Effect of gastric emptying and entero-hepatic circulation on bioequivalence assessment of ranitidine.

The aim of study was to compare the bioavailability of ranitidine obtained from either Ranitidine (300 mg tablet; LPH® S.C. LaborMed Pharma S.A. Romania: the test formulation) and Zantac® (300 mg tablet; GlaxoSmithKline, Austria: the reference formulation). Twelve, Romanian, healthy volunteers were enrolled in the study. An open-label, two-period, crossover, randomized design was used. Plasma levels of ranitidine were determined using the validated, high-pressure liquid chromatography (HPLC) method. The physiologically motivated time-delayed model was used for the data evaluation and a paired Student's t-test and Schuirmann's two one-sided tests were carried out to compare parameters. Nonmodeling parameters (AUC(t), AUC, C(max), T(max)) were tested by the paired Student's t-test and the 90 confidence intervals of the geometric mean ratios were determined by Schuirmann's tests. Paired Student's t-test showed no significant differences between nonmodeling and modeling parameters. The results of the Schuirmann's tests however indicated significant statistical differences with reference to AUC(t), AUC, C(max), T(max) and other modeling parameters, especially MT(c) and τ(c). Schuirmann's tests revealed significant bioequivalence between ranitidine formulations using the modeling parameters MRT and n. The presented model can be useful as an additional tool to assess drug bioequivalence, by screening for disruptive parameters.

Mathematical model indicates nonlinearity of noradrenaline effect on rat renal artery.

The aim of this work is to present the efficacy of a previously introduced computational procedure, developed for evaluation of vascular responsiveness. On this reason, as an example a common study of noradrenaline (NA) effect on a rat renal artery under in vitro conditions was arbitrarily selected. The response of the arterial segment to NA doses (0.1-10 microg) was digitally recorded on a PC and employed to develop mathematical model of NA effect. Using the model, the following NA effect variables were determined: the vessel sensitivity parameter, mean effect time and rate constant, respectively, characterizing the effect intensity, duration, and regression and also classic response variables: the maximal effect and time of the maximal effect. The two-way analysis of variance followed by Bonferroni's test revealed a significant influence of the increasing NA dose on the vessel sensitivity parameter and mean effect time. These findings indicated nonlinearity of processes underlying NA effect on the rat renal artery over the given range of NA doses. The procedure exemplified has the potential for use as an effective adjunct to routine studies of vascular responsiveness as it enables the extraction of meaningful information which cannot by obtained by common manual evaluation procedures.

Computer-based methods for measurement, recording and modeling vessel responses in vitro: a pilot study with noradrenaline.

This paper reports the first results of an ongoing methodological pilot study aimed at designing techniques for the automatic measurement and digital recording of vessel responses to biologically active substances under in vitro conditions and for the mathematical modeling of the underlying processes. The techniques presented in this pilot study allowed us to determine model-based estimates of the parameters characterizing vasoconstrictor responses, i.e., the vessel sensitivity parameter, the mean time of vasoconstrictor response and the rate constant of vessel relaxation. The given parameters are not dependent on doses of biologically active substances, provided that the underlying processes satisfy the principle of superposition. Use of these techniques is shown in the classic study of vasoconstrictor responses to noradrenaline in the rat renal artery.

System approach to modeling metabolite formation from parent drug: a working example with methotrexate.

The aim of this methodological study was to present and exemplify a system-approach-based technology in modeling the formation of the metabolite from the parent drug. To represent this process, the parent-metabolite dynamic system was defined in such a way that the concentration-time profile of the parent drug was considered the input, while the concentration-time profile of the metabolite the output, of this system. The system-approach-based modeling technology was used to determine the model of the parent-metabolite dynamic system and to obtain the model-based estimates of the rate of metabolite formation, the rate of metabolic ratio and the mean time of metabolite formation. The technology was applied to concentration data for methotrexate and 7-hydroxymethotrexate in patients with psoriasis after a single oral methotrexate dose. Third-order linear models were selected as optimal to approximate the parent-metabolite dynamic systems representing the formation of 7-hydroxymethotrexate from methotrexate of these patients. The model-based estimates of the metabolic ratios ranged from 0.53 to 0.95. The model-based estimates of the mean times of formation of 7-hydroxymethotrexate from methotrexate ranged from 9.13 to 25.13 h. The model-based estimates of the rates of formation of 7-hydroxymethotrexate from methotrexate reached peak values (ranging from 0.03 to 0.11 h-1) in the time interval 1.5-4.5 h after administration of methotraxate. This study does not only introduce the method that may be useful in gaining insight into metabolite formation, but also presents a new example of the methodological, conceptual and computational uniformity of the system-approach-based technology in modeling various biomedical systems.

Modeling drug absorption from enteric-coated granules.

A system-approach-based method is proposed for modeling drug absorption from enteric-coated granules. This method was exemplified using enteric-coated granules of aspirin given to healthy subjects. Based on the results obtained, it can be concluded that absorption of salicylate from the granules can be sufficiently described using a first-order linear model with an absorption rate constant of salicylate similar to that reported for an aqueous solution of aspirin administered orally to healthy subjects. The method proposed in this study may contribute to the working library of modeling techniques in pharmacokinetics since it allows direct modeling of the drug absorption process and estimates the absorption rate constant of a drug when its behavior in the body is significantly influenced by a gastric emptying process. i.e., when the absorption rate constant of the drug cannot be estimated on the basis of its cumulative absorption-time profile.

Weighting function used for adjustment of multiple-bolus drug dosing.

This paper presents a new method for the adjustment of the multiple-bolus dosing of a drug. The method is based on the weighting function of the system describing the behavior (absorption, distribution and elimination) of the drug in the patient, identified employing a test dose administration of the drug to a patient. This method can be employed for the adjustment of the multiple-bolus dosing of the drugs whose behavior in the patient can be sufficiently described by linear time invariant models. The method allows to estimate loading and maintenance bolus doses of the drug, necessary to reach and maintain prescribed trough levels of the drug in a patient at desired time-points, both (the levels and time-points) specified by treatment requirements. The method is particularly suitable for the adjustment of multiple-bolus dosing of drugs with narrow therapeutical windows or of very expensive products such as the clotting factors. The method is exemplified by the adjustment of the multiple-bolus dosing of factor VIII in postoperative treatment of hemophilia A.

Bioavailability and pharmacokinetic studies in the development of an oral formulation of stobadine dipalmitate.

The pyridoindole stobadine is a novel drug with antioxidant and cardioprotective properties. The objective of this study was to compare the bioavailability and the main pharmacokinetic parameters of two different stobadine dosage forms, STBtest and STBref, after single oral dosing in the form of gelatine capsules to 6 dogs. The dose ranged from 2.9 to 4.7 mg/kg and a randomized two-period crossover design was applied. To quantify the drug in plasma, a GC/MS method was developed with a quantification limit of 1 ng/ml. The time profiles of stobadine plasma concentrations were fitted by pharmacokinetic models. The extent of relative bioavailability ranged between 0.71 and 1.56. Practically no difference was found between the bioavailability rate of the two capsules, expressed as Cmax/AUC, with values ranging from 0.0022-0.0047 min-1 for STBtest and 0.0022-0.0045 min-1 for STBref. In conclusion, the technological difference of the capsules investigated did not yield deviations in either their extent or rate of absorption. Therefore the two stobadine formulations were concluded to be bioequivalent.

Pharmacokinetic study of stobadine.

The aim of this paper is to provide a brief overview of most important results of stobadine kinetic studies in rats, dogs, and human volunteers. In these studies, stobadine dihydrochloride and stobadine dipalmitate was used for intravenous and oral administration, respectively. To evaluate kinetic properties of stobadine and its metabolites, TLC, HPLC, GLC, GC-MS, radiometric, and fluorometric methods were developed and used.

Numerical simulations of stochastic circulatory models.

Properties of two of the stochastic circulatory models theoretically introduced by Smith et al., 1997, Bull. Math. Biol. 59, 1-22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov-Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.

Model of lymphocyte migration in Merino ewes under physiological conditions.

The paper presents an example of a new type of a structured model containing time delays in parallel branches. This model was selected as optimal to describe mathematically the lymphocyte migration between the venous blood and prescapular lymph in Merino ewes under physiological conditions. The model allowed to identify and quantify several lymphocyte fractions exhibiting different migration dynamics.

Pharmacokinetics of factor VIII in hemophilia A patients assessed by frequency response method.

The frequency response method, having its mathematical underpinnings in the theory of linear dynamic systems, was utilized to model pharmacokinetic systems describing the fate of factor VIII (F VIII) administered to hemophilia A patients before surgery. The pharmacokinetic system was defined on the basis of the patient's data in such a way that the injection of F VIII during 5-15 min was considered the input, and the corresponding plasma F VIII concentration profile consisting of both the injection and post-injection part the output of this system. The approach is an alternative to routine procedures based only on evaluation of the post-injection part of the F VIII concentration profile. With respect to the common sampling schedule of F VIII, simple second-order models were found acceptable for all the patients involved in the study. However, in the patients whose plasma F VIII concentration profiles did not decrease monotonously after the injection, these models failed to approximate secondary peaks indicating the presence of time delays in F VIII kinetics. The results obtained were discussed with respect to applications of pharmacokinetic models for the adjusted dose continuous infusion of F VIII in hemophilia A patients during and after surgical interventions.

Modeling in frequency domain used for assessment of in vivo dissolution profile.

PURPOSE: To present a model-dependent approach for the assessment of the in vivo drug dissolution profile based on in vitro data for the multiple unit dosage form, as an alternative to the numerical method proposed in the study by Hayashi et al., Pharm Res. 12:1333-1337 (1995). METHODS: The data for aspirin granules administered to healthy subjects obtained in the above mentioned study were re-evaluated. The subject dissolution system was considered to consist of two subsystems connected in series, i.e. the subsystem describing the gastric-emptying process and the subsystem describing the intestinal dissolution process. The frequency response method was used to model the subject dissolution system. RESULTS: The model in vivo dissolution profile of aspirin, assessed as the integral of the model weighting function of the subject dissolution system, was in agreement with the in vivo cumulative absorption profile calculated by the Wagner-Nelson method. CONCLUSIONS: Comparison of dynamic properties of the subject dissolution system with the subsystem describing the gastric-emptying process yielded quantitative confirmation of the decisive role of the gastric-emptying process in the in vivo drug dissolution after administration in the multi unit dosage form.

Effect of long-term administration of stobadine on exploratory behaviour and on striatal levels of dopamine and serotonin in rats and their offspring.

Stobadine (STB), a cardioprotective drug, was evaluated for its effect on the intensity and habituation of exploratory behaviour in open field testing and on the levels of striatal dopamine (DA), serotonin (5-HT) and their metabolites (3,4-dihydroxyphenylacetic acid, homovanillic acid, 5-hydroxyindole-3-acetic acid) in rats and their offspring. Dams were treated by oral gavage with STB (50 mg kg-1) for a total of 56 days from 14 days before mating to day 21 postpartum (pp). The first open field measurements of the dams were performed over 4 days at the beginning of the experiment, the second on days 21-24 pp and the third on days 49-52 pp (recovery period). Their offspring were tested on postnatal (pn) days 30-33 and 60-63. The biochemical analysis (HPLC with electrochemical detection) in the dams was performed at the same time schedule as given for the open field testing, but in their offspring only on pn day 60. Motor activity of the dams was decreased on days 21-24 pp. The increase of motor activity in female offspring was observed on pn days 30-33. Neurochemical analysis of the striatum of the dams revealed a significant increase of the levels of DA, 5-HT and 5-hydroxyindole-3-acetic acid. In male offspring the levels of DA were significantly decreased, whereas in females the levels were increased. These results suggest that maternal administration of STB resulted both in dams and their offspring in minor alterations in spontaneous behaviour components and changes in the dopaminergic and serotonergic system, but without inducing overtly detectable toxicity.

CXT-MAIN: a software package for determination of the analytical form of the pharmacokinetic system weighting function.

A new procedure specific for the determination of the analytical form of the model weighting function of a complex multicomponent pharmacokinetic system with or without a shunt and time delays is described. The procedure is based on the theory of linear dynamic systems and on a circulatory pharmacokinetic model of the living body. The model transfer function of the system under study was obtained by the frequency response method in the form of the ratio of two frequency dependent polynomials. Subsequently, the technique of the partial fraction inversion was employed to determine the analytical form of the model weighting function. Two examples from bioavailability studies in pharmacokinetics are given. The first example presents two estimates of the model weighting function of a pharmacokinetic system obtained by the new procedure and by a polyexponential deconvolution method. To compare these results, two models of the measured system output were determined using the two estimates of the model weighting function, the actual system input and a convolution method. The model weighting function obtained by the new procedure yielded a better model approximation of the output data than that obtained by the polyexponential deconvolution method. The second example, using the new procedure, presents the determination of the model weighting function of such a system that the deconvolution methods, commonly used in pharmacokinetics, cannot be applied to.

Determination of analytical form of system weighting function.

This paper presents the determination of the analytical form of the weighting function of the three following complex multicomponent systems: 1) the system describing human pharmacokinetics of pentacaine after oral administration; 2) the system describing the hepatal elimination of indocyanine green in pig, and 3) the system describing the fate of indocyanine green in human esophageal varixes. The determination of the weighting function is based on the system transfer function and the technique of the partial-fraction inversion.

Building a structured model of a complex pharmacokinetic system with time delays.

This paper presents a description of the procedure for building a structured model of a complex pharmacokinetic system on using its transfer function. The example employed is that of the pharmacokinetic system based on gentamicin plasma concentrations after intravenous and intratracheal administration to guinea pigs, describing the pathway of the drug into the systemic circulation after the extravascular injection mentioned. The structured model selected consisted of a submodel of a proportional linear subsystem, two submodels of simple linear dynamic subsystems with time constants of 0.135 +/- 0.065 hr (95% I.C.) and 0.052 +/- 0.049 hr, and two submodels of parallel subsystems with time delays of 0.25 +/- 0.046 hr and 1.135 +/- 0.288 hr, connected in serial. Two estimates of the mean residence time of the total amount of gentamicin in the system, i.e., 0.347 and 0.335 hr, were obtained, based on the system frequency and structured model, respectively. From the methodological point of view, our paper demonstrates the efficiency of combination of modelling in the frequency and in the time domain, designed to facilitate studies of pharmacokinetic systems.

CXT: a programme for analysis of linear dynamic systems in the frequency domain.

In this paper, the computer programme CXT (CompleX Tools for Linear Dynamic System Analysis), using the frequency response method, is described and exemplified. The method is based on the approximation of the frequency response of the linear or linearised dynamic system, measured or calculated from input-output measurements, by the frequency model of the system transfer function in the form of the ratio of two frequency-dependent polynomials. The form of the programme is sufficiently general to permit application in many areas, e.g., in modelling linear or linearised dynamic biological systems consisting of several subsystems arranged in serial and/or parallel fashion, with or without time delays. The programme is a menu-driven software taking data from a keyboard or disk file to produce outputs on a screen, printer, or disk file in tables and plots. The programme can run interactively or in an automatic tutorial mode, under DOS and/or WINDOWS. Numerical examples are taken from pharmacokinetics and indocyanine green liver function tests.

[Transplacental transfer of stobadine in rabbits in various stages of pregnancy--an approximation using a pharmacokinetic model]. / Transplacentárny prechod stobadínu u králikov v rôznych stádiach gravidity--aproximácia farmakokinetickým modelom.

Stobadine (STB), a cardioprotective drug, was investigated for its placental transfer in rabbits on the 20th and 27th day of gestation. The concentration of 3H-STB and its metabolites was determined in maternal and foetal plasma and organs at 0.5; 1; 2; and 6 h after the oral administration of 5 mg/kg STB. The third and fifth order linear models were selected as the optimal models of the fate of STB in the maternal plasma at the 20th and 27th day of gestation, respectively. The high order of the latter model indicated recirculation of STB in the maternal body at the last stage of gestation. The concentrations of STB and its metabolites in the uterus were found to be higher at mid- than late-pregnancy. At the 27th day of pregnancy the concentration of STB and its metabolites were higher in all foetal organs than on the concentrations at the 20th day of pregnancy, indicating active placental barrier function in mid-pregnancy.

Frequency response method in pharmacokinetics.

The paper presents the demonstration of applicability of the frequency response method in a bioavailability study. The frequency response method, common in system engineering, is based on an approximation of the frequency response of a linear dynamic system, calculated from input-output measurements, by a frequency model of the system transfer function in the frequency domain. In general, the influence of the system structure on the form of the system frequency response is much more distinct than on the form of the system output. This is of great advantage in modeling the system frequency response instead of the system output, commonly used in pharmacokinetics. After a brief theoretical section, the method is demonstrated on the estimation of the rate and extent of gentamicin bioavailability after intratracheal administration to guinea pigs. The optimal frequency model of the system describing the gentamicin pathway into the systemic circulation and point estimates of its parameters were selected by the approximation of the system frequency response in the frequency domain, using a noniterative algorithm. Two similar estimates of the system weighing function were independently obtained: the weighting function of the selected frequency model and the weighting function estimated by the numerical deconvolution procedure. Neither of the estimates of the weighting function does decrease monotonously after the maximum of about 2.2-2.5 unit of dose hr-1 recorded approximately 0.1 hr after drug administration. Both estimates show a marked additional peak approximately at 0.3 hr after administration and possible peaks in the further time period. We hypothesized that the loop found in the frequency response calculated and in the selected optimal frequency model, the high-order of this model, and several peaks identified in the estimates of the system weighting function indicated the complexity of the system and the presence of time delays. Three estimates of the extent of gentamicin intratracheal bioavailability obtained by the three different ways: directly from the calculated frequency response, calculated using the selected frequency model, and by the deconvolution method were 0.950, 0.934, and 0.907 respectively. Thus the conclusion can be made that gentamicin injected intratracheally to guinea pigs is almost completely available.