Harold Boxenbaum

Statistical estimations in pharmacokinetics

Several important statistical aspects of pharmacokinetic analyses by digital computer are discussed. These include selection of appropriate equations, weighting of data, precision of parameter estimates, comparisons of parameters, analysis of weighted residuals, and criteria useful in the selection of particular models. Data obtained after administration of isoniazid and isonicotinuric acid to man are analyzed to illustrate the usefulness of the discussed methods.

Interspecies scaling, allometry, physiological time, and the ground plan of pharmacokinetics

Interspecies variation in pharmacokinetics is considered and treated as a property and consequence of body size (allometry). Consequently, it is possible to reference (scale) pharmacokinetic parameters to the organisms individual anatomy, biochemistry, and/or physiology in such a manner that differences between species are nullified. Thus, in the mouse, rat, dog, monkey, and human, methotrexate plasma clearance always equals 133% of creatinine clearance and as such becomes invariant. Pharmacokinetic time (a variable in terms of chronological time) is shown to be a form of physiological time in which a pharmacokinetic event becomes the independent variable, e.g., disposition halflife. A relationship between pharmacokinetic time and body size is demonstrated. It is suggested that mans lesser quantitative ability to metabolize many drugs may be correlated with his enhanced longevity.

Interspecies variation in liver weight, hepatic blood flow, and antipyrine intrinsic clearance : extrapolation of data to benzodiazepines and phenytoin

The literature was reviewed to obtain data from 11 mammalian species on liver weight, hepatic blood flow, and antipyrine intrinsic clearance. It was demonstrated that liver weight and hepatic blood flow in all species could be readily related to body weight by a simple equation. Additionally, hepatic blood flow in all species was directly proportional to liver weight. With the exception of man, antipyrine intrinsic clearance was also directly proportional to liver weight. Mans intrinsic clearance was approximately one-seventh of that which would be predicted from other species. Data on benzodiazepines and phenytoin showed a similar pattern.

First‐Time‐in‐Human Dose Selection: Allometric Thoughts and Perspectives

Some of the many factors that influence dose selection in first‐time‐in‐human studies are examined. These include animal toxicology, toxicokinetics, allometric scaling, pharmacokinetics, body surface area correlations, and integration of preclinical pharmacologic and toxicologic data. Appropriate preclinical evaluation and analysis may reduce the frequency and severity of unexpected toxic events arising during single‐dose, phase I testing. However, significant intrinsic uncertainties in this process presently exist and will continue to exist well into the foreseeable future. With our present state of knowledge, we cannot provide a realistic and reasonable algorithm for ascertaining first‐time‐in‐human doses: any decision tree would be too unwieldy. There are several rules of thumb that do have a place in the evaluation and decision‐making process, however.

Scaling of antipyrine intrinsic clearance of unbound drug in 15 mammalian species

SummaryThe intrinsic clearance of unbound drug (CLuint) for antipyrine in 15 mammalian species was characterized by an equation of the form, CLuint=ϕ1 (body weight)ϕ2 (brain weight)ϕ3, where thetas are constants. Maximum lifespan potential in mammals can also be characterized by an equation of this form. It is suggested that the set of genetic mechanisms regulating longevity and other constitutional characteristics in species is also linked to rates of drug metabolism. The ability to scale interspecies data in pharmacokinetics is taken as an expression of this design principle.

Comparative pharmacokinetics of benzodiazepines in dog and man

The pharmacokinetic parameters disposition half-life, metabolic clearance, volume of distribution, intrinsic clearance of unbound drug, and (distributive tissue volume/unbound fraction in tissue) were compared for 12 benzodiazepines in dog and man. With the exception of volume of distribution, statistically significant correlations were obtained when parameters were plotted on a double logarithmic grid. In general, benzodiazepines were metabolized more rapidly and exhibited greater tissue distribution in dog than in man. The variability in parameters was such, however, as to make extrapolations from one species to another subject to considerable error.

Effective Half‐Life in Clinical Pharmacology

T he concept of an “effective half-life” for drug accumulation was initially posited by Kwan and Duggan in 19771 and was formally examined in 1984.2 In principle, an effective half-life is one that reflects drug accumulation, as opposed to one or more aspects of exponential disposition. Unfortunately, this concept has not received wide acceptance. The purpose of this commentary is to discuss effective half-life in simple mathematical terms and thus stimulate its use in clinical pharmacology. The concept of an effective half-life subsumes Wagner’s accumulation factor, R.3 Accordingly, R will initially be discussed, after which its relation to effective half-life will be examined. To simplify and focus the discussion, linear monoexponential disposition will initially be assumed.

Pharmacokinetics and Clinical Effects of Alprazolam Following Single and Multiple Oral Doses in Patients With Panic Disorder

The anxiolytic triazolobenzodiazepine alprazolam was administered to six male patients, aged 26 to 46 years, with panic disorder or agoraphobia (with panic attacks) to assess clinical effects and steady‐state pharmacokinetics following multiple dosing at three levels: 3.0 mg/d, 6.0 mg/d, and 9.0 mg/d. Multiple‐dose kinetics of alprazolam were compared with alprazolam disposition after a 1.0‐mg oral dose in the same patients. Kinetic variables after the single dose were very similar to those reported previously for healthy young male volunteers. Mean values were peak plasma concentration, 19 ng/mL; time of peak, 1.33 hours after dosage; elimination half‐life, 10.0 hours; total oral clearance, 1.11 mL/min/kg. During multiple dosage, mean steady‐state plasma concentrations (Css) was proportional to dosing rate, and steady‐state clearance was independent of dosage. Clinical improvement was rapid, with the greatest decrement in symptoms at the 3‐mg/d dosage, at a mean Css of 30 ng/mL. Further improvement was not seen at 6 mg/d (Css 62 ng/mL), or at 9 mg/d (Css, 103 ng/mL). Side effects, however, were directly related to dosage and plasma level, and increased progressively in number at the 3‐, 6‐, and 9‐mg/d dosage levels. Thus, the disposition of alprazolam in young male patients with panic disorder is essentially identical to that in healthy male volunteers of similar age. Alprazolam clearance is independent of dose and plasma concentration up to daily doses of at least 9 mg/d, with steady‐state plasma level proportional to dosing rate.

Desmethyldiazepam Pharmacokinetics: Studies Following Intravenous and Oral Desmethyldiazepam, Oral Clorazepate, and Intravenous Diazepam

After single 10‐mg intravenous (IV) doses of desmethyldiazepam (DMDZ) to 12 healthy human volunteers, (mean age, 62 years) blood samples were obtained over the next 14 or more days. Mean kinetic variables were volume of distribution (Vd), 90 liters; elimination half‐life (t1/2), 93 hours; and clearance, 12.3 mL/min. Vd was significantly correlated with body weight (r = .73, P <.01) and with percent ideal body weight (r = .91, P <.001). Eleven of the same subjects also received 5‐ to 15‐mg doses of IV diazepam (DZ). Mean kinetic variables were Vd, 180 liters; t1/2, 83 hours; and clearance, 28 mL/min. Clearances of DZ and DMDZ were significantly correlated (r = .73, P <.02). Based on area analysis, the extent of conversion of DZ to systemic DMDZ averaged 53%. After oral administration of DMDZ in tablet form (10 mg), or of clorazepate dipotassium in capsule form (15 mg), systemic availability of DMDZ from each of the oral dosage forms was not significantly different from 100%.

Pharmacokinetic Determinants in the Design and Evaluation of Sustained-Release Dosage Forms

A new method employing the principle of superimposition was developed to aid in the formulation of sustained-release dosage forms. Independently absorbed components of a product, e.g., waxed pellets for an oral capsule, are administered separately and their plasma level-time profiles determined. Using a trial and error procedure, the ratios of pellets are varied to obtain a desired plasma level-time profile. The use of (1) time averaged plasma concentration-time data, (2) amount remaining to be absorbed (excreted) plots, and (3) cumulative amount absorbed (excreted) plots were all shown to be inappropriate for pharmacokinetic analyses in general, and evaluation of sustained-release products in particular. It was recommended that raw plasma concentration-time data be made available for sustained-released products, and that individual rate of absorption plots be used to assess absorption kinetics. It was concluded that much of the sustained-release pharmacokinetic data presently in the literature have been presented in such a manner, e.g. averaged data, as to be of limited value.