Asymptotics and bioavailability in a 17-compartment pharmacokinetic model with enterohepatic circulation and remetabolization

A 17-compartment linear pharmacokinetic model is designed, describing the complex process of enterohepatic circulation as a superposition of the net (remetabolizationfree) enterohepatic circulation, and remetabolization with subsequent intestinal absorption of the parent drug. Basically, the model is built by doubling the model describing the circulation of the parent drug in the body, so that the remetabolizable metabolite circulates in a model of the same structure as does the parent compound. The two submodels are cross-connected with arrows denoting the transition of the particular substance into the complementary part of the complex model. Asymptotic properties of the model are investigated, in particular, explicit formulas for its pharmacokinetic endpoints are given using the elements of its transition probability matrix. Conversely, taking account of the effect of bile cannulation, intravenous, intraportal and oral administration of the drug, as well as of the intravenous and intraportal administration of the remetabolizable metabolite, the transition probabilities of the system are determined in terms of certain measurable pharmacokinetic endpoints and the flow rates through the kidneys, liver and the cardiac output. Finally, the influence of the enterohepatic circulation and remetabolization process on bioavailability is examined. In particular, the inclusion-exclusion formula is derived, expressing its joint efficiency (defined as the relative increase of bioavailability) by means of the efficiencies of the net enterohepatic circulation and of the remetabolization process.     

Portacaval shunt and measurement of canine bile acid enterohepatic circulation: effects of cholecystectomy

Studies were made of the usefulness of serial serum bile acid determinations in dogs with end-to-side portacaval shunt for determining relative rates of bile acid enterohepatic circulation (EHC). Studies in intact and cholecystectomized dogs with shunt showed that bile acid EHC in fasting cholecystectomized animals was about three times faster than in intacts. As expected, feeding greatly increased EHC in intacts, but caused smaller but definite increases in cholecystectomized animals. Cholecystokinin (Kinevac) administration caused transient increases in intact dog bile acid EHC, but had no effect in cholecystectomized animals. These results confirm most previous studies and demonstrate that the method is sensitive and useful for comparing rates of bile acid enterohepatic circulation under different circumstances.     

Effects of sphincterectomy on bile acid enterohepatic circulation in dogs

Relative rates of bile enterohepatic circulation (EHC) and bile acid pool distribution were compared in intact and sphincterectomized dogs with portacaval shunt. There was no significant difference in the rates of EHC or in the bile acid pool distribution in the groups of animals. Feeding and cholecystokinin administration caused similar increases in bile acid EHC rates in sphincterectomized and intact animals. It was concluded that the sphincter of Oddi has little or no effect on these aspects of bile acid metabolism in dogs.     

Canine bile acid enterohepatic circulation

The enterohepatic circulation (EHC) of bile acids has been studied in fasting dogs with portacaval shunt maintained in the steady state. In such animals the rate of EHC is proportional to systemic blood bile acid concentration. Bile acid EHC was irregular (20 to 100% variation) when measured at 15 minute or hourly intervals. Studies showed that the variations persisted in cholecystectomized and sphincterectomized animals. The irregularities were enhanced by bethanechol chloride which increases intestinal peristalsis and suppressed by diphenoxylate HCl which slows peristalsis. The variations appear to arise from irregular patterns of intestinal peristalsis. This phenomenon may explain some variations in blood bile acid concentration observed in patients with liver disease.     

Multistate modeling and simulation of patient trajectories after allogeneic hematopoietic stem cell transplantation to inform drug development

We present a case study for developing clinical trial scenarios in a complex progressive disease with multiple events of interest. The idea is to first capture the course of the disease in a multistate Markov model, and then to simulate clinical trials from this model, including a variety of hypothesized drug effects. This case study focuses on the prevention of graft‐versus‐host disease (GvHD) after allogeneic hematopoietic stem cell transplantation (HSCT). The patient trajectory after HSCT is characterized by a complex interplay of various events of interest, and there is no established best method of measuring and/or analyzing treatment benefits. We characterized patient trajectories by means of multistate models that we fitted to a subset of the Center for International Blood and Marrow Transplant Research (CIBMTR) database. Events of interest included acute GvHD of grade III or IV, severe chronic GvHD, relapse of the underlying disease, and death. The transition probability matrix was estimated using the Aalen‐Johansen estimator, and patient characteristics were identified that were associated with different transition rates. In a second step, clinical trial scenarios were simulated from the model assuming various drug effects on the background transition rates, and the operating characteristics of different endpoints and analysis strategies were compared in these scenarios. This helped devise a drug development strategy in GvHD prevention after allogeneic HSCT. More generally, multistate models provide a rich framework for exploring complex progressive diseases, and the availability of a corresponding simulation machinery provides great flexibility for clinical trial planning.     

Bile acids via FXR initiate the expression of major transporters involved in the enterohepatic circulation of bile acids in newborn mice

The enterohepatic circulation (EHC) of bile acids (BAs) plays a pivotal role in facilitating lipid absorption. Therefore, initiation of the EHC in newborns is of crucial importance for lipid absorption from milk. The purpose of this study was to determine at what age BA transporters in liver are expressed, and the mechanism for their initiation. Serum and liver samples were collected from C57BL/6 mice at 2 days before birth and various postnatal ages. Messenger RNA assays revealed a dramatic increase at birth in the expression of the BA transporters (Ntcp, Bsep, Mrp4, Ostβ), as well as the phospholipid floppase Mdr2 in mouse liver, with the highest expression at 1 day of age. The mRNA expression of the ileal BA transporters (Ostα and Ostβ) also markedly increased at birth. Meanwhile, taurine-conjugated cholic acid markedly increased in both serum and liver of newborns, correlated with upregulation of the classic pathway of BA biosynthesis in newborn liver. The mRNA levels of the major BA sensors, FXR and PXR, were increased at 1 day of age, and their prototypical target genes were upregulated in liver. The mRNA expression of transporters involved in the EHC of BAs was similar in wild-type and PXR-null mice. In contrast, in FXR-null mice, the "day 1 surge" pattern of Ntcp, Bsep, Ostβ, and Mdr2 was blocked in newborn mouse liver, and the induction of Ostα and Ostβ was also abolished in ileums of FXR-null mice. In conclusion, at birth, BAs from the classic pathway of synthesis trigger the induction of transporters involved in EHC of BAs in mice, through activation of the nuclear receptor FXR.     

Short- and long-term effects of biliary drainage on hepatic cholesterol metabolism in the rat.

The present study concerns short- and long-term effects of interruption of the enterohepatic circulation (EHC) on hepatic cholesterol metabolism and biliary secretion in rats. For this purpose, we employed a technique that allows reversible interruption of the EHC, during normal feeding conditions, and excludes effects of anaesthesia and surgical trauma. [3H]Cholesteryl oleate-labelled human low-density lipoprotein (LDL) was injected intravenously in rats with (1) chronically (8 days) interrupted EHC, (2) interrupted EHC at the time of LDL injection and (3) intact EHC. During the first 3 h after interruption of the EHC, bile flow decreased to 50% and biliary bile acid, phospholipid and cholesterol secretion to 5%, 11% and 19% of their initial values respectively. After 8 days of bile diversion, biliary cholesterol output and bile flow were at that same level, but bile acid output was increased 2-3-fold and phospholipid output was about 2 times lower. The total amount of cholesterol in the liver decreased after interruption of the EHC, which was mainly due to a decrease in the amount of cholesteryl ester. Plasma disappearance of LDL was not affected by interruption of the EHC. Biliary secretion of LDL-derived radioactivity occurred 2-4 times faster in chronically interrupted rats as compared with the excretion immediately after interruption of the EHC. Radioactivity was mainly in the form of bile acids under both conditions. This study demonstrates the very rapid changes that occur in cholesterol metabolism and biliary lipid composition after interruption of the EHC. These changes must be taken into account in studies concerning hepatic metabolism of lipoprotein cholesterol and subsequent secretion into bile.     

Distinct distributions of D-erythro-neopterin in arteries and veins and its recovery by an enterohepatic circulation.

Large amounts of D-erythro-neopterin, a pteridine derivative, are formed from guanosine triphosphate (GTP) by human macrophages upon stimulation with interferon-gamma. In addition, in humans a basal neopterin level in all body fluids is evident also in absence of immunological stimuli. Extremely high concentrations of D-erythro-neopterin were detected in biliary fluid. We therefore investigated, if an enterohepatic circulation might exist for this substance. We quantified concentrations of pteridines in serum obtained from various vessels and in biliary fluid. Samples were collected during surgery of five patients with duodenal ulcer or adenocarcinoma of the stomach. Our data clearly demonstrate the existence of an enterohepatic circulation for the recovery of neopterin which seems to be specific for this substance. The relative distributions of neopterin concentrations in the gastrointestinal tract and vessels were seen invariably in all patients and were consistent with findings in five corpses examined post mortem. In addition, significantly higher neopterin concentrations, were found in arteries than in veins. The data indicate that neopterin derivatives are consumed in the peripheral capillary system and an enterohepatic circulation is established to maintain constant blood levels of neopterin derivatives. Furthermore, we suppose that the liver is the source of constitutive neopterin concentrations.     

Absorption and enterohepatic circulation of baicalin in rats

Pharmacokinetics of baicalin, in form of its parent drug (BG) and conjugated metabolites (BGM), were studied following intravenous and oral administration of baicalin to intact rats. The enterohepatic circulation of BG and BGM was also assessed in a linked-rat model. Multiple plasma and urine samples were collected, and concentrations of BG and BGM were determined using a liquid chromatography/tandem mass spectrometry method. The concentration of BGM was assayed in the form of baicalein after treatment with beta-glucuronidase/sulfatase. After i.v. administration, plasma concentration of BG rapidly declined with the elimination half-life (T1/2) of 0.1 till 4 h post dose, followed by slight increase from 4-8 h in plasma concentrations after drug administration. These plasma concentrations resulted in a significant prolongation of the terminal elimination half-life of BG (T1/2 TER, 9.7 h). BG also displayed slight increase in plasma concentrations (12-24 h) after oral administration, with T1/2 TER of 12.1 h. Based on the AUC of BG and BGM, the absolute bioavailability of baicalin was 2.2+/-0.2% and 27.8+/-5.6%, respectively. The exposure of baicalin to the systemic circulation was approximately 118-fold lower than that of BGM after oral administration (AUC0-t, 4.43 versus 523.97 nmol.h/mL). The high extent of glucuronidation suggested the possible presence of enterohepatic circulation, which was confirmed in the linked-rat model since plasma concentrations of BG and BGM were observed in bile-recipient rats at 4 to 36 h. The extent of enterohepatic circulation after intravenous administration of baicalin was 4.8% and 13.3% for BG and BGM, respectively. It was determined that 18.7% and 19.3% of the administered baicalin were subjected to enterohepatic circulation for BG and BGM, respectively, after oral administration. These results confirm that BG undergoes extensive first-pass glucuronidation and that enterohepatic circulation contributes significantly to the exposure of BG and BGM in rats.     

An analytical solution for a class of delay-differential equations in pharmacokinetic compartment modeling

The authors obtain the analytic expression for the solution of a differential system with time lags for any n-compartment linear model with a single input, and, by convolution, for all intakes. The theoretical result is applied to the case of one-, two-, and three-compartment models and gives insight into the pharmacokinetics of drug undergoing enterohepatic circulation: the amount of drug in any compartment is expressed for all time. Statistical results, such as the mean residence time of drug, are obtained by the same calculation.     

Drug recirculation model with multiple cycles occurring at unequal time intervals

A pharmacokinetic model for enterohepatic recycling has been developed to take into account multiple recirculations likely to occur at various times after intravenous or subcutaneous injection, after infusion, or after a single oral administration of a drug. The times when the gall bladder empties, the duration of infusion and the number of recirculations may be arbitrarily chosen (for simulations) or computed (for optimization) to express the concentration in the central compartment at any time. Without a new theoretical calculation, the area under the concentration curve may be obtained as a function of the model parameters. As an example, the model is applied to an experimental case of four recirculations after oral administration and to a new drug data fitting.     

2,4-diamino-7-hydroxy-pteridines, a new class of catabolites of methotrexate

Methotrexate remains a commonly used drug in the chemotherapy of various malignancies. The known catabolites are 7-hydroxy-methotrexate, formed in the liver, and diamino-methyl-pteroic acid formed in the gut. We report for the first time evidence that 2,4-diamino-7-hydroxy-pteridine derivatives are present in the biological fluids of patients on high-dose methotrexate protocols. So far, two major derivatives have been identified as 2,4-diamino-6-hydroxymethyl-7-hydroxy-pteridine and 2,4-diamino-6-methyl-7-hydroxy-pteridine. In regard to the actual knowledge of the catabolism of pteridines, these compounds are presumably formed by intestinal bacteria during enterohepatic circulation of the drug. Their slow clearance from the body raises the question of possible interference of these compounds on pteridine-dependent enzymes, which might explain in part some of the toxic effects of methotrexate.     

A review of the common properties of drugs with idiosyncratic hepatotoxicity and the "multiple determinant hypothesis" for the manifestation of idiosyncratic drug toxicity

Idiosyncratic drug toxicity is generally believed to be a phenomenon that cannot be readily evaluated experimentally. Reasons for this difficulty include the following: 1. It is a rare event (<1/5,000) and therefore impossible to be studied in clinical trials; 2. It is a human-specific event not detectable in experimental animals. To aid the understanding of idiosyncratic toxicity and to develop an experimental strategy for this phenomenon, a hypothesis is proposed. The hypothesis states that the low frequency of idiosyncratic drug toxicity is due to the requirements for the occurrence of multiple critical and discrete events, with the probability for the occurrence of idiosyncratic drug toxicity as a product of the probabilities of each event. The key determinants of these critical events are proposed to be: 1. Chemical properties; 2. exposure; 3. environmental factors; and 4. genetic factors. Based on this hypothesis, idiosyncratic drug toxicity can be evaluated experimentally via studying these key determinants. The chemical properties critical to idiosyncratic drug toxicity are identified via a review of the common properties of drugs that cause idiosyncratic liver toxicity. These properties include: 1. Formation of reactive metabolites. 2. Metabolism by P450 isoforms. 3. Preponderance of P450 inducers, and 4. Occurrence of clinically significant pharmacokinetic interactions with co-administered drugs. Based on this review, it is proposed that these common properties may be useful experimental endpoints for the prediction and therefore avoidance of the selection of drug candidates with idiosyncratic drug toxicity for further development.     

Importance of correlations among matrix entries in stochastic models in relation to number of transition matrices

Stochastic matrix models are used to predict population viability and the risk of extinction. Different stochastic methods require different amounts of estimation effort and may lead to divergent estimates. We used 16 transition matrices collected from ten populations of the perennial herb Primula veris to compare population estimates produced by different stochastic methods, such as selection of matrices, selection of vital rates, selection of matrix elements, and Tuljapurkar's approximation. Specifically, we tested the reliability of the methods using different numbers of transition matrices, and examined the importance of correlations among matrix entries. When correlations among matrix entries were included in the models, selection of vital rates produced the lowest and Tuljapurkar's approximation produced the highest estimates of mean population growth rates. Selection of matrices and matrix elements often produced nearly similar population estimates. Simulations based on incompletely estimated correlations among matrix entries considerably differed from those based on all correlations estimated, particularly when correlations were strong. The magnitude of correlations among matrix entries depended on the number of matrices, which made it difficult to generalize correlations within a species. Given that selection of vital rates or matrix elements is used, correlations among matrix entries should usually be included in the model, and they should preferably be estimated from the present data rather than according to other information of the species.     

Stochastic matrix models for conservation and management: a comparative review of methods

Stochastic matrix models are frequently used by conservation biologists to measure the viability of species and to explore various management actions. Models are typically parameterized using two or more sets of estimated transition rates between age/size/stage classes. While standard methods exist for analyzing a single set of transition rates, a variety of methods have been employed to analyze multiple sets of transition rates. We review applications of stochastic matrix models to problems in conservation and use simulation studies to compare the performance of different analytic methods currently in use. We find that model conclusions are likely to be robust to the choice of parametric distribution used to model vital rate fluctuations over time. However, conclusions can be highly sensitive to the within-year correlation structure among vital rates, and therefore we suggest using analytical methods that provide a means of conducting a sensitivity analysis with respect to correlation parameters. Our simulation results also suggest that the precision of population viability estimates can be improved by using matrix models that incorporate environmental covariates in conjunction with experiments to estimate transition rates under a range of environmental conditions.     

On Assessment of Bioequivalence for Drugs with Negligible Plasma Levels

In bioavailability studies, bioequivalence between drug products is usually determined based on some pharmacokinetic responses such as area under the blood or plasma concentration-time curve and maximum concentration. For some drug products, however, we may have negligible plasma levels because their intended routes of administration. In this case, assessment of bioequivalence between drug products of this kind may be established using clinical endpoints such as therapeutic response and time to the onset of a therapeutic response. In this paper, we propose two procedures which modify the method of generalized estimating equations (Liang and Zeger, 1986) and the proportional hazard models for paired failure times to assess bioequivalence between two drug products under the structure of a standard two-sequence, two-period crossover design. An example concerning a bioequivalence trial for albuterol metered dose inhaler indicated for acute bronchospasm (Herson, 1991) is used to illustrate the proposed procedures.     

Hepatocytes--the choice to investigate drug metabolism and toxicity in man: in vitro variability as a reflection of in vivo

The pharmaceutical industry is committed to marketing safer drugs with fewer side effects, predictable pharmacokinetic properties and quantifiable drug-drug interactions. Drug metabolism is a major determinant of drug clearance and interindividual pharmacokinetic differences, and an indirect determinant of the clinical efficacy and toxicity of drugs. Progressive advances in the knowledge of metabolic routes and enzymes responsible for drug biotransformation have contributed to understanding the great metabolic variations existing in human beings. Phenotypic as well genotypic differences in the expression of the enzymes involved in drug metabolism are the main causes of this variability. However, only a minor part of phenotypic variability in man is attributable to gene polymorphisms, thus making the definition of a normal liver complex. At present, the use of human in vitro hepatic models at early preclinical stages means that the process of selecting drug candidates is becoming much more rational. Cultured human hepatocytes are considered to be the closest model to human liver. However, the fact that hepatocytes are located in a microenvironment that differs from that of the cell in the liver raises the question: to what extent does drug metabolism variability observed in vitro actually reflect that of the liver in vivo? By comparing the metabolism of a model compound both in vitro and in vivo in the same individual, a good correlation between the in vitro and in vivo relative abundance of oxidized metabolites and the hydrolysis of the compound was observed. Thus, it is reasonable to consider that the variability observed in human hepatocytes reflects the existing phenotypic heterogeneity of the P450 expression in human liver.     

Estimating compliance to study medication from serum drug levels: application to an AIDS clinical trial of zidovudine.

This paper examines the use of serum drug levels to assess compliance to study medication in a clinical trial. We discuss problems of false-positivity, false-negativity, and bias that arise because of experimental errors in the drug assays, pharmacokinetic variations of the drug, and differential dosing levels. Basic concepts in probability are applied to derive a simple model that quantifies these problems. This model is used to obtain an estimate of compliance rate that corrects for these problems. However, derivation of this estimate requires additional information about false-positive and false-negative rates of the assay as well as some knowledge of the pharmacokinetic properties of the drug. We illustrate the evaluation of such a compliance estimate in the setting of an AIDS clinical trial of zidovudine (ZDV), in which some accessory data are available on the properties of ZDV serum assays and on the pharmacokinetic behavior of ZDV. We also describe a method that uses the accessory data to provide the additional information needed for computing the compliance estimate.