Chapter 10 Model library

10.1 PK section

10.1.1 1cpt_fo

Description: One-compartment PK model with first-order absorption and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - CL/VC*A_CENTRAL

10.1.2 1cpt_fo_lag

Description: One-compartment PK model with first-order absorption (+ lag time) and linear elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - CL/VC*A_CENTRAL

10.1.3 1cpt_fo_lag_mixed

Description: One-compartment PK model with first-order absorption (+ lag time) and mixed elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)

10.1.4 1cpt_fo_lag_mm

Description: One-compartment PK model with first-order absorption (+ lag time) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)

10.1.5 1cpt_fo_mixed

Description: One-compartment PK model with first-order absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)

10.1.6 1cpt_fo_mm

Description: One-compartment PK model with first-order absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)

10.1.7 1cpt_fo_transit

Description: One-compartment PK model with first-order absorption (+ transit compartments) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - CL/VC*A_CENTRAL

10.1.8 1cpt_fo_transit_mixed

Description: One-compartment PK model with first-order absorption (+ transit compartments) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)

10.1.9 1cpt_fo_transit_mm

Description: One-compartment PK model with first-order absorption (+ transit compartments) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)

10.1.10 1cpt_mmabs

Description: One-compartment PK model with Michaelis-Menten absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS - CL/VC*A_CENTRAL

10.1.11 1cpt_mmabs_mixed

Description: One-compartment PK model with Michaelis-Menten absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)

10.1.12 1cpt_mmabs_mm

Description: One-compartment PK model with Michaelis-Menten absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)

10.1.13 1cpt_weibull

Description: One-compartment PK model with Weibull absorption (GAM) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
CL	3.0	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - CL/VC*A_CENTRAL

10.1.14 1cpt_weibull_double

Description: One-compartment PK model with double Weibull absorption (GAM1, GAM2) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
CL	3.0	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - CL/VC*A_CENTRAL

10.1.15 1cpt_weibull_double_mixed

Description: One-compartment PK model with double Weibull absorption (GAM1, GAM2) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
CL	3.0	Clearance	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)

10.1.16 1cpt_weibull_double_mm

Description: One-compartment PK model with double Weibull absorption (GAM1, GAM2) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)

10.1.17 1cpt_weibull_mixed

Description: One-compartment PK model with Weibull absorption (GAM) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
CL	3.0	Clearance	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)

10.1.18 1cpt_weibull_mm

Description: One-compartment PK model with Weibull absorption (GAM) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)

10.1.19 1cpt_weibull_original

Description: One-compartment PK model with Weibull absorption (TAU, SH) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - CL/VC*A_CENTRAL

10.1.20 1cpt_weibull_original_mixed

Description: One-compartment PK model with Weibull absorption (TAU, SH) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)

10.1.21 1cpt_weibull_original_mm

Description: One-compartment PK model with Weibull absorption (TAU, SH) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)

10.1.22 1cpt_zo

Description: One-compartment PK model with zero-order absorption and linear elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h

ODEs:

d/dt(A_CENTRAL)=-CL/VC*A_CENTRAL

10.1.23 1cpt_zo_mixed

Description: One-compartment PK model with zero-order absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_CENTRAL)=-(VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)

10.1.24 1cpt_zo_mm

Description: One-compartment PK model with zero-order absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_CENTRAL)=-VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)

10.1.25 2cpt_fo

Description: Two-compartment PK model with first-order absorption and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.26 2cpt_fo_lag

Description: Two-compartment PK model with first-order absorption (+ lag time) and linear elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.27 2cpt_fo_lag_mixed

Description: Two-compartment PK model with first-order absorption (+ lag time) and mixed elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.28 2cpt_fo_lag_mm

Description: Two-compartment PK model with first-order absorption (+ lag time) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.29 2cpt_fo_mixed

Description: Two-compartment PK model with first-order absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.30 2cpt_fo_mm

Description: Two-compartment PK model with first-order absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.31 2cpt_fo_transit

Description: Two-compartment PK model with first-order absorption (+ transit compartments) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.32 2cpt_fo_transit_mixed

Description: Two-compartment PK model with first-order absorption (+ transit compartments) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.33 2cpt_fo_transit_mm

Description: Two-compartment PK model with first-order absorption (+ transit compartments) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.34 2cpt_mmabs

Description: Two-compartment PK model with Michaelis-Menten absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.35 2cpt_mmabs_mixed

Description: Two-compartment PK model with Michaelis-Menten absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.36 2cpt_mmabs_mm

Description: Two-compartment PK model with Michaelis-Menten absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.37 2cpt_weibull

Description: Two-compartment PK model with Weibull absorption (GAM) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
CL	3.0	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.38 2cpt_weibull_double

Description: Two-compartment PK model with double Weibull absorption (GAM1, GAM2) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
CL	3.0	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.39 2cpt_weibull_double_mixed

Description: Two-compartment PK model with double Weibull absorption (GAM1, GAM2) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
CL	3.0	Clearance	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.40 2cpt_weibull_double_mm

Description: Two-compartment PK model with double Weibull absorption (GAM1, GAM2) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.41 2cpt_weibull_mixed

Description: Two-compartment PK model with Weibull absorption (GAM) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
CL	3.0	Clearance	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.42 2cpt_weibull_mm

Description: Two-compartment PK model with Weibull absorption (GAM) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.43 2cpt_weibull_original

Description: Two-compartment PK model with Weibull absorption (TAU, SH) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.44 2cpt_weibull_original_mixed

Description: Two-compartment PK model with Weibull absorption (TAU, SH) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.45 2cpt_weibull_original_mm

Description: Two-compartment PK model with Weibull absorption (TAU, SH) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.46 2cpt_zo

Description: Two-compartment PK model with zero-order absorption and linear elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.47 2cpt_zo_mixed

Description: Two-compartment PK model with zero-order absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.48 2cpt_zo_mm

Description: Two-compartment PK model with zero-order absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL

10.1.49 3cpt_fo

Description: Three-compartment PK model with first-order absorption and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.50 3cpt_fo_lag

Description: Three-compartment PK model with first-order absorption (+ lag time) and linear elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.51 3cpt_fo_lag_mixed

Description: Three-compartment PK model with first-order absorption (+ lag time) and mixed elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.52 3cpt_fo_lag_mm

Description: Three-compartment PK model with first-order absorption (+ lag time) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
LAG	1	Lag time	h
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.53 3cpt_fo_mixed

Description: Three-compartment PK model with first-order absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.54 3cpt_fo_mm

Description: Three-compartment PK model with first-order absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.55 3cpt_fo_transit

Description: Three-compartment PK model with first-order absorption (+ transit compartments) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.56 3cpt_fo_transit_mixed

Description: Three-compartment PK model with first-order absorption (+ transit compartments) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.57 3cpt_fo_transit_mm

Description: Three-compartment PK model with first-order absorption (+ transit compartments) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
MTT	10	Mean transit time	h
KA	1	Absorption rate	1/h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

KTR=5/MTT
d/dt(A_DEPOT)=-KTR*A_DEPOT
d/dt(A_TRANS1)=KTR*A_DEPOT - KTR*A_TRANS1
d/dt(A_TRANS2)=KTR*A_TRANS1 - KTR*A_TRANS2
d/dt(A_TRANS3)=KTR*A_TRANS2 - KTR*A_TRANS3
d/dt(A_TRANS4)=KTR*A_TRANS3 - KTR*A_TRANS4
d/dt(A_ABS)=KTR*A_TRANS4 - KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.58 3cpt_mmabs

Description: Three-compartment PK model with Michaelis-Menten absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.59 3cpt_mmabs_mixed

Description: Three-compartment PK model with Michaelis-Menten absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.60 3cpt_mmabs_mm

Description: Three-compartment PK model with Michaelis-Menten absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
VMABS	50	Max. absorption rate
KMABS	50	Amount at 50% max. absorption rate	mg
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

MM=VMABS/(KMABS + A_ABS)
d/dt(A_ABS)=-MM*A_ABS
d/dt(A_CENTRAL)=MM*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.61 3cpt_weibull

Description: Three-compartment PK model with Weibull absorption (GAM) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
VP2	200.0	Volume of peripheral compartment 2	L
Q2	10.0	Inter-compartment flow 2	L/h
CL	3.0	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.62 3cpt_weibull_double

Description: Three-compartment PK model with double Weibull absorption (GAM1, GAM2) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
VP2	200.0	Volume of peripheral compartment 2	L
Q2	10.0	Inter-compartment flow 2	L/h
CL	3.0	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.63 3cpt_weibull_double_mixed

Description: Three-compartment PK model with double Weibull absorption (GAM1, GAM2) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
VP2	200.0	Volume of peripheral compartment 2	L
Q2	10.0	Inter-compartment flow 2	L/h
CL	3.0	Clearance	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.64 3cpt_weibull_double_mm

Description: Three-compartment PK model with double Weibull absorption (GAM1, GAM2) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
FR	0.5	Fraction absorbed by 1st Weibull function
KA1	2.0	Absorption rate 1	1/h
GAM1	0.5	Weibull shape parameter 1
KA2	0.5	Absorption rate 2	1/h
GAM2	4.0	Weibull shape parameter 2
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
VP2	200.0	Volume of peripheral compartment 2	L
Q2	10.0	Inter-compartment flow 2	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1 - FR * (1-exp(-pow(KA1*TSUB,GAM1))) - (1-FR)*(1-exp(-pow(KA2*TSUB,GAM2)))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.65 3cpt_weibull_mixed

Description: Three-compartment PK model with Weibull absorption (GAM) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
VP2	200.0	Volume of peripheral compartment 2	L
Q2	10.0	Inter-compartment flow 2	L/h
CL	3.0	Clearance	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.66 3cpt_weibull_mm

Description: Three-compartment PK model with Weibull absorption (GAM) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1.0	Bioavailability
KA	1.0	Absorption rate	1/h
GAM	0.5	Weibull shape parameter
VC	10.0	Volume of central compartment	L
VP	40.0	Volume of peripheral compartment	L
Q	20.0	Inter-compartment flow	L/h
VP2	200.0	Volume of peripheral compartment 2	L
Q2	10.0	Inter-compartment flow 2	L/h
VMAX	20.0	Maximal elimination rate	mg/h
KM	5.0	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=1-exp(-pow(KA*TSUB,GAM))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.67 3cpt_weibull_original

Description: Three-compartment PK model with Weibull absorption (TAU, SH) and linear elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.68 3cpt_weibull_original_mixed

Description: Three-compartment PK model with Weibull absorption (TAU, SH) and mixed elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.69 3cpt_weibull_original_mm

Description: Three-compartment PK model with Weibull absorption (TAU, SH) and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
BIO	1	Bioavailability
TAU	5	Weibull parameter
SH	2	Weibull shape parameter
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

TSUB=t - TDOS
if (TSUB < 0) TSUB=0
WF=(SH/TAU)*pow((TSUB/TAU),(SH-1))
d/dt(A_ABS)=-WF*A_ABS
d/dt(A_CENTRAL)=WF*A_ABS + Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.70 3cpt_zo

Description: Three-compartment PK model with zero-order absorption and linear elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - CL/VC*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.71 3cpt_zo_mixed

Description: Three-compartment PK model with zero-order absorption and mixed elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
CL	3	Clearance	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - (VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM) + CL/VC*A_CENTRAL)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.1.72 3cpt_zo_mm

Description: Three-compartment PK model with zero-order absorption and Michaelis-Menten elimination

Parameter table:

Name	Value	Label	Unit
DUR	4	Duration of 0-order input	h
VC	10	Volume of central compartment	L
VP	40	Volume of peripheral compartment	L
Q	20	Inter-compartment flow	L/h
VP2	200	Volume of peripheral compartment 2	L
Q2	10	Inter-compartment flow 2	L/h
VMAX	20	Maximal elimination rate	mg/h
KM	5	Concentration at 50% max. elimination	mg/L

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL + Q2/VP2*A_PERIPHERAL2 - Q/VC*A_CENTRAL - Q2/VC*A_CENTRAL - VMAX/VC*A_CENTRAL/(A_CENTRAL/VC+KM)
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_PERIPHERAL2)=Q2/VC*A_CENTRAL - Q2/VP2*A_PERIPHERAL2

10.2 TMDD section

10.2.1 1cpt_fo_tmdd_full

Description: Full TMDD model including one-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KDEG	2.0	Degradation rate of free target	1/d
KON	50.0	Association rate	1/nM/d
KD	1.0	Dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.2 1cpt_fo_tmdd_full_cst_rtot

Description: Full TMDD model with constant receptor concentration including one-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KON	50.0	Association rate	1/nM/d
KD	1.0	Dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.3 1cpt_fo_tmdd_full_cst_rtot_ib

Description: Full TMDD model with constant receptor concentration and irreversible binding including one-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KON	50.0	Association rate	1/nM/d
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.4 1cpt_fo_tmdd_full_ib

Description: Full TMDD model with irreversible binding including one-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KDEG	2.0	Degradation rate of free target	1/d
KON	50.0	Association rate	1/nM/d
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.5 1cpt_fo_tmdd_qe

Description: Quasi-Equilibrium (QE) TMDD model including one-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KDEG	2.0	Degradation rate of free target	1/d
KD	1.0	Dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - A_RTOT - KD, 2) + 4*KD*A_CENTRAL
L=0.5*(A_CENTRAL - A_RTOT - KD + sqrt(DELTA))
d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - (CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_RTOT)=KSYN - (KINT - KDEG)*(A_CENTRAL - L) - KDEG*A_RTOT
RTOT=A_RTOT
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.6 1cpt_fo_tmdd_qss

Description: Quasi steady-state (QSS) TMDD model including one-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KDEG	2.0	Degradation rate of free target	1/d
KSS	1.0	Approximate dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - A_RTOT - KSS, 2) + 4*KSS*A_CENTRAL
L=0.5*(A_CENTRAL - A_RTOT - KSS + sqrt(DELTA))
d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - (CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_RTOT)=KSYN - (KINT - KDEG)*(A_CENTRAL - L) - KDEG*A_RTOT
RTOT=A_RTOT
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.7 1cpt_fo_tmdd_wagner

Description: Wagner TMDD model including one-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KD	1.0	Dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - RTOT - KD, 2) + 4*KD*A_CENTRAL
L=0.5*(A_CENTRAL - RTOT - KD + sqrt(DELTA))
d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS - (CL/VC - KINT)*L - KINT*A_CENTRAL
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.8 1cpt_zo_tmdd_full

Description: Full TMDD model including one-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KDEG	2e+00	Degradation rate of free target	1/d
KON	5e+01	Association rate	1/nM/d
KD	1e+00	Dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_CENTRAL)=-CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.9 1cpt_zo_tmdd_full_cst_rtot

Description: Full TMDD model with constant receptor concentration including one-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KON	5e+01	Association rate	1/nM/d
KD	1e+00	Dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_CENTRAL)=-CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.10 1cpt_zo_tmdd_full_cst_rtot_ib

Description: Full TMDD model with constant receptor concentration and irreversible binding including one-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KON	5e+01	Association rate	1/nM/d
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_CENTRAL)=-CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.11 1cpt_zo_tmdd_full_ib

Description: Full TMDD model with irreversible binding including one-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KDEG	2e+00	Degradation rate of free target	1/d
KON	5e+01	Association rate	1/nM/d
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_CENTRAL)=-CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.12 1cpt_zo_tmdd_qe

Description: Quasi-Equilibrium (QE) TMDD model including one-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KDEG	2e+00	Degradation rate of free target	1/d
KD	1e+00	Dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - A_RTOT - KD, 2) + 4*KD*A_CENTRAL
L=0.5*(A_CENTRAL - A_RTOT - KD + sqrt(DELTA))
d/dt(A_CENTRAL)=-(CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_RTOT)=KSYN - (KINT - KDEG)*(A_CENTRAL - L) - KDEG*A_RTOT
RTOT=A_RTOT
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.13 1cpt_zo_tmdd_qss

Description: Quasi steady-state (QSS) TMDD model including one-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KDEG	2e+00	Degradation rate of free target	1/d
KSS	1e+00	Approximate dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - A_RTOT - KSS, 2) + 4*KSS*A_CENTRAL
L=0.5*(A_CENTRAL - A_RTOT - KSS + sqrt(DELTA))
d/dt(A_CENTRAL)=-(CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_RTOT)=KSYN - (KINT - KDEG)*(A_CENTRAL - L) - KDEG*A_RTOT
RTOT=A_RTOT
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.14 1cpt_zo_tmdd_wagner

Description: Wagner TMDD model including one-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KD	1e+00	Dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - RTOT - KD, 2) + 4*KD*A_CENTRAL
L=0.5*(A_CENTRAL - RTOT - KD + sqrt(DELTA))
d/dt(A_CENTRAL)=-(CL/VC - KINT)*L - KINT*A_CENTRAL
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.15 2cpt_fo_tmdd_full

Description: Full TMDD model including two-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
VP	3.0	Volume of peripheral compartment	L
Q	0.5	Inter-compartment flow	L/d
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KDEG	2.0	Degradation rate of free target	1/d
KON	50.0	Association rate	1/nM/d
KD	1.0	Dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.16 2cpt_fo_tmdd_full_cst_rtot

Description: Full TMDD model with constant receptor concentration including two-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
VP	3.0	Volume of peripheral compartment	L
Q	0.5	Inter-compartment flow	L/d
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KON	50.0	Association rate	1/nM/d
KD	1.0	Dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.17 2cpt_fo_tmdd_full_cst_rtot_ib

Description: Full TMDD model with constant receptor concentration and irreversible binding including two-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
VP	3.0	Volume of peripheral compartment	L
Q	0.5	Inter-compartment flow	L/d
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KON	50.0	Association rate	1/nM/d
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.18 2cpt_fo_tmdd_full_ib

Description: Full TMDD model with irreversible binding including two-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
VP	3.0	Volume of peripheral compartment	L
Q	0.5	Inter-compartment flow	L/d
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KDEG	2.0	Degradation rate of free target	1/d
KON	50.0	Association rate	1/nM/d
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.19 2cpt_fo_tmdd_qe

Description: Quasi-Equilibrium (QE) TMDD model including two-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
VP	3.0	Volume of peripheral compartment	L
Q	0.5	Inter-compartment flow	L/d
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KDEG	2.0	Degradation rate of free target	1/d
KD	1.0	Dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - A_RTOT - KD, 2) + 4*KD*A_CENTRAL
L=0.5*(A_CENTRAL - A_RTOT - KD + sqrt(DELTA))
d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*L - (CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*L - Q/VP*A_PERIPHERAL
d/dt(A_RTOT)=KSYN - (KINT - KDEG)*(A_CENTRAL - L) - KDEG*A_RTOT
RTOT=A_RTOT
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.20 2cpt_fo_tmdd_qss

Description: Quasi steady-state (QSS) TMDD model including two-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
VP	3.0	Volume of peripheral compartment	L
Q	0.5	Inter-compartment flow	L/d
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KDEG	2.0	Degradation rate of free target	1/d
KSS	1.0	Approximate dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - A_RTOT - KSS, 2) + 4*KSS*A_CENTRAL
L=0.5*(A_CENTRAL - A_RTOT - KSS + sqrt(DELTA))
d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*L - (CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*L - Q/VP*A_PERIPHERAL
d/dt(A_RTOT)=KSYN - (KINT - KDEG)*(A_CENTRAL - L) - KDEG*A_RTOT
RTOT=A_RTOT
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.21 2cpt_fo_tmdd_wagner

Description: Wagner TMDD model including two-compartment disposition model with first-order absorption

Parameter table:

Name	Value	Label	Unit
BIO	0.6	Bioavailability
KA	0.2	Absorption rate	1/d
VC	3.0	Volume of central compartment	L
VP	3.0	Volume of peripheral compartment	L
Q	0.5	Inter-compartment flow	L/d
CL	0.5	Linear clearance	L/d
R0	20.0	Baseline target concentration	nM
KD	1.0	Dissociation constant	nM
KINT	1.0	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - RTOT - KD, 2) + 4*KD*A_CENTRAL
L=0.5*(A_CENTRAL - RTOT - KD + sqrt(DELTA))
d/dt(A_ABS)=-KA*A_ABS
d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*L - (CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*L - Q/VP*A_PERIPHERAL
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.22 2cpt_zo_tmdd_full

Description: Full TMDD model including two-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
VP	3e+00	Volume of peripheral compartment	L
Q	5e-01	Inter-compartment flow	L/d
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KDEG	2e+00	Degradation rate of free target	1/d
KON	5e+01	Association rate	1/nM/d
KD	1e+00	Dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.23 2cpt_zo_tmdd_full_cst_rtot

Description: Full TMDD model with constant receptor concentration including two-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
VP	3e+00	Volume of peripheral compartment	L
Q	5e-01	Inter-compartment flow	L/d
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KON	5e+01	Association rate	1/nM/d
KD	1e+00	Dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.24 2cpt_zo_tmdd_full_cst_rtot_ib

Description: Full TMDD model with constant receptor concentration and irreversible binding including two-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
VP	3e+00	Volume of peripheral compartment	L
Q	5e-01	Inter-compartment flow	L/d
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KON	5e+01	Association rate	1/nM/d
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.25 2cpt_zo_tmdd_full_ib

Description: Full TMDD model with irreversible binding including two-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
VP	3e+00	Volume of peripheral compartment	L
Q	5e-01	Inter-compartment flow	L/d
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KDEG	2e+00	Degradation rate of free target	1/d
KON	5e+01	Association rate	1/nM/d
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
d/dt(A_R)=KSYN - KDEG*A_R - KON*A_CENTRAL*A_R + KOFF*A_COMPLEX
d/dt(A_COMPLEX)=KON*A_CENTRAL*A_R - KOFF*A_COMPLEX - KINT*A_COMPLEX
LTOT=A_CENTRAL + A_COMPLEX
RTOT=A_R + A_COMPLEX
RO=1-A_R/RTOT
RR=A_R/R0

10.2.26 2cpt_zo_tmdd_qe

Description: Quasi-Equilibrium (QE) TMDD model including two-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
VP	3e+00	Volume of peripheral compartment	L
Q	5e-01	Inter-compartment flow	L/d
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KDEG	2e+00	Degradation rate of free target	1/d
KD	1e+00	Dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - A_RTOT - KD, 2) + 4*KD*A_CENTRAL
L=0.5*(A_CENTRAL - A_RTOT - KD + sqrt(DELTA))
d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*L - (CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*L - Q/VP*A_PERIPHERAL
d/dt(A_RTOT)=KSYN - (KINT - KDEG)*(A_CENTRAL - L) - KDEG*A_RTOT
RTOT=A_RTOT
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.27 2cpt_zo_tmdd_qss

Description: Quasi steady-state (QSS) TMDD model including two-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
VP	3e+00	Volume of peripheral compartment	L
Q	5e-01	Inter-compartment flow	L/d
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KDEG	2e+00	Degradation rate of free target	1/d
KSS	1e+00	Approximate dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - A_RTOT - KSS, 2) + 4*KSS*A_CENTRAL
L=0.5*(A_CENTRAL - A_RTOT - KSS + sqrt(DELTA))
d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*L - (CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*L - Q/VP*A_PERIPHERAL
d/dt(A_RTOT)=KSYN - (KINT - KDEG)*(A_CENTRAL - L) - KDEG*A_RTOT
RTOT=A_RTOT
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.2.28 2cpt_zo_tmdd_wagner

Description: Wagner TMDD model including two-compartment disposition model with zero-order absorption

Parameter table:

Name	Value	Label	Unit
DUR	1e-05	Duration of 0-order input	d
VC	3e+00	Volume of central compartment	L
VP	3e+00	Volume of peripheral compartment	L
Q	5e-01	Inter-compartment flow	L/d
CL	5e-01	Linear clearance	L/d
R0	2e+01	Baseline target concentration	nM
KD	1e+00	Dissociation constant	nM
KINT	1e+00	Internalization/Degradation rate of drug-target complex	1/d

ODEs:

DELTA=pow(A_CENTRAL - RTOT - KD, 2) + 4*KD*A_CENTRAL
L=0.5*(A_CENTRAL - RTOT - KD + sqrt(DELTA))
d/dt(A_CENTRAL)=Q/VP*A_PERIPHERAL - Q/VC*L - (CL/VC - KINT)*L - KINT*A_CENTRAL
d/dt(A_PERIPHERAL)=Q/VC*L - Q/VP*A_PERIPHERAL
COMPLEX=A_CENTRAL - L
R=RTOT - COMPLEX
RO=1-R/RTOT
RR=R/R0

10.3 NONMEM section

10.3.1 advan1_trans1

Description: One-compartment PK model with zero-order absorption (K, V)

Parameter table:

Name	Value
K	0.0625
V	80.0000

ODEs:

d/dt(A_CENTRAL)=-K*A_CENTRAL
d/dt(A_OUTPUT)=K*A_CENTRAL
F=A_CENTRAL/S1

10.3.2 advan1_trans2

Description: One-compartment PK model with zero-order absorption (CL, V)

Parameter table:

Name	Value
CL	5
V	80

ODEs:

d/dt(A_CENTRAL)=-CL*A_CENTRAL/V
d/dt(A_OUTPUT)=CL*A_CENTRAL/V
F=A_CENTRAL/S1

10.3.3 advan11_trans4

Description: Three-compartment PK model with zero-order absorption (CL, V1, V2, V3, Q2, Q3)

Parameter table:

Name	Value
CL	5.0
V1	80.0
V2	225.0
V3	1225.0
Q2	5.0
Q3	1.5

ODEs:

d/dt(A_CENTRAL)=Q2*A_PERIPHERAL1/V2 + Q3*A_PERIPHERAL2/V3 + (-CL/V1 - Q2/V1 - Q3/V1)*A_CENTRAL
d/dt(A_PERIPHERAL1)=-Q2*A_PERIPHERAL1/V2 + Q2*A_CENTRAL/V1
d/dt(A_PERIPHERAL2)=-Q3*A_PERIPHERAL2/V3 + Q3*A_CENTRAL/V1
d/dt(A_OUTPUT)=CL*A_CENTRAL/V1
F=A_CENTRAL/S1

10.3.4 advan12_trans4

Description: Three-compartment PK model with first-order absorption (KA, CL, V1, V2, V3, Q2, Q3)

Parameter table:

Name	Value
KA	1.0
CL	5.0
V1	80.0
V2	225.0
V3	1225.0
Q2	5.0
Q3	1.5

ODEs:

d/dt(A_DEPOT)=-KA*A_DEPOT
d/dt(A_CENTRAL)=KA*A_DEPOT + Q3*A_PERIPHERAL1/V3 + Q4*A_PERIPHERAL2/V4 + (-CL/V2 - Q3/V2 - Q4/V2)*A_CENTRAL
d/dt(A_PERIPHERAL1)=-Q3*A_PERIPHERAL1/V3 + Q3*A_CENTRAL/V2
d/dt(A_PERIPHERAL2)=-Q4*A_PERIPHERAL2/V4 + Q4*A_CENTRAL/V2
d/dt(A_OUTPUT)=CL*A_CENTRAL/V2
F=A_CENTRAL/S2

10.3.5 advan2_trans1

Description: One-compartment PK model with first-order absorption (KA, K, V)

Parameter table:

Name	Value
KA	1.000
K	0.065
V	80.000

ODEs:

d/dt(A_DEPOT)=-KA*A_DEPOT
d/dt(A_CENTRAL)=-K*A_CENTRAL + KA*A_DEPOT
d/dt(A_OUTPUT)=K*A_CENTRAL
F=A_CENTRAL/S2

10.3.6 advan2_trans2

Description: One-compartment PK model with first-order absorption (KA, CL, V)

Parameter table:

Name	Value
KA	1
CL	5
V	80

ODEs:

d/dt(A_DEPOT)=-KA*A_DEPOT
d/dt(A_CENTRAL)=-CL*A_CENTRAL/V + KA*A_DEPOT
d/dt(A_OUTPUT)=CL*A_CENTRAL/V
F=A_CENTRAL/S2

10.3.7 advan3_trans1

Description: Two-compartment PK model with zero-order absorption (K, V, K12, K21)

Parameter table:

Name	Value
K	0.0625
V	80.0000
K12	0.0500
K21	0.2000

ODEs:

d/dt(A_CENTRAL)=K21*A_PERIPHERAL + (-K - K12)*A_CENTRAL
d/dt(A_PERIPHERAL)=K12*A_CENTRAL - K21*A_PERIPHERAL
d/dt(A_OUTPUT)=K*A_CENTRAL
F=A_CENTRAL/S1

10.3.8 advan3_trans3

Description: Two-compartment PK model with zero-order absorption (CL, V, Q, VSS)

Parameter table:

Name	Value
CL	5
V	80
Q	4
VSS	300

ODEs:

d/dt(A_CENTRAL)=Q*A_PERIPHERAL/(-V + VSS) + (-CL/V - Q/V)*A_CENTRAL
d/dt(A_PERIPHERAL)=-Q*A_PERIPHERAL/(-V + VSS) + Q*A_CENTRAL/V
d/dt(A_OUTPUT)=CL*A_CENTRAL/V
F=A_CENTRAL/S1

10.3.9 advan3_trans4

Description: Two-compartment PK model with zero-order absorption (CL, V1, V2, Q)

Parameter table:

Name	Value
CL	5
V1	80
V2	20
Q	4

ODEs:

d/dt(A_CENTRAL)=Q*A_PERIPHERAL/V2 + (-CL/V1 - Q/V1)*A_CENTRAL
d/dt(A_PERIPHERAL)=-Q*A_PERIPHERAL/V2 + Q*A_CENTRAL/V1
d/dt(A_OUTPUT)=CL*A_CENTRAL/V1
F=A_CENTRAL/S1

10.3.10 advan3_trans5

Description: Two-compartment PK model with zero-order absorption (AOB, ALPHA, BETA)

Parameter table:

Name	Value
AOB	5.0
ALPHA	0.2
BETA	1.0

ODEs:

d/dt(A_CENTRAL)=(ALPHA + AOB*BETA)*A_PERIPHERAL/(AOB + 1) + (-ALPHA*BETA/K21 - ALPHA - BETA + K + K21)*A_CENTRAL
d/dt(A_PERIPHERAL)=-(ALPHA + AOB*BETA)*A_PERIPHERAL/(AOB + 1) + (ALPHA + BETA - K - K21)*A_CENTRAL
d/dt(A_OUTPUT)=ALPHA*BETA*A_CENTRAL/K21
F=A_CENTRAL/S1

10.3.11 advan4_trans1

Description: Two-compartment PK model with first-order absorption (KA, K, V, K23, K32)

Parameter table:

Name	Value
KA	1.0000
K	0.0625
V	80.0000
K23	0.0500
K32	0.2000

ODEs:

d/dt(A_DEPOT)=-KA*A_DEPOT
d/dt(A_CENTRAL)=K32*A_PERIPHERAL + KA*A_DEPOT + (-K - K23)*A_CENTRAL
d/dt(A_PERIPHERAL)=K23*A_CENTRAL - K32*A_PERIPHERAL
d/dt(A_OUTPUT)=K*A_CENTRAL
F=A_CENTRAL/S2

10.3.12 advan4_trans3

Description: Two-compartment PK model with first-order absorption (KA, CL, V, Q, VSS)

Parameter table:

Name	Value
KA	1
CL	5
V	80
Q	4
VSS	300

ODEs:

d/dt(A_DEPOT)=-KA*A_DEPOT
d/dt(A_CENTRAL)=KA*A_DEPOT + Q*A_PERIPHERAL/(-V + VSS) + (-CL/V - Q/V)*A_CENTRAL
d/dt(A_PERIPHERAL)=-Q*A_PERIPHERAL/(-V + VSS) + Q*A_CENTRAL/V
d/dt(A_OUTPUT)=CL*A_CENTRAL/V
F=A_CENTRAL/S2

10.3.13 advan4_trans4

Description: Two-compartment PK model with first-order absorption (KA, CL, V2, V3, Q)

Parameter table:

Name	Value
KA	1
CL	5
V2	80
V3	20
Q	4

ODEs:

d/dt(A_DEPOT)=-KA*A_DEPOT
d/dt(A_CENTRAL)=KA*A_DEPOT + Q*A_PERIPHERAL/V3 + (-CL/V2 - Q/V2)*A_CENTRAL
d/dt(A_PERIPHERAL)=-Q*A_PERIPHERAL/V3 + Q*A_CENTRAL/V2
d/dt(A_OUTPUT)=CL*A_CENTRAL/V2
F=A_CENTRAL/S2

10.3.14 advan4_trans5

Description: Two-compartment PK model with first-order absorption (KA, AOB, ALPHA, BETA)

Parameter table:

Name	Value
AOB	5.0
ALPHA	0.2
BETA	1.0
KA	0.5

ODEs:

d/dt(A_DEPOT)=-KA*A_DEPOT
d/dt(A_CENTRAL)=KA*A_DEPOT + (ALPHA + AOB*BETA)*A_PERIPHERAL/(AOB + 1) + (-ALPHA*BETA/K32 - ALPHA - BETA + K + K32)*A_CENTRAL
d/dt(A_PERIPHERAL)=-(ALPHA + AOB*BETA)*A_PERIPHERAL/(AOB + 1) + (ALPHA + BETA - K - K32)*A_CENTRAL
d/dt(A_OUTPUT)=ALPHA*BETA*A_CENTRAL/K32
F=A_CENTRAL/S2