#------------------------------------------------------------------------------ # An adult man model # A PK model for man, based on our previous woman model. # # May 2005 - El Hadji Kone - various modifications for # transformation of our PK model for woman,to a man model. # # July 2005 - Frederic Bois - addition of upper respiratory tract and # mucociliary clearance. # # Units: # Volumes: L # Time: min # Flows: L/min # Concentrations: mM (ie mmol/L) # Vmax: mM/min # Km: mM # Masses: kg # Height: m # Perfusion rates: L/min/kg of tissue # # Copyright (c) 1993-2008 Free Software Foundation, Inc. # #------------------------------------------------------------------------------ States = {Q_adip, # Quantity of chemical in body adipose (mmol) Q_adrenal, # ... in adrenal (mmol) Q_art, # ... in arterial blood (mmol) Q_brain, # ... in brain (mmol) Q_breast, # ... in breast(mmol) Q_gonads, # ... in gonads(mmol) Q_gut, # ... in gut (mmol) Q_gut_lumen, # ... in gut lumen (mmol) Q_heart, # ... in heart (mmol) Q_kidney, # ... in kidney (mmol) Q_liver, # ... in liver (mmol) Q_lung, # ... in lung (mmol) Q_marrow, # ... in bone marrow + perf bone (mmol) Q_muscle, # ... in muscle (mmol) Q_other, # ... in other (mmol) Q_pancreas, # ... in pancreas (mmol) Q_skin, # ... in skin (mmol) Q_spleen, # ... in spleen (mmol) Q_stomach, # ... in stomach (mmol) Q_stom_lumen, # ... in stomach lumen (mmol) Q_thyroid, # ... in thyroid (mmol) Q_ven, # ... in venous blood (mmol) Q_met_liver, # ... metabolized in liver (mmol) Q_met_lung, # ... metabolized in lung (mmol) Q_met_gut, # ... metabolized in gut (mmol) Q_ing, # ... ingested (mmol) Q_inh, # ... inhaled (mmol) Q_exhaled, # ... exhaled (mmol) Q_feces, # ... fecally excreted (mmol) Q_urine, # ... renally excreted (mmol) Q_urt}; # ... in upper respiratory tract (mmol) Outputs = {C_exh, # Concentration of chemical in exhaled air (mM) C_adip, # ... in adipose (mM) C_adrenal, # ... in adrenal (mM) C_art, # ... in arterial blood (mM) C_brain, # ... in brain (mM) C_breast, # ... in breast(mM) C_gonads, # ... in gonads(mM) C_gut, # ... in gut (mM) C_gut_lumen, # ... in gut lumen (mM) C_heart, # ... in heart (mM) C_kidney, # ... in kidney (mM) C_liver, # ... in liver (mM) C_lung, # ... in lung (mM) C_marrow, # ... in bone marrow (mM) C_muscle, # ... in muscle (mM) C_other, # ... in other (mM) C_pancreas, # ... in pancreas (mM) C_skin, # ... in skin (mM) C_spleen, # ... in spleen (mM) C_stomach, # ... in stomach (mM) C_stom_lumen, # ... in stomach lumen (mM) C_thyroid, # ... in venous thyroid (mM) C_ven, # ... in venous blood (mM) C_null, # Null output, e.g. bone or gas (set to zero) Q_total}; # Total quantity in body and excreted (mmol) Inputs = {C_inh, # Concentration inhaled (mM) Q_ing_rate}; # Ingestion rate (mmol/min) # Nominal parameter values # ======================== # Physiological and pharmacokinetic parameters # -------------------------------------------- # Fraction of dead space in lung F_dead_space = 0.67; # Volume of dead space V_urt = 0.15; # (L), ref ICRP 2002. # Age in years Age = 30; # Fraction of arterial blood # Calculated from Filser 2000 p.43 Fr_art_blood = 0.0178 / (0.0178 + 0.0533); # Tissue volumic weight are assumed to be equal to 1 # excepted for adipose tissue (cf Brown et al. 97 p.433) density_adip = 0.9; density_bone = 2.0; # Scaling factors for the volume of the organs # Unit = L/meter of height # sc_V_ have been calculated for a standard man : 1.76m 73kg # and using the organ weights given by the ICRP 2002 Pub 89 # [ p.18(T 2.8) p.19(T 2.9)] # density for the organs is supposed equal to 1 excepted for # adipose tissues (0.9) and bones (2) # these have been calculated as follows: # sc_V_organ=organ_weight/(organ_density*body_height) sc_V_adrenal = 7.955E-3; sc_V_bone = 1.562; sc_V_brain = 0.824; sc_V_gonads = 0.032; sc_V_gut = 0.58; sc_V_gut_lumen = 0.369; sc_V_heart = 0.186; sc_V_kidney = 0.176; sc_V_liver = 1.023; sc_V_lung = 0.284; sc_V_marrow = 2.074; # yellow + red sc_V_muscle = 16.477; sc_V_other = 4.012; sc_V_pancreas = 0.08; sc_V_skin = 1.875; sc_V_spleen = 0.085; sc_V_stomach = 0.085; sc_V_stom_lumen= 0.142; sc_V_thyroid = 0.011; # Perfusion per unit mass of organ. # These have been calculated as follows: # sc_F_organ = %blood_flow_rate * Card_output / organ_weight # the values have been taken from ICRP 2002 Pub 89 # Organ weight : Table 2.8 p18-19, # Cardiac output : Table 2.39 p28 [ Card_output = 6.5(L/min)] # Blood_flow : Table 2.40 p29 or William & Leggett # Unit: L/min/kg of tissue sc_F_adip = 0.03; sc_F_adrenal = 1.3928; sc_F_brain = 0.538; sc_F_breast = 5.95; sc_F_eport = 0.25; sc_F_gonads = 0.0625; sc_F_gut = 0.96; sc_F_heart = 1.08; sc_F_kidney = 3.9838; sc_F_marrow = 0.0786; sc_F_muscle = 0.0381; sc_F_pancreas= 0.4642; sc_F_skin = 0.0984; sc_F_spleen = 1.3; sc_F_stomach = 0.4333; sc_F_thyroid = 4.8750; sc_F_other = 0.027; # Transits; Unit: L/min Fl_stom_lumen = 0.250 / 45.0; # Intestinal transit for stomach -> gut # ICRP 2002 Pub 89 p28 T 2.37 and p18 T 2.8 # Intestinal transit for gut_lumen (feces) # gut_lumen := contents of small and large intestine # large intestine := {right colon, left colon, rectosigmoid} # ICRP 2002 Pub 89 p28 T 2.37 and p18 T 2.8 # Fl_small_intestine = 0.350/(4*60) # Fl_right_colon = 0.15/(12*60) # Fl_left_colon = Fl_rectosigmoid = 0.075/(12*60) # Fl_gut_lumen has been considered as the mean. Fl_gut_lumen = 0.4625E-3; # Parameters indicating the fraction of fat in each organ # comming from Fiserova-Bergerova 1983 # or references found in Van der Mollen 1996 frac_fat_blood = 0.0052; # Papke et al 89. frac_fat_adip = 0.859; # Beck 90, Duarte-Davidson 93, Patterson 86 # Ryan 86 Ryan 85b Schecter 85 # refs in Van der Molen 96 frac_fat_adrenal = 0.049; # Default value corresponding to # "Remaining organs de Van der Molen" frac_fat_brain = 0.11; # Fiserova-Bergerova 1983 frac_fat_breast = 0.049; # Default value frac_fat_gonads = 0.049; # Default value frac_fat_gut = 0.065; # Fiserova-Bergerova 1983 frac_fat_gut_lumen = 0.049; # Default value frac_fat_heart = 0.083; # Fiserova-Bergerova 1983 frac_fat_kidney = 0.052; # Fiserova-Bergerova 1983 frac_fat_liver = 0.049; # Lenter 81, ref in Van der Molen 96 frac_fat_lung = 0.017; # Fiserova-Bergerova 1983 frac_fat_marrow = 0.186; # Clarys & Martin 85,ref in Van der Molen 96 frac_fat_muscle = 0.064; # Lenter 81 & Ryan 85, # ref in Van der Molen 96 frac_fat_other = 0.049; # Default value frac_fat_pancreas = 0.105; # Fiserova-Bergerova 1983 frac_fat_skin = 0.150; # Fiserova-Bergerova 1983 frac_fat_spleen = 0.030; # Fiserova-Bergerova 1983 frac_fat_stomach = 0.049; # Default value frac_fat_stom_lumen = 0.049; # Default value frac_fat_thymus = 0.049; # Default value frac_fat_thyroid = 0.049; # Default value # Parameters specific of the chemical studied # ------------------------------------------- # Transferts depending on the agent; Unit: L/min Ka_stomach = 0.1; # Absorption rate constant for stomach Ka_gut = 0.1; # Absorption rate constant for gut Ke_bile = 0.0; # Biliary excretion rate constant # Lung/air PC PC_lung_over_air = 1; # Pulmonary deadspace deposition (the higher the better) PC_urt = 1; # Adipose tissue over blood partition coefficent PC_adip = 1; # Renal elimination flow rate (L/min) Ke_renal = 1E-3; # Hepatic metabolic rate constant scaling factor ((kg^0.25)/min) # Scaling to the 0.25 is supported by Hattis et al. and used by Gentry et al. scKm_liver = 0; # Gut metabolic rate constant scaling factor ((kg^0.25)/min) scKm_gut = 0; # Lung metabolic rate constant scaling factor ((kg^0.25)/min) scKm_lung = 0; # Pulmonary mucociliary clearance (L/min) Cl_mc_lung = 0; # Other parameters that will be computed in Initialize PC_fat; PC_adrenal; PC_brain; PC_breast; PC_gonads; PC_gut; PC_heart; PC_kidney; PC_liver; PC_lung; PC_marrow; PC_muscle; PC_other; PC_pancreas; PC_skin; PC_spleen; PC_stomach; PC_thymus; PC_thyroid; # Parameters changing with time. # ------------------------------------------- height; dtmp; Km_liver; Km_gut; Km_lung; W_lean; W_total; # Total weight of the man, bone V_blood; V_adip; V_adrenal; V_art; V_ven; V_bone; V_brain; V_breast; V_gonads; V_gut; V_gut_lumen; V_heart; V_kidney; V_liver; V_lung; V_marrow; V_muscle; V_other; V_pancreas; V_skin; V_spleen; V_stomach; V_stom_lumen; V_thyroid; F_adip; F_adrenal; F_alv; F_brain; F_breast; F_eport; F_gonads; F_gut; F_heart; F_kidney; F_marrow; F_muscle; F_other; F_pancreas; F_pul; F_skin; F_spleen; F_stomach; F_thyroid; F_liver; F_blood; Initialize { # Pure fat /blood partition coef. PC_fat = PC_adip / frac_fat_adip; # Tissue over blood partition coefficients PC_adrenal = frac_fat_adrenal * PC_fat; PC_brain = frac_fat_brain * PC_fat; PC_breast = frac_fat_breast * PC_fat; PC_gonads = frac_fat_gonads * PC_fat; PC_gut = frac_fat_gut * PC_fat; PC_heart = frac_fat_heart * PC_fat; PC_kidney = frac_fat_kidney * PC_fat; PC_liver = frac_fat_liver * PC_fat; PC_lung = frac_fat_lung * PC_fat; PC_marrow = frac_fat_marrow * PC_fat; PC_muscle = frac_fat_muscle * PC_fat; PC_other = frac_fat_other * PC_fat; PC_pancreas = frac_fat_pancreas * PC_fat; PC_skin = frac_fat_skin * PC_fat; PC_spleen = frac_fat_spleen * PC_fat; PC_stomach = frac_fat_stomach * PC_fat; PC_thymus = frac_fat_thymus * PC_fat; PC_thyroid = frac_fat_thyroid * PC_fat; # Tissue volumes (L) are supposed to be proportionnal to the # height, excepted for the adipose tissue # ICRP 2002 Pub 89 p19 T 2.9 height = (Age < 1 ? 51 + Age * (76-51) : (Age < 5 ? 76 + (Age-1) * (109-76) / 4.0 : (Age < 10 ? 109 + (Age-5) * (138-109) / 5.0 : (Age < 15 ? 138 + (Age-10) * (167-138) / 5.0 : (Age < 20 ? 167 + (Age-15) * (176-167) / 5.0 : 176))))) * 0.01; V_adrenal = sc_V_adrenal * height; V_bone = sc_V_bone * height; V_brain = sc_V_brain * height; V_gut = sc_V_gut * height; V_gut_lumen = sc_V_gut_lumen * height; V_heart = sc_V_heart * height; V_kidney = sc_V_kidney * height; V_liver = sc_V_liver * height; V_lung = sc_V_lung * height; V_marrow = sc_V_marrow * height; V_muscle = sc_V_muscle * height; V_other = sc_V_other * height; V_pancreas = sc_V_pancreas * height; V_skin = sc_V_skin * height; V_spleen = sc_V_spleen * height; V_stomach = sc_V_stomach * height; V_stom_lumen = sc_V_stom_lumen* height; V_thyroid = sc_V_thyroid * height; # Volumes of the organs changing with the time, # computed with the equations from Luecke 94 and from ICRP data and Van # Molen model after age 14 # ICRP 2002 Pub 89 p18-19 T 2.8 V_adip = (Age < 1 ? 0.93 + Age * (3.8-0.93) : (Age < 5 ? 3.8 + (Age-1) * (5.5-3.8) / 4.0 : (Age < 10 ? 5.5 + (Age-5) * (8.6-5.5) / 5.0 : (Age < 15 ? 8.6 + (Age-10) * (12-8.6) / 5.0 : 12 + (Age-15) * 18.2 / 55.0)))) / density_adip; V_blood = (Age < 1 ? 0.29 + Age * (0.53-0.29) : (Age < 5 ? 0.53 + (Age-1) * (1.5-0.53) / 4.0 : (Age < 10 ? 1.5 + (Age-5) * (2.5-1.5) / 5.0 : (Age < 15 ? 2.5 + (Age-10) * (4.8-2.5) / 5.0 : (Age < 20 ? 4.8 + (Age-15) * (5.6-4.8) / 5.0 : 5.6))))); V_art = V_blood * Fr_art_blood; V_ven = V_blood - V_art; V_breast = (Age < 10 ? 0.01 : (Age < 15 ? 0.01 + (Age-10) * (0.015-0.01) / 5. : (Age < 20 ? 0.015 + (Age-15) * (0.025-0.015) / 5. : 0.025))); V_gonads = sc_V_gonads * height; W_lean = V_adrenal + V_blood + V_bone * density_bone + V_brain + V_breast + V_gut + V_gut_lumen + V_heart + V_kidney + V_liver + V_lung + V_marrow + V_muscle + V_other + V_pancreas + V_skin + V_spleen + V_stomach + V_stom_lumen + V_thyroid + V_gonads; W_total = W_lean + V_adip * density_adip; # Scale metabolism to body masses dtmp = pow(W_lean, 0.25); Km_liver = scKm_liver / dtmp; Km_gut = scKm_gut / dtmp; Km_lung = scKm_lung / dtmp; # Compute actual blood flows # Unit: L/min F_adip = sc_F_adip * V_adip; F_adrenal = sc_F_adrenal * V_adrenal; F_brain = sc_F_brain * V_brain; F_breast = sc_F_breast * V_breast; F_eport = sc_F_eport * V_liver; F_gonads = sc_F_gonads * V_gonads; F_gut = sc_F_gut * V_gut; F_heart = sc_F_heart * V_heart; F_kidney = sc_F_kidney * V_kidney; F_marrow = sc_F_marrow * V_marrow; F_muscle = sc_F_muscle * V_muscle; F_other = sc_F_other * V_other ; F_pancreas = sc_F_pancreas * V_pancreas; F_skin = sc_F_skin * V_skin; F_spleen = sc_F_spleen * V_spleen; F_stomach = sc_F_stomach * V_stomach; F_thyroid = sc_F_thyroid * V_thyroid; F_liver = F_eport + F_spleen + F_pancreas + F_gut + F_stomach; F_blood = F_adip + F_adrenal + F_brain + F_breast + F_heart + F_kidney + F_liver + F_marrow + F_muscle + F_other + F_skin + F_thyroid + F_gonads; # Note: lung is irrigated by a bifurcation and does not enter in the # formula above. # Pulmonary Flow rate (L/min) (ref ICRP Pub 89, p 99). F_pul = (Age < 1 ? 1.5 + Age * (3.7-1.5) : (Age < 5 ? 3.7 + (Age-1) * (5.3-3.7) / 4.0 : (Age < 10 ? 5.3 + (Age-5) * (6.3-5.3) / 5.0 : (Age < 15 ? 6.3 + (Age-10) * (7.95-6.3) / 5.0 : (Age < 20 ? 7.95 + (Age-15) * (9-7.95) / 5.0 : 9))))); # Alveolar flow rate F_alv = F_pul * F_dead_space; } # End of initialize Dynamics { # Concentrations in venous blood at the organ exit and in tissues C_adip = Q_adip / V_adip; C_adip_v = C_adip / PC_adip; C_adrenal = Q_adrenal / V_adrenal; C_adrenal_v = C_adrenal / PC_adrenal; C_brain = Q_brain / V_brain; C_brain_v = C_brain / PC_brain; C_breast = Q_breast / V_breast; C_breast_v = C_breast / PC_breast; C_gut = Q_gut / V_gut; C_gut_v = C_gut / PC_gut; C_heart = Q_heart / V_heart; C_heart_v = C_heart / PC_heart; C_kidney = Q_kidney / V_kidney; C_kidney_v = C_kidney / PC_kidney; C_liver = Q_liver / V_liver; C_liver_v = C_liver / PC_liver; C_lung = Q_lung / V_lung; C_lung_v = C_lung / PC_lung; C_marrow = Q_marrow / V_marrow; C_marrow_v = C_marrow / PC_marrow; C_muscle = Q_muscle / V_muscle; C_muscle_v = C_muscle / PC_muscle; C_other = Q_other / V_other; C_other_v = C_other / PC_other; C_pancreas = Q_pancreas / V_pancreas; C_pancreas_v = C_pancreas / PC_pancreas; C_skin = Q_skin / V_skin; C_skin_v = C_skin / PC_skin; C_spleen = Q_spleen / V_spleen; C_spleen_v = C_spleen / PC_spleen; C_stomach = Q_stomach / V_stomach; C_stomach_v = C_stomach / PC_stomach; C_thyroid = Q_thyroid / V_thyroid; C_thyroid_v = C_thyroid / PC_thyroid; C_gonads = Q_gonads / V_gonads; C_gonads_v = C_gonads / PC_gonads; # Other compartment concentrations for which PC_ is not needed # because equal to 1 (PC_ven and PC_art) or because # they are not directly irrigated by blood (diffusion, deposition) C_gut_lumen = Q_gut_lumen / V_gut_lumen; C_stom_lumen = Q_stom_lumen / V_stom_lumen; C_art = Q_art / V_art; C_ven = Q_ven / V_ven; C_urt = Q_urt / V_urt; # Differentials dt(Q_ing) = Q_ing_rate; dt(Q_stom_lumen) = Q_ing_rate + Cl_mc_lung * C_lung - (Fl_stom_lumen + Ka_stomach) * C_stom_lumen; dt(Q_stomach ) = Ka_stomach * C_stom_lumen + F_stomach * (C_art - C_stomach_v); dt(Q_feces) = Fl_gut_lumen * C_gut_lumen; dt(Q_gut_lumen) = Fl_stom_lumen * C_stom_lumen + Ke_bile * C_liver - Ka_gut * C_gut_lumen - dt(Q_feces); dt(Q_met_gut) = Km_gut * Q_gut; dt(Q_gut) = Ka_gut * C_gut_lumen + F_gut * (C_art - C_gut_v) - dt(Q_met_gut); dt(Q_met_liver) = Km_liver * Q_liver; dt(Q_liver) = F_eport * C_art + F_spleen * C_spleen_v + F_pancreas * C_pancreas_v + F_gut * C_gut_v + F_stomach * C_stomach_v - F_liver * C_liver_v - Ke_bile * C_liver - dt(Q_met_liver); dt(Q_adip) = F_adip * (C_art - C_adip_v); dt(Q_adrenal) = F_adrenal * (C_art - C_adrenal_v); dt(Q_brain) = F_brain * (C_art - C_brain_v); dt(Q_breast) = F_breast * (C_art - C_breast_v); dt(Q_heart) = F_heart * (C_art - C_heart_v); dt(Q_inh) = F_pul * C_inh; dt(Q_exhaled) = F_pul * (C_urt / PC_urt); dt(Q_met_lung) = Km_lung * Q_lung; dt(Q_urt) = dt(Q_inh) - dt(Q_exhaled) - F_alv * (C_urt - C_lung / PC_lung_over_air); dt(Q_lung) = F_blood * (C_ven - C_lung_v) + F_alv * (C_urt - C_lung / PC_lung_over_air) - Cl_mc_lung * C_lung - dt(Q_met_lung); dt(Q_urine) = Ke_renal * C_kidney; dt(Q_kidney) = F_kidney * (C_art - C_kidney_v) - dt(Q_urine); dt(Q_marrow) = F_marrow * (C_art - C_marrow_v); dt(Q_muscle) = F_muscle * (C_art - C_muscle_v); dt(Q_other) = F_other * (C_art - C_other_v); dt(Q_pancreas) = F_pancreas * (C_art - C_pancreas_v); dt(Q_skin) = F_skin * (C_art - C_skin_v); dt(Q_spleen) = F_spleen * (C_art - C_spleen_v); dt(Q_thyroid) = F_thyroid * (C_art - C_thyroid_v); dt(Q_art) = F_blood * (C_lung_v - C_art); dt(Q_ven) = C_skin_v * F_skin + C_heart_v * F_heart + C_other_v * F_other + C_liver_v * F_liver + C_adip_v * F_adip + C_adrenal_v * F_adrenal + C_marrow_v * F_marrow + C_breast_v * F_breast + C_muscle_v * F_muscle + C_brain_v * F_brain + C_thyroid_v * F_thyroid + C_gonads_v * F_gonads + C_kidney_v * F_kidney - F_blood * C_ven; dt(Q_gonads) = F_gonads * (C_art - C_gonads_v); # Mass balance check Q_total = Q_adip + Q_adrenal + Q_art + Q_brain + Q_breast + Q_gut + Q_gut_lumen + Q_heart + Q_kidney + Q_liver + Q_lung + Q_marrow + Q_muscle + Q_other + Q_pancreas + Q_skin + Q_spleen + Q_stomach + Q_stom_lumen + Q_thyroid + Q_gonads + Q_ven + Q_met_liver + Q_met_lung + Q_met_gut + Q_exhaled + Q_feces + Q_urine; } # End of Dynamics CalcOutputs { # Exhaled air concentration (mM) C_exh = 0.7 * C_ven + 0.3 * C_inh; C_null = 0; } # End of CalcOutputs # END