William R. Gillespie

A polyexponential deconvolution method. Evaluation of the «gastrointestinal bioavailability» and mean In vivo dissolution time of some ibuprofen dosage forms

A new deconvolution algorithm (DCON) suitable for pharmacokinetic applications is presented. It requires that both the impulse and input responses, typically systemic drug levels, be well described by polyexponential equations. DCON has a wider range of applications than an earlier method (DECONV) from which it is derived. A FORTRAN program is provided, making implementation of the technique a simple matter. DCON is demonstrated to evaluate the “GI bioavailability,” defined as the rate and the extent of gastrointestinal drug release, of various ibuprofen dosage forms. The GI drug release kinetics exemplifies a pharmacokinetic system which cannot be evaluated using the previous deconvolution algorithm (DECONV) because of an initial zero drug level response. This limitation is not found in DCON. It is also demonstrated how the mean in vivo dissolution time MDT can be evaluated by deconvolution.

Theorems and implications of a model-independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. II. Clearance concepts applied to the evaluation of distribution kinetics

The disposition decomposition approach is employed to derive clearance parameters descriptive of drug distribution kinetics. The name distribution clearance, CLd,is given to a characteristic constant of linear and some nonlinear pharmacokinetic systems. CLdis the clearance associated with the steady-state rate of drug transfer from the peripheral tissues to the systemic circulation. Also introduced is the elimination clearance, CLe,which is associated with the total drug transfer rate from the systemic circulation in linear systems. Estimates of CLdand CLeare presented for several drugs.

Theorems and implications of a model-independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. III: Peripheral bioavailability and distribution time concepts applied to the evaluation of distribution kinetics

Disposition decomposition analysis (DDA) is applied to evaluate the rate and extent of drug delivery from the sampling compartment to the peripheral system, i.e., peripheral bioavailability. Four parameters are introduced which are useful in quantifying peripheral bioavailability. The compounded peripheral bioavailability, Fcomp,is the ratio between the total compounded amount of drug transferred to the peripheral system and the injected dose, D.The AUCperipheral bioavailability, FAUC,is the ratio between the area under the amount vs.time curves for the peripheral system and the sampling compartment. The distribution time td,is the time following an i.v. bolus at which the net transfer of drug to the peripheral system reverses in direction. The maximum peripheral bioavailability, Fmax,is the maximum fraction of an i.v. bolus dose that is present in the peripheral system at any one time. Equations are derived which permit estimation of those parameters from drug concentrations in the sampling compartment. Simple algorithms and a computer program are provided for estimating Fcomp, FAUC, td, Fmax,and other parameters relevant to DDA for drugs that exhibit a linear polyexponential bolus response. Estimates of Ecomp, FAUC, td,are presented for several drugs.

The determination of mean residence time using statistical moments:It is correct

The present communication seeks to end a controversy created by a recent publication regarding the applicability of statistical moment principles for determination of mean residence time of drug in the body ¯tb.It is shown that the equation ¯tb=AUMC/AUC iscorrect when applied to pharmacokinetic systems in which the total drug elimination rate is directly proportional to the drug concentration in the systemic circulation, i.e., firstorder central elimination. More general equations for ¯tbin terms of elimination rate, amount eliminated, and amount in the body are presented along with demonstrations of their utility.

A note on appropriate constraints on the initial input response when applying deconvolution

When deconvolution is employed to estimate cumulative input profiles, nonzero initial values may result unless certain constraints are imposed on the function used to approximate the input response c(t).It is shown that the initial value of the response to a nonimpulse input is zero, i.e., c(t0)=0,where t0is the input lag time. If, in addition, the initial value of the impulse response is zero, i.e.,cδ(0)=0,then c′(t0)=0.Therefore, it is appropriate to impose the constraint c(t0)=0in general and c′(t0)=0whencδ(0)=0if c(t)is the response to a nonimpulse input. The use of such constraints is demonstrated in an example where the cumulative in vivodissolution profile is estimated by deconvolution.

Linear systems approach to the analysis of an induced drug removal process. Phenobarbital removal by oral activated charcoal

The theory of linear systems analysis is applied to the evaluation of induced drug removal processes. The rate and extent of removal are determined by deconvolution for the case of phenobarbital removal from the systemic circulation by orally administered activated charcoal. The proposed method is model independent in the sense that no specific models of intrinsic or induced pharmacokinetic processes are required, and it is readily adapted to the analysis of most types of induced removal processes (hemodialysis, peritoneal dialysis, etc.). Application of the approach indicates that phenobarbital was removed from the systemic circulation to an extent of 25–53% following multiple oral doses of activated charcoal in healthy human subjects.

Theorems and implications of a model-independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. IV. Exact relationship between the terminal log-linear slope parameter beta and drug clearance

An exact formula relating the terminal log-linear beta parameter and the drug clearance is derived. The expression is valid for drugs with a linear, polyexponential disposition kinetics. The formula is useful for calculating the clearance when the clearance has changed between drug administrations and requires only drug level data from the terminal, log-linear elimination phase in addition to data from a single separate i.v. administration in the same subject. Data from an i. v. administration are necessary in order to apply the disposition decomposition technique to isolate and uniquely define the distribution kinetics in terms of the distribution function h(t).The different clearances can then be calculated from the beta values of the log-linear terminal drug level data and the parameters of h(t).The theoretical basis of the method and its assumptions and limitations are discussed and various pertinent theorems are presented. A computer program enabling an easy implementation of the proposed method is also presented. The mathematical and computational procedures of the method are demonstrated using kinetic data from i.v. and oral administrations of cimetidine, diazepam, and pentobarbital in human subjects. The classical V. beta method of approximating the clearance as the product of volume of distribution and beta is considered for comparison. For the three drugs considered the V. beta method which assumes a single exponential disposition kinetics leads to excessive errors when applied in absolute clearance comparisons. However, when applied in relative comparisons in the form of the “beta correction” the errors cancel out to some extent depending on the magnitude of the distribution kinetic effect. Whenever possible it is advisable to apply the proposed method to avoid such errors.