calc_fetal_phys {httk}

Calculate maternal-fetal physiological parameters

Description

This function uses the equations from Kapraun (2019) to calculate chemical- independent physiological paramreters as a function of gestational age in weeks.

Usage

calc_fetal_phys(week = 12, ...)

Arguments

week

Gestational week

...

Additional arguments to parameterize_fetal_pbtk

Details

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 ;

Value

list containing:

BW

Maternal body weight, kg

Wadipose

Maternal adipose fraction of total weight

Wfkidney

Fetal kidney fraction of total weight

Wfthyroid

Fetal thyroid fraction of total weight

Wfliver

Fetal liver fraction of total weight

Wfbrain

Fetal brain fraction of total weight

Wfgut

Fetal gut fraction of total weight

Wflung

Fetal lung fraction of total weight

hematocrit

Maternal hematocrit fraction of blood

Rblood2plasma

Maternal Rblood2plasma

fhematocrit

Fetal hematocrit fraction of blood

Rfblood2plasma

Fetal Rfblood2plasma

fBW

Fetal body weight, kg

Vplacenta

Volume of Vplacenta, L

Vamnf

Volume of amniotic fluid, L

Vplasma

Maternal volume of plasma, L

Vrbcs

Maternal volume of red blood cells, L

Vven

Maternal volume of venous blood, L

Vart

Maternal volume of arterial blood, L

Vadipose

Maternal volume of adipose, L

Vffmx

Fetal volume ofVffmx, L

Vallx

Vallx, L

Vrest

Maternal volume of rest of body, L

Vfart

Fetal volume of arterial blood, L

Vfven

Fetal volume of venous blood, L

Vfkidney

Fetal volume of kidney, L

Vfthyroid

Fetal volume of thyroid, L

Vfliver

Fetal volume of liver, L

Vfbrain

Fetal volume of brain, L

Vfgut

Fetal volume of gut, L

Vflung

Fetal volume of lung, L

Vfrest

Fetal volume of rest of body, L

Qcardiac

Maternal cardiac output blood flow, L/day

Qgut

Maternal blood flow to gut, L/day

Qkidney

Maternal blood flow to kidney, L/day

Qliver

Maternal blood flow to liver, L/day

Qthyroid

Maternal blood flow to thyroid, L/day

Qplacenta

Maternal blood flow to placenta, L/day

Qadipose

Maternal blood flow to adipose, L/day

Qrest

Maternal blood flow to rest, L/day

Qgfr

Maternal glomerular filtration rate in kidney, L/day

Qfrvtl

Fetal blood flow to right ventricle, L/day

Qflvtl

Fetal blood flow to left ventircle, L/day

Qfda

Fetal blood flow to Qfda, L/day

Qfartb

Fetal blood flow to Qfartb, L/day

Qfcardiac

Fetal cardiac output blood flow, L/day

Qflung

Fetal blood flow to lung, L/day

Qfplacenta

Fetal blood flow to placenta, L/day

Qfdv

Fetal blood flow to Qfdv, L/day

Qfgut

Fetal blood flow to gut, L/day

Qfkidney

Fetal blood flow to kidney, L/day

Qfbrain

Fetal blood flow to brain, L/day

Qfliver

Fetal blood flow to liver, L/day

Qfthyroid

Fetal blood flow to thyroid, L/day

Qfrest

Fetal blood flow to rest, L/day

Qfbypass

Fetal blood flow to Qfbypass, L/day

Author(s)

John Wambaugh

References

Kapraun DF, Wambaugh JF, Setzer RW, Judson RS (2019). “Empirical models for anatomical and physiological changes in a human mother and fetus during pregnancy and gestation.” PLOS ONE, 14(5), 1-56. doi:10.1371/journal.pone.0215906.