#-----------------------------------------------------------------------
#                         Initial Comments
#-----------------------------------------------------------------------


#-----------------------------------------------------------------------
# 			            Initial Parameters 
#               (plus params for added compartments)
#-----------------------------------------------------------------------
#region

# Chemical Parameters
#--------------------
MW_APAP = 151.17;   # Molecualar Weight of APAP
MW_AG = 327.28;     # Molecular Weight of APAP-glucoronide
MW_AS = 231.22;     # Molecular Weight of APAP-suphate
#fa = 0.87; lnfa = log(0.87);          # Bioavailability of APAP


# Anatomical Parameters
#---------------------- 
BW    = 70.; lnBW = log(70.);       # Body weight (kg).
QCC   = 16.2;         # Cardiac output (L/hr/kg^0.75).

# Fractional volumes (fraction of body weight).
VFC  = 0.214;            # Fat.
VKC  = 0.0044;          # Kidney.
VGC  = 0.0144;          # Gut.
VLC  = 0.0257;          # Liver.
VMC  = 0.4;             # Muscle
VBLAC= 0.0243;        # Arterial Blood.
VBLVC= 0.0557;         # Venous Blood.
VSC = 0.185;            # Slowly Perfused
VRC = 0.0765;           # Rapidly Perfused (1- everything else)


# Fractional blood flows (fraction of cardiac output).
QFC  = 0.052;           # Fat. **
QKC  = 0.175;          # Kidney.
QGC  = 0.181;          # Gut. **
QLBC = 0.046;          # Hepatic artery. **
QMC  = 0.191;          # Muscle
QSC = 0.14;           # Slowly Perfused
QRC = 0.215;           # Rapidly Perfused (1 -  everything else)


# Chemical Specific Transport Params
#-----------------------------------
kSG_Vm = 2332.5; lnkSG_Vm = log(2332.5);     # Kmax for abs to portal
kSG_Km = 1765.49; lnkSG_Km = log(1765.49);     # Km for abs to portal
Tg = 0.233;     lnTg = log(0.233);
Tp = 0.033; lnTp = log(0.033);


CLC_APAP = 0.059; lnCLC_APAP = log(0.059); # Total APAP blood clearance (L/hr/kg)
CLC_AS = 0.29; lnCLC_AS = log(0.29);       # Total AS blood clearance (L/hr/kg)
CLC_AG = 0.22; lnCLC_AG = log(0.22);      # Total AG blood clearance (L/hr/kg)
alpha_APAP = 1.;
alpha_AS = 1.;
alpha_AG = 1.;

BP_APAP = 0.9; lnBP_APAP = log(0.9);    # Blood:Plasma Ratio

# Partition Coefficients
    # Rodgers et al. APAP: pKa1 = 9.46, pKa2 = -4.4, zwitterion, logP = 0.91, fu = 0.819, BP = 0.98
    PF_APAP = 0.447; lnPF_APAP = log(0.447);    # Fat:blood
    PG_APAP = 0.907; lnPG_APAP = log(0.907);    # Gut:blood
    PK_APAP = 0.711; lnPK_APAP = log(0.711);    # Kidney:blood
    PL_APAP = 0.687; lnPL_APAP = log(0.687);    # Liver:blood
    PM_APAP = 0.687; lnPM_APAP = log(0.687);    # Muscle:blood
    
    PR_APAP = 0.676; lnPR_APAP = log(0.676);    # rapidly perfused:blood [brain, lung, spleen]
    PS_APAP = 0.606; lnPS_APAP = log(0.606);    # slowly perfused:blood [bone, heart, skin]

    # Rodgers et al. AS: pKa1 = -2.2, pKa2 = -4.4, zwitterion, logP = -1, fu = 0.46, BP = 0.98
    PF_AS = 0.088; lnPF_AS = log(0.088);
    PG_AS = 0.297; lnPG_AS = log(0.297);
    PK_AS = 0.261; lnPK_AS = log(0.261);
    PL_AS = 0.203; lnPL_AS = log(0.203);
    PM_AS = 0.199; lnPM_AS = log(0.199);
    
    PR_AS = 0.207; lnPR_AS = log(0.207);
    PS_AS = 0.254; lnPS_AS = log(0.254);

    # Rodgers et al. AG: pKa1 = 3.17, pKa2 = -3.7, zwitterion, logP = -0.68, fu = 0.923, BP = 0.98
    PF_AG = 0.128; lnPF_AG = log(0.128);
    PG_AG = 0.436; lnPG_AG = log(0.436);
    PK_AG = 0.392; lnPK_AG = log(0.392);
    PL_AG = 0.321; lnPL_AG = log(0.321);
    PM_AG = 0.336; lnPM_AG = log(0.366);

    PR_AG = 0.364; lnPR_AG = log(0.364);
    PS_AG = 0.351; lnPS_AG = log(0.351);

# Biochemical Parameters
#-----------------------

# PAPS second order rate constant
#--------------------------------
kPAPS = 0.018; lnkPAPS = log(0.018);
kPAPS_syn = 1E-20; lnkPAPS_syn = log(1E-20); # Zeroth order PAPS synthesis

# GA second order rate constant
#-------------------------------
kGA = 0.008; lnkGA = log(0.008);
kGA_syn = 1E-20; lnkGA_syn = log(1E-20); # Zeroth order GA synthesis

#CYP Oxidase Params (Liver)
#--------------------------
CYP_Km = 2082.; lnCYP_Km = log(2082.);
CYP_VmaxC = 4623.; lnCYP_VmaxC = log(4623.);

# Glucoronidation (Liver)
#------------------------
UGT_Km = 6000.; lnUGT_Km = log(6000.);    # Km for entire UGT 2
UGT_Ki = 1E10; lnUGT_Ki = log(1E10);       # Partial substrate inhibition for UGT
UGT_VmaxC = 1551.; lnUGT_VmaxC = log(1551.); # Vmax in Liver
UGT_Km_GA = 10.; lnUGT_Km_GA = log(10.); # Km for UGT cofactor
Vmax_AG = 1E20; lnVmax_AG = log(1E20); # Vmax for transport out of hepatocyte
Km_AG = 20000.; lnKm_AG = log(20000.); # Km for transport out of hepatocyte

# Sulfation by PAPS (Liver)
#-------------------------------
SULT_Km_apap = 300.; lnSULT_Km_apap = log(300.);
SULT_Km_paps = 19.65; lnSULT_Km_paps = log(19.65);
SULT_Ki = 1E10; lnSULT_Ki = log(1E10);      # Partial substrate inhibition for SULT
SULT_VmaxC = 43100.; lnSULT_VmaxC = log(43100.); # Vmax in Liver
Vmax_AS = 1.0E20; lnVmax_AS = log(1.0E20); # Vmax for AS transport out of hepatocyte
Km_AS = 22900.; lnKm_AS = log(22900.); # Km for AS transport out of hepatocyte


#endregion

#-----------------------------------------------------------------------
#                   Parameters for Exposure/Dose
#-----------------------------------------------------------------------
#region
mgkg_flag=1.; # If the flag is 1, we have a mg/kg dose

# Oral Regimen
OralDose_APAP_mgkg = 0.; lnOralDose_APAP_mgkg = log(2E-9);     # Oral Dose given (mg/kg)
OralDose_APAP_mg = 0.;  lnOralDose_APAP_mg = log(2E-9);         # Oral Dose given (mg)

OralDur_APAP = 0.001;   # Oral Duration of chemical (hr)
ODose_APAP_mg;  # Calculated Dose of APAP (mg)
fa;             # Calculated, dose dependent fa
ODose_APAP;     # Dose of chemical (muM/hr)
true_dose;      # Calculated dose (muM)

# IV Regimen
IVDose_APAP_mgkg = 0.; lnIVDose_APAP_mgkg = log(2E-9);      # IV Dose given (mg/kg)
IVDose_APAP_mg = 0.; lnIVDose_APAP_mg = log(2E-9);      # IV Dose given (mg)

IVDur_APAP = 0.001;     # IV Duration (hr): Default is 5 min duration
IVD_APAP_mg; # Calculated Dose of APAP (mg) 
IVDR_APAP; # Actual Dose of APAP (muM)
#endregion

#-----------------------------------------------------------------------
#                   Defined Scaled Parameters
#-----------------------------------------------------------------------
#region
# Metabolism Vmax
CYP_Vmax; UGT_Vmax; SULT_Vmax;

# Compartment Volumes
VTC; VF; VK; VG; VM; VL; VBLA; VBLV; VR; VS;

# Compartment Flow Rates
QTC; QC; QF; QK; QG; QM; QLB; QR; QS; QL;

# Clearance Rates
CLR_APAP; CLR_AS; CLR_AG;
#endregion

#-----------------------------------------------------------------------
#                   Reverse Dosimetry Parameters
#-----------------------------------------------------------------------
#region
M_OralDose_APAP; Var_OralDose_APAP;
M_IVDose_APAP; Var_IVDose_APAP;
M_lnOralDose_APAP; Var_lnOralDose_APAP;
M_lnIVDose_APAP; M_lnVar_IVDose_APAP;
#endregion


#-----------------------------------------------------------------------
#                   Calibration Parameters
#-----------------------------------------------------------------------
#region

#-----------------------------------------------------------------------
#                   Population Mean Parameters (M_...)
#-----------------------------------------------------------------------
#region
# Phyisiological Params
#----------------------
M_BW; M_lnBW;
M_fa; M_lnfa;

# Chemical Specific Transport Params
#-----------------------------------
M_kSG_Vm; M_lnkSG_Vm;
M_kSG_Km; M_lnkSG_Km;
M_Tg;     M_lnTg;
M_Tp;     M_lnTp;

M_CLC_APAP; M_lnCLC_APAP; # Total APAP blood clearance (L/hr/kg)
M_CLC_AS; M_lnCLC_AS;       # Total AS blood clearance (L/hr/kg)
M_CLC_AG; M_lnCLC_AG;      # Total AG blood clearance (L/hr/kg)

M_BP_APAP; M_lnBP_APAP;    # Blood:Plasma Ratio
# Rodgers et al.
# APAP
M_PF_APAP; M_lnPF_APAP;    # Fat:blood
M_PG_APAP; M_lnPG_APAP;    # Gut:blood
M_PK_APAP; M_lnPK_APAP;    # Kidney:blood
M_PL_APAP; M_lnPL_APAP;    # Liver:blood
M_PM_APAP; M_lnPM_APAP;    # Muscle:blood
M_PR_APAP; M_lnPR_APAP;    # rapidly perfused:blood
M_PS_APAP; M_lnPS_APAP;    # slowly perfused:blood

# AS
M_PK_AS; M_lnPK_AS;
M_PF_AS; M_lnPF_AS;
M_PL_AS; M_lnPL_AS;
M_PG_AS; M_lnPG_AS;
M_PM_AS; M_lnPM_AS;
M_PR_AS; M_lnPR_AS;
M_PS_AS; M_lnPS_AS;

# AG
M_PK_AG; M_lnPK_AG;
M_PF_AG; M_lnPF_AG;
M_PL_AG; M_lnPL_AG;
M_PG_AG; M_lnPG_AG;
M_PM_AG; M_lnPM_AG;
M_PR_AG; M_lnPR_AG;
M_PS_AG; M_lnPS_AG;

# Biochemical Parameters
#-----------------------

# PAPS second order rate constant
#--------------------------------
M_kPAPS; M_lnkPAPS;
M_kPAPS_syn; M_lnkPAPS_syn;

# GA second order rate constant
#-------------------------------
M_kGA; M_lnkGA;
M_kGA_syn; M_lnkGA_syn;

#CYP Oxidase Params (Liver)
#--------------------------
M_CYP_Km; M_lnCYP_Km;
M_CYP_VmaxC; M_lnCYP_VmaxC;

# Glucoronidation (Liver)
#------------------------
M_UGT_Km; M_lnUGT_Km;    # Km for entire UGT 2
M_UGT_VmaxC; M_lnUGT_VmaxC; # Vmax in Liver
M_UGT_Km_GA; M_lnUGT_Km_GA;
M_UGT_Ki;   M_lnUGT_Ki;
M_Vmax_AG; M_lnVmax_AG;
M_Km_AG; M_lnKm_AG;

# Sulfation by PAPS (Liver)
#-------------------------------
M_SULT_Km_apap; M_lnSULT_Km_apap;
M_SULT_Km_paps; M_lnSULT_Km_paps;
M_SULT_Ki;   M_lnSULT_Ki;
M_SULT_VmaxC; M_lnSULT_VmaxC; # Vmax in Liver
M_Vmax_AS; M_lnVmax_AS;
M_Km_AS; M_lnKm_AS;
#endregion

#-----------------------------------------------------------------------
#                   Population Variance Parameters (Var_...)
#-----------------------------------------------------------------------
#region
# Phyisiological Params
#----------------------
Var_BW; Var_lnBW;
Var_fa; Var_lnfa;

# Chemical Specific Transport Params
#-----------------------------------
Var_kSG_Vm; Var_lnkSG_Vm;
Var_kSG_Km; Var_lnkSG_Km;
Var_Tg;     Var_lnTg;
Var_Tp;     Var_lnTp;

Var_CLC_APAP; Var_lnCLC_APAP; # Total APAP blood clearance (L/hr/kg)
Var_CLC_AS; Var_lnCLC_AS;       # Total AS blood clearance (L/hr/kg)
Var_CLC_AG; Var_lnCLC_AG;      # Total AG blood clearance (L/hr/kg)

Var_BP_APAP; Var_lnBP_APAP;    # Blood:Plasma Ratio
# Rodgers et al.
# APAP
Var_PF_APAP; Var_lnPF_APAP;    # Fat:blood
Var_PG_APAP; Var_lnPG_APAP;    # Gut:blood
Var_PK_APAP; Var_lnPK_APAP;    # Kidney:blood
Var_PL_APAP; Var_lnPL_APAP;    # Liver:blood
Var_PM_APAP; Var_lnPM_APAP;    # Muscle:blood
Var_PR_APAP; Var_lnPR_APAP;    # rapidly perfused:blood
Var_PS_APAP; Var_lnPS_APAP;    # slowly perfused:blood

# AS
Var_PK_AS; Var_lnPK_AS;
Var_PF_AS; Var_lnPF_AS;
Var_PL_AS; Var_lnPL_AS;
Var_PG_AS; Var_lnPG_AS;
Var_PM_AS; Var_lnPM_AS;
Var_PR_AS; Var_lnPR_AS;
Var_PS_AS; Var_lnPS_AS;

# AG
Var_PK_AG; Var_lnPK_AG;
Var_PF_AG; Var_lnPF_AG;
Var_PL_AG; Var_lnPL_AG;
Var_PG_AG; Var_lnPG_AG;
Var_PM_AG; Var_lnPM_AG;
Var_PR_AG; Var_lnPR_AG;
Var_PS_AG; Var_lnPS_AG;

# Biochemical Parameters
#-----------------------

# PAPS second order rate constant
#--------------------------------
Var_kPAPS; Var_lnkPAPS;
Var_kPAPS_syn; Var_lnkPAPS_syn;

# GA second order rate constant
#-------------------------------
Var_kGA; Var_lnkGA;
Var_kGA_syn; Var_lnkGA_syn;

#CYP Oxidase Params (Liver)
#--------------------------
Var_CYP_Km; Var_lnCYP_Km;
Var_CYP_VmaxC; Var_lnCYP_VmaxC;

# Glucoronidation (Liver)
#------------------------
Var_UGT_Km; Var_lnUGT_Km;    # Km for entire UGT 2
Var_UGT_VmaxC; Var_lnUGT_VmaxC; # Vmax in Liver
Var_UGT_Km_GA; Var_lnUGT_Km_GA;
Var_UGT_Ki;   Var_lnUGT_Ki;
Var_Vmax_AG; Var_lnVmax_AG;
Var_Km_AG; Var_lnKm_AG;

# Sulfation by PAPS (Liver)
#-------------------------------
Var_SULT_KVar_apap; Var_lnSULT_Km_apap;
Var_SULT_KVar_paps; Var_lnSULT_Km_paps;
Var_SULT_Ki;   Var_lnSULT_Ki;
Var_SULT_VmaxC; Var_lnSULT_VmaxC; # Vmax in Liver
Var_Vmax_AS; Var_lnVmax_AS;
Var_Km_AS; Var_lnKm_AS;
#endregion


#endregion

#-----------------------------------------------------------------------
#                          Data Error (Verr_...)
#-----------------------------------------------------------------------
#region
# Needed if you are using an error distribution, rather than error at specific time points.

Verr_CPL_APAP_mcmolL; Verr_CPL_APAP_mcgL;
Verr_CPL_AG_mcmolL; Verr_CPL_AG_mcgL;
Verr_CPL_AS_mcmolL; Verr_CPL_AS_mcgL;

Verr_lnCPL_APAP_mcmolL_samp; Verr_lnCPL_APAP_mcgL_samp;
Verr_lnCPL_AG_mcmolL_samp; Verr_lnCPL_AG_mcgL_samp;
Verr_lnCPL_AS_mcmolL_samp; Verr_lnCPL_AS_mcgL_samp;

Verr_CU_APAP_mcg;
Verr_CU_AG_mcg;
Verr_CU_AS_mcg;

Verr_lnCU_APAP_mcg_samp;
Verr_lnCU_AG_mcg_samp;
Verr_lnCU_AS_mcg_samp;


#endregion

#-----------------------------------------------------------------------
#                 State Variables (Dependent Variables in ODE)
#-----------------------------------------------------------------------
#region

States = {
#================
# Meabolism Rates
#================
# Liver
#------
# CYP                  # Sulfation          # Glucoronidation
CL_APAP_to_NAPQI_CYP, CL_APAP_to_AS_SULT, CL_APAP_to_AG_UGT,


#=========================
# Chemical Amounts (mcmol)
#=========================
# Stomach
AST_Oral_APAP, AST_APAP, AST_to_Gut_APAP,

		# Adipose   # Rapid # Slow
		AF_APAP, AR_APAP, AS_APAP,
            AF_AS,   AR_AS,  AS_AS,
            AF_AG,   AR_AG,  AS_AG,

# Kidney
AKE_APAP, AKE_AS, AKE_AG,
AK_APAP, AK_AS, AK_AG,
# Liver
AL_APAP, AL_AS, AL_AG, AL_PAPS, AL_GA, CH_AG, CH_AG_to_CL_AG, CH_AS, CH_AS_to_CL_AS,

# Muscle
AM_APAP, AM_AS, AM_AG,

# Blood         Arterial
                ABLA_APAP, ABLA_AS, ABLA_AG,
#               Venous
ABL_IV_APAP, ABLV_APAP, ABLV_AS, ABLV_AG,

# Urine
AU_APAP, AU_AS, AU_AG, pct_abs

# Inactive Cofactor
#AL_PAPS_inact, AL_GA_inact 

};
#endregion

#-----------------------------------------------------------------------
#                    Inputs (Switches for Exposures)
#-----------------------------------------------------------------------
#region

Inputs = {
# ORAL EXPOSURE
#--------------
OralExp_APAP, IVExp_APAP,

};

#endregion

#-----------------------------------------------------------------------
#                       Outputs from the Model
#-----------------------------------------------------------------------
#region
Outputs = {
# Anything in CalcOutputs must go here

CF_APAP, CK_APAP, CL_APAP, CR_APAP, CS_APAP,

CF_AS, CK_AS, CL_AS, CR_AS, CS_AS,

CF_AG, CK_AG, CL_AG, CR_AG, CS_AG,

CA_APAP, CV_APAP, CPL_APAP,

CA_AS, CV_AS, CPL_AS,

CA_AG, CV_AG, CPL_AG, 

CPL_APAP_mcmolL, CPL_APAP_mcgL, CPL_AG_mcmolL,
CPL_AG_mcgL, CPL_AS_mcmolL, CPL_AS_mcgL,
CL_APAP_mcmolL, CL_APAP_mcgL,
CU_APAP_mcg, CU_AG_mcg, CU_AS_mcg,
f_abs,

lnCPL_APAP_mcgL, lnCPL_AG_mcgL, lnCPL_AS_mcgL,
lnCU_APAP_mcg, lnCU_AG_mcg, lnCU_AS_mcg,
lnf_abs,

Verr_lnCPL_APAP_mcmolL, Verr_lnCPL_APAP_mcgL,
Verr_lnCPL_AG_mcmolL, Verr_lnCPL_AG_mcgL,
Verr_lnCPL_AS_mcmolL, Verr_lnCPL_AS_mcgL,

Verr_lnCU_APAP_mcg,
Verr_lnCU_AG_mcg,
Verr_lnCU_AS_mcg,

};

#endregion

#-----------------------------------------------------------------------
#                       Initialize the Model
#-----------------------------------------------------------------------
#region

Initialize {

# Rescale log-transformed params
#-------------------------------
#region
# Rescale the log transformed params here, comment out if no log re-scale needed

#fa = exp(lnfa);
BW = exp(lnBW);

# Inital Dosing
#--------------
OralDose_APAP_mgkg = exp(lnOralDose_APAP_mgkg);
OralDose_APAP_mg = exp(lnOralDose_APAP_mg);
IVDose_APAP_mgkg = exp(lnIVDose_APAP_mgkg);
IVDose_APAP_mg = exp(lnIVDose_APAP_mg);

# Chemical Specific Transport Params
#-----------------------------------
kSG_Vm = exp(lnkSG_Vm);     # Kmax for abs to portal
kSG_Km = exp(lnkSG_Km);     # Km for abs to portal
Tg = exp(lnTg);
Tp = exp(lnTp);

CLC_APAP = exp(lnCLC_APAP);     # Total APAP blood clearance (L/hr/kg)
CLC_AS = exp(lnCLC_AS);       # Total AS blood clearance (L/hr/kg)
CLC_AG = exp(lnCLC_AG);      # Total AG blood clearance (L/hr/kg)

BP_APAP = exp(lnBP_APAP);    # Blood:Plasma Ratio
# Rodgers et al.
# APAP
PF_APAP = exp(lnPF_APAP);    # Fat:blood
PG_APAP = exp(lnPG_APAP);    # Gut:blood
PK_APAP = exp(lnPK_APAP);    # Kidney:blood
PL_APAP = exp(lnPL_APAP);    # Liver:blood
PM_APAP = exp(lnPM_APAP);    # Muscle:blood
PR_APAP = exp(lnPR_APAP);   # rapidly perfused:blood
PS_APAP = exp(lnPS_APAP);   # slowly perfused:blood

# AS
PK_AS = exp(lnPK_AS);
PF_AS = exp(lnPF_AS);
PL_AS = exp(lnPL_AS);
PG_AS = exp(lnPG_AS);
PM_AS = exp(lnPM_AS);
PR_AS = exp(lnPR_AS);
PS_AS = exp(lnPS_AS);

# AG
PK_AG = exp(lnPK_AG);
PF_AG = exp(lnPF_AG);
PL_AG = exp(lnPL_AG);
PG_AG = exp(lnPG_AG);
PM_AG = exp(lnPM_AG);
PR_AG = exp(lnPR_AG);
PS_AG = exp(lnPS_AG);

# Biochemical Parameters
#-----------------------

# PAPS second order rate constant
#--------------------------------
kPAPS = exp(lnkPAPS);
kPAPS_syn = exp(lnkPAPS_syn);

# GA second order rate constant
#-------------------------------
kGA = exp(lnkGA);
kGA_syn = exp(lnkGA_syn);

#CYP Oxidase Params (Liver)
#--------------------------
CYP_Km = exp(lnCYP_Km);
CYP_VmaxC = exp(lnCYP_VmaxC);

# Glucoronidation (Liver) -> GA Cofactor
#---------------------------------------
UGT_Km = exp(lnUGT_Km);    # Km for entire UGT 2
UGT_VmaxC = exp(lnUGT_VmaxC); # Vmax in Liver
UGT_Km_GA = exp(lnUGT_Km_GA);
UGT_Ki = exp(lnUGT_Ki);
Vmax_AG = exp(lnVmax_AG);
Km_AG = exp(lnKm_AG);

# Sulfation (Liver) -> PAPS Cofactor
#-----------------------------------
SULT_Km_apap = exp(lnSULT_Km_apap);
SULT_Km_paps = exp(lnSULT_Km_paps);
SULT_Ki = exp(lnSULT_Ki);
SULT_VmaxC = exp(lnSULT_VmaxC); # Vmax in Liver
Vmax_AS = exp(lnVmax_AS);
Km_AS = exp(lnKm_AS);

#endregion

# APAP oral dose rate (rate of input to stomach (mcmol/hr)).
ODose_APAP_mg = (mgkg_flag>0.5 ? OralDose_APAP_mgkg*BW: OralDose_APAP_mg);
fa = (ODose_APAP_mg<1000 ? 0.0005*ODose_APAP_mg + 0.37: 0.88);
ODose_APAP  = (fa*ODose_APAP_mg/OralDur_APAP)*(1000./MW_APAP);
true_dose = (fa*ODose_APAP_mg)*(1000./MW_APAP);

# APAP IV dose rate (rate of input to venous blood (mcmol/hr)).
IVD_APAP_mg = (mgkg_flag>0.5 ? IVDose_APAP_mgkg*BW: IVDose_APAP_mg);
IVDR_APAP = (IVD_APAP_mg/IVDur_APAP)*(1000./MW_APAP);

#---------------------------------------------------------------------------
# Specify the compartment volumes (L)
#---------------------------------------------------------------------------
VTC  = VFC+VKC+VGC+VLC+VMC+VBLAC+VBLVC+VRC+VSC;
VF = VFC*BW/VTC;         # Fat.
VK = VKC*BW/VTC;         # Kidney.
VG = VGC*BW/VTC;         # Gut.
VL = VLC*BW/VTC;         # Liver.
VM = VMC*BW/VTC;         # Muscle.
VBLA = VBLAC*BW/VTC;     # Arterial
VBLV = VBLVC*BW/VTC;     # Venous
VR = VRC*BW/VTC;         # Rapidly Perfused
VS = VSC*BW/VTC;         # Slowly Perfused

#---------------------------------------------------------------------------
# Specify the flow rates (L/hr)
#---------------------------------------------------------------------------
QTC  = QFC+QKC+QGC+QLBC+QMC+QRC+QSC;
QC  = QCC*pow(BW,0.75);      # Cardiac output (L/hr).

QF = QFC*QC/QTC;         # Fat.
QK = QKC*QC/QTC;         # Kidney.
QG = QGC*QC/QTC;         # Gut.
QM = QMC*QC/QTC;         # Gut.
QLB = QLBC*QC/QTC;       # Hepatic artery.
QR = QRC*QC/QTC;         # Rapidly Perfused
QS = QSC*QC/QTC;         # Slowly Perfused
QL  = QG+QLB;            # Total liver flow.

#---------------------------------------------------------------------------
# Compute the clearance rates (L/hr)
#---------------------------------------------------------------------------
CLR_APAP  = (alpha_APAP)*CLC_APAP*BW;        # Renal clearance (L/hr).
CLR_AS = (alpha_AS)*(CLC_AS)*BW;
CLR_AG = (alpha_AG)*CLC_AG*BW;

#------------------------------------
# Compute Allometric Scaling for Vmax
#------------------------------------

CYP_Vmax = CYP_VmaxC*pow(BW, 0.75);
UGT_Vmax = UGT_VmaxC*pow(BW, 0.75);
SULT_Vmax = SULT_VmaxC*pow(BW, 0.75);

#---------------------------------------
# Initialize PAPSn and GA at 100% at t=0
#---------------------------------------
AL_PAPS = 1.;
AL_GA = 1.;


};
#endregion

#-----------------------------------------------------------------------
#                       The Model (Actual ODEs)
#-----------------------------------------------------------------------
#region
Dynamics {

#---------------------------------------------------------------------------
# Compute the drug tissue/organ concentrations (mcmol/L)
#---------------------------------------------------------------------------
CF_APAP = AF_APAP/VF;      # APAP Fat
CVF_APAP = CF_APAP/PF_APAP;
CK_APAP = AK_APAP/VK;      # APAP Kidney
CVK_APAP = CK_APAP/PK_APAP;
CM_APAP = AM_APAP/VM;      # APAP Muscle
CVM_APAP = CM_APAP/PM_APAP;
CL_APAP = AL_APAP/VL;      # APAP Liver
CVL_APAP = CL_APAP/PL_APAP;
CR_APAP = AR_APAP/VR;      # APAP Rapidly Perfused
CVR_APAP = CR_APAP/PR_APAP;
CS_APAP = AS_APAP/VS;      # APAP Slowly Perfused
CVS_APAP = CS_APAP/PS_APAP;

CF_AS = AF_AS/VF;          # AS Fat
CVF_AS = CF_AS/PF_AS;
CK_AS = AK_AS/VK;          # AS Kidney
CVK_AS = CK_AS/PK_AS;
CL_AS = AL_AS/VL;          # AS Liver
CVL_AS = CL_AS/PL_AS;
CM_AS = AM_AS/VM;          # AS Muscle
CVM_AS = CM_AS/PM_AS;
CR_AS = AR_AS/VR;          # AS Rapidly Perfused
CVR_AS = CR_AS/PR_AS;
CS_AS = AS_AS/VS;          # AS Slowly Perfused
CVS_AS = CS_AS/PS_AS;

CF_AG = AF_AG/VF;          # AG Fat
CVF_AG = CF_AG/PF_AG;
CK_AG = AK_AG/VK;          # AG Kidney
CVK_AG = CK_AG/PK_AG;
CL_AG = AL_AG/VL;          # AG Liver
CVL_AG = CL_AG/PL_AG;
CM_AG = AM_AG/VM;          # AG Muscle
CVM_AG = CM_AG/PM_AG;
CR_AG = AR_AG/VR;          # AG Rapidly Perfused
CVR_AG = CR_AG/PR_AG;
CS_AG = AS_AG/VS;          # AG Slowly Perfused
CVS_AG = CS_AG/PS_AG;

#---------------------------------------------------------------------------
# Compute the blood/plasma concentrations (mcmol/L)
#---------------------------------------------------------------------------
CA_APAP = ABLA_APAP/VBLV;   # APAP Blood
CV_APAP = ABLV_APAP/VBLA;
CPL_APAP = CV_APAP/BP_APAP;

CA_AS = ABLA_AS/VBLA;       # AS Blood
CV_AS = ABLV_AS/VBLV;
CPL_AS = CV_AS/BP_APAP;

CA_AG = ABLA_AG/VBLA;       # AG Blood
CV_AG = ABLV_AG/VBLV;
CPL_AG = CV_AG/BP_APAP;

#================
# Meabolism Rates
#================

#---------------------------------------------
# Liver Metabolism (Michaelis-Menten Kinetics)
#---------------------------------------------

dt(CL_APAP_to_NAPQI_CYP) = CYP_Vmax*CL_APAP/(CYP_Km + CL_APAP);
dt(CL_APAP_to_AS_SULT) = SULT_Vmax*(CL_APAP)*(AL_PAPS)/((SULT_Km_apap + CL_APAP + pow(CL_APAP, 2)/SULT_Ki)*(SULT_Km_paps + AL_PAPS));
dt(CL_APAP_to_AG_UGT) = UGT_Vmax*(CL_APAP)*(AL_GA)/((UGT_Km + CL_APAP + pow(CL_APAP, 2)/UGT_Ki)*(UGT_Km_GA + AL_GA));

# Cofactor amounts
dt(AL_PAPS) = -dt(CL_APAP_to_AS_SULT) + kPAPS_syn*(1 - AL_PAPS);
dt(AL_GA) = -dt(CL_APAP_to_AG_UGT) + kGA_syn*(1 - AL_GA);

#==============================
# Individual Substrate Dynamics
#==============================

# APAP
#=====
dt(AST_Oral_APAP) = OralExp_APAP*ODose_APAP;

# Stomach (Dissolution Absorption)
dt(AST_to_Gut_APAP) = true_dose*(exp(-t/Tg)-exp(-t/Tp))/(Tg-Tp);
dt(AST_APAP) = dt(AST_Oral_APAP) - dt(AST_to_Gut_APAP);

# Liver
dt(AL_APAP) =  QL*CA_APAP + dt(AST_to_Gut_APAP) - QL*CVL_APAP - dt(CL_APAP_to_NAPQI_CYP) - dt(CL_APAP_to_AS_SULT) - dt(CL_APAP_to_AG_UGT);
dt(pct_abs) =  dt(AST_to_Gut_APAP)/true_dose;

# Venous Blood
dt(ABL_IV_APAP) = IVExp_APAP*IVDR_APAP;
dt(ABLV_APAP)  =  QF*CVF_APAP + QM*CVM_APAP + QK*CVK_APAP + QL*CVL_APAP + QR*CVR_APAP + QS*CVS_APAP - QC*CV_APAP + dt(ABL_IV_APAP);

# Arterial Blood
dt(ABLA_APAP) = QC*(CV_APAP - CA_APAP);

# Fat
dt(AF_APAP) = QF*(CA_APAP - CVF_APAP);

# Muscle
dt(AM_APAP) = QM*(CA_APAP - CVM_APAP);

# Kidney
dt(AKE_APAP) = CLR_APAP*CA_APAP; # APAP Kidney Elimination
dt(AK_APAP)  = QK*(CA_APAP - CVK_APAP) - dt(AKE_APAP);

# Rapidly Perfused
dt(AR_APAP) = QR*(CA_APAP - CVR_APAP);

# Slowly Perfused
dt(AS_APAP) = QS*(CA_APAP - CVS_APAP);

# Urine
dt(AU_APAP) = dt(AKE_APAP);

#AS
#==

# liver
dt(CH_AS_to_CL_AS) = Vmax_AS*CH_AS/(Km_AS + CH_AS);
dt(CH_AS) = dt(CL_APAP_to_AS_SULT) - dt(CH_AS_to_CL_AS);
dt(AL_AS) = QL*(CA_AS - CVL_AS) + dt(CH_AS_to_CL_AS);

# fat
dt(AF_AS) = QF*(CA_AS - CVF_AS);

# muscle
dt(AM_AS) = QM*(CA_AS - CVM_AS);

# rapidly perfused
dt(AR_AS) = QR*(CA_AS - CVR_AS);

# slowly perfused
dt(AS_AS) = QS*(CA_AS - CVS_AS);

# venous blood
dt(ABLV_AS) = QK*CVK_AS + QL*CVL_AS + QF*CVF_AS + QM*CVM_AS + QR*CVR_AS + QS*CVS_AS - QC*CV_AS;

# arterial blood
dt(ABLA_AS) = QC*(CV_AS - CA_AS);

# kidney
dt(AKE_AS) = CLR_AS*CA_AS; # AS kidney elimination
dt(AK_AS) = QK*(CA_AS - CVK_AS) - dt(AKE_AS);

# Urine
dt(AU_AS) = dt(AKE_AS);

#AG
#==

# liver
dt(CH_AG_to_CL_AG) = Vmax_AG*CH_AG/(Km_AG + CH_AG);
dt(CH_AG) = dt(CL_APAP_to_AG_UGT) - dt(CH_AG_to_CL_AG);
dt(AL_AG) = QL*(CA_AG - CVL_AG) + dt(CH_AG_to_CL_AG);

# fat
dt(AF_AG) = QF*(CA_AG - CVF_AG);

# fat
dt(AM_AG) = QM*(CA_AG - CVM_AG);

# rapidly perfused
dt(AR_AG) = QR*(CA_AG - CVR_AG);

# slowly perfused
dt(AS_AG) = QS*(CA_AG - CVS_AG);

# venous blood
dt(ABLV_AG) = QK*CVK_AG + QL*CVL_AG + QF*CVF_AG + QM*CVM_AG + QR*CVR_AG + QS*CVS_AG  - QC*CV_AG;

# arterial blood
dt(ABLA_AG) = QC*(CV_AG - CA_AG);

# kidney
dt(AKE_AG) = CLR_AG*CA_AG; # AS kidney elimination
dt(AK_AG) = QK*(CA_AG - CVK_AG) - dt(AKE_AG);

# Urine
dt(AU_AG) = dt(AKE_AG);



};
#endregion

#-----------------------------------------------------------------------
#                       Calculate the Model Outputs
#-----------------------------------------------------------------------
#region
CalcOutputs {
CPL_APAP_mcmolL = CPL_APAP; CPL_APAP_mcgL = CPL_APAP*MW_APAP;
CPL_AG_mcmolL = CPL_AG; CPL_AG_mcgL = CPL_AG*MW_AG;
CPL_AS_mcmolL = CPL_AS; CPL_AS_mcgL = CPL_AS*MW_AS;
CL_APAP_mcmolL = CL_APAP; CL_APAP_mcgL = CL_APAP*MW_APAP;

CU_APAP_mcg = AU_APAP*MW_APAP;
CU_AG_mcg = AU_AG*MW_AG;
CU_AS_mcg = AU_AS*MW_AS;
f_abs = AST_to_Gut_APAP/true_dose;

lnCPL_APAP_mcgL = (CPL_APAP_mcgL > 0 ? log(CPL_APAP_mcgL):-20.); # APAP in Plasma
lnCPL_AG_mcgL = (CPL_AG_mcgL > 0 ? log(CPL_AG_mcgL):-20.); # AG in Plasma
lnCPL_AS_mcgL = (CPL_AS_mcgL > 0 ? log(CPL_AS_mcgL):-20.); # AS in Plasma
lnCU_APAP_mcg = (CU_APAP_mcg > 0 ? log(CU_APAP_mcg):-20.); # APAP in Urine
lnCU_AG_mcg = (CU_AG_mcg > 0 ? log(CU_AG_mcg):-20.); # AG in Urine
lnCU_AS_mcg = (CU_AS_mcg > 0 ? log(CU_AS_mcg):-20.); # AS in Urine
lnf_abs = (f_abs > 0 ? log(f_abs): -20);  

# Sampled error from measured data points
Verr_lnCPL_APAP_mcmolL=Verr_lnCPL_APAP_mcmolL; 
Verr_lnCPL_APAP_mcgL=Verr_lnCPL_APAP_mcgL;
Verr_lnCPL_AG_mcmolL=Verr_lnCPL_AG_mcmolL; 
Verr_lnCPL_AG_mcgL=Verr_lnCPL_AG_mcgL;
Verr_lnCPL_AS_mcmolL=Verr_lnCPL_AS_mcmolL; 
Verr_lnCPL_AS_mcgL=Verr_lnCPL_AS_mcgL;
   
Verr_lnCU_APAP_mcg=Verr_lnCU_APAP_mcg;
Verr_lnCU_AG_mcg=Verr_lnCU_AG_mcg;
Verr_lnCU_AS_mcg=Verr_lnCU_AS_mcg;
}
End.