TITLE Methyl mercury in rats. : : This model is a SCOP version by Alberto Protzel of the methyl mercury : model of Farris et al., (Physiological model for the pharmacokinetics of : methyl mercury in the growing rat), which appeared in Toxicol. Appl. : Pharmacol. 119:74-90 (1993). : PARAMETER { : ==== Intercompartmental Mass Transport Parameters. ======== : These k-values are multiplied by the appropriate growth function to give : the K-values used in the model equations. : The k_ refers to methyl mercury and the k1_ refers to mercuric mercury. k_Br = 3.5E-5 : Blood to brain (ml blood/min/g tissue) k1_Br = 3.2E-5 k_Cs = 7.7E-4 : Blood to carcass (ml blood/min/g tissue) k1_Cs = 3.1E-4 k_Lv_k_Gt = 9.1E-4 : Blood to liver (ml blood/min/g tissue) k1_Lv_k1_Gt = 9.1E-2 k_Ki = 2.0E-2 : Blood to kidney (ml blood/min/g tissue) k1_Ki = 8.4E-3 k_Sk = 1.0E-3 : Blood to skin (ml blood/min/g tissue) k1_Sk = 4.2E-4 k_Gt = 8.6E-3 : Blood to GI tissue (ml blood/min/g tissue) k1_Gt = 3.5E-3 k_Gl = 1.0E-2 : GI tissue to lumen (ml tissue/min/g tissue) k1_Gl = 2.0E-4 : GI mucosal cell exfoliation (ml tissue/min/g tissue) k_In = 1.2E-4 : Skin to hair (ml skin/min/g skin) k1_In = 1.2E-4 k_Lv = 9.5E-3 : For liver only; obtained by A. Protzel k1_Lv = 9.45E-2 : ===== Physiological Flow rates and Clearances in the rat ===== : : These q- and cl- values are multiplied by the appropriate growth : function to obtain the Q- and CL- values used in the model equations. q_Ur = 5.6E-3 : Urine flow rate (ml/min/g kidney) q_Fs = 8.5E-4 : Fecal flow rate (ml/min/g GI lumen) cl_Bi = 9.7E-4 : Biliary clearance (ml liver/min/g liver) cl1_Rf = 3.5E-4 : Renal filtration clearance for mercuric : mercury (ml blood/min/g kidney) : ===== Partition Coefficients and biliary clearances ======== : : R-values are for methyl mercury, R1-values are for mercuric Hg. R_Br = 0.08 : Brain to Blood R1_Br = 0.80 R_Cs = 0.10 : Carcass to Blood R1_Cs = 0.45 R_Gt = 0.10 : GI tissue to Blood R1_Gt = 0.45 R_Lv = 0.18 : Liver to Blood R1_Lv = 11.5 R_Ki = 1.5 : Kidney to Blood R1_Ki = 600 R_Sk = 0.08 : Skin to Blood R1_Sk = 2.7 R_Gl = 0.28 : GI lumen to Tissue R1_Gl = 10 R_Ur = 0.008 : Urine to Blood CR = 0.5 : Biliary clearance ratio of NPSH compounds from liver : to mercury from liver. CR1 = 3.0 : ======= Rate Constants =========== k_GD = 3.0E-3 : Demethylation in GI lumen (min-1) k_LD = 2.0E-4 : Demethylation in liver (min-1) k_KU = 2.8E-6 : Loss of mercuric Hg by tubular cell exfoliation (min-1) k_HS = 2.4E-6 : Loss of Hg in hair to surroundings (min-1) k_HG = 3.4E-6 : Ingestion of Hg in hair during grooming (min-1) : ======= Growth Equation parameters =========== : Blood Vo_Bl = 19.86 : weight at start (g) Vf_Bl = 35.35 : weight at time infinity (g) kCG_Bl = 1.18E-5 : time constant in exponential (min-1) : Brain Vo_Br = 1.83 Vf_Br = 2.08 kCG_Br = 1.07E-5 : Carcass Vo_Cs = 198.07 Vf_Cs = 349.69 kCG_Cs = 1.28E-5 : Gut tissue Vo_Gt = 9.49 Vf_Gt = 14.35 kCG_Gt = 1.26E-5 : Gut lumen Vo_Gl = 9.49 Vf_Gl = 14.35 kCG_Gl = 1.26E-5 : Hair Vo_Hr = 4.61 Vf_Hr = 10.85 kCG_Hr = 1.15E-5 : Liver Vo_Lv = 13.42 Vf_Lv = 17.44 kCG_Lv = 1.93E-5 : Kidney Vo_Ki = 1.94 Vf_Ki = 2.81 kCG_Ki = 2.37E-5 : Skin Vo_Sk = 48.54 Vf_Sk = 108.51 kCG_Sk = 7.36E-6 : Body Weight Vo_Bw = 307.21 Vf_Bw = 548.43 kCG_Bw = 1.17E-5 : ======= Experimental Parameters ========== } INDEPENDENT { t FROM 0 TO 141120 WITH 14 (minutes) : time is t } STATE : C_ corresponds to methyl mercury concentrations; C1_ corresponds to : mercuric mercury concentrations. { : Methyl Mercury C_Ki FROM 0 TO 10 START 0.0 : Conc. MM in kidney C_Bl FROM 0 TO 10 START 0.0 : Conc. MM in blood C_Lv FROM 0 TO 10 START 0.0 : Conc. MM in liver C_Gt FROM 0 TO 10 START 0.0 : Conc. MM in Gut tissue C_Gl FROM 0 TO 10 START 10.54 : Conc. MM in Gut lumen C_Sk FROM 0 TO 10 START 0.0 : Conc. MM in Skin C_Hr FROM 0 TO 10 START 0.0 : Conc. MM in Hair C_Br FROM 0 TO 5 START 0.0 : Conc. MM in Brain C_Cs FROM 0 TO 10 START 0.0 : Conc. MM in Carcass Cum_MM_Urine FROM 0 TO 100 START 0.0 : Cummulative excretion in urine Cum_MM_Feces FROM 0 TO 100 START 0.0 : Cummulative excretion in feces Cum_MM_Sh_Hair FROM 0 TO 100 START 0.0 : Cumm. excret. in shed hair : Mercuric Mercury C1_Ki FROM 0 TO 10 START 0.0 : Conc. MM in kidney C1_Bl FROM 0 TO 10 START 0.0 : Conc. MM in blood C1_Lv FROM 0 TO 10 START 0.0 : Conc. MM in liver C1_Gt FROM 0 TO 10 START 0.0 : Conc. MM in Gut tissue C1_Gl FROM 0 TO 10 START 0.0 : Conc. MM in Gut lumen C1_Sk FROM 0 TO 10 START 0.0 : Conc. MM in Skin C1_Hr FROM 0 TO 10 START 0.0 : Conc. MM in Hair C1_Br FROM 0 TO 5 START 0.0 : Conc. MM in Brain C1_Cs FROM 0 TO 10 START 0.0 : Conc. MM in Carcass Cum_MercM_Urine FROM 0 TO 100 START 0.0 : Cummulative excretion in urine Cum_MercM_Feces FROM 0 TO 100 START 0.0 : Cummulative excretion in feces Cum_MercM_Sh_Hair FROM 0 TO 100 START 0.0 : Cummul. excret. in shed hair } ASSIGNED { : K_ values for transport (flow) : Methyl Mercury K_Ki : Blood flow to kidney (ml/min) K_Br : Blood flow to brain (ml/min) K_Cs : Blood flow to carcass (ml/min) K_Lv : Blood flow to liver (ml/min) K_Sk : Blood flow to skin (ml/min) K_Gt : Whole blood flow to gut (ml/min) K_In : flow from skin to hair (ml skin/min) K_Gl : whole blood flow to gut lumen (ml/min) : Mercuric Mercury K1_Ki : Blood flow to kidney (ml/min) K1_Br : Blood flow to brain (ml/min) K1_Cs : Blood flow to carcass (ml/min) K1_Lv : Blood flow to liver (ml/min) K1_Sk : Blood flow to skin (ml/min) K1_Gt : Whole blood flow to gut (ml/min) K1_In : flow from skin to hair (ml skin/min) K1_Gl : whole blood flow to gut lumen (ml/min) : Kidney equation V_Ki : Vol. kidney (g) Q_Ur : Urine flow rate (ml/min) DV_Ki_Dt : dV/dt for kidney CL1_Rf : Renal filtration clearance for mercuric Hg : (ml blood/min) : Blood equation V_Bl : Vol. blood (g) DV_Bl_Dt : dV/dt for blood : Liver equation V_Lv : Vol. liver (g) CL_Bi : Biliary clearance from hepatic pool (ml liver/min) DV_Lv_Dt : dV/dt for liver : Gut tissue equation V_Gt : Vol. gut tissue (g) DV_Gt_Dt : dV/dt for gut tissue : Gut lumen equation V_Gl : Vol. gut lumen (g) DV_Gl_Dt : dV/dt for gut lumen Q_Fs : Fecal flow rate (ml/min) : Skin equation V_Sk : Vol. of skin (g) DV_Sk_Dt : dV/dt for skin : Hair equation V_Hr : Vol. hair (g) DV_Hr_Dt : dV/dt for hair : Brain equation V_Br : Vol. brain (g) DV_Br_Dt : dV/dt for brain : Carcass equation V_Cs : Vol. carcass (g) DV_Cs_Dt : dV/dt for carcass : Excretion Tot_Inorg : Total excretion of inorganic mercury Tot_MM : Total excretion of methyl mercury Cum_Urine : Cumulative urinary MM plus Mercuric Mercury excretion. Cum_Feces : Cummulative fecal MM plus Mercuric Mercury excretion. } INITIAL { : Initial volumes of compartments V_Ki = Vo_Ki : kidney V_Bl = Vo_Bl : blood V_Lv = Vo_Lv : liver V_Gt = Vo_Gt : gut tissue V_Gl = Vo_Gl : gut lumen V_Sk = Vo_Sk : skin V_Hr = Vo_Hr : hair V_Br = Vo_Br : brain V_Cs = Vo_Cs : carcass : Initial transport rates K_Ki = k_Ki * V_Ki K_Br = k_Br * V_Br K_Cs = k_Cs * V_Cs K_Lv = k_Lv * V_Lv K_Sk = k_Sk * V_Sk K_Gt = k_Gt * V_Gt K_In = k_In * V_Sk K_Gl = k_Gl * V_Gl : Flow rates and Clearances Q_Ur = q_Ur * V_Ki : Urine Q_Fs = q_Fs * V_Gl : Feces CL_Bi = cl_Bi * V_Lv : Biliary clearance } DERIVATIVE pbpk : Contains the equations of the model { : Calculation of time-dependent parameters : Growth equations V_Ki = Vo_Ki + (Vf_Ki - Vo_Ki)*(1.0 - exp(-kCG_Ki*t)) : kidney V_Bl = Vo_Bl + (Vf_Bl - Vo_Bl)*(1.0 - exp(-kCG_Bl*t)) : blood V_Lv = Vo_Lv + (Vf_Lv - Vo_Lv)*(1.0 - exp(-kCG_Lv*t)) : liver V_Gt = Vo_Gt + (Vf_Gt - Vo_Gt)*(1.0 - exp(-kCG_Gt*t)) : gut tissue V_Gl = Vo_Gl + (Vf_Gl - Vo_Gl)*(1.0 - exp(-kCG_Gl*t)) : gut lumen V_Sk = Vo_Sk + (Vf_Sk - Vo_Sk)*(1.0 - exp(-kCG_Sk*t)) : skin V_Hr = Vo_Hr + (Vf_Hr - Vo_Hr)*(1.0 - exp(-kCG_Hr*t)) : hair V_Br = Vo_Br + (Vf_Br - Vo_Br)*(1.0 - exp(-kCG_Br*t)) : brain V_Cs = Vo_Cs + (Vf_Cs - Vo_Cs)*(1.0 - exp(-kCG_Cs*t)) : carcass : Rate of growth formulas DV_Ki_Dt = kCG_Ki * (Vf_Ki - Vo_Ki) * exp(-kCG_Ki*t) : kidney DV_Bl_Dt = kCG_Bl * (Vf_Bl - Vo_Bl) * exp(-kCG_Bl*t) : blood DV_Lv_Dt = kCG_Lv * (Vf_Lv - Vo_Lv) * exp(-kCG_Lv*t) : liver DV_Gt_Dt = kCG_Gt * (Vf_Gt - Vo_Gt) * exp(-kCG_Gt*t) : gut tissue DV_Gl_Dt = kCG_Gl * (Vf_Gl - Vo_Gl) * exp(-kCG_Gl*t) : gut lumen DV_Sk_Dt = kCG_Sk * (Vf_Sk - Vo_Sk) * exp(-kCG_Sk*t) : skin DV_Hr_Dt = kCG_Hr * (Vf_Hr - Vo_Hr) * exp(-kCG_Hr*t) : hair DV_Br_Dt = kCG_Br * (Vf_Br - Vo_Br) * exp(-kCG_Br*t) : brain DV_Cs_Dt = kCG_Cs * (Vf_Cs - Vo_Cs) * exp(-kCG_Cs*t) : carcass : Intercompartamental transport coefficients : Methyl Mercury K_Ki = k_Ki * V_Ki K_Br = k_Br * V_Br K_Cs = k_Cs * V_Cs K_Lv = k_Lv * V_Lv K_Sk = k_Sk * V_Sk K_Gt = k_Gt * V_Gt K_In = k_In * V_Sk K_Gl = k_Gl * V_Gl : Mercuric Mercury K1_Ki = k1_Ki * V_Ki K1_Br = k1_Br * V_Br K1_Cs = k1_Cs * V_Cs K1_Lv = k1_Lv * V_Lv K1_Sk = k1_Sk * V_Sk K1_Gt = k1_Gt * V_Gt K1_In = k1_In * V_Sk K1_Gl = k1_Gl * V_Gl : Flow rates and clearances Q_Ur = q_Ur * V_Ki : Urine Q_Fs = q_Fs * V_Gl : Feces CL_Bi = cl_Bi * V_Lv : Biliary clearance CL1_Rf = cl1_Rf * V_Ki : Renal filtration clearance for : mercuric mercury : ======= Equations for methyl mercury ======= : Kidney C_Ki' = (-C_Ki * DV_Ki_Dt + K_Ki * (C_Bl - C_Ki/R_Ki) - Q_Ur * C_Bl * R_Ur) / V_Ki : Blood C_Bl' = (-C_Bl * DV_Bl_Dt + K_Br * (C_Br/R_Br - C_Bl) + K_Cs * (C_Cs/R_Cs - C_Bl) + K_Lv * (C_Lv/R_Lv - C_Bl) + K_Ki * (C_Ki/R_Ki - C_Bl) + K_Sk * (C_Sk/R_Sk - C_Bl))/V_Bl : Liver C_Lv' = (-C_Lv * DV_Lv_Dt + (K_Lv - K_Gt) * C_Bl + K_Gt * C_Gt / R_Gt -K_Lv * C_Lv / R_Lv - k_LD * C_Lv * V_Lv - CL_Bi * C_Lv / CR) / V_Lv : Gut tissue C_Gt' = (-C_Gt * DV_Gt_Dt + K_Gt * (C_Bl - C_Gt / R_Gt) + K_Gl * (C_Gl / R_Gl - C_Gt)) / V_Gt : Gut lumen C_Gl' = (-C_Gl * DV_Gl_Dt + CL_Bi * C_Lv / CR + k_HG * C_Hr * V_Hr - k_GD * C_Gl * V_Gl - Q_Fs * C_Gl + K_Gl * (C_Gt - C_Gl / R_Gl)) / V_Gl : Skin C_Sk' = (-C_Sk * DV_Sk_Dt + K_Sk * (C_Bl - C_Sk / R_Sk) - K_In * C_Sk) / V_Sk : Hair C_Hr' = (-C_Hr * DV_Hr_Dt + K_In * C_Sk -(k_HG + k_HS) * C_Hr * V_Hr) / V_Hr : Brain C_Br' = (-C_Br * DV_Br_Dt + K_Br * (C_Bl - C_Br / R_Br)) / V_Br : Carcass C_Cs' = (-C_Cs * DV_Cs_Dt + K_Cs * (C_Bl - C_Cs / R_Cs)) / V_Cs : Urine (cumulative excretion) Cum_MM_Urine' = Q_Ur * C_Bl * R_Ur : Feces (cumulative excretion) Cum_MM_Feces' = Q_Fs * C_Gl : Shed Hair (cumulative excretion) Cum_MM_Sh_Hair' = (k_HS + k_HG) * C_Hr * V_Hr : ====== Equations for Mercuric mercury ====== : Kidney C1_Ki' = (-C1_Ki * DV_Ki_Dt + K1_Ki * (C1_Bl - C1_Ki/R1_Ki) - CL1_Rf * C1_Bl - k_KU * C1_Ki * V_Ki) / V_Ki : Blood C1_Bl' = (-C1_Bl * DV_Bl_Dt + K1_Br * (C1_Br/R1_Br - C1_Bl) + K1_Cs * (C1_Cs/R1_Cs - C1_Bl) + K1_Lv * (C1_Lv/R1_Lv - C1_Bl) + K1_Ki * (C1_Ki/R1_Ki - C1_Bl) + K1_Sk * (C1_Sk/R1_Sk - C1_Bl))/V_Bl : Liver C1_Lv' = (-C1_Lv * DV_Lv_Dt + (K1_Lv - K1_Gt) * C1_Bl + K1_Gt * C1_Gt / R1_Gt - K1_Lv * C1_Lv / R1_Lv + k_LD * C_Lv * V_Lv - CL_Bi * C1_Lv / CR1) / V_Lv : Gut tissue C1_Gt' = (-C1_Gt * DV_Gt_Dt + K1_Gt * (C1_Bl - C1_Gt / R1_Gt) + K1_Gl * (C1_Gl / R1_Gl - C1_Gt)) / V_Gt : Gut lumen C1_Gl' = (-C1_Gl * DV_Gl_Dt + CL_Bi * C1_Lv / CR1 + k_HG * C1_Hr * V_Hr + k_GD * C_Gl * V_Gl - Q_Fs * C1_Gl + K1_Gl * (C1_Gt - C1_Gl/R1_Gl)) / V_Gl : Skin C1_Sk' = (-C1_Sk * DV_Sk_Dt + K1_Sk * (C1_Bl - C1_Sk / R1_Sk) - K1_In * C1_Sk) / V_Sk : Hair C1_Hr' = (-C1_Hr * DV_Hr_Dt + K1_In * C1_Sk -(k_HG + k_HS) * C1_Hr * V_Hr) / V_Hr : Brain C1_Br' = (-C1_Br * DV_Br_Dt + K1_Br * (C1_Bl - C1_Br / R1_Br)) / V_Br : Carcass C1_Cs' = (-C1_Cs * DV_Cs_Dt + K1_Cs * (C1_Bl - C1_Cs / R1_Cs)) / V_Cs : Urine (cumulative excretion) Cum_MercM_Urine' = (CL1_Rf * C1_Bl) + (k_KU * C1_Ki * V_Ki) : Feces (cumulative excretion) Cum_MercM_Feces' = Q_Fs * C1_Gl : Shed Hair (cumulative excretion) Cum_MercM_Sh_Hair' = (k_HS + k_HG) * C1_Hr * V_Hr } BREAKPOINT { SOLVE pbpk METHOD clsoda : solve with Gear algorithm Tot_Inorg = Cum_MercM_Feces + Cum_MercM_Urine + Cum_MercM_Sh_Hair Tot_MM = Cum_MM_Feces + Cum_MM_Urine + Cum_MM_Sh_Hair } PLOT C_Ki, C_Bl, Cum_MM_Feces, Cum_MercM_Feces VS t