Mean time parameters in pharmacokinetics. Definition, computation and clinical implications (Part II)

A Complete Extension of Classical Hepatic Clearance Models Using Fractional Distribution Parameter fd in Physiologically Based Pharmacokinetics

The classical organ clearance models have been proposed to relate the plasma clearance CLp to probable mechanism(s) of hepatic clearance. However, the classical models assume the intrinsic capability of drug elimination (CLu,int) that is physically segregated from the vascular blood but directly acts upon the unbound drug concentration in the blood (fubCavg), and do not handle the transit-time delay between the inlet/outlet concentrations in their closed-form clearance equations. Therefore, we propose unified model structures that can address the internal blood concentration patterns of clearance organs in a more mechanistic/physiological manner, based on the fractional distribution parameter fd operative in PBPK. The basic partial/ordinary differential equations for four classical models are revisited/modified to yield a more complete set of extended clearance models, i.e., the Rattle, Sieve, Tube, and Jar models, which are the counterparts of the dispersion, series-compartment, parallel-tube, and well-stirred models. We demonstrate the feasibility of applying the resulting extended models to isolated perfused rat liver data for 11 compounds and an example dataset for in vitro-in vivo extrapolation of the intrinsic to the systemic clearances. Based on their feasibilities to handle such real data, these models may serve as an improved basis for applying clearance models in the future.

Investigations on the Transfer of Quinolizidine Alkaloids from Lupinus angustifolius into the Milk of Dairy Cows

Lupin varieties with a low content of quinolizidine alkaloids (QAs) like blue sweet lupin (BSL) have long been used as a protein source for dairy cows. A health concern for humans may arise from the transfer of acute toxic QAs from feed into cow's milk. This study is the first to quantify the transfer of QAs from BSL into cow's milk with experimental and modeling methods. Four lactating dairy cows were subjected to two 7 day feeding periods with 1 and 2 kg/d BSL, respectively, each followed by a depuration period. BSL contained 1774 mg/kg dry matter total QAs. Individual milk samples were taken twice daily and QA contents in feed and milk determined with liquid chromatography-tandem mass spectrometry. Transfer of QAs into the milk was already seen with the administration of 1 kg/d BSL, with differences in transfer rates (TRs) between individual QAs. A toxicokinetic model was derived to quantify and predict QA feed-to-food transfer. For the four most prominent QAs, our model shows an α-half-life of around 0.27 d. TRs were obtained for six QAs and were between 0.13 (sparteine) and 3.74% (multiflorine). A toxicological assessment of milk containing QAs as measured in this study indicated a potential health concern.

The non-compartmental steady-state volume of distribution revisited

The lack in the literature of a simple, yet general and complete derivation of the widely used equation for non-compartmental calculation of steady-state volume of distribution is pointed out. It is demonstrated that the most frequently cited references contain an overly simplified explanation. The logical gap consists in doubly defining the same quantities without a proof the definitions are equivalent. Two alternative solutions are proposed: analytical derivation and hydrodynamic analogy. It is shown, that the problem can be analyzed in a purely macroscopic framework by utilizing the integral mean value of the function, without the need to resort to statistical distributions.

Mean remaining life span: a new clinically relevant parameter to assess the quality of transfused red blood cells

BACKGROUND

The quality of transfused red blood cells (RBCs) to treat anemia depends on its potential for oxygen delivery, governed by two properties: 1) initial posttransfusion recovery and 2) life span of initially surviving RBCs. The latter property is poorly evaluated by the traditional mean potential life span (MPL) or mean cell age (MA), because these parameters do not evaluate how long transfused RBCs remain in circulation. Furthermore, evaluation of MPL is based on two problematic assumptions regarding transfused RBCs: 1) they were produced at a constant steady-state rate and 2) they have similar storage life spans.

STUDY DESIGN AND METHODS

This work introduces a new parameter, the mean remaining life span (MRL) to quantify transfused RBC survival (TRCS) and presents a simple algorithm for its evaluation. The MRL was calculated for four adult subjects with sickle cell disease and four adult diabetic and nondiabetic subjects using RBC survival data sets with existing TRCS parameters.

RESULTS

The RBC survival curves in the sickle cell subjects were nonlinear with rapid decline in survival within the first 5 days. The MRL was approximately 4.6 days. Thus, the MRL was indicative of the survival of all transfused RBCs. For the diabetic and nondiabetic subjects, the RBC disappearance curves did not deviate substantially from a linear decline. Thus, the estimates for MRL ranging from 39 to 51 days are similar to the MA previously computed.

CONCLUSION

MRL overcomes limitations of previously proposed TRCS parameters, is simpler to calculate, and is physiologically and clinically more appropriate.

Progesterone pharmacokinetics in the mouse: implications for potential stroke therapy

OBJECTIVES

Progesterone has been shown to be neuroprotective in a number of preclinical central nervous system injury models including cerebral ischaemia. The aim of this study was to clarify differences in outcomes owing to different dosing regimens and the pharmacokinetic profile of progesterone, particularly in relation to brain levels.

METHODS

Male C57 Bl/6 mice were injected intraperitoneally with progesterone (8 mg/kg in dimethylsulfoxide) or with a bolus injection followed by continuous subcutaneous infusion (1.0 µl/h of a 50 mg/ml progesterone solution) via implanted osmotic minipumps. Plasma and brain samples were collected over 24 h from bolus-injected mice and 48 h from mice implanted with minipumps. Progesterone concentrations were measured by an enzyme-linked immunoassay and pharmacokinetic profiles were constructed.

KEY FINDINGS

Intraperitoneally injected progesterone had a short half-life (fast component half-life of 0.2 h) in both plasma and brain. Minipump delivery resulted in higher concentrations of progesterone in plasma and particularly in brain over a longer period. The volume of distribution with intraperitoneal injection was 172.78 versus 1641.84 ng/h per g via minipump in the first 24 h.

CONCLUSIONS

A bolus intraperitoneal loading dose of progesterone followed by continuous delivery via osmotic minipump is an effective way of delivering progesterone to the brain.

In silico labeling reveals the time-dependent label half-life and transit-time in dynamical systems

Background

Mathematical models of dynamical systems facilitate the computation of characteristic properties that are not accessible experimentally. In cell biology, two main properties of interest are (1) the time-period a protein is accessible to other molecules in a certain state - its half-life - and (2) the time it spends when passing through a subsystem - its transit-time. We discuss two approaches to quantify the half-life, present the novel method of in silico labeling, and introduce the label half-life and label transit-time. The developed method has been motivated by laboratory tracer experiments. To investigate the kinetic properties and behavior of a substance of interest, we computationally label this species in order to track it throughout its life cycle. The corresponding mathematical model is extended by an additional set of reactions for the labeled species, avoiding any double-counting within closed circuits, correcting for the influences of upstream fluxes, and taking into account combinatorial multiplicity for complexes or reactions with several reactants or products. A profile likelihood approach is used to estimate confidence intervals on the label half-life and transit-time.

Results

Application to the JAK-STAT signaling pathway in Epo-stimulated BaF3-EpoR cells enabled the calculation of the time-dependent label half-life and transit-time of STAT species. The results were robust against parameter uncertainties.

Conclusions

Our approach renders possible the estimation of species and label half-lives and transit-times. It is applicable to large non-linear systems and an implementation is provided within the PottersWheel modeling framework (http://www.potterswheel.de).

Assessment of exposure to PCB 153 from breast feeding and normal food intake in individual children using a system approach model

Investigators have typically relied on a single or few discrete time points as measures of polychlorinated biphenyl (PCB) body burden, however health effects are more likely to be the result of integrative exposure in time, optionally expressed as an area under the time curve (AUC) of PCB serum concentration. Using data from a subgroup of 93 infants from a birth cohort in eastern Slovakia-a region highly polluted by PCBs-we fit a system type model, customized to our longitudinal measures of serum PCB concentrations in cord, 6, 16, and 45 month blood specimens. The most abundant congener, PCB 153, was chosen for modeling purposes. In addition to currently used methods of exposure assessment, our approach estimates a concentration time profile for each subject, taking into account mean residence time of PCB 153 molecules in the body, duration of breast feeding, hypothetical PCB 153 concentration in steady-state without breast feeding and alternately without normal food intake. Hypothetical PCB 153 concentration in steady-state without normal food intake correlates with AUC (r=0.84, p<0.001) as well as with duration of breast feeding (r=0.64, p<0.001). It makes possible to determine each subject's exposure profile expressed as AUC of PCBs serum concentration with a minimum model parameters. PCB body burden in most infants was strongly associated with duration of breast feeding in most, but not all children, was apparent from model output.

Residual fraction of the area under the curve as a qualitative criterion in pharmacokinetic studies

The aim of the present study was to determine whether the residual area under the curve (AUC(res%); expressed as % of total value of AUC) could be used as a parameter for the qualitative evaluation of pharmacokinetic studies.We propose new criteria for the qualitative evaluation of pharmacokinetic analysis. Two sets of hypothetical data that illustrate the relationship between concentration and time were used for the analysis of drug pharmacokinetics. Non-compartmental analysis was applied for the calculations. The results obtained from the hypothetical data were compared with those obtained from an in vivo study in which 3-week-old broiler chickens were administered 10 mg/kg b.w. enrofloxacin intravenously (iv) or per os (po). In the first set of data (A-D), AUC(res%) values were as follows: A= 16.29% and B = 20.79% for iv administration and C = 29.61% and D = 27.90% for po administration. In the next set of data (E-G), AUC(res%) values after oral administration were 25.30% (E), 23.18% (F), and 20.79% (G). The AUC(res%) values after iv administration of enrofloxacin were similar to po administration; the range of iv and po administration values were 14.35% to 17.50% and 11.14% to 28.33% of the total AUC, respectively. The analysis of the hypothetical data indicates that AUC(res%) is not an optimal method for the evaluation of pharmacokinetic studies.

Pharmacokinetic differentiation of drug candidates using system analysis and physiological-based modelling. Comparison of C.E.R.A. and erythropoietin

Evaluation of the pharmacokinetics (PKs) in a proper physiological context is paramount to elucidate the factors that may improve a drug's PK properties. Using modern system analysis-based physiological modelling principles, this work applies a novel kinetic analysis framework to a PK comparison of two erythropoietically active drugs, C.E.R.A. (continuous erythropoietin receptor activator) and recombinant human erythropoietin (Epo), aimed at elucidating the main factors responsible for the substantial PK differences seen. The evaluation according to the new model is compared with a compartmental model analysis. Sheep (n = 7 for Epo; n = 8 for C.E.R.A.) received intravenous bolus injections of Epo and C.E.R.A. Baseline and 20–30 blood samples per injection were assayed by radioimmunoassay. Fundamental physiologically based PK building block principles were introduced, proceeding to the construction of a general PK model and several sub-models from which a final PK model was selected based on information theoretical principles. The compartmental comparison analysis use a two-compartment model with central Michaelis-Menten elimination. Several lines of evidence support the hypothesis that the desirable slow elimination of C.E.R.A. relative to Epo is mainly caused by a smaller recirculation extraction fraction, which appears more influential on the elimination kinetics than the mean circulation transit time. The compartmental analysis demonstrates large differences in several PK parameters that contribute to C.E.R.A.'s slower elimination, consistent with the recirculation model analysis. It is hypothesized that C.E.R.A.'s smaller recirculatory extraction fraction is due to a reduced receptor-mediated elimination, consistent with in-vitro measurements where C.E.R.A. shows Epo-receptor binding with a lower association constant and a larger dissociation constant.

Pharmacokinetic differentiation of drug candidates using system analysis and physiological-based modelling. Comparison of C.E.R.A. and erythropoietin

Evaluation of the pharmacokinetics (PKs) in a proper physiological context is paramount to elucidate the factors that may improve a drug's PK properties. Using modern system analysis-based physiological modelling principles, this work applies a novel kinetic analysis framework to a PK comparison of two erythropoietically active drugs, C.E.R.A. (continuous erythropoietin receptor activator) and recombinant human erythropoietin (Epo), aimed at elucidating the main factors responsible for the substantial PK differences seen. The evaluation according to the new model is compared with a compartmental model analysis. Sheep (n = 7 for Epo; n = 8 for C.E.R.A.) received intravenous bolus injections of Epo and C.E.R.A. Baseline and 20-30 blood samples per injection were assayed by radioimmunoassay. Fundamental physiologically based PK building block principles were introduced, proceeding to the construction of a general PK model and several sub-models from which a final PK model was selected based on information theoretical principles. The compartmental comparison analysis use a two-compartment model with central Michaelis-Menten elimination. Several lines of evidence support the hypothesis that the desirable slow elimination of C.E.R.A. relative to Epo is mainly caused by a smaller recirculation extraction fraction, which appears more influential on the elimination kinetics than the mean circulation transit time. The compartmental analysis demonstrates large differences in several PK parameters that contribute to C.E.R.A.'s slower elimination, consistent with the recirculation model analysis. It is hypothesized that C.E.R.A.'s smaller recirculatory extraction fraction is due to a reduced receptor-mediated elimination, consistent with in-vitro measurements where C.E.R.A. shows Epo-receptor binding with a lower association constant and a larger dissociation constant.

Mean lifetime and first-passage time of the enzyme species involved in an enzyme reaction. Application to unstable enzyme systems

Taking as starting point the complete analysis of mean residence times in linear compartmental systems performed by Garcia-Meseguer et al. (Bull. Math. Biol. 65:279-308, 2003) as well as the fact that enzyme systems, in which the interconversions between the different enzyme species involved are of first or pseudofirst order, act as linear compartmental systems, we hereby carry out a complete analysis of the mean lifetime that the enzyme molecules spend as part of the enzyme species, forms, or groups involved in an enzyme reaction mechanism. The formulas to evaluate these times are given as a function of the individual rate constants and the initial concentrations of the involved species at the onset of the reaction. We apply the results to unstable enzyme systems and support the results by using a concrete example of such systems. The practicality of obtaining the mean times and their possible application in a kinetic data analysis is discussed.

The Connection Between the Steady State (Vss) and Terminal (Vβ) Volumes of Distribution in Linear Pharmacokinetics and The General Proof That Vβ ≥ Vss

The steady state and terminal (area) volumes of distribution are important pharmacokinetic parameters defined as the ratio of the total quantity of drug in the body, A(b)(t), to drug plasma concentration C(p)(t) at steady state and the terminal phase of drug elimination, respectively. The general equations for the approach of C(p)(t), A(b)(t) and the distribution volume A(b)(t)/C(p)(t) to the steady state values (for a continuous constant rate drug infusion) are derived. It is shown that the time course of A(b)(t) near the asymptotic steady state value depends on both the terminal and steady state volumes of distribution, and an accurate equation to determine the time required to reach the steady state is obtained. For a general linear pharmacokinetic system (i.e., with possible drug elimination at any state from any compartment and drug exchange between compartments) it is proven that V(beta) >/= V(ss). A physiologically determined feature, which is the drug input into plasma for reaching the steady state or terminal phase, underlies the proof. If the steady state is reached by a continuous input of drug into some compartment other than plasma, and the terminal volume of distribution is considered after dosing of a drug in the same compartment, then both cases V(ss) <> V(beta) are possible. It is shown that the general exponential series for C(p)(t) after intravenous bolus dose may have negative pre-exponents, unlike a common assumption that all pre-exponents should be positive. Its is figured out that the commonly used equations for the estimation of V(ss) and V(beta) (V(ss) = D x AUMC/AUC(2) and V(beta) = D/(AUC x beta) may yield V(ss) > V(beta) for a linear pharmacokinetic system, contrary to the usual statement (V(ss) < V(beta)) and its seemingly simple proof, which has a flaw. It is shown that the time required to reach the steady state concentration of drug in plasma could be much shorter than a commonly used estimation of 5t(1/2), where t(1/2) is the terminal half-life obtained from the intravenous bolus drug plasma concentration time course.

Bronchoscopic assessment of airway retention time of aerosolized xylitol

Background

Human airway surface liquid (ASL) has abundant antimicrobial peptides whose potency increases as the salt concentration decreases. Xylitol is a 5-carbon sugar that has the ability to lower ASL salt concentration, potentially enhancing innate immunity. Xylitol was detected for 8 hours in the ASL after application in airway epithelium in vitro. We tested the airway retention time of aerosolized iso-osmotic xylitol in healthy volunteers.

Methods

After a screening spirometry, volunteers received 10 ml of nebulized 5% xylitol. Bronchoscopy was done at 20 minutes (n = 6), 90 minutes (n = 6), and 3 hours (n = 5) after nebulization and ASL was collected using microsampling probes, followed by bronchoalveolar lavage (BAL). Xylitol concentration was measured by nuclear magnetic resonance spectroscopy and corrected for dilution using urea concentration.

Results

All subjects tolerated nebulization and bronchoscopy well. Mean ASL volume recovered from the probes was 49 ± 23 μl. The mean ASL xylitol concentration at 20, 90, and 180 minutes was 1.6 ± 1.9 μg/μl, 0.6 ± 0.6 μg/μl, and 0.1 ± 0.1 μg/μl, respectively. Corresponding BAL concentration corrected for dilution was consistently lower at all time points. The terminal half-life of aerosolized xylitol obtained by the probes was 45 minutes with a mean residence time of 65 minutes in ASL. Corresponding BAL values were 36 and 50 minutes, respectively.

Conclusion

After a single dose nebulization, xylitol was detected in ASL for 3 hours, which was shorter than our in vitro measurement. The microsampling probe performed superior to BAL when sampling bronchial ASL.

Steady-state serum concentrations of progesterone following continuous intravenous infusion in patients with acute moderate to severe traumatic brain injury

Progesterone (PG) has been shown to provide substantial neuroprotection after traumatic brain injury (TBI) in multiple animal models. As a first step in assessing applicability to humans, the authors examined the effects of acute TBI and extracranial trauma on the pharmacokinetics of PG given by intravenous infusion. Multiple blood samples were obtained from 11 female and 21 male trauma patients receiving PG and 1 female and 3 male patients receiving placebo infusions for 72 hours. Values for C(SS), CL, t(1/2), and Vd were obtained using AUC((0-72)) and postinfusion blood samples. C(SS) values were 337 +/- 135 ng/mL, which were significantly lower than the target concentration of 450 +/- 100 ng/mL. The lower C(SS) is attributed to the CL, which was higher than anticipated. In addition, t(1/2) was longer and V(d) was higher than anticipated. These results demonstrate that stable PG concentrations can be rapidly achieved following TBI.

Time to reach tacrolimus maximum blood concentration,mean residence time, and acute renal allograft rejection: an open-label, prospective, pharmacokinetic study in adult recipients

OBJECTIVES

The aims of this study were to determine whether disposition-related pharmacokinetic parameters such as T(max) and mean residence time (MRT) could be used as predictors of clinical efficacy of tacrolimus in renal transplant recipients, and to what extent these parameters would be influenced by clinical variables.

METHODS

We previously demonstrated, in a prospective pharmacokinetic study in de novo renal allograft recipients, that patients who experienced early acute rejection did not differ from patients free from rejection in terms of tacrolimus pharmacokinetic exposure parameters (dose interval AUC, preadministration trough blood concentration, C(max), dose). However, recipients with acute rejection reached mean (SD) tacrolimus T(max) significantly faster than those who were free from rejection (0.96 [0.56] hour vs 1.77 [1.06] hours; P < 0.001). Taking into account that neither differences in tacrolimus steady-state clearance nor T(1/2) could explain this unusual finding, we used data from the previous study to calculate MRT from the concentration-time curves.

RESULTS

As part of the previous study, 100 patients (59 male, 41 female; mean [SD] age, 51.4 [13.8] years;age range, 20-75 years) were enrolled in the study The calculated MRT was significantly shorter in recipients with acute allograft rejection (11.32 [031] hours vs 11.52 [028] hours; P = 0.02), just like T(max) was an independent risk factor for acute rejection in a multivariate logistic regression model (odds ratio, 0.092 [95% CI, 0.014-0.629]; P = 0.01). Analyzing the impact of demographic, transplantation-related, and biochemical variables on MRT, we found that increasing serum albumin and hematocrit concentrations were associated with a prolonged MRT (P < 0.05). Conversely, serum albumin and hematocrit concentrations were significantly lower in recipients with acute rejection (P < (101).

CONCLUSIONS

In this selected population of de novo renal allograft recipients, a shorter tacrolimus T(max) and calculated MRT were associated with a higher incidence of early acute graft rejection. These findings suggest that a shorter transit time of tacrolimus in certain tissue compartments, rather than failure to obtain a maximum absolute tacrolimus blood concentration, might lead to inadequate immunosuppression early after transplantation.

Comparison of plasma disposition of alkaloids after lupine challenge in cattle that had given birth to calves with lupine-induced arthrogryposis or clinically normal calves

OBJECTIVE

To compare plasma disposition of alkaloids after lupine challenge in cattle that had given birth to calves with lupine-induced arthrogryposis and cattle that had given birth to clinically normal calves and determine whether the difference in outcome was associated with differences in plasma disposition of anagyrine.

ANIMALS

6 cows that had given birth to calves with arthrogryposis and 6 cows that had given birth to clinically normal calves after being similarly exposed to lupine during pregnancy.

PROCEDURES

Dried lupine (2 g/kg) was administered via gavage. Blood samples were collected before and at various time points for 48 hours after lupine administration. Anagyrine, 5,6-dehydrolupanine, and lupanine concentrations in plasma were measured by use of gas chromatography. Plasma alkaloid concentration versus time curves were generated for each alkaloid, and pharmacokinetic parameters were determined for each cow.

RESULTS

No significant differences in area under the plasma concentration versus time curve, maximum plasma concentration, time to reach maximum plasma concentration, and mean residence time for the 3 alkaloids were found between groups.

CONCLUSIONS AND CLINICAL RELEVANCE

Because no differences were found in plasma disposition of anagyrine following lupine challenge between cattle that had given birth to calves with arthrogryposis and those that had not, our findings do not support the hypothesis that between-cow differences in plasma disposition of anagyrine account for within-herd differences in risk for lupine-induced arthrogryposis.

Bioavailability and its assessment

Bioavailability is a key pharmacokinetic parameter which expresses the proportion of a drug administered by any nonvascular route that gains access to the systemic circulation. Presented in this review are the different approaches to measurement of bioavailability (absolute and relative), including the case in which intravenous administration is impossible. The rate of drug absorption is also discussed with special emphasis on the possible difficulties encountered using C(max) and T(max) or curve fitting to evaluate the rate of drug absorption.

The effect of age on the early disposition of doxorubicin

PURPOSE

Clinical studies indicate that anthracycline cardiotoxicity increases with patient age. This may be due to altered pharmacokinetics or pharmacodynamics. A parameter termed 'early clearance' has been shown to decrease with age in patients receiving intravenous doxorubicin. This parameter, as defined, has no immediate relationship to any physiologically based pharmacokinetic parameter. We therefore reevaluated the pharmacokinetic data to better define the relationship between doxorubicin disposition and patient age.

METHODS

Four studies provided a total of 56 patients with evaluable pharmacokinetics. The volume of the central compartment, V(c), the distribution clearance, CL(d), and total body clearance, CL, were determined for each patient and regressed against age. A physiologically based pharmacokinetic (PBPK) model for doxorubicin was also used to evaluate the effects of age on doxorubicin disposition. Published blood flows associated with various patient ages were used to simulate plasma and tissue doxorubicin concentrations. The relationship between CL(d) and initial tumor regression was also evaluated.

RESULTS

No correlation was found between V(c) and age ( P>0.05). A highly significant correlation was observed between CL(d) and age ( P<0.0005) and there was a mild but significant relationship between CL and age ( P<0.01). Use of the PBPK model with different age-related blood flows yielded virtually identical parameter values to the clinical data analyzed. Furthermore, relative tissue AUCs simulated in old and young patients compared well with those reported for daunorubicin disposition in young and old rats. In addition, a linear relationship was observed between initial tumor regression and CL(d).

CONCLUSIONS

Initial concentrations of doxorubicin following intravenous administration are higher in the elderly due to a decrease in CL(d) rather than in V(c). On the basis of simulations with the PBPK model, the reduced CL(d) appears to be related to altered regional blood flows in the elderly, and such changes may be of clinical significance.

Rapid determination of PEGylated liposomal doxorubicin and its major metabolite in human plasma by ultraviolet-visible high-performance liquid chromatography

A high-performance liquid chromatographic method was developed for the quantification of doxorubicin derived from PEGylated liposomal doxorubicin (Doxil) and its major metabolite in human plasma. This method utilizes Triton X-100 to disperse the liposome, followed by a protein precipitation step with 5-sulfosalicylic acid. Analytes in the resultant supernatant are separated on a Discovery RP amide C(16) column (250 x 3 mm I.D., 5 microm) using an isocratic elution with a mobile phase consisting of 0.05 M sodium acetate (pH 4.0) and acetonitrile (72:28). The retention times for doxorubicin and the internal standard daunorubicin were 4.8 and 10.1 min, respectively. The column eluate was monitored by UV-visible detection at 487 nm. The determination of doxorubicin was found to be linear in the range of 1.0 ng/mL to 25 microg/mL, with intra-day and inter-day coefficients of variation and percent error < or =10%. The recovery of doxorubicin from plasma was >69.3%, with a liposomal dispersion efficiency of >95.7%. Our analytical method for free and PEGylated doxorubicin in human plasma is rapid, avoids organic extractions, and maintains sensitivity for the parent compound and its major metabolite, doxorubicinol.

Pharmacokinetics of sulfamethoxazole and trimethoprim in donkeys, mules, and horses

OBJECTIVE

To compare serum disposition of sulfamethoxazole and trimethoprim after IV administration to donkeys, mules, and horses.

ANIMALS

5 donkeys, 5 mules, and 3 horses.

PROCEDURE

Blood samples were collected before (time 0) and 5, 15, 30, and 45 minutes and 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 8, 10, and 24 hours after IV administration of sulfamethoxazole (12.5 mg/kg) and trimethoprim (2.5 mg/kg). Serum was analyzed in triplicate with high-performance liquid chromatography for determination of sulfamethoxazole and trimethoprim concentrations. Serum concentration-time curve for each animal was analyzed separately to estimate noncompartmental pharmacokinetic variables.

RESULTS

Clearance of trimethoprim and sulfamethoxazole in donkeys was significantly faster than in mules or horses. In donkeys, mean residence time (MRT) of sulfamethoxazole (2.5 hours) was less than half the MRT in mules (6.2 hours); MRT of trimethoprim in donkeys (0.8 hours) was half that in horses (1.5 hours). Volume of distribution at steady state (Vdss) for sulfamethoxazole did not differ, but Vdss of trimethoprim was significantly greater in horses than mules or donkeys. Area under the curve for sulfamethoxazole and trimethoprim was higher in mules than in horses or donkeys.

CONCLUSIONS AND CLINICAL RELEVANCE

Dosing intervals for IV administration of trimethoprim-sulfamethoxazole in horses may not be appropriate for use in donkeys or mules. Donkeys eliminate the drugs rapidly, compared with horses. Ratios of trimethoprim and sulfamethoxazole optimum for antibacterial activity are maintained for only a short duration in horses, donkeys, and mules.

Time course equations of the amount of substance in a linear compartmental system and their computerized derivation

In this contribution, we present the symbolic time course equations corresponding to a general model of a linear compartmental system, closed or open, with or without traps and with zero input. The steady state equations are obtained easily from the transient phase equations by setting the time --> infinity. Special attention has been given to the open systems, for which an exhaustive kinetic analysis has been developed to obtain important properties. Besides, the results have been particularized to open systems without traps and an alternative expression for the distribution function of exit times has been provided. We have implemented a versatile computer program, that is easy to use and with a user-friendly format of the input of data and the output of results. This computer program allows the user to obtain all the information necessary to derive the symbolic time course equations for closed or open systems as well as for the derivation of the distribution function of exit times.

Pharmacokinetic aspects of measurement of glomerular filtration rate in the dog: a review

Glomerular filtration rate (GFR) is estimated by means of clearance, defined as the volume of plasma that has been cleared of a particular substance per unit time. Glomerular filtration rate may be estimated by measuring the renal clearance of a filtration marker using data from both urine and plasma or by plasma clearance using only plasma data. Several alternative pharmacokinetic models are used for the calculation of clearance using various filtration markers with slightly different pharmacokinetic properties. The purpose of this article is to discuss how the choice of marker and pharmacokinetic model may influence estimated GFR values and to elucidate commonly used methods and reported GFR values in the dog.

Ascorbic acid disposition kinetics in the plasma and tissues of calves

Kinetic plasma disposition parameters and tissue distribution of ascorbic acid (AA) and dihydroascorbic acid (DHA) were determined in newborn calves. After a radiolabeled AA intravenous administration, the plasma clearance (Cl) was low (40.8 +/- 9.5 ml.kg-1.h-1), the steady-state volume of distribution (Vss) was very high (8.9 +/- 2.2 l/kg), and the AA mean residence time (MRT) was long (230 +/- 85 h). After administration of a 3-g dose of AA, the Cl was high (450 +/- 146 ml.kg-1.h-1), the Vss was low (0.658 +/- 0.236 l/kg), and the MRT was short (1.49 +/- 0.41 h), indicating a strong nonlinearity of AA disposition in calves and the impossibility of preventing scurvy with the use of a loading AA dose. Nonlinearity was explained by the saturation of both kidney reabsorption and tissue uptake. The estimated AA body pool size was 23.1 +/- 6.8 mg/kg. On the basis of a compartmental analysis and actual tissue concentration measurements, it is suggested that the lung (19% of the pool) constitutes a low-capacity but rapidly mobilized pool able to cover an acute need for AA, whereas muscle and liver (40 and 33% of the pool, respectively) are high-capacity AA pools, but slowly mobilized and involved in covering the calf's long-term AA requirements. The average daily AA entry rate over the first 7 days of life was 3.43 +/- 1.16 mg/kg, and it is suggested that the calf is able to synthesize AA at an early stage.

Effect of polyaspartic acid on pharmacokinetics of gentamicin after single intravenous dose in the dog

The effects of poly-L-aspartic acid on the pharmacokinetics of gentamicin were examined by using a randomized crossover trial design with the dog. When analyzed according to a three-compartment open model, poly-L-aspartic acid reduced some first-order rate equation constants (A3, lambda 1, and lambda 3), the deep peripheral compartment exit microconstant (k31), the elimination rate constant (k(el)), and the area under the concentration-time curve from 0 to 480 h (AUC0-480) (0.21-, 0.60-, 0.26-, 0.27-, 0.72-, and 0.76-fold, respectively; P < 0.05) but increased the volume of distribution at steady state (Vss), the volume of distribution calculated by the area method (V(area)), the apparent volume of the peripheral compartment (Vp), and all mean time parameters. These results suggested that poly-L-aspartic acid increased the distribution of gentamicin to or binding within the deep peripheral compartment and that poly-L-aspartic acid may have delayed gentamicin transit through the peripheral tissues. In contrast, poly-L-aspartic acid did not alter pharmacokinetic parameters relevant to the central or shallow peripheral compartments to a clinically significant extent. Although gentamicin's pharmacokinetic parameters of relevance to therapeutic drug monitoring were not directly altered, this study has provided pharmacokinetic evidence that poly-L-aspartic acid alters the peripheral distribution of gentamicin. This pharmacokinetic interaction occurred after a single intravenous dose of each drug. Therefore, this interaction should be investigated further, before polyaspartic acid can be considered for use as a clinical nephroprotectant.

Metoclopramide increases the bioavailability of dantrolene in spinal cord injury

A study was conducted to determine the effect of metoclopramide on the disposition of dantrolene in patients with spinal cord injury (SCI) and in neurologically intact, able-bodied volunteers. Fifteen serum samples each were collected from 6 able-bodied volunteers and 13 patients with SCI (7 paraplegics, 6 quadriplegics) in a prospective, open-label, pharmacokinetic study of a single 100-mg oral dose of dantrolene. After a washout period, a single 10-mg intravenous dose of metoclopramide was given along with dantrolene to the patients with SCI only, and the study was repeated in sequential, crossover fashion. Concentrations of dantrolene were measured by a high-performance liquid chromatography (HPLC) assay. Numerical integration was used to calculate area under the curve (AUC) and mean residence time (MRT). Differences were studied using paired and two-sample, nonparametric tests, with 0.05 as the significance level. Without metoclopramide, the AUC of dantrolene was larger in able-bodied volunteers than in patients with SCI, and the MRT of dantrolene was similar both groups. When patients with SCI received metoclopramide before treatment with dantrolene, the median increase in the AUC for dantrolene was 57%, with no change in MRT. This pharmacokinetic interaction is probably attributable to augmented absorption and could alter the pharmacologic action of dantrolene. Concurrent treatment of patients with SCI with metoclopramide and dantrolene should be accompanied by careful surveillance to avoid toxicity and preserve efficacy.

Accuracy of noncompartmental pharmacokinetic parameters estimated from bolus injection and steady-state infusion data

A Monte Carlo simulation study was carried out to examine the accuracy of parameters derived from curve moments. Impulse response (IR) and washout (WO) concentration-time curves, based on a triexponential model, were analyzed by numerical integration and regression analysis. Both designs were tested according to their robustness to measurement error and model misspecification. Performance of the methods was judged using the median error (ME) and the median absolute error (MAE) of 1000 simulations. The WO design provided better estimates of mean disposition residence time and worse estimates of the normalized variance of disposition residence times (CVD2) than its rival. At 20% measurement noise, the MAE of CVD2 was less than 13%. The WO design was much more robust to model misspecification. Numerical integration performed as good as, or better than, regression analysis. Both methods are very sensitive to tail-area error, meaning that special attention needs to be paid to this aspect of experimental design. This study demonstrates that it is possible to obtain good estimates of higher moment parameters in a well-designed experiment.

Duration of opioid antagonism by nalmefene and naloxone in the dog: an integrated pharmacokinetic/pharmacodynamic comparison

A continuous fentanyl infusion was administered to eight adult, male beagle dogs for a duration of approximately 400 min at a rate of 30 micrograms/kg/h. The extent of respiratory depression was quantified by continuous, noninvasive, transcutaneous pCO2 recordings. Upon reaching a pseudosteady-state of respiratory depression at approximately 120 min of fentanyl infusion, the animals then received, in a 2 x 2 crossover fashion separated by approximately 3 weeks, 30-minute equiefficacious infusions of nalmefene (12 micrograms/kg/h) or naloxone (48 micrograms/kg/h). Multiple venous blood samples were taken throughout the dosing regimen, and the resulting fentanyl, nalmefene, or naloxone plasma concentrations were determined. The concentration-time data were analyzed by noncompartmental methods and subsequently linked to the pharmacodynamic effect data by a competitive antagonism link model. Separately, the biophase concentrations were linked to the plasma concentration-time profiles through a single-exponential conduction function. The various pharmacokinetic/pharmacodynamic parameters resulting from this semiparametric analysis were analyzed by ANOVA, using a statistical model that considers carryover effects. The results of these analyses indicate that several pharmacokinetic/pharmacodynamic parameters of the two antagonists were comparable. However, nalmefene had a significantly more protracted terminal disposition and a significantly greater persistency in the biophase evaluated over the experimental time frame from 0 to 450 min.

Pharmacokinetics of an extended-dose halofantrine regimen in patients with malaria and in healthy volunteers

The pharmacokinetics and tolerance of a 4.5 gm 7-day halofantrine loading dose regimen were evaluated in 10 Thai patients with malaria and in 10 noninfected volunteers. Halofantrine peak plasma concentrations and bioavailability on the first day of treatment were significantly lower in patients with malaria than in healthy volunteers. Halofantrine elimination half-life was significantly shorter in patients with malaria than healthy control subjects (9.5 versus 15.8 days). These data show a distinct effect of acute malaria on the absorption and elimination of the drug. In addition, marked intersubject and intrasubject variability in peak and trough halofantrine levels was observed, indicating variable drug absorption. This dosing regimen was effective and well tolerated, with mild transient diarrhea during the first few days of treatment in both groups. To produce consistently effective drug levels, the currently recommended dosing regimens may be suboptimal. Slow halofantrine elimination raises concern for induction of parasite resistance when the drug is used in endemic areas of the world.

The effects on the pharmacokinetics of intravenous ceftiofur sodium in dairy cattle of simultaneous intravenous acetyl salicylate (aspirin) or probenecid

Ceftiofur sodium is a third-generation cephalosporin antibiotic. It is possible that non-steroidal anti-inflammatory drugs such as acetyl salicylate (aspirin) may be used concomitantly with ceftiofur sodium in dairy cattle. Therefore this study evaluated potential pharmacokinetic interactions between ceftiofur sodium and aspirin. In addition, this study evaluated the potential for interaction between ceftiofur and its active metabolites and the organic anion transporter. The organic anion transporter substrate used in this evaluation was probenecid. Ten healthy, non-pregnant, non-lactating dairy cows were used in a randomized complete three-way crossover design. In repeated experiments all cows were administered: (1) 2 mg of ceftiofur sodium per kg body weight by intravenous bolus or (2) 10 mg of probenecid per kg body weight by intravenous bolus, followed immediately by 2 mg of ceftiofur sodium per kg body weight by intravenous bolus or (3) 26 mg of aspirin per kg body weight by intravenous bolus, followed immediately by 2 mg of ceftiofur sodium per kg body weight by intravenous bolus. For treatment with ceftiofur sodium alone, the mean volume of distribution at steady-state Vd(ss) was 0.2 +/- 0.06 L/kg, the mean volume of distribution by the area method Vd(area) was 0.38 +/- 0.22 L/kg, mean residence time (MRT) was 6.5 +/- 1.8 h, mean residence time in peripheral tissues (MRTp) was 2.6 +/- 1.0 h, total body clearance (Cl) was 0.032 +/- 0.013 L/kg/h and elimination rate constant (beta) was 0.097 +/- 0.044 h-1 (mean +/- standard deviation). No statistically significant changes were detected as a result of preceding treatment with aspirin.(ABSTRACT TRUNCATED AT 250 WORDS)

General linear compartment model with zero input: III. First passage residence time of enzyme systems

In this paper, we present an alternative procedure to derive the residence times of enzyme and compartment systems. This procedure allows to express the residence time by a general, symbolic and simplified formula relating it directly with the rate constants. It is applicable to any enzyme reaction scheme which can be formulated as a set of first-order or pseudo-first order interconversions, without any other restriction. A computer program has been developed that greatly facilitates the task of the residence time derivations. The above analysis was extrapolated to any linear compartment model.

General linear compartment model with zero input: II. The computerized derivation of the kinetic equations

The final equations obtained in the first article of this series describing the concentrations of substances in any of the compartments of a model are here cast in an easily programmable form. A computer program with an easy input method and the ability to expand all of the coefficients in the kinetic equations in terms of the model parameters has been developed. The program has been written in the BASIC language.

General linear compartment model with zero input: I. Kinetic equations

The derivation of kinetic equations is described for n-compartment linear models, in which the substance may be simultaneously introduced into one or more compartments at t = 0 and eliminated from any compartment. For a given zero-input, general formulas are derived which describe the amount of tracer in any of the compartments as a function of time and the model parameters. New algorithms have been developed which allow the expression of the kinetic equations.

Effect of famotidine on ciprofloxacin pharmacokinetics after single intravenous and oral doses in rats

The effect of intravenous (3.5 mg/kg) and oral (5 mg/kg) famotidine on ciprofloxacin pharmacokinetics after single (i.v.) intravenous (5 mg/kg) and oral (20 mg/kg) doses were examined in the rat. Famotidine co-administration significantly increased the terminal elimination half-life of ciprofloxacin (54% and 29% following i.v. and oral administration, respectively) and tended to reduce the total body clearance by 27% and 34% following i.v. and oral routes, respectively. The area under the plasma concentration-time curve and the mean residence time in the body after i.v. and oral doses were significantly increased following famotidine co-administration. No changes in the steady-state apparent volume of distribution was observed after i.v. administration. The maximum plasma concentration and the time to peak concentration after oral dosing were also unaffected. These results suggest a possible reduction in the total clearance of ciprofloxacin, owing to inhibition of its renal tubular excretion by famotidine. Further studies are warranted to determine whether this interaction occurs in humans.

Quantitative structure-pharmacokinetic relationships for systemic drug distribution kinetics not confined to a congeneric series

Many attempts have been made to describe quantitative structure-pharmacokinetic relationships within a congeneric series of drug molecules. The goal is to develop a predictive relationship that could predict in vivo results for other drugs within that series. These studies typically evaluate pharmacokinetic parameters that are reflective of both distribution and elimination processes. This work utilizes the results from 17 noncongeneric drugs reported in 18 pharmacokinetic studies. The objective was to determine if drug distribution parameters that were independent of elimination could be predicted from easily measured physicochemical parameters with a data base that included a wide variety of drugs that were not congeners of one another. Regression models utilizing a linear and a quadratic response surface were used to predict the various distribution parameters from physicochemical parameters, including molecular weight, intrinsic solubility, alcohol solubility, protein binding, and the distribution coefficient. Analogous to the extent of absorption, the extent of drug distribution can be predicted reasonably well by the probability that the drug will distribute into the peripheral system before being eliminated and by the volume of distribution at steady state. The duration of distribution, analogous to the rate of absorption, can be predicted by the mean transit time through the peripheral system the mean residence time of the drug in the peripheral system and the intrinsic mean residence time in the peripheral system. The ability to use statistical models to approximate drug distribution parameters without the constraints of working within a congeneric series provides some valuable opportunities.

Pharmacokinetics of enrofloxacin and its metabolite ciprofloxacin after intravenous and oral administration of enrofloxacin in dogs

Four dogs were given 5 mg/kg body weight enrofloxacin intravenously (i.v.) and orally (p.o.) in a cross-over study. Plasma concentrations of the active ingredient enrofloxacin and its main metabolite ciprofloxacin were determined by a reversed phase liquid chromatographic method. Pharmacokinetic parameters of both substances were calculated by use of statistical moments and were compared to those of enrofloxacin described in the veterinary literature. Mean enrofloxacin t1/2 lambda z was 2.4 h, mean Cls was 27.1 ml/min.kg, and mean Vss was 7.0 l/kg. After i.v. and p.o. administration, concentrations of ciprofloxacin exceeding minimal inhibitory concentrations of several microorganisms were reached (Cmax = 0.2 microgram/ml, tmax = 2.2 h after intravenous administration; Cmax = 0.2 microgram/ml, tmax = 3.6 h after oral administration). A considerable part of the antimicrobial activity is due to ciprofloxacin, the main metabolite of enrofloxacin.

Mean residence time in multicompartmental models with time delays

Calculation of the mean residence time (MRT) of a drug in a stationary compartmental model is classically carried out from several expressions. Nevertheless, one or more time delays between compartments modify the mean residence times. It is the aim of this paper to propose a general method for MRT calculations, in any n-compartmental models which may include time delays. As examples, catenary and mammillary models are considered.

Comparative pharmacokinetics of aditoprim in milk-fed and conventionally fed calves of different ages

Aditoprim body disposition was described after intravenous and oral administration of 5 or 10 mg kg-1 bodyweight to milk-fed and conventionally fed calves with bodyweights of 80 kg, 160 kg and 210 kg. After intravenous administration to conventionally fed calves, aditoprim total body clearance increased and elimination half-life decreased with age. Oral administration of aditoprim with feed was associated with a longer absorption half-life and consequently longer elimination half-life in the older calves, because the drug was deposited in a functionally mature rumen. The weak base aditoprim is slowly absorbed from the rumen according to the pH partition hypothesis and probable binding to dietary fibres and other macromolecules. The favourable pharmacokinetics of aditoprim indicate a potential use for this antimicrobial in bovine practice, pending further studies on residue depletion profile, safety and therapeutic efficacy.

Bias and variance of extrapolated tails for area-under-the-curve (AUC) and area-under-the-moment-curve (AUMC)

The usual formulas for the extrapolated values of AUC and AUMC from tn to infinity produce estimates that are biased. An empirical correction factor is shown to reduce both bias and variance of estimates. The fitted value Cz at the last time-point tn should normally be used in the formulas, rather than the measured concentration Cn. Nonlinear least squares methods offer no advantage over the fitting of a straight line to ln (C).

The effect of a protein meal on zidovudine pharmacokinetics in HIV-infected patients

Eleven HIV-infected men participated in a randomized, two-treatment, two-period crossover study to determine the effect of a 25 g protein meal on zidovudine pharmacokinetics. On two separate occasions, 1 week apart, each patient received 200 mg zidovudine in a fasting state or immediately following the protein meal. A protein meal significantly decreased Cmax [532 (228 s.d.) vs 802 (452 s.d.) ng ml-1, P = 0.004] and increased mean residence time (138 (26 s.d.) vs 114 (26 s.d.) min, corrected for lag times, P = 0.001). However, AUC, tmax, terminal half-life and renal clearance were not significantly altered (P greater than 0.05). The power to detect a 20% change in AUC was 98% at the 5% significance level. In contrast to fat-containing foods, protein-based meals may not alter the extent of zidovudine absorption.

Optimum numerical integration methods for estimation of area-under-the-curve (AUC) and area-under-the-moment-curve (AUMC)

Eleven numerical methods for estimation of AUC (including 4 new methods) and 22 methods for AUMC (including 8 new methods) were tested on large simulated noisy datasets representing bolus, oral and infusion concentration-time profiles. Some methods were unacceptable because their mean error was large; these included a commonly recommended form of the linear trapezoidal rule for AUMC. Others, notably Lagrange and cubic spline methods, were unacceptable because the variance of their estimates was large. These methods should be abandoned. A simple and easily programmed new method, parabolas-through-the-origin then log-trapezoidal rule, performed especially well.

Glycated low density lipoprotein catabolism is increased in rabbits with alloxan-induced diabetes mellitus

Hyperglycaemia in diabetes mellitus is responsible for the process of non-enzymatic glycosylation of different proteins. Since we did not find elevated glycated apolipoprotein B levels in diabetic patients, an altered glycated apolipoprotein B metabolism was suspected in diabetic patients. Experiments in normal rabbits showed that non-reductive (in vitro) glycated low density lipoprotein (gly-LDL) was cleared at a slower rate than control LDL and thus stayed longer in the circulation (vascular mean residence time: 10 vs 8 h, p less than 0.001). The body mean residence time for gly-LDL was 22 h vs 17 h for control LDL. In diabetic animals the catabolic parameters of both LDL preparations changed towards a faster clearance, the effect being greatest for gly-LDL (total mean residence times of gly-LDL pre-diabetic: 19 h, diabetic: 16 h; control LDL pre-diabetic and diabetic: 14 h). The difference in clearance between glycated and control LDL was thus strongly reduced. Virtually no antibody complexed to gly-LDL could be measured. The results suggest an increased activity of the non-receptor mediated pathway in diabetes mellitus, possibly co-responsible for an increased atherosclerotic risk.

Pharmacokinetics and efficacy of rectal versus oral sustained-release morphine in cancer patients

Sustained-release morphine (MST) given by the rectal route was compared with oral MST in an open randomised cross-over trial in ten patients with cancer who received stable doses of MST. No significant difference was found in the areas under the curve of the concentration-time profiles (AUC) following oral or rectal administration for parent morphine. The AUCs determined for morphine-6-glucuronide (M6G) and morphine-3-glucuronide (M3G) after oral administration were approximately twice those obtained following rectal administration. The maximal concentration achieved was lower and the time to maximal concentration was longer following rectal administration for morphine, M6G and M3G. The relative mean arrival times following rectal administration were significantly longer for morphine and M3G but not for M6G. These findings suggest slower absorption but less first-pass metabolism of MST after rectal administration. No significant difference was noted between the oral and the rectal route in measurements on visual-analogue scales for pain or side effects. We recommend the rectal route as being suitable for MST administration when the oral route is no longer available. In changing from oral to rectal administration, the same dose and dose interval may be used, but dose adjustment may be needed.

Optimal extravascular dosing intervals

An explicit formula is presented for simple calculations of the dosing time, tau, that results in a steady-state peak-to-trough ratio of 2 in extravascular dosings. Contrary to other formulae presented, the calculations are guaranteed to be well bound in the percentage error (less than 1%) for any parameter value combination. It is shown that the biexponential dosing interval problem can be transformed into a general, dimensionless problem enabling a global error analysis in the approximation. The proposed formula is demonstrated in the calculation of an "optimal" dosing interval for quinidine. An algorithm and FORTRAN computer program OPTAU for exact calculation of tau and dosing simulations is also demonstrated in the quinidine example.