Relationships between the area under the first moment curve after single bolus injection and the integral of plasma concentrations after constant-rate intravenous infusion.
Explore the source record for details and available documents.
Humans↗
Biomedical subjects
W R Gillespie
Publications and source records attributed to W R Gillespie.
Simple methods for estimation of mean residence time and steady-state volume of distribution from continuous-infusion data.
The following equations are derived for amount of drug in the body (xbss), volume of distribution (vss), and mean residence time in the body (tb) at steady state during a continuous constant rate infusion of drug. (formula; see text) where c(t) identical to drug concentration in the systemic circulation at time t following the start of a constant-rate infusion, css identical to steady-state systemic drug concentration, and R identical to infusion rate. The equations are based on the assumption that the rate of drug elimination is proportional to the systemic drug concentration. The equations provide the basis for simple methods that are presented for estimating xbss, vss, and tb directly from experimental data. More general relationships are also derived for cases where the continuous infusion is preceded by other modes of administration, e.g., a bolus loading dose followed by a constant-rate infusion.
Infusions, Intravenous↗
Noncompartmental versus compartmental modelling in clinical pharmacokinetics.
Explore the source record for details and available documents.
Humans↗
Estimation of theophylline clearance during continuous arteriovenous hemofiltration.
Pharmacologic agents and other non-protein-bound compounds smaller than 5,000 daltons have the potential to be removed by continuous arteriovenous hemofiltration (CAVH). A proposed method for estimating drug clearance by CAVH (ClCAVH) equates ultrafiltrate clearance to the product of the sieving coefficient and the average ultrafiltration rate. This simplified approach for estimating ClCAVH would be a clinically useful method for calculating replacement doses, as it economizes on the sampling and analytical requirements associated with the conventional method. Presented are some theoretical considerations and a brief evaluation of the accuracy of this proposed method. The evaluation was conducted using an animal model whereby CAVH was performed in four male beagles. During the hemofiltration period, an i.v. bolus of theophylline, 6 mg/kg, was administered over 15 s. Samples for analysis of theophylline were collected from the arterial, venous, and ultrafiltrate ports at 0, 5, 15, 30, 45, 60, 90, 120, 180, 240, 360, and 480 min following dosage administration. The volume of ultrafiltrate produced during each collection interval was measured. Theophylline serum concentrations were determined by a high performance liquid chromatography assay. Statistically, the simplified method was found to result in significantly (p less than 0.05) larger estimates of ultrafiltrate clearance when compared to the conventional method. However, the average magnitude of difference was only 9% and does not constitute a clinically significant margin between the two methods.
Animals↗
A system approach to pharmacodynamics. I: Theoretical framework.
A general theoretical framework is constructed for the relationship between a pharmacokinetic response r (e.g., systemic drug concentration or input rate), and an observed pharmacologic effect response E. The overall relationship may be described mathematically by E = omega(r) = omega p(omega b(omega r(r))) where omega is an operator that describes the overall relationship, and omega r, omega b, and omega p are operators that describe the contributions of components of the pharmacodynamic system. The kinetic basis for applying certain general mathematical properties such as linearity are discussed. The result is the introduction of various specific mathematical structures that may be applied to pharmacodynamic systems [e.g., E = phi t(r), E = phi t(psi r*r), E = phi p(psi p*phi b(r)), and E = phi p(psi p*phi b(psi r*r))].
Biotransformation↗
A system approach to pharmacodynamics. II: Glyburide pharmacodynamics and estimation of optimal drug delivery.
A system approach to the analysis of pharmacodynamic systems is applied to the relationship between the glyburide serum concentration (Cd) and a resulting pharmacologic effect response, that is, the C-peptide serum concentration (Cc) in patients with non-insulin dependent diabetes mellitus (NIDDM). Glyburide, glucose, and C-peptide serum concentrations were measured in eight patients with NIDDM following each of five treatments: Treatment A: one glyburide 5-mg tablet (formulation 1); Treatment B: one glyburide 5-mg tablet (formulation 2); Treatment C: glyburide solution as an intragastric infusion (4.67 mg over 12 h); Treatment D: glyburide solution as an intragastric infusion (9.33 mg over 12 h); and Treatment E: no glyburide. The overall relationship between the C-peptide (Cc), glyburide (Cd), and glucose (Cg) serum concentrations is successfully described by operator equations of the form, Cc(t) = t-infinity psi p(t-u)phi t(Cd(u), Cg(u)) du or Cc(t) = t-infinity psi p(t-u)phi t(Cd(u), Cg(u),u) du. The forms of the individual functions are selected empirically based on the results of the present study and those of previous investigations, and are estimated by conventional curve-fitting procedures. The resulting operator equations are used to describe glyburide pharmacodynamics in NIDDM patients and to estimate the optimal glyburide systemic concentration and delivery rate profiles for such patients based on pharmacodynamic response.
Blood Glucose↗
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, F comp, is the ratio between the total compounded amount of drug transferred to the peripheral system and the injected dose, D. The AUC peripheral 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, and Fmax are presented for several drugs.
Biological Availability↗
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.
Cimetidine↗
Ibuprofen kinetics in plasma and synovial fluid of arthritic patients.
After administration of a single dose and at steady state, ibuprofen concentrations were measured simultaneously in plasma and synovial fluid obtained from eight patients with rheumatoid arthritis. By seven hours after a dose at steady state, the mean synovial fluid: plasma ibuprofen concentration ratios were constant, and the synovial fluid levels were, on average, greater than those in plasma. The extent to which ibuprofen was bound to protein was somewhat greater in plasma than in synovial fluid. As a result, the mean synovial fluid:plasma free concentration ratio for seven-hour and later specimens was greater than that based on total concentrations. The degree of accumulation of ibuprofen in each fluid was minimal, consistent with its short half-life.
Adult↗
Single pass mean residence time in peripheral tissues: a distribution parameter intrinsic to the tissue affinity of a drug.
The single pass mean residence time in peripheral tissues, tp1, is a characteristic constant of linear pharmacokinetic systems and nonlinear systems with linear distribution kinetics. It is descriptive of distribution kinetics in such systems and is not dependent on elimination kinetics as are other related parameters, e.g., mean residence time in peripheral tissues, tp. Equations are derived which permit estimation of tp1 from experimental data for systems in which no peripheral elimination occurs. The type of data required are systemic drug levels resulting from iv administration. The probability density function for single pass residence time in peripheral tissues is derived. It is shown that tp1 is related to the amount of drug in the peripheral tissues at steady state according to (Ap)ss = CLdCsstp1, where CLd is the distribution clearance, and Css is the steady-state systemic drug level. Values of tp1 are presented for several drugs.
Humans↗
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 t0 is the input lag time. If, in addition, the initial value of the impulse response is zero, i.e., c delta (0) = 0, then c'(t0) = 0. Therefore, it is appropriate to impose the constraint c(t0) = 0 in general and c'(t0) = 0 when c delta (0) = 0 if c(t) is the response to a nonimpulse input. The use of such constraints is demonstrated in an example where the cumulative in vivo dissolution profile is estimated by deconvolution.
Animals↗
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.
Charcoal↗
Deconvolution applied to the kinetics of extracorporal drug removal. Haemodialysis of cefsulodin.
A novel approach to the evaluation of the kinetics of drug removal by an extracorporal device (ECD), e.g., haemodialysis, haemofiltration, and haemoperfusion, is presented. The rate and extent of extracorporal drug removal (ECR) are determined by deconvolution. The proposed method is model independent in the sense that no specific models of corporal or extracorporal disposition are required. The estimation of various derived functions and parameters useful for describing ECR such as clearance and fractional drug removal are facilitated by the technique. The kinetics of cefsulodin elimination by haemodialysis in 3 patients were evaluated using the deconvolution approach. The results indicated that cefsulodin was dialyzable with approximately 50% of the drug in the body removed by haemodialysis over 3-4 h.
Cefsulodin↗
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 is correct 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., first-order central elimination. More general equations for tb in terms of elimination rate, amount eliminated, and amount in the body are presented along with demonstrations of their utility.
Body Burden↗
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. CLd is 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 CLd and CLe are presented for several drugs.
Animals↗
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.
Biological Availability↗
Plasma protein binding of prednisolone in normal volunteers and arthritic patients.
Explore the source record for details and available documents.
Adult↗
Theoretical decrease in systemic availability with decrease in input rate at steady-state for first-pass drugs.
Explore the source record for details and available documents.
Animals↗