Analysis of methylmercury disposition in humans utilizing a PBPK model and animal pharmacokinetic data.

Physiologically based pharmacokinetic (PBPK) models are excellent tools to aid in the extrapolation of animal data to humans. When the fate of the chemical is the same among species being compared, animal data can appropriately be considered as a model for human exposure. For methylmercury exposure, sufficient data exist to allow comparison of numerous mammalian species to humans. PBPK model validation entails obtaining blood and tissue concentrations of the parent chemical and metabolite(s) at various times following a known exposure. From ethical and practical considerations, human tissue concentrations following a known exposure to an environmental toxicant are scarce. While animal-to-human extrapolation demands that sufficient human data exist to validate the model, the validation requirements are less stringent if multiple animal models are utilized within a single model template. A versatile PBPK model was used to analyze the distribution and elimination of methylmercury and its metabolite, inorganic mercury. Uniquely, the model is formed in a generic way from a single basic template during the initial program compilation. Basic parameters are defined for diffferent PBPK models for mammalian species that span a relatively large range of sizes. In this article, the analyses include 12 species (mouse, hamster, rat, guinea pig, cat, rabbit, monkey, sheep, pig, goat, cow, and human). Allometric (weight-based) correlations of tissue binding coefficients, metabolism rate constants, and elimination parameters for both methylmercury and inorganic mercury are presented for species for which sufficient data are available. The resulting human model, in accord with the animal models, predicts relatively high inorganic mercury levels in the kidneys long after the disappearance of methylmercury from the blood.

Mathematical modeling of human embryonic and fetal growth rates.

A mathematical model for human embryonic/fetal growth data from implantation to birth is developed. In previous work, it was shown that an unbiased estimate for human fetal growth data from about day 50 post-conception until term could be calculated from the Gompertz equation. This period represents a range of embryonic/fetal weights from one to 3500 g. When the Gompertz equation is extended, with no change of parameters, to the prenatal period before 50 days, the predicted weights have a consistent bias which might have a biological basis. Early embryonic growth immediately following fertilization is exponential; i.e., one cell goes to 2, then 4, then 8... etc., with essentially no decrease in relative growth rate. Except for possible small changes in cell size and cell mitosis cycle time, such exponential growth can be considered as a special case of the Gompertz equation with a, the relative rate of decrease of the relative growth rate, equal to zero. The relative growth rate begins to decrease about 20 days post-conception, at the time of cell differentiation into organ precursors. Although the "Hayflick Limit" of the maximum of 50 to 60 cell divisions for human cells would tend to cause a decrease in growth rate, it can be shown that the effect is insignificant during embryonic/fetal growth. The observed decrease in the growth rate might be a result of a decreasing fraction of cells in the pool of dividing cells. For the Gompertz equation model, a at this time changes from zero to a positive number. Analysis of fetal growth data shows that a rapidly becomes large and then decreases over a period of several days to become a constant positive value for the remainder of the prenatal term. Good fits of empirical embryonic/fetal growth data were obtained by nonlinear regression with calculation of the embryonic/fetal weights through numerical integration of the differential Gompertz equations and the functionality of alpha.

Physiological "constants" for PBPK models for pregnancy.

Physiologically based pharmacokinetic (PBPK) models for pregnancy are inherently more complex than conventional PBPK models due to the growth of the maternal and embryo/fetal tissues. Physiological parameters such as compartmental volumes or flow rates are relatively constant at any particular time during gestation when an acute experiment might be conducted, but vary greatly throughout the course of gestation (e.g., contrast relative fetal weight during the first month of gestation with the ninth month). Maternal physiological parameters change during gestation, depending upon the particular system; for example, cardiac output increases by approximately 50% during human gestation; plasma protein concentration decreases during pregnancy; overall metabolism remains fairly constant. Maternal compartmental volumes may change by 10-30%; embryo/fetal volume increases over a billionfold from conception to birth. Data describing these physiological changes in the human are available from the literature. Human embryo/fetal growth can be well described using the Gompertz equation. By contrast, very little of these same types of data is available for the laboratory animal. In the rodent there is a dearth of information during organogenesis as to embryo weights, and even less organ or tissue weight or volume data during embryonic or fetal periods. Allometric modeling offers a reasonable choice to extrapolate (approximately) from humans to animals; validation, however, is confined to comparisons with limited data during the late embryonic and fetal periods of development (after gestation d 11 in the rat and mouse). Embryonic weight measurements are limited by the small size of the embryo and the current state of technology. However, the application of the laser scanning confocal microscope (LSCM) to optically section intact embryos offers the capability of precise structural measurements and computer-generated three-dimensional reconstruction of early embryos. Application of these PBPK models of pregnancy in laboratory animal models at teratogenically sensitive periods of development provides exposure values at specific target tissues. These exposures provide fundamentally important data to help design and interpret molecular probe investigations into mechanisms of teratogenesis.

A computer model and program for xenobiotic disposition during pregnancy.

A physiologically based pharmacokinetic computer model and program have been developed that depict internal disposition of chemicals during pregnancy in the mother and embryo/fetus. The model is based on human physiology but has been extended to simulate laboratory animal data. The model represents the distribution, metabolism, and elimination of two chemicals in both the maternal and embryo/fetal systems; the program handles the two chemicals completely independently or interactively with the two chemicals sharing routes of metabolism and/or elimination. The FORTRAN program computes the concentration of the two chemicals in 26 organs/tissues in the pregnant mother and 15 organs/tissues in the embryo/fetus using a 486DX4 or Pentium PC. Adjustments for embryo/fetal organ and tissue volumes as a function of developmental age are made utilizing the Gompertz growth equation for the developing embryo/fetus and allometric relationships for the developing organs. Various changes in the maternal compartments which could affect the distribution of a xenobiotic during pregnancy are also included in the model. Input files require estimates of binding coefficients, first- and/or second-order metabolism constants, level of interaction between the two chemicals, and dosing information. Different possible routes of administration are included (e.g., i.v., infusion, oral, dermal, and inhalation, as well as repeated doses or exposures). Regression analysis can be conducted on any combination of these various parameters to fit actual data. Output concentration-time curves are available simultaneously from all 82 differential equations. An illustrative example compares observed data with simulations for imipramine and its demethylated metabolite, desipramine, in both the maternal rat and her fetuses. Methyl mercury data for the non-pregnant and pregnant rat also are compared with human data. Based on parameters determined from analysis of rat data, the model is readjusted for human physiology and predicts human maternal and fetal tissue concentrations as a function of time.

Mathematical analysis for teratogenic sensitivity.

A mathematical structure is described for determining teratogenic sensitivity or susceptibility from analysis of malformation incidence, dose-response, and pharmacokinetic data obtained during pregnancy as a result of exposure to a teratogenic agent. From the dosage or exposure of laboratory animals, embryonic and maternal concentrations of the xenobiotic are calculated using a physiologically based pharmacokinetic (PBPK) model. Malformations observed in the progeny are linked to the PBPK-derived target tissue concentrations with a model for the sensitivity calculated as a function of the embryonic age. The PBPK model for internal disposition of chemicals during pregnancy was developed previously. This report focuses on the development of the mathematical relations for the sensitivity of the embryo and effect functions on different organs. The concentrations of a xenobiotic calculated for the site of action or target tissue(s) in the embryo are weighted using both a nonlinear dose-response curve and a sensitivity distribution function that depends on the age or stage of development of the embryo. This weighted "exposure" of the target tissue is regressed with the number of observed malformations to quantify the parameters of the model. This approach lends itself to integration of diverse sources of experimental data, with hydroxyurea data taken from several sources in the literature as an example. This sensitivity function obtained from laboratory animal data serves as a vehicle for prediction and extrapolation to human pregnancy for the teratogenic potential of a substance.

Mathematical representation of organ growth in the human embryo/fetus.

During human pregnancy, there is a huge increase in the total weight of the embryo/fetus from conception to term. The total growth, which is the summation of growth of the various organs and tissues that make up the organism, was analyzed in a previous paper and fitted to the Gompertz equation for growth. In the present study, allometry, the quantitative representation of the consequence of size, was utilized to describe the correlation of individual fetal organ/tissue weights with the total fetal weight. The organ/tissue weight and the total fetal weight data used in the analyses were pooled from various sources that provided data ranging from 25 days to 300 days post-conception. Allometric equations are presented for 16 embryo/fetal organs and tissues. The standard allometric equation gave adequate fits for embryo/fetal adrenal, bone, bone marrow, brain, heart, liver, pancreas, plasma, skeletal muscle, extracellular water, thymus and thyroid; but it was necessary to use a quadratic form of the allometric equation for embryo/fetal fat, kidney, lung and spleen. Parameters were also calculated for crown-to-rump and crown-to-heels for fetal lengths that occur during pregnancy.

A physiologically based pharmacokinetic computer model for human pregnancy.

A physiologically based pharmacokinetic (PBPK) model for human pregnancy must incorporate many factors that are not usually encountered in PBPK models of mature animals. Models for pregnancy must include the large changes that take place in the mother, the placenta and the embryo/fetus over the period of pregnancy. The embryo/fetal weight change was modeled using the Gompertz equation for growth which gave a good fit to extensive pooled weight data of the human embryo/fetus from 25 to 300 days of gestation. This equation is based on a growth rate that is proportional to the total weight of the organism with the proportionality factor decreasing exponentially with time. Allometric equations, which are widely used to relate organ weights, blood flow rates and other attributes of mature animals to total weight, were adapted to correlate fetal organ weights with total fetal weight. Allometric relationships were also developed for plasma flow rates and other organ-related parameters. The computer model, written in FORTRAN 77, included 27 compartments for the mother and 16 for the fetus; it also accommodates two substances allowing representation of a parent compound and a metabolite (or a second drug or environmental substance). Although this model is large, the inherent sparsity in the equations allow it to be solved numerically in a reasonable time on currently available, reasonably priced desktop computers. A nonlinear regression routine is included to fit key model parameters to experimental data. Concentrations of chemicals administered and measured in the mother may be simulated in both maternal and fetal organs at any day(s) between 25 days and 300 days of gestation. Allometric relationships are also utilized to adopt this human model for use with data obtained from animal experiments.

A mathematical analysis of human embryonic and fetal growth data.

There is no set of growth data from a single source for the human embryo/fetus which spans the full range of pregnancy. For mathematical and statistical analysis of the full gestational period, it was necessary to pool data from several sources. Three growth equations, which have been reported in the literature for various purposes, were tested and compared for possible use as a tool to describe the growth of the human embryo/fetus. Parameters were estimated using statistical procedures on the pooled data for the Verhulst logistic equation, a polynomial equation, and the Gompertz equation. The polynomial and Gompertz equations provided the best fit for the growth of the normal human embryo/fetus over the broadest range of 25 to 300 days, and especially in the critical period of development (gestational days 40 to 70). The relative rate of growth of the embryo/fetus was about 15% per day on the 25th day and declined progressively thereafter; the absolute rate of growth was the greatest at about the 240th day.

Multifactorial modeling, drug interactions, liver damage and aging.

A well designed physiological flow model can be used not only to describe and analyze the basic elimination of a drug but also it can form the basis for multifactorial analysis in situations of multiple organ dysfunction and drug therapy. Physiological flow models use existent knowledge of anatomical structure and physiological processes along with the biochemical basis of drug elimination to calculate concentration-vs-time profiles of drugs in various organs and tissue regions. A tissue region or organ must be included in the model if it is an important site of storage, toxicity, elimination, or other significant pharmacological action. Such models can be a powerful tool in medicine providing a rational basis for multiple drug therapy in high risk patients with altered organ function--especially for drugs with a narrow margin of safety. For some specific types of drug systems, physiological flow model models exist which can accurately describe drug concentration profiles in tissues for a variety of situations. A definitive general model is theoretically possible; but, in practice, has not yet been developed. Future research could provide the necessary information to make multifactorial analysis a clinically useful tool in rational drug therapy.

Drug interactions affecting the elimination of doxorubicin in the rat.

Radioactive 14C-doxorubicin (10 mg/kg iv; 2 microCi/kg) disappeared rapidly from the plasma of anaesthetized male Sprague-Dawley rats. Radioactivity appeared in the bile within 5 to 7 min, reached a peak concentration in 10 to 15 min and declined rapidly thereafter for 150 min during which about 22% of the injected dose appeared in the bile. Tissue concentrations measured 10 min after injection were compared with tissue samples obtained at 150 min. Polyexponential analysis of the amount of doxorubicin remaining in the body (based upon the amount injected minus the cumulative amount excreted) suggested a two-compartment model. In acute studies, the injection of bromosulphophthalein (50 mg/kg) or rifampicin (53 mg/kg) 60 min after the injection of doxorubicin reduced the excretion of doxorubicin. The daily administration of phenobarbital (75 mg/kg X 3) increased the cumulative excretion of doxorubicin; the administration of CCl4 (1 ml/kg, ip) 24 hrs before the experiment reduced the cumulative excretion of doxorubicin.

Estimation of drug binding parameters.

Many methods have been suggested and tested to estimate the association constants and binding capabilities of ligand-macromolecule interactions from experimental data. This problem is a subset of the general problem of parameter estimation for nonlinear algebraic models where both the independent and dependent variables are subject to measurement error. It is often difficult to anticipate the effect on the parameter estimates that is caused by error in the primary measurements. In this work, a computer algorithm is described which finds the maximum likelihood estimate for the true values of the parameters and also estimates for the values of the measurements. It is applied to experimental binding data in two examples for fitting the association constants and binding capacities.

A mathematical model and computer program for adriamycin distribution and elimination.

A mathematical physiological flow model is described for the distribution and elimination of adriamycin in the rat. The model includes the volume or mass of, and blood flow to the following tissues: heart, plasma, muscle, skin, kidney, bone marrow, gut, liver and bile. A compartment is also included for tight or almost irreversible binding which occurs with this drug. The program was written in FORTRAN to compute the concentration of drug in each tissue as a function of time after bolus injection or short term infusion. The computed data is printed on a line printer and recorded on disk for use in a SAS program GPLOT to obtain precision plots.

Competition between serum albumin and soluble fraction of liver for binding of warfarin and other drugs.

The binding of Warfarin by human serum albumin (HSA) and subcellular fractions from rat liver was investigated to evaluate the roles of such interactions in the pharmacokinetic properties of the anticoagulant. In vitro intracellular distribution studies showed that Warfarin was bound primarily by the soluble fraction of rat liver. Equilibrium dialysis studies were carried out to test the hypothesis that the hepatic extraction of Warfarin and drug interactions between Warfarin and other drugs involved competition between albumin and the soluble fraction of liver. A three compartment dialysis cell was designed and constructed for such studies. Three types of competitive binding interactions were identified. Iopanoic acid displaced Warfarin from HSA resulting in increased Warfarin in the protein-free compartment and in the compartment containing the soluble fraction. On the other hand, tolbutamide displaced Warfarin from HSA to the liver soluble fraction with relatively little effect on unbound anticoagulant. Sulfinpyrazone produced a third type of interaction characterized by displacement of Warfarin from HSA with an increase in the concentration of unbound drug. It was concluded that competitive binding between albumin and soluble liver proteins, is important in the hepatic uptake of Warfarin. The three compartment dialysis cells may be useful to simulate the distribution of drugs and drug combinations between non-dialyzable macromolecules.

Uptake of anticoagulants by isolated rat hepatocytes.

Various studies were carried out on the uptake of 14C-labeled warfarin and dicumarol by isolated rat hepatocytes. The uptake was rapid, reaching a steady-state level in the isolated cells in about one-half minute. Concentration studies showed that the uptake of warfarin by the cells approached saturation at about 4.5 nmoles per million cells, whereas the uptake of dicumarol did not approach saturation over the range studied. The effects of the anticoagulants on respiration were complex, having little or no effect on respiration at the lowest concentrations, stimulating respiration at the intermediate levels, and reducing respiration at the highest levels. Metabolic inhibitors such as 2,4-dinitrophenol and antimycin reduced the uptake of warfarin but not that of dicumarol. Serum albumin reduced the uptake of anticoagulants by the hepatocytes and the uptake was reciprocally related to the concentration of serum albumin. Computations showed that most of the binding of the drugs would be at the high-affinity sites on the albumin. The cells metabolized warfarin progressively for at least two hours, and serum albumin reduced the rate of metabolism of the drug. The rate of metabolism was relatively slow compared with the uptake; about 1% of the warfarin taken up by the cells was metabolized per minute.

Physiological flow model for drug elimination interactions in the rat.

Drug elimination interactions in the rat are modelled based on physiological blood flow rates and organ weights. A previous model has been substantially improved by the addition of a compartment representing the skin and the interactions are computed using Michaelis-Menten kinetics for competitive inhibition in the shared pathways. Furthermore, the results of repetitive dosing may also be simulated. The programs, which are extensively annotated and user oriented, are illustrated on the results of an acute warfarin--BSP interaction experiment in rats.

Drug elimination interactions: analysis using a mathematical model.

A mathematical model was developed to analyze the elimination kinetics of drug interactions in the rat. The model is based on physiological blood flow rates and organ weights and includes Michaelis-Menten equations for enzymatic processes which are involved in the elimination of the drug; competitive inhibition interactions are computed for shared pathways. Using data from the single drugs, the model can simulate the results of experiments of the acute warfarin-BSP interactions in rats.

The effects of oleic acid, tolbutamide, and oxyphenbutazone on the binding of warfarin by human serum albumin.

Equilibrium dialysis studies showed that, at low levels, stearate, palmitate and oleate enhanced the binding of warfarin by human serum albumin, but at high levels of FFA, warfarin was displaced. Tolbutamide and oxyphenbutazone separately desplaced warfarin, and this dispplacement was reduced by the presence of low concentrations of oleate while at higher concentrations of oleate displacement occurred. Thus, the binding of warfarin was affected in a complex fashion depending upon the drugs present and the concentration of the FFA.

A program to simulate drug elimination interactions: warfarin and BSP - an illustrative example.

The kinetics of drug elimination of interactive drug systems is stimulated by a set of differential equations based on mass balances, the mass of organs and blood flow rates. Experimentally determined concentration profiles of the drugs in the plasma and bile are used to evaluate clearance rate parameters. An example is shown in which the clearance of the anticoagulant warfarin is reduced to less than 50% of its normal rate due to the interference by BSP.