WNL Classic Models

Pharmacokinetic models

Phoenix includes nineteen pharmacokinetic (PK) models. Each is available in the PK Model object.

Model	Input	Number of compartments	Parameterization	Lag time	Elimination rate
Model 1	IV-bolus	1	-	no	1st order
Model 2	IV-infusion	1	-	no	1st order
Model 3	1st order	1	-	no	1st order
Model 4	1st order	1	-	yes	1st order
Model 5	1st order	1	K10=K01	no	1st order
Model 6	1st order	1	K10=K01	yes	1st order
Model 7	IV-bolus	2	micro	no	1st order
Model 8	IV-bolus	2	macro	no	1st order
Model 9	IV-infusion	2	micro	no	1st order
Model 10	IV-infusion	2	macro	no	1st order
Model 11	1st order	2	micro	no	1st order
Model 12	1st order	2	micro	yes	1st order
Model 13	1st order	2	macro	no	1st order
Model 14	1st order	2	macro	yes	1st order
Model 15	IV-bolus plus IV-infusion	1	micro	no	1st order
Model 16	IV-bolus plus IV-infusion	2	micro	no	1st order
Model 17	IV-bolus plus IV-infusion	2	macro	no	1st order
Model 18	IV-bolus	3	macro	no	1st order
Model 19	IV-infusion	3	macro	no	1st order

Note:All models except models 15–17 accept multiple dose data.

The models shown in this section give equations for compartment 1 (central).

Model 1

One-compartment with bolus input and first-order output.

Required constants	Estimated parameters	Secondary parameters	Clearance estimated	Clearance secondary
N doses	V is the volume	AUC=D/V/K10	V	AUC
dose N	K10 is the elimination rate	K10 half-life	CL	K10 half-life
time of dose N		Cmax=D/V		Cmax
(Repeat for each dose)		CL		K10
		AUMC		AUMC
		MRT		MRT
		Vss		VSS

Model 2

One-compartment with constant IV input, first-order absorption.

where:

Required constants	Estimated parameters	Secondary parameters	Clearance estimated	Clearance secondary
N doses	V is the volume	AUC=D/V/K10	V	AUC
dose N	K10 is the elimination rate	K10 half-life	CL	K10 half-life
start time N		Cmax=C(TI)		Cmax
end time N		CL		K10
(Repeat for each dose)		AUMC		AUMC
		MRT		MRT
		Vss		VSS

Model 3

One-compartment with first-order input and output, no lag time.

Required constants	Estimated parameters	Secondary parameters	Clearance estimated	Clearance secondary
N doses	V_F	AUC=D/V/K10	V_F	AUC
dose N	K01 is the absorption rate	K01 half-life	K01	K01 half-life
time of dose N	K10 is the elimination rate	K10 half-life	CL_F	K10 half-life
(Repeat for each dose)		CL_F		K10
		Tmax=time of Cmax		Tmax
		Cmax is the max concentration		Cmax

Model 4

One-compartment with first-order input and output with lag time.

Identical to Model 3, with an additional estimated parameter: Tlag=lag time.

Model 5

One-compartment, equal first-order input and output, no lag time.

Required constants	Estimated parameters	Secondary parameters	Clearance estimated	Clearance secondary
N doses	V_F	AUC=D/V/K	V_F	AUC
dose N	K is the absorption and elimination rate	K half-life	CL_F	K half-life
time of dose N	K is the absorption and elimination rate	CL_F		K
(Repeat for each dose)		Tmax is the time of Cmax=1/K		Tmax
(Repeat for each dose)		Cmax is the max concentration		Cmax

Model 6

One-compartment, equal first-order input and output with lag time.

Identical to Model 5, with an additional estimated parameter: Tlag=lag time.

Model 7

Two-compartment with bolus input and first-order output; micro-constants as primary parameters.

where:

–ALPHA and –BETA (ALPHA > BETA) are the roots of the quadratic equation:

Required constants	Estimated parameters	Secondary parameters	Clearance estimated	Clearance secondary
N doses	V1 is Volume1	AUC=AUC=A/Alpha+B/Beta	V1	AUC
dose N	K10 is the elimination rate	K10 half-life	CL	K10 half-life
time of dose N	K12 is the transfer rate, 1 to 2	ALPHA	V2	ALPHA
(Repeat for each dose)	K21 is the transfer rate, 2 to 1	BETA	CLD2	BETA
		ALPHA half-life		ALPHA half-life
		BETA half-life		BETA half-life
		A		A
		B		B
		Cmax=D/V		Cmax
		CL		K10
		AUMC		AUMC
		MRT		MRT
		Vss		Vss
		V2		K12
		CLD2		K21

Model 8

Two-compartment with bolus input and first-order output; macro-constants as primary parameters.

As Model 7 with macroconstants as the primary (estimated) parameters. Clearance parameters are not available for Model 8.

Required constants	Estimated parameters	Secondary parameters
stripping dose	A	AUC=A/ALPHA+B/BETA	V1
N doses	B	K10 half-life	CL
dose N	ALPHA	ALPHA half-life	AUMC
time of dose N	BETA	BETA half-life	MRT
(Repeat for each dose)		K10	Vss
		K12	V2
		K21	CLD2
		Cmax

Model 9

Two-compartment with constant IV input and first-order output; micro-constants as primary parameters.

where:

–ALPHA and –BETA (ALPHA > BETA) are the roots of the quadratic equation:

Required constants	Estimated parameters	Secondary parameters	Clearance estimated	Clearance secondary
N doses	V1 is Volume1	AUC=D/V/K10	V1	AUC
dose N	K10 is the elimination rate	K10 half-life	CL	K10 half-life
start time N	K12 is the transfer rate, 1 to 2	ALPHA	V2	ALPHA
end time N	K21 is the transfer rate, 2 to 1	BETA	CLD2	BETA
(Repeat for each dose)		ALPHA half-life		ALPHA half-life
		BETA half-life		BETA half-life
		A		A
		B		B
		Cmax=C(TI)		Cmax
		CL		K10
		AUMC		AUMC
		MRT		MRT
		Vss		Vss
		V2		K12
		CLD2		K21

Model 10

Two-compartment with constant IV input and first-order output; macro-constants as primary parameters.

As Model 9 with macroconstants as the primary (estimated) parameters. Clearance parameters are not available in Model 10.

Required constants	Estimated parameters	Secondary parameters
N doses	V1	K10	Cmax
dose N	K21	K12	CL
start time N	ALPHA	K10 half-life	AUMC
end time N	BETA	AUC	MRT
(Repeat for each dose)		ALPHA half-life	Vss
		BETA half-life	V2
		A	CLD2
		B

Model 11

Two-compartment with first-order input, first-order output, no lag time and micro-constants as primary parameters.

where:

–ALPHA and –BETA (ALPHA > BETA) are the roots of the quadratic equation:

Required constants	Estimated parameters	Secondary parameters	Clearance estimated	Clearance secondary
N doses	V1_F	AUC=D/V/K10	V1_F	AUC
dose N	K01 is the absorption rate	K01 half-life	K01	K01 half-life
time of dose N	K10 is the elimination rate	K10 half-life	CL_F	K10 half-life
(Repeat for each dose)	K12 is the transfer rate, 1 to 2	ALPHA	V2_F	ALPHA
	K21 is the transfer rate, 2 to 1	BETA	CLD2_F	BETA
		ALPHA half-life		ALPHA half-life
		BETA half-life		BETA half-life
		A		A
		B		B
		CL_F		K10
		V2_F		K12
		CLD2_F		K21
		Tmax ^a		Tmax
		Cmax^a		Cmax

^aEstimated for the compiled model only.

Model 12

Two-compartment with first-order input, first-order output, lag time and micro-constants as primary parameters.

As Model 11, with an additional estimated parameter: Tlag=lag time.

Model 13

Two-compartment with first-order input, first-order output, no lag time and macro-constants as primary parameters.

As Model 11, with macroconstants as the primary (estimated) parameters. Clearance parameters are not available for Model 13.

Required constants	Estimated parameters	Secondary parameters
Stripping dose	A	K10	BETA half-life
N doses	B	K12	V1_F
dose N	K01 is the absorption rate	K21	CL_F
time of dose N	ALPHA	AUC=D/V/K10	V2_F
(Repeat for each dose)	BETA	K01 half-life	CLD2_F
	Note: C=–(A+B)	K10 half-life	Tmax ^a
		ALPHA half-life	Cmax^a

^aEstimated for the compiled model only.

Model 14

Two-compartment with first-order input, first-order output, lag time and macro-constants as primary parameters.

As Model 13, with an additional estimated parameter: Tlag=lag time.

Model 15

One-compartment with simultaneous bolus IV and constant IV infusion.

where:

Model 16

Two-compartment with simultaneous bolus IV and constant infusion input; micro constants as primary parameters.

where:

and

where:

–ALPHA and –BETA (ALPHA > BETA) are the roots of the quadratic equation:

Required constants	Estimated parameters	Secondary parameters	Clearance estimated	Clearance secondary
bolus dose	V1	K10 half-life	V1	K10 half-life
IV dose	K10	ALPHA	CL	ALPHA
length of infusion (= TI)	K12	BETA	V2	BETA
	K21	ALPHA half-life	CLD2	ALPHA half-life
		BETA half-life		BETA half-life
		A		A
		B		B
		CL		K10
		V2		K12
		CLD2		K21

Model 17

Two-compartment with simultaneous bolus IV and constant infusion input and macro constants as primary parameters.

As Model 16 with macroconstants as the primary (estimated) parameters.

Required constants	Estimated parameters	Secondary parameters
stripping dose	A	K10	BETA half-life
bolus dose	B	K12	V1
IV dose	ALPHA	K21	CL
length of infusion (= TI)	BETA	K10 half-life	V2
		ALPHA half-life	CLD2

Clearance parameters are not available in Model 17.

Model 18

Three-compartment with bolus input, first-order output; macro constants as primary parameters.

Required constants	Estimated parameters	Secondary parameters
stripping dose	A	Cmax	GAMMA half-life
N doses	B	V1	AUC
dose N	C	K21	CL
time of dose N	ALPHA	K31	AUMC
(Repeat for each dose)	BETA	K10	MRT
	GAMMA	K12	Vss
		K13	V2
		K10 half-life	CLD2
		ALPHA half-life	V3
		BETA half-life	CLD3

Clearance parameters are not available in Model 18.

Model 19

Three compartment model with constant IV infusion; macro constants as primary parameters.

where:

Required constants	Estimated parameters	Secondary parameters
N doses	V1	Cmax	K10 half-life	MRT
dose N	K21	K10	ALPHA half-life	Vss
start time of dose N	K31	K12	BETA half-life	V2
end time of dose N	ALPHA	K13	GAMMA half-life	CLD2
(Repeat for each dose)	BETA	A	AUC	V3
	GAMMA	B	CL	CLD3
		C	AUMC

A, B, and C are the zero time intercepts following an IV injection.
Clearance parameters are not available in Model 19.