Fig 1.
Mass of a human mother vs. gestational age.
The cubic model (solid line) given by Eq 1 was selected as the most parsimonious model in our analysis. The models of Abduljalil et al. [28] and Gaohua et al. [29], both quadratic, were calibrated using the same curated data set [28] used by us. The maternal mass gain data (or “growth data”) depicted here were modified from the source [48] to account for an assumed initial mass as described in the text. Note that all models depicted here describe the mass of the entire maternal body plus the products of conception (including the fetus, placenta, and amniotic fluid).
Table 1.
Itemized comparison of selected publications that contain one or more formulae related to human gestation and pregnancy.
Table 2.
Data sources, preferred models, and relevant figures for various quantities of interest.
Table 3.
Types of models used to describe changes in masses, volumes, percentages, and physiological rates during pregnancy and gestation.
Table 4.
Four-letter codes used to represent compartments in a human mother or fetus.
Table 5.
Maternal mass models (mass in kg vs. gestational age in weeks).
Table 6.
Fetal mass models (mass in g vs. gestational age in weeks).
Fig 2.
Volume (mL) or mass (g) of a human fetus vs. gestational age.
The Gompertz model (solid line) given by Eq 2 was selected as the most parsimonious model in our analysis. The models of Abduljalil et al. [28] and Wosilait et al. [27] were also Gompertz models, though the model parameters used by those authors were different. Dallmann et al. [3] used a log-logistic model for fetal volume. The model of Abduljalil et al. [28] was calibrated using the same curated data set [28] used by us, while the models of Wosilait et al. [27] and Dallmann et al. [3] were calibrated using different data sets.
Table 7.
Maternal fat mass models (mass in kg vs. fetal mass in kg for power law models, mass in kg vs. gestational age in weeks for all other models).
Fig 3.
Adipose tissue mass of a human mother of vs. gestational age.
The linear model (solid line) given by Eq 3 was selected as the most parsimonious model in our analysis. The models of Abduljalil et al. [28] and Gaohua et al. [29], both quadratic, were calibrated using the same curated data set [28] used by us. The latter of these models was modified as described in the text. The model of Luecke et al. [15] was calibrated using different data. It predicts maternal fat mass as a function of total fetal mass, and was interpreted as described in the text. Dallmann et al. [3] also selected a linear model, but they calibrated their model with different data.
Table 8.
Percent of total body mass and density (references listed) for various human organs and tissues.
Table 9.
Maternal plasma volume models (volume in L vs. fetal mass in kg for power law models, volume in L vs. gestational age in weeks for all other models).
Fig 4.
Maternal plasma volume vs. gestational age.
The modified logistic model (solid line) given by Eq 5 was selected as the most parsimonious model in our analysis. The models of Abduljalil et al. [28] and Gaohua et al. [29], both cubic polynomials, were calibrated using the same curated data set [28] used by us. The model of Luecke et al. [15] was calibrated using different data. It assumes an initial maternal plasma volume of 2.6 L (or an initial plasma mass of 2.6 kg) and predicts an increase in maternal plasma volume (or mass) as a function of total fetal mass. Dallmann et al. [3] calibrated their cubic model with different data.
Table 10.
Maternal RBC volume models (volume in L vs. fetal mass in kg for power law models, volume in L vs. gestational age in weeks for all other models).
Fig 5.
Maternal RBC volume vs. gestational age.
The modified logistic model (solid line) given by Eq 6 was selected as the most parsimonious model in our analysis, but the hematocrit-based model (second in legend) of Eq 7 ensures consistency with models for plasma volume (Eq 5) and hematocrit (Eq 24). The models of Abduljalil et al. [28] and Gaohua et al. [29], both of which are linear models, were calibrated using the same curated data set [28] used by us. Dallmann et al. [3] did not create a model for maternal RBC volume, so the model attributed to them here is algebraically derived from their models for plasma volume and hematocrit.
Table 11.
Placenta volume models (volume in mL vs. fetal mass in kg for power law models, volume in mL vs. gestational age in weeks for all other models).
Fig 6.
Placenta volume vs. gestational age.
The cubic growth model (solid line) given by Eq 8 was selected as the most parsimonious model in our analysis. The model of Abduljalil et al. [28], also a cubic polynomial model, was calibrated using the same curated data set [28] used by us. The model of Luecke et al. [15] was calibrated using different data and assumes a relationship between placenta volume and fetal mass. Dallmann et al. [3] calibrated their cubic model with different data.
Table 12.
Amniotic fluid volume models (volume in mL vs. fetal mass in kg for power law models, volume in mL vs. gestational age in weeks for all other models).
Fig 7.
Amniotic fluid volume vs. gestational age.
The logistic model (solid line) given by Eq 9 was selected as the most parsimonious model in our analysis. The model of Abduljalil et al. [28], which is a fifth degree polynomial model, was calibrated using the same curated data set [28] used by us. The model of Luecke et al. [15] was calibrated using different data and assumes a relationship between amniotic fluid volume and fetal mass. That model is shown here both as originally stated (in the publication) and after correcting a presumed error (to obtain the “Adjusted Model”) as described in the text. Dallmann et al. [3] calibrated their fourth degree polynomial model with different data.
Table 13.
Volumes of (some) maternal compartments that do not change during pregnancy.
Fig 8.
Volume of maternal “rest of body” compartment vs. gestational age.
The formula for the depicted model, which is based on mass balance, is provided as Eq 12.
Table 14.
Maternal cardiac output models (flow rate in L/h vs. maternal mass in kg for power law models, flow rate in L/h vs. gestational age in weeks for all other models).
Fig 9.
Maternal cardiac output vs. gestational age.
The cubic model (solid line) given by Eq 13 was selected as the most parsimonious model in our analysis. The models of Abduljalil et al. [28] and Gaohua et al. [29], both of which are quadratic models, were calibrated using the same curated data set [28] used by us. Dallmann et al. [3] calibrated their model with different data.
Table 15.
Maternal kidney blood flow models (flow rate in L/h vs. maternal mass in kg for power law models, flow rate in L/h vs. gestational age in weeks for all other models).
Fig 10.
Maternal kidney blood flow vs. gestational age.
The cubic model (solid line) given by Eq 17 was selected as the most parsimonious model in our analysis. The linear transition model given by Eq 16 is also shown. The model of Abduljalil et al. [28], which is a quadratic model, was calibrated using the same curated data set [28] used by us. Dallmann et al. [3] calibrated their model with different data.
Fig 11.
Maternal blood flow to the placenta vs. gestational age.
The proportional-to-volume model (solid line) given by Eq 22, the linear transition model given by Eq 21, and two published models [3, 29, 32] are shown.
Fig 12.
Maternal blood flow to the “rest of body” compartment vs. gestational age (cf. Eq 23).
Table 16.
Maternal hematocrit models (percentage vs. maternal mass in kg for power law models, percentage vs. gestational age in weeks for all other models).
Fig 13.
Maternal hematocrit vs. gestational age.
The quadratic model (solid line) given by Eq 24 was selected as the most parsimonious model in our analysis. The “ratio model” given by Eq 25 is also shown. The models of Abduljalil et al. [28] and Gaohua et al. [29], both of which are quadratic models, were calibrated using the same curated data set [28] used by us. Dallmann et al. [3] calibrated their model with different data.
Table 17.
Maternal GFR models (rate in mL/min vs. maternal mass in kg for power law models, rate in mL/min vs. gestational age in weeks for all other models).
Fig 14.
Maternal glomerular filtration rate vs. gestational age.
The quadratic model (solid line) given by Eq 26 was selected as the most parsimonious model in our analysis. The model of Abduljalil et al. [28], also a quadratic model, was calibrated using the same curated data set [28] used by us. The Dallmann et al. [3] model depicted here has been modified from the published version, which contained typographical errors, based on personal correspondence with the lead author. The model attributed to Pearce et al. [61] is evaluated as described in the text.
Table 18.
Fetal brain mass models (g vs. fetal mass in g for power law models, g vs. gestational age in weeks for all other models).
Fig 15.
Fetal brain mass vs. gestational age.
The quadratic growth model (solid line) given by Eq 28 was selected as the most parsimonious model in our analysis; however, that model gives negative brain mass values during early gestation. The Gompertz model (dashed line) given by Eq 29 is strictly positive on the time domain of interest. The model of Luecke et al. [15], which is a power law model based on fetal mass, was calibrated using a different data set [25]. The model of Zhang et al. [32] was also calibrated using a distinct compiled data set. The Zhang et al. [32] model describes brain volume, so the units were converted assuming a tissue density of 1 g/mL.
Table 19.
Fetal liver mass models (g vs. fetal mass in g for power law models, g vs. gestational age in weeks for all other models).
Fig 16.
Fetal liver mass vs. gestational age.
The cubic growth model (solid line) given by Eq 31 was selected as the most parsimonious model in our analysis; however, that model gives negative liver mass values during early gestation. The Gompertz model (dashed line) given by Eq 32 is strictly positive on the time domain of interest. The model of Luecke et al. [15], which is a power law model based on fetal mass, was calibrated using a different data set [25]. The model of Zhang et al. [32] was also calibrated using a distinct compiled data set. The Zhang et al. [32] model describes liver volume, so the units were converted assuming a tissue density of 1 g/mL.
Table 20.
Fetal kidney mass models (g vs. fetal mass in g for power law models, g vs. gestational age in weeks for all other models).
Fig 17.
Fetal kidney mass vs. gestational age.
The power law model (solid line) given by Eq 34 was selected as the most parsimonious model in our analysis; however, that model is a function of fetal mass. The Gompertz model (dashed line) given by Eq 35 may be preferred since it is a function of gestational age and does not require an intermediate model for fetal mass. Note that the Gompertz model and the power law model are virtually indistinguishable in this plot. The model of Luecke et al. [15], which is also a power law model based on fetal mass, was calibrated using a different data set [25]. The model of Zhang et al. [32] was also calibrated using a distinct compiled data set. The Zhang et al. [32] model describes kidney volume, so the units were converted assuming a tissue density of 1 g/mL. The apparently poor fit of the model of Abduljalil et al. [33] to their own curated data set is probably due to precision-related errors—they only reported the leading coefficient of their polynomial model to one significant figure.
Table 21.
Fetal lung mass models (g vs. fetal mass in g for power law models, g vs. gestational age in weeks for all other models).
Fig 18.
Fetal lung mass vs. gestational age.
The Gompertz model (solid line) given by Eq 37 was selected as the most parsimonious model in our analysis. The model of Luecke et al. [15], which is a power law model based on fetal mass, was calibrated using a different data set [25]. The version of the Luecke et al. [15] model depicted here has been adjusted as described in the text. Note that our Gompertz model and the model of Abduljalil et al. [33] are virtually indistinguishable in this plot.
Table 22.
Fetal thyroid mass models (g vs. fetal mass in g for power law models, g vs. gestational age in weeks for all other models).
Fig 19.
Fetal thyroid mass vs. gestational age.
The Gompertz model (solid line) given by Eq 39 was selected as the most parsimonious model in our analysis. The model of Luecke et al. [15], which is a power law model based on fetal mass, was calibrated using a different data set [25].
Table 23.
Fetal gut mass models (g vs. fetal mass in g for power law models, g vs. gestational age in weeks for all other models).
Fig 20.
Fetal gut mass vs. gestational age.
The Gompertz model (solid line) given by Eq 41 was selected as the most parsimonious model in our analysis. The model of Zhang et al. [32] was calibrated using a different data set. The Zhang et al. [32] model describes gut volume, so the units were converted assuming a tissue density of 1 g/mL.
Fig 21.
Fetal rest of body vs. gestation age (cf. Eq 43).
The volume of the whole fetal body (cf. Eq 2) is shown for comparison.
Table 24.
Fetal right ventricle blood flow models (mL/min vs. fetal mass in g for power law models, mL/min vs. gestational age in weeks for all other models).
Fig 22.
Fetal blood flow through the right ventricle vs. gestational age.
The logistic model (solid line) given by Eq 44 was selected as the most parsimonious model in our analysis. The model of Kiserud et al. [38] was calibrated using the same data set [38] used by us.
Table 25.
Fetal left ventricle blood flow models (mL/min vs. fetal mass in g for power law models, mL/min vs. gestational age in weeks for all other models).
Fig 23.
Fetal blood flow through the left ventricle vs. gestational age.
The logistic model (solid line) given by Eq 45 was selected as the most parsimonious model in our analysis. The model of Kiserud et al. [38] was calibrated using the same data set [38] used by us.
Table 26.
Fetal ductus arteriosus blood flow models (mL/min vs. fetal mass in g for power law models, mL/min vs. gestational age in weeks for all other models).
Fig 24.
Fetal blood flow through the ductus arteriosus vs. gestational age.
The logistic model (solid line) given by Eq 46 was selected as the most parsimonious model in our analysis, which utilized data of Mielke and Benda [39].
Table 27.
Models for fetal blood flow to the placenta (mL/min vs. fetal mass in g for power law models, mL/min vs. gestational age in weeks for all other models).
Fig 25.
Fetal blood flow through the placenta vs. gestational age.
The logistic model (solid line) given by Eq 50 was selected as the most parsimonious model in our analysis. The model of Kiserud et al. [40] was calibrated using the same data set [40] used by us, whereas the model of Zhang et al. [32] was calibrated using a different compiled data set.
Table 28.
Models for fetal blood flow through the ductus venosus (mL/min vs. fetal mass in g for power law models, mL/min vs. gestational age in weeks for all other models).
Fig 26.
Fetal blood flow through the ductus venosus vs. gestational age.
The Gompertz model (solid line) given by Eq 51 was selected as the most parsimonious model in our analysis. The model of Kiserud et al. [40] was calibrated using the same data set [40] used by us, whereas the model of Zhang et al. [32] was calibrated using a different compiled data set.
Fig 27.
Comparison of flow rates through the placenta and through the ductus venosus vs. gestational age (cf. Eqs 50 and 51).
Because blood flow through the ductus venosus should always be less than blood flow through the placenta, these models should not be used prior to gestational age 12 weeks.
Table 29.
Average blood flow rates to various fetal tissues.
Fig 28.
Fetal blood flow to the “rest of body” compartment vs. gestational age (cf. Eq 57).
Fetal blood flow to the arterial blood compartment (cf. Eq 47) and the placenta (cf. Eq 50) are shown for comparison.
Table 30.
Fetal hematocrit models (percentage vs. gestational age in weeks).
Fig 29.
Fetal hematocrit vs. gestational age.
The quadratic growth model (solid line) given by Eq 58 was selected as the most parsimonious model in our analysis, but the cubic growth model given by Eq 59 gives a better visual fit to the data while yielding only a slightly (0.8%) larger AIC score. We calibrated our models using the data curated by Ohls [41]. Dallmann et al. [3] calibrated their model with different data.