This function uses the equations from Kapraun (2019) to calculate chemical- independent physiological paramreters as a function of gestational age in weeks.
calc_fetal_phys(week = 12, ...)list containing:
Maternal body weight, kg
Maternal adipose fraction of total weight
Fetal kidney fraction of total weight
Fetal thyroid fraction of total weight
Fetal liver fraction of total weight
Fetal brain fraction of total weight
Fetal gut fraction of total weight
Fetal lung fraction of total weight
Maternal hematocrit fraction of blood
Maternal Rblood2plasma
Fetal hematocrit fraction of blood
Fetal Rfblood2plasma
Fetal body weight, kg
Volume of Vplacenta, L
Volume of amniotic fluid, L
Maternal volume of plasma, L
Maternal volume of red blood cells, L
Maternal volume of venous blood, L
Maternal volume of arterial blood, L
Maternal volume of adipose, L
Fetal volume ofVffmx, L
Vallx, L
Maternal volume of rest of body, L
Fetal volume of arterial blood, L
Fetal volume of venous blood, L
Fetal volume of kidney, L
Fetal volume of thyroid, L
Fetal volume of liver, L
Fetal volume of brain, L
Fetal volume of gut, L
Fetal volume of lung, L
Fetal volume of rest of body, L
Maternal cardiac output blood flow, L/day
Maternal blood flow to gut, L/day
Maternal blood flow to kidney, L/day
Maternal blood flow to liver, L/day
Maternal blood flow to thyroid, L/day
Maternal blood flow to placenta, L/day
Maternal blood flow to adipose, L/day
Maternal blood flow to rest, L/day
Maternal glomerular filtration rate in kidney, L/day
Fetal blood flow to right ventricle, L/day
Fetal blood flow to left ventircle, L/day
Fetal blood flow to Qfda, L/day
Fetal blood flow to Qfartb, L/day
Fetal cardiac output blood flow, L/day
Fetal blood flow to lung, L/day
Fetal blood flow to placenta, L/day
Fetal blood flow to Qfdv, L/day
Fetal blood flow to gut, L/day
Fetal blood flow to kidney, L/day
Fetal blood flow to brain, L/day
Fetal blood flow to liver, L/day
Fetal blood flow to thyroid, L/day
Fetal blood flow to rest, L/day
Fetal blood flow to Qfbypass, L/day
Gestational week
Additional arguments to parameterize_fetal_pbtk
John Wambaugh
$$BW = pre_pregnant_BW + BW_cubic_theta1 * tw + BW_cubic_theta2 * tw^2 + BW_cubic_theta3 * tw^3 $$
$$ Wadipose = Wadipose_linear_theta0 + Wadipose_linear_theta1 * tw ; $$
$$ Wfkidney = 0.001 * Wfkidney_gompertz_theta0 * exp ( Wfkidney_gompertz_theta1 / Wfkidney_gompertz_theta2 * ( 1 - exp ( - Wfkidney_gompertz_theta2 * tw ) ) ) ; $$
$$ Wfthyroid = 0.001 * Wfthyroid_gompertz_theta0 * exp ( Wfthyroid_gompertz_theta1 / Wfthyroid_gompertz_theta2 * ( 1 - exp ( - Wfthyroid_gompertz_theta2 * tw ) ) ) ; $$
$$ Wfliver = 0.001 * Wfliver_gompertz_theta0 * exp ( Wfliver_gompertz_theta1 / Wfliver_gompertz_theta2 * ( 1 - exp ( - Wfliver_gompertz_theta2 * tw ) ) ) ; $$
$$ Wfbrain = 0.001 * Wfbrain_gompertz_theta0 * exp ( Wfbrain_gompertz_theta1 / Wfbrain_gompertz_theta2 * ( 1 - exp ( - Wfbrain_gompertz_theta2 * tw ) ) ) ; $$
$$ Wfgut = 0.001 * Wfgut_gompertz_theta0 * exp ( Wfgut_gompertz_theta1 / Wfgut_gompertz_theta2 * ( 1 - exp ( - Wfgut_gompertz_theta2 * tw ) ) ) ; $$
$$ Wflung = 0.001 * Wflung_gompertz_theta0 * exp ( Wflung_gompertz_theta1 / Wflung_gompertz_theta2 * ( 1 - exp ( - Wflung_gompertz_theta2 * tw ) ) ) ; $$
$$ hematocrit = ( hematocrit_quadratic_theta0 + hematocrit_quadratic_theta1 * tw + hematocrit_quadratic_theta2 * pow ( tw , 2 ) ) / 100 ; $$
$$ Rblood2plasma = 1 - hematocrit + hematocrit * Krbc2pu * Fraction_unbound_plasma ; $$
$$ fhematocrit = ( fhematocrit_cubic_theta1 * tw + fhematocrit_cubic_theta2 * pow ( tw , 2 ) + fhematocrit_cubic_theta3 * pow ( tw , 3 ) ) / 100 ; $$
$$ Rfblood2plasma = 1 - fhematocrit + fhematocrit * Kfrbc2pu * Fraction_unbound_plasma_fetus ; $$
$$ fBW = 0.001 * fBW_gompertz_theta0 * exp ( fBW_gompertz_theta1 / fBW_gompertz_theta2 * ( 1 - exp ( - fBW_gompertz_theta2 * tw ) ) ) ; $$
$$ Vplacenta = 0.001 * ( Vplacenta_cubic_theta1 * tw + Vplacenta_cubic_theta2 * pow ( tw , 2 ) + Vplacenta_cubic_theta3 * pow ( tw , 3 ) ) ; $$
$$ Vamnf = 0.001 * Vamnf_logistic_theta0 / ( 1 + exp ( - Vamnf_logistic_theta1 * ( tw - Vamnf_logistic_theta2 ) ) ) ; $$
$$ Vplasma = Vplasma_mod_logistic_theta0 / ( 1 + exp ( - Vplasma_mod_logistic_theta1 * ( tw - Vplasma_mod_logistic_theta2 ) ) ) + Vplasma_mod_logistic_theta3 ; $$
$$ Vrbcs = hematocrit / ( 1 - hematocrit ) * Vplasma ; $$
$$ Vven = venous_blood_fraction * ( Vrbcs + Vplasma ) ; $$
$$ Vart = arterial_blood_fraction * ( Vrbcs + Vplasma ) ; $$
$$ Vadipose = 1 / adipose_density * Wadipose ; $$
$$ Vffmx = 1 / ffmx_density * ( BW - Wadipose - ( fBW + placenta_density * Vplacenta + amnf_density * Vamnf ) ) ; $$
$$ Vallx = Vart + Vven + Vthyroid + Vkidney + Vgut + Vliver + Vlung ; $$
$$ Vrest = Vffmx - Vallx ; $$
$$ Vfart = 0.001 * arterial_blood_fraction * fblood_weight_ratio * fBW ; $$
$$ Vfven = 0.001 * venous_blood_fraction * fblood_weight_ratio * fBW ; $$
$$ Vfkidney = 1 / kidney_density * Wfkidney ; $$
$$ Vfthyroid = 1 / thyroid_density * Wfthyroid ; $$
$$ Vfliver = 1 / liver_density * Wfliver ; $$
$$ Vfbrain = 1 / brain_density * Wfbrain ; $$
$$ Vfgut = 1 / gut_density * Wfgut ; $$
$$ Vflung = 1 / lung_density * Wflung ; $$
$$ Vfrest = fBW - ( Vfart + Vfven + Vfbrain + Vfkidney + Vfthyroid + Vfliver + Vfgut + Vflung ) ; $$
$$ Qcardiac = 24 * ( Qcardiac_cubic_theta0 + Qcardiac_cubic_theta1 * tw + Qcardiac_cubic_theta2 * pow ( tw , 2 ) + Qcardiac_cubic_theta3 * pow ( tw , 3 ) ) ; $$
$$ Qgut = 0.01 * ( Qgut_percent_initial + ( Qgut_percent_terminal - Qgut_percent_initial ) / term * tw ) * Qcardiac ; $$
$$ Qkidney = 24 * ( Qkidney_cubic_theta0 + Qkidney_cubic_theta1 * tw + Qkidney_cubic_theta2 * pow ( tw , 2 ) + Qkidney_cubic_theta3 * pow ( tw , 3 ) ) ; $$
$$ Qliver = 0.01 * ( Qliver_percent_initial + ( Qliver_percent_terminal - Qliver_percent_initial ) / term * tw ) * Qcardiac ; $$
$$ Qthyroid = 0.01 * ( Qthyroid_percent_initial + ( Qthyroid_percent_terminal - Qthyroid_percent_terminal ) / term * tw ) * Qcardiac ; $$
$$ Qplacenta = 24 * Qplacenta_linear_theta1 * 1000 * Vplacenta ; $$
$$ Qadipose = 0.01 * ( Qadipose_percent_initial + ( Qadipose_percent_terminal - Qadipose_percent_initial ) / term * tw ) * Qcardiac ; $$
$$ Qrest = Qcardiac - ( Qgut + Qkidney + Qliver + Qthyroid + Qplacenta + Qadipose ) ; $$
$$ Qgfr = 60 * 24 * 0.001 * ( Qgfr_quadratic_theta0 + Qgfr_quadratic_theta1 * tw + Qgfr_quadratic_theta2 * pow ( tw , 2 ) ) ; $$
$$ Qfrvtl = 60 * 24 * 0.001 * Qfrvtl_logistic_theta0 / ( 1 + exp ( - Qfrvtl_logistic_theta1 * ( tw - Qfrvtl_logistic_theta2 ) ) ) ; $$
$$ Qflvtl = 60 * 24 * 0.001 * Qflvtl_logistic_theta0 / ( 1 + exp ( - Qflvtl_logistic_theta1 * ( tw - Qflvtl_logistic_theta2 ) ) ) ; $$
$$ Qfda = 60 * 24 * 0.001 * Qfda_logistic_theta0 / ( 1 + exp ( - Qfda_logistic_theta1 * ( tw - Qfda_logistic_theta2 ) ) ) ; $$
$$ Qfartb = Qflvtl + Qfda ; $$
$$ Qfcardiac = Qfartb ; $$
$$ Qflung = Qfrvtl - Qfda ; $$
$$ Qfplacenta = 60 * 24 * 0.001 * Qfplacenta_logistic_theta0 / ( 1 + exp ( - Qfplacenta_logistic_theta1 * ( tw - Qfplacenta_logistic_theta2 ) ) ) ; $$
$$ Qfdv = 60 * 24 * 0.001 * Qfdv_gompertz_theta0 * exp ( Qfdv_gompertz_theta1 / Qfdv_gompertz_theta2 * ( 1 - exp ( - Qfdv_gompertz_theta2 * tw ) ) ) ; $$
$$ Qfgut = Qfgut_percent / Qfnonplacental_percent * ( 1 - Qfplacenta / Qfartb ) * Qfartb ; $$
$$ Qfkidney = Qfkidney_percent / Qfnonplacental_percent * ( 1 - Qfplacenta / Qfartb ) * Qfartb ; $$
$$ Qfbrain = Qfbrain_percent / Qfnonplacental_percent * ( 1 - Qfplacenta / Qfartb ) * Qfartb ; $$
$$ Qfliver = Qfliver_percent / ( 100 - ( Qbrain_percent + Qkidney_percent + Qgut_percent ) ) * ( 1 - ( Qfbrain_percent + Qfkidney_percent + Qfgut_percent ) / Qfnonplacental_percent ) * ( 1 - Qfplacenta / Qfartb ) * Qfartb ; $$
$$ Qfthyroid = Qfthyroid_percent / ( 100 - ( Qbrain_percent + Qkidney_percent + Qgut_percent ) ) * ( 1 - ( Qfbrain_percent + Qfkidney_percent + Qfgut_percent ) / Qfnonplacental_percent ) * ( 1 - Qfplacenta / Qfartb ) * Qfartb ; $$
$$ Qfrest = Qfcardiac - ( Qfplacenta + Qfgut + Qfliver + Qfthyroid + Qfkidney + Qfbrain ) ; $$
$$ Qfbypass = Qfcardiac - Qflung ; $$
Kapraun, Dustin F., et al. "Empirical models for anatomical and physiological changes in a human mother and fetus during pregnancy and gestation." PloS one 14.5 (2019): e0215906.