Pharmacokinetic

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

Table 2: Pharmacokinetic Models
Model	Input	Number of Compartments	Parameterization	Lag Time	Elimination Rate
Model 1	IV-bolus	1		no lag	1st order
Model 2	IV-infusion	1		no lag	1st order
Model 3	1st order	1		no lag	1st order
Model 4	st order	1		yes lag	1st order
Model 5	1st order	1	K10=K01	no lag	1st order
Model 6	1st order	1	K10=K01	yes lag	1st order
Model 7	IV-bolus	2	micro	no lag	1st order
Model 8	IV-bolus	2	macro	no lag	1st order
Model 9	IV-infusion	2	micro	no lag	1st order
Model 10	IV-infusion	2	macro	no lag	1st order
Model 11	1st order	2	micro	no lag	1st order
Model 12	1st order	2	micro	yes lag	1st order
Model 13	1st order	2	macro	no lag	1st order
Model 14	1st order	2	macro	yes lag	1st order
Model 15	IV-bolus + IV-infusion	1	micro	no lag	1st order
Model 16	IV-bolus + IV-infusion	2	micro	no lag	1st order
Model 17	IV-bolus + IV-infusion	2	macro	no lag	1st order
Model 18	IV-bolus	3	macro	no lag	1st order
Model 19	IV-infusion	3	macro	no lag	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 IV-bolus input and first-order output (1cp bolus).

mdllib_pk1

Phoenix_UserDocs_Maximum_Likelihood_Models_image2830

Required constants: N doses, dose N, time of dose N (Repeat for each dose)

Estimated parameters: V (volume), K10 (elimination rate)

Secondary parameters: AUC=D/V/K10, K10 half-life, Cmax=D/V, AUMC, MRT, Vss

Clearance estimated: V, CL

Clearance secondary: AUC, K10 half-life, Cmax, AUMC, MRT, VSS

Model 2

One-compartment with constant IV input, first-order absorption (1cp infus).

mdllib_pk2

Phoenix_UserDocs_Maximum_Likelihood_Models_image2834

where:

Tinf = infusion length

t* = t – Tinf for t > Tinf

t* = 0 for t £ Tinf

Required constants: N doses, dose N, start time N, end time N (Repeat for each dose)

Estimated parameters: V (volume), K10 (elimination rate)

Secondary parameters: AUC=D/V/K10, K10 half-life, Cmax=C(Tinf), CL, AUMC, MRT, Vss

Clearance estimated: V, CL

Clearance secondary: AUC, K10 half-life, Cmax, K10, AUMC, MRT, VSS

Model 3

One-compartment with first-order input and output, no lag time (1cp extravascular).

mdllib_pk3

Phoenix_UserDocs_Maximum_Likelihood_Models_image2838

Required constants: N doses, dose N, time of dose N (Repeat for each dose)

Estimated parameters: V_F, K01 (absorption rate), K10 (elimination rate)

Secondary parameters: AUC=D/V/K10, K01 half-life, K10 half-life, CL_F, Tmax=time of Cmax = [ln(K01/K10)] / [(K01 – K10)]

Clearance estimated: V_F, K01, CL_F

Clearance secondary: AUC, K01 half-life, K10 half-life, K10, Tmax, Cmax

Model 4

One-compartment with first-order input and output with lag time (1cp xvas lag).

Identical to Model 3, with an additional estimated parameter: Tlag=lag time. In the Model 3 equation, substitute (t - Tlag) for t.

Model 5

One-compartment, equal first-order input and output, no lag time (1cp k01=ke).

mdllib_pk5

Phoenix_UserDocs_Maximum_Likelihood_Models_image2842

Required constants: N doses, dose N, time of dose N (Repeat for each dose)

Estimated parameters: V_F, K (absorption and elimination rate)

Secondary parameters: AUC=D/V/K, K half-life, CL_F, Tmax=time of Cmax=1/K

Clearance estimated: V_F, CL_F

Clearance secondary: AUC, K half-life, K, Tmax, Cmax

Model 6

One-compartment, equal first-order input and output with lag time (1cp k01=ke lag).

Identical to Model 5, with an additional estimated parameter: Tlag=lag time. In the Model 5 equation, substitute (t - Tlag) for t.

Model 7

Two-compartment with bolus input and first-order output; micro-constants as primary parameters (2cp micro bolus).

mdllib_pk7

Phoenix_UserDocs_Maximum_Likelihood_Models_image2846

where:

Phoenix_UserDocs_Maximum_Likelihood_Models_image2848

–a and –b (a > b) are the roots of the quadratic equation:

r² + (K12 + K21 + K10)r + K21(K10) = 0

Required constants: N doses, dose N, time of dose N, (Repeat for each dose)

Estimated parameters: V1 is Volume1, K10 (elimination rate), K12 (transfer rate, 1 to 2), K21 (transfer rate, 2 to 1)

Secondary parameters: AUC=A/Alpha+B/Beta, K01 half-life, Alpha, Beta, Alpha half-life, Beta half-life, A, B, Cmax=D/V, CL, AUMC, MRT, Vss, V2, CLD2

Clearance estimated: V1, CL, V2, CLD2

Clearance secondary: AUC, K10 half-life, Alpha, Beta, Alpha half-life, Beta half-life, A, B, Cmax, K10, AUMC, MRT, Vss, K12, K21

Model 8

Two-compartment with bolus input and first-order output; macro-constants as primary parameters (2cp macro bolus).

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

Required constants: Stripping dose, N doses, dose N, time of dose N (Repeat for each dose)

Estimated parameters: A, B, Alpha, Beta

Secondary parameters: AUC=A/Alpha+B/Beta, K10 half-life, Alpha half-life, Beta half-life, K10, K12, K21, Cmax, V1, CL, AUMC, MRT, Vss, V2, CLD2

Model 9

Two-compartment with constant IV input and first-order output; micro-constants as primary parameters (2cp micro infus).

mdllib_pk9

Phoenix_UserDocs_Maximum_Likelihood_Models_image2852

where:

Tinf = infusion length

t* = t – Tinf for t > Tinf

t* = 0 for t £ Tinf

Phoenix_UserDocs_Maximum_Likelihood_Models_image2854

–a and –b (a > b) are the roots of the quadratic equation:

r² + (K12 + K21 + K10)r + K21(K10) = 0

Required constants: N doses, dose N, start time N, end time N,

Estimated parameters: V1 is Volume1, K10 (elimination rate), K12 (transfer rate, 1 to 2), K21 (transfer rate, 2 to 1) (Repeat for each dose)

Secondary parameters: AUC=D/V/K10, K10 half-life, Alpha, Beta, Alpha half-life, Beta half-life, A, B, Cmax=C(T_inf), AUMC, MRT, Vss, V2, CLD2

Clearance estimated: V1, CL, V2, CLD2,

Clearance secondary: AUC, K10 half-life, Alpha, Beta, Alpha half-life, Beta half-life, A, B, Cmax, AUMC, MRT, Vss, K12, K21

Model 10

Two-compartment with constant IV input and first-order output; macro-constants as primary parameters (2cp macro infus).

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

Required constants: N doses, dose N, start time N, end time N (Repeat for each dose)

Estimated parameters: V1, K21, Alpha, Beta

Secondary parameters: K10, K12, K10 half-life, AUC, Alpha half-life, Beta half-life, A, B, Cmax, CL, AUMC, MRT, Vss, V2, CLD2

Model 11

Two-compartment with first-order input, first-order output, no lag time and micro-constants as primary parameters (2cp micro xvas).

mdllib_pk11

Phoenix_UserDocs_Maximum_Likelihood_Models_image2858

where:

Phoenix_UserDocs_Maximum_Likelihood_Models_image2860

–a and –b (a > b) are the roots of the quadratic equation:

r² + (K12 + K21 + K10)r + K21(K10) = 0

Required constants: N doses, dose N, time of dose N (Repeat for each dose)

Estimated parameters: V1_F, K01 (absorption rate), K10 (elimination rate), K12 (transfer rate, 1 to 2). K21 (transfer rate, 2 to 1)

Secondary parameters: AUC=D/V/K10, K01 half-life, K10 half-life, Alpha, Beta, Alpha half-life, Beta half-life, A, B, CL_F, V2_F, CLD2_F, Tmax^a, Cmax^a

Clearance estimated: V1_F, K01, CL_F, V2_F, CLD2_F

Clearance secondary: AUC, K01 half-life, K10 half-life, Alpha, Beta, Alpha half-life, Beta half-life, A, B, K10, K12, K21, Tmax, 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 (2cp micro xvas lag).

As Model 11, with an additional estimated parameter: Tlag=lag time. In the Model 11 equation, substitute (t - Tlag) for t.

Model 13

Two-compartment with first-order input, first-order output, no lag time and macro-constants as primary parameters (2cp macro xvas).

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

Required constants: Stripping dose, N doses, dose N, time of dose N (Repeat for each dose)

Estimated parameters: A, B, K01 (absorption rate), Alpha, Beta, Note: C=–(A+B)

Secondary parameters: K10, K12, K21, AUC=D/V/K10, K01 half-life, K10 half-life, Alpha half-life, Beta half-life, V1_F, CL_F, V2_F, CLD2_F, Tmax^a, 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 (2cp macro xvas lag).

As Model 13, with an additional estimated parameter: Tlag=lag time. In the Model 13 equation, substitute (t - Tlag) for t.

Model 15

One-compartment with simultaneous bolus IV and constant IV infusion (1cp micro bol+inf).

mdllib_pk15

Phoenix_UserDocs_Maximum_Likelihood_Models_image2864

Phoenix_UserDocs_Maximum_Likelihood_Models_image2866

Phoenix_UserDocs_Maximum_Likelihood_Models_image2868

where:

Tinf = infusion length

t* = t – Tinf for t > Tinf

t* = 0 for t £ Tinf

Model 16

Two-compartment with simultaneous bolus IV and constant infusion input; micro constants as primary parameters (2cp micro bol+inf).

mdllib_pk16

Phoenix_UserDocs_Maximum_Likelihood_Models_image2872

where:

Phoenix_UserDocs_Maximum_Likelihood_Models_image2874

and

Phoenix_UserDocs_Maximum_Likelihood_Models_image2876

where:

Phoenix_UserDocs_Maximum_Likelihood_Models_image2878

Tinf = infusion length

t* = t – Tinf for t > Tinf

t* = 0 for t £ Tinf

–a and –b (a > b) are the roots of the quadratic equation:

r² + (K12 + K21 + K10)r + K21(K10) = 0

Phoenix_UserDocs_Maximum_Likelihood_Models_image2880

Required constants: Bolus dose, IV dose, length of infusion (= Tinf)

Estimated parameters: V1, K10, K12, K21

Secondary parameters: K10 half-life, Alpha, Beta, Alpha half-life, Beta half-life, A, B, CL, V2, CLD2

Clearance estimated: V1, CL, V2, CLD2

Clearance secondary: K10 half-life, Alpha, Beta, Alpha half-life, Beta half-life, A, B, K10, K12, K21

Model 17

Two-compartment with simultaneous bolus IV and constant infusion input and macro constants as primary parameters (2cp macro bol_inf).

As Model 10 with macroconstants as the primary (estimated) parameters.

Required constants: Stripping dose, bolus dose, IV dose, length of infusion (= Tinf)

Estimated parameters: A, B, Alpha, Beta

Secondary parameters: K10, K12, K21, K10 half-life, Alpha half-life, Beta half-life, V1, CL, V2, CLD2

Clearance parameters are not available in Model 17.

Model 18

Three-compartment with bolus input, first-order output; macro constants as primary parameters (3cp macro bolus).

mdllib_pk18

Phoenix_UserDocs_Maximum_Likelihood_Models_image2884

Required constants: Stripping dose, N doses, dose N, time of dose N (Repeat for each dose)

Estimated parameters: A, B, C, Alpha, Beta, Gamma

Secondary parameters: Cmax, V1, K21, K31, K10, K12, K13, K10 half-life, Alpha half-life, Beta half-life, Gamma half-life, AUC, CL, AUMC, MRT, Vss, V2, CLD2, V3, CLD3

Clearance parameters are not available in Model 18.

Model 19

Three compartment model with constant IV infusion; macro constants as primary parameters (3cp macro infus).

mdllib_pk19

Phoenix_UserDocs_Maximum_Likelihood_Models_image2888

where:

Phoenix_UserDocs_Maximum_Likelihood_Models_image2890

Tinf = infusion length

t* = t – Tinf for t > Tinf

t* = 0 for t £ Tinf

Required constants: N doses, dose N, start time and end time of dose N (Repeat for each dose)

Estimated parameters: V1, K21, K31, Alpha, Beta, Gamma

Secondary parameters: Cmax, K10, K12, K13, A, B, C, K10 half-life, Alpha half-life, Beta half-life, Gamma half-life, AUC, CL, AUMC, MRT, Vss, V2, CLD2, V3, CLD3

A, B, and C are the zero time intercepts following an IV injection.

Clearance parameters are not available in Model 19.