weeks when phenytoin was administered at an appropriate rate. In the case of a low-to-average Vmax value and an average-to-high Km value, an initial maintenance dose of 3–4 mg phenytoin sodium/kg/day would, within a few days, result in serum phenytoin levels above the usual therapeutic range. On the other hand, if Vmax and Km values were both low (3.8 mg/kg/day and 1.45 mg/liter, respectively), a very slow rate of accumulation would ensue. Thirty days after the start of 4 mg phenytoin sodium/kg/day, a serum level of about 16 μg/ml would likely occur. The magnitude of continued accumulation beyond this level would be significantly influenced by the rate of renal elimination of unchanged phenytoin. It is recommended that, after initiation or adjustment of phenytoin therapy, serum phenytoin levels be monitored weekly for 3–4 weeks, then monthly for 2 additional months. Long-term follow-up should include serum phenytoin levels every 3– 6 months or as clinically indicated. Appreciation of the characteristics of phenytoin accumulation in relation to rate of administration and individual pharmacokinetic parameters is important for accurate interpretation of serum phenytoin levels and rational adjustment of dosage regimens.

Volume of Distribution and Tissue Level Errors in Instantaneous Intravenous Input Assumptions

A comparison was made between instantaneous input assumption and short-term zero-order infusion for 1 and 2 min for several drugs showing fast distribution to the tissue compartments. The errors ranged from 9 to 40% for the volume of the central compartment, from 0.7 to 11% for the volume of distribution following pseudo-distribution equilibrium, and from 11 to 34% for the volume of distribution change at the end of the 2-min infusion period. Significant errors in the tissue levels also were observed. It was suggested that all intravenous administrations be considered as short-term zero-order inputs.