Richard H. Luecke

Human organ/tissue growth algorithms that include obese individuals and black/white population organ weight similarities from autopsy data.

Physiologically based pharmacokinetic (PBPK) models need the correct organ/tissue weights to match various total body weights in order to be applied to children and the obese individual. Baseline data from Reference Man for the growth of human organs (adrenals, brain, heart, kidneys, liver, lungs, pancreas, spleen, thymus, and thyroid) were augmented with autopsy data to extend the describing polynomials to include the morbidly obese individual (up to 250 kg). Additional literature data similarly extends the growth curves for blood volume, muscle, skin, and adipose tissue. Collectively these polynomials were used to calculate blood/organ/tissue weights for males and females from birth to 250 kg, which can be directly used to help parameterize PBPK models. In contrast to other black/white anthropomorphic measurements, the data demonstrated no observable or statistical difference in weights for any organ/tissue between individuals identified as black or white in the autopsy reports.

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 different 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 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.

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.

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.

A mathematical biothermal model of the california sea lion

Abstract The thermal behavior of the California sea lion is modeled by a set of seventeen simultaneous partial differential equations. Numerical solution of these equations yields temperature profiles in the sea lion that closely reproduce experimental data obtained with the animals at rest in air. The model predicts that exercise is necessary to maintain body temperature while immersed in very cold water (0°C) but that very efficient heat conservation occurs during diving because of bradycardia, limited circulation, and absence of respiration.

Windows ® based general PBPK/PD modeling software

A physiologically based pharmacokinetic (PBPK) model and program (called PostNatal) was developed which focuses on postnatal growth. Algorithms defining organ/tissue growth curves from birth through adulthood for male and female humans, dogs, rats, and mice are utilized to calculate the appropriate weight and blood flow for the internal organs/tissues. This Windows based program is actually four linked PBPK models with each PBPK model acting independently or totally integrated with the others through metabolism by first order or Michaelis-Menten kinetics. Data fitting is accomplished by a weighted least square regression algorithm. The model includes linkages for the simulation of pharmacodynamic (PD) effects.

Air temperature and direct partitional calorimetry of the California sea lion (Zalophus Californianus)

Abstract The objective of these experiments was to study the partitional heat exchange of the California sea lion as affected by air temperature (Ta) through the use of direct and indirect calorimetry. o 1. Throughout the temperature range of 10°–25°C the total heat production remained quite constant. Radiant loss fell from 58% at 10° to 40% at 28°C Ta. Conduction-convection accounted for 35% at 15° and 20°C Ta but declined to 15% at 28°C. Evaporative loss was 21% at 10°C Ta, fell to 14% at 15°C and rose to account for over 50% of the exchange at 28°C. 2. At 25°C Ta, hyperpyrexia was usually apparent although an accompanying increase in heat production (O2 consumption) was not. It is hypothesized that a metabolic depression and/or a temporary heat sequestration might account for the observation. Oxygen consumption increased and effective heat loss diminished at a Ta of 28°C. 3. An abrupt rise in recorded Tb accompanied by postural adjustments followed removal of the animals from the higher Tas, indicating the occurrence of a circulatory sequestration of heat. It is postulated that a temporary storage of blood in the splanchnic circulation might account for this observation.

Postnatal growth considerations for PBPK modeling.

A physiologically based pharmacokinetic (PBPK) model and Windows-based program (called PostNatal) was developed that focuses on postnatal growth, from birth through adulthood, using appropriate growth curves for each species and gender. Postnatal growth algorithms relating organs/tissues weights with total body weight for male and female humans, dogs, rats, and mice are an integral part of the software and are utilized to assign the appropriate weight and blood flow for each of 22 organs/tissues for each simulation. Upper limits of body weight were chosen that reflect the available data used to define the algorithms; above these limits a set percent body weight was assigned to all organs/tissues.