Research Article: Empirical models for anatomical and physiological changes in a human mother and fetus during pregnancy and gestation

Date Published: May 2, 2019

Publisher: Public Library of Science

Author(s): Dustin F. Kapraun, John F. Wambaugh, R. Woodrow Setzer, Richard S. Judson, Frank T. Spradley.


Many parameters treated as constants in traditional physiologically based pharmacokinetic models must be formulated as time-varying quantities when modeling pregnancy and gestation due to the dramatic physiological and anatomical changes that occur during this period. While several collections of empirical models for such parameters have been published, each has shortcomings. We sought to create a repository of empirical models for tissue volumes, blood flow rates, and other quantities that undergo substantial changes in a human mother and her fetus during the time between conception and birth, and to address deficiencies with similar, previously published repositories. We used maximum likelihood estimation to calibrate various models for the time-varying quantities of interest, and then used the Akaike information criterion to select an optimal model for each quantity. For quantities of interest for which time-course data were not available, we constructed composite models using percentages and/or models describing related quantities. In this way, we developed a comprehensive collection of formulae describing parameters essential for constructing a PBPK model of a human mother and her fetus throughout the approximately 40 weeks of pregnancy and gestation. We included models describing blood flow rates through various fetal blood routes that have no counterparts in adults. Our repository of mathematical models for anatomical and physiological quantities of interest provides a basis for PBPK models of human pregnancy and gestation, and as such, it can ultimately be used to support decision-making with respect to optimal pharmacological dosing and risk assessment for pregnant women and their developing fetuses. The views expressed in this article are those of the authors and do not necessarily represent the views or policies of the U.S. Environmental Protection Agency.

Partial Text

Human health chemical risk assessments frequently consider pregnant women as a subpopulation of interest based on the relatively high exposure rates and/or susceptibility of this group to various compounds [1, 2]. Unfortunately, pregnant women are generally underrepresented in pharmaceutical clinical studies [3] and non-therapeutic chemicals are rarely studied in humans at any life-stage [4–6]. In order to assess the risk posed by a chemical, pharmacokinetic (PK) modeling can be used to relate chemical exposure to potential toxicity in tissues [7]. PK models describe chemical absorption, distribution, metabolism, and elimination by the body [8, 9]. Furthermore, such models allow one to quantify the tissue concentrations resulting from external doses, whether they are controlled (e.g., doses administered in a clinical trial or animal toxicity study [10]) or uncontrolled (e.g., through complex environmental exposures [11]).

For each quantity of interest discussed in this section, we describe: (1) the data we used for model calibration, (2) the model selected by us after considering both parsimony and plausibility, and (3) previously published models for the same quantity of interest. Our recommended, or “preferred”, models for all quantities of interest are identified by equation number in Table 2.

Here we have presented a comprehensive collection of empirical models for anatomical and physiological changes related to human pregnancy and gestation. (See Table 2 for our list of preferred models.) Several similar repositories have been published [3, 15, 25, 28, 29, 31–33], but in evaluating each of these we found shortcomings that we sought to address in our own set of empirical models. One distinguishing feature of the current collection of models derives from our recognition that the fetal circulatory system differs fundamentally from the adult circulatory system. Thus, in addition to describing models for those pregnancy- and gestation-related changes that have been included in other collections, we have provided models for blood flow rates in the fetus that do not have analogs in the adult; in particular, we have included models for blood flow rates through the ductus venosus, the ductus arteriosus, and the foramen ovale of the human fetus. To establish a single best model for each quantity of interest, we applied a rigorous set of statistical and mathematical procedures for calibrating a variety of models and selecting an optimal model. Finally, to better inform potential users of the models described herein, we have compared our models to previously-published alternative models wherever possible.

All PBPK models involve parameters that describe the anatomy and physiology of an organism, but defining values for these parameters requires special care when designing a PBPK model to represent a mother and fetus during the period from conception to birth. Because pregnancy and gestation represent a time of dramatic changes, many of the PBPK model parameters that are traditionally treated as constants for adult organisms or shorter-duration simulations must be described by time-varying functions in any PBPK model intended for studying this period, either in its entirety or for shorter time periods during which pregnancy- and gestation-related changes might be substantial. To facilitate the development of human pregnancy and gestation PBPK models, we have provided a repository of empirical models describing tissue volumes, blood flow rates, hematocrits, and glomerular filtration rates in an “average” mother and fetus. This collection of models offers advantages over similar repositories in that it includes descriptions for many fetal parameters that have previously been neglected and it uses rigorous and well-defined methods for model calibration and selection. We anticipate that the formulae provided in this collection will provide an improved basis for PBPK models of human pregnancy and gestation, and ultimately support decision-making with respect to optimal pharmacological dosing and risk assessment for pregnant women and their developing fetuses. In fact, we are currently preparing a manuscript that describes a high-throughput toxicokinetic (HTTK) model for pregnancy and gestation that is based upon the formulae provided herein.




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