A Physiologically Based Pharmacokinetic Model of Amiodarone and its Metabolite Desethylamiodarone in Rats: Pooled Analysis of Published Data

Abstract

Background and Objective

Amiodarone (AMD) is one of the most effective drugs for rhythm control of atrial fibrillation. The use of AMD is also associated with adverse effects in multiple tissues. Both the parent compound and its major metabolite desethylamiodarone (DEA) contribute to the drug’s therapeutic and toxic action. The present study aimed to build a whole-body physiologically based pharmacokinetic (PBPK) model for AMD and DEA in rats.

Methods

Pharmacokinetic data from multiple studies were collected. Some of the data were pooled together to develop the PBPK model; others were used to evaluate the model. Development of the model also involved in vitro to in vivo extrapolation based on in vitro metabolism data.

Results

The final model consisted of 11 tissue compartments, including therapeutic target organs and those to which AMD and DEA may be harmful. Model simulations were in good agreement with the observed time courses of the drug–metabolite pair in tissues, under various dosing scenarios. The key pharmacokinetic properties of AMD, such as extensive tissue distribution, substantial storage in the fat tissue, and long half-lives in many tissues, were closely reflected.

Conclusion

The developed PBPK model can be regarded as the first step towards a PBPK–pharmacodynamic model that can used to mechanistically evaluate and explain the high adverse event rate and potentially to determine which factors are the primary drives for experiencing an adverse event.

Appendix

1.1 I. Model parameter abbreviations

Abbreviations	Parameter
QC	Cardiac output
Q Tissue	Blood flow to tissue
V VB	Volume of venous blood
V AB	Volume of arterial blood
V Tissue	Volume of tissue
V VTissueC	Fraction of vascular space in tissue
PS Tissue	Permeability-surface area product between vascular space and extravascular space in tissue
F u,Tissue	Fraction of unbound drug in tissue
F u,Bld	Fraction of unbound drug in blood
F u,plasma	Fraction of unbound drug in plasma
F u,mic	Fraction of unbound drug in liver microsomes
K a,Tissue	First-order association rate constant for drug binding to ‘deep tissue’ of tissue
K d,Tissue	First-order dissociation rate constant for drug binding to ‘deep tissue’ of tissue
K BP	Blood to plasma concentration ratio
V max,LivMet,AMD	Maximum metabolic rate of AMD to DEA in liver
K M,LivMet,AMD	AMD concentration at which half of V max,LivMet,AMD is achieved
CL OthMet,AMD	Clearance of unbound AMD mediated by conversion to other metabolites rather than DEA
CL Met,DEA	Clearance of unbound DEA mediated by metabolism
A VTissue	Drug amount in vascular space of tissue
A Tissue	Drug amount in tissue extravascular space except in ‘deep tissue’
A TissueDeep	Drug amount in ‘deep tissue’ of tissue extravascular space
A AB	Drug amount in arterial blood
A VB	Drug amount in venous blood
C VTissue	Drug concentration in vascular space of tissue
C Tissue	Drug concentration in tissue extravascular space except in ‘deep tissue’
C VMix	Drug concentration in mixed venous blood
C V	Drug concentration in venous blood
C plasma	Drug concentration in venous plasma
C A	Drug concentration in arterial blood
DoseRate	Dosing rate

1.2 II. Equations

Since model equations describing drug disposition in different tissue compartments are very similar, only the equations for liver, arterial blood pool and venous blood pool were presented.

1.2.1 A. Liver

1. For AMD

Liver vascular space:

$$\begin{aligned} \frac{{{\text{d}}A_{\text{VLiv,AMD}} }}{{{\text{d}}t}} =\, Q_{\text{Liv}} \times C_{\text{A,AMD}} + Q_{\text{Sp}} \times C_{\text{VSp,AMD}} - (Q_{\text{Liv}} + Q_{\text{Sp}} )\times C_{\text{VLiv,AMD}} + {\text{PS}}_{\text{Liv,AMD}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\; \times (C_{\text{Liv,AMD}} \times F_{\text{u,Liv,AMD}} - C_{\text{VLiv,AMD}} \times F_{\text{u,Bld,AMD}} ) \hfill \\ \end{aligned}$$

(3)

$$C_{\text{VLiv,AMD}} = \frac{{A_{\text{VLiv,AMD}} }}{{V_{\text{Liv}} \times V_{\text{VLivC}} }}$$

(4)

Liver extravascular space:

$$\begin{aligned} \frac{{{\text{d}}A_{\text{Liv,AMD}} }}{{{\text{d}}t}} = {\text{PS}}_{\text{Liv,AMD}} \times ( - C_{\text{Liv,AMD}} \times F_{\text{u,Liv,AMD}} + C_{\text{VLiv,AMD}} \times F_{\text{u,Bld,AMD}} )\hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; - \frac{{V_{\text{max,LivMet,AMD}} \times C_{\text{Liv,AMD}} \times F_{\text{u,Liv,AMD}} }}{{K_{\text{M,LivMet,AMD}} \times F_{\text{u,mic,AMD}} + C_{\text{Liv,AMD}} \times F_{\text{u,Liv,AMD}} }} - {\text{CL}}_{\text{OthMet,AMD}} \times C_{\text{Liv,AMD}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \times F_{\text{u,Liv,AMD}} - K_{\text{a,Liv,AMD}} \times A_{\text{Liv,AMD}} \times F_{\text{u,Liv,AMD}} + K_{\text{d,Liv,AMD}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \times A_{\text{LivDeep,AMD}} \hfill \\ \end{aligned}$$

(5)

$$C_{\text{Liv,AMD}} = \frac{{A_{\text{Liv,AMD}} }}{{V_{\text{Liv}} \times (1 - V_{\text{VLivC}} )}}$$

(6)

$$\frac{{{\text{d}}A_{\text{LivDeep,AMD}} }}{{{\text{d}}t}} = K_{\text{a,Liv,AMD}} \times A_{\text{Liv,AMD}} \times F_{\text{u,Liv,AMD}} - K_{\text{d,Liv,AMD}} \times A_{\text{LivDeep,AMD}}$$

(7)

$$C_{\text{LivExtraV,AMD}} = \frac{{A_{\text{Liv,AMD}} + A_{\text{LivDeep,AMD}} }}{{V_{\text{Liv}} \times (1 - V_{\text{VLivC}} )}}$$

(8)

Equation 3 describes the changing rate of AMD amount in vascular space of liver; Eq. 5 describes the changing rate of AMD amount in extravascular space of liver except in ‘deep tissue’; Eq. 7 describes the changing rate of AMD amount in ‘deep tissue’ of liver; Eq. 8 describes the AMD concentration in extravascular space of liver.

2. For DEA

Liver vascular space:

$$\begin{aligned} \frac{{{\text{d}}A_{\text{VLiv,DEA}} }}{{{\text{d}}t}} = (Q_{\text{Liv}} \times C_{\text{A,DEA}} + Q_{\text{Sp}} \times C_{\text{VSp,DEA}} - (Q_{\text{Liv}} + Q_{\text{Sp}} )\times C_{\text{VLiv,DEA}} + {\text{PS}}_{\text{Liv,DEA}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \times (C_{\text{Liv,DEA}} \times F_{\text{u,Liv,DEA}} - C_{\text{VLiv,DEA}} \times F_{\text{u,Bld,DEA}} ) \hfill \\ \end{aligned}$$

(9)

$$C_{\text{VLiv,DEA}} = \frac{{A_{\text{VLiv,DEA}} }}{{V_{\text{Liv}} \times V_{\text{VLivC}} }}$$

(10)

Liver extravascular space:

$$\begin{aligned} \frac{{{\text{d}}A_{{{\text{Liv}},{\text{DEA}}}} }}{{{\text{d}}t}} = {\text{PS}}_{{{\text{Liv}},{\text{DEA}}}} \times \left( { - C_{{{\text{Liv}},{\text{DEA}}}} \times F_{{{\text{u}},{\text{Liv}},{\text{DEA}}}} + C_{{{\text{VLiv}},{\text{DEA}}}} \times F_{{{\text{u}},{\text{Bld}},{\text{DEA}}}} } \right) \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; + \frac{{V_{{{ \hbox{max} },{\text{LivMet}},{\text{AMD}}}} \times C_{{{\text{Liv}},{\text{AMD}}}} \times F_{{{\text{u}},{\text{Liv}},{\text{AMD}}}} }}{{K_{{{\text{M}},{\text{LivMet}},{\text{AMD}}}} \times F_{{{\text{u}},{\text{mic}},{\text{AMD}}}} + C_{{{\text{Liv}},{\text{AMD}}}} \times F_{{{\text{u}},{\text{Liv}},{\text{AMD}}}} }} - {\text{CL}}_{{{\text{Met}},{\text{DEA}}}} \times C_{{{\text{Liv}},{\text{DEA}}}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \times F_{{{\text{u}},{\text{Liv}},{\text{DEA}}}} - K_{{{\text{a}},{\text{Liv}},{\text{DEA}}}} \times A_{{{\text{Liv}},{\text{DEA}}}} \times F_{{{\text{u}},{\text{Liv}},{\text{DEA}}}} + K_{{{\text{d}},{\text{Liv}},{\text{DEA}}}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\,\; \times A_{{{\text{LivDeep}},{\text{DEA}}}} \hfill \\ \end{aligned}$$

(11)

$$C_{{{\text{Liv}},{\text{DEA}}}} = \frac{{A_{{{\text{Liv}},{\text{DEA}}}} }}{{V_{\text{Liv}} \times (1 - V_{\text{VLivC}} )}}$$

(12)

$$\frac{{{\text{d}}A_{{{\text{LivDeep}},{\text{DEA}}}} }}{{{\text{d}}t}} = K_{{{\text{a}},{\text{Liv}},{\text{DEA}}}} \times A_{{{\text{Liv}},{\text{DEA}}}} \times F_{{{\text{u}},{\text{Liv}},{\text{DEA}}}} - K_{{{\text{d}},{\text{Liv}},{\text{DEA}}}} \times A_{{{\text{LivDeep}},{\text{DEA}}}}$$

(13)

$$C_{{{\text{LivExtraV}},{\text{DEA}}}} = \frac{{A_{{{\text{Liv}},{\text{DEA}}}} + A_{{{\text{LivDeep}},{\text{DEA}}}} }}{{V_{\text{Liv}} \times (1 - V_{\text{VLivC}} )}}$$

(14)

1.2.2 B. Venous blood

1. For AMD

$$\begin{aligned} C_{{{\text{VMix}},{\text{AMD}}}} = ((Q_{\text{Liv}} + Q_{\text{Sp}} ) \times C_{{{\text{VLiv}},{\text{AMD}}}} + Q_{\text{Kid}} \times C_{{{\text{VKid}},{\text{AMD}}}} + Q_{\text{H}} \times C_{{{\text{VH}},{\text{AMD}}}} + Q_{\text{Br}} \times C_{{{\text{VBr}},{\text{AMD}}}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; + Q_{\text{Thy}} \times C_{{{\text{VThy}},{\text{AMD}}}} + Q_{\text{F}} \times C_{{{\text{VF}},{\text{AMD}}}} + Q_{\text{Sk}} \times C_{{{\text{VSk}},{\text{AMD}}}} + Q_{\text{Re}} \times C_{{{\text{VRe}},{\text{AMD}}}} ) \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\, \times \frac{1}{QC} \hfill \\ \end{aligned}$$

(15)

$$\frac{{dA_{{{\text{VB}},{\text{AMD}}}} }}{dt} = QC \times (C_{{{\text{VMix}},{\text{AMD}}}} - C_{{{\text{V}},{\text{AMD}}}} ) + DoseRate_{AMD}$$

(16)

$$C_{{{\text{V}},{\text{AMD}}}} = \frac{{A_{{{\text{VB}},{\text{AMD}}}} }}{{V_{\text{VB}} }}$$

(17)

$$C_{\text{Plasma,AMD}} = \frac{{C_{\text{V,AMD}} }}{{K_{\text{BP,AMD}} }}$$

(18)

Equation 16 describes the changing rate of AMD amount in venous blood.

2. For DEA

$$\begin{aligned} C_{{{\text{VMix}},{\text{DEA}}}} = ((Q_{\text{Liv}} + Q_{\text{Sp}} ) \times C_{{{\text{VLiv}},{\text{DEA}}}} + Q_{\text{Kid}} \times C_{{{\text{VKid}},{\text{DEA}}}} + Q_{\text{H}} \times C_{{{\text{VH}},{\text{DEA}}}} + Q_{\text{Br}} \times C_{{{\text{VBr}},{\text{DEA}}}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\; + Q_{\text{Thy}} \times C_{{{\text{VThy}},{\text{DEA}}}} + Q_{\text{F}} \times C_{{{\text{VF}},{\text{DEA}}}} + Q_{\text{Sk}} \times C_{{{\text{VSk}},{\text{DEA}}}} + Q_{\text{Re}} \times C_{{{\text{VRe}},{\text{DEA}}}} ) \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\; \times \frac{1}{QC} \hfill \\ \end{aligned}$$

(19)

$$\frac{{{\text{d}}A_{{{\text{VB}},{\text{DEA}}}} }}{{{\text{d}}t}} = {\text{QC}} \times (C_{{{\text{VMix}},{\text{DEA}}}} - C_{{{\text{V}},{\text{DEA}}}} ) + {\text{Dose Rate}}_{\text{DEA}}$$

(20)

$$C_{{{\text{V}},{\text{DEA}}}} = \frac{{A_{{{\text{VB}},{\text{DEA}}}} }}{{V_{\text{VB}} }}$$

(21)

$$C_{{{\text{Plasma}},{\text{DEA}}}} = \frac{{C_{{{\text{V}},{\text{DEA}}}} }}{{K_{{{\text{BP}},{\text{DEA}}}} }}$$

(22)

1.2.3 C. Arterial blood

1. For AMD

$$\frac{{{\text{d}}A_{{{\text{AB}},{\text{AMD}}}} }}{{{\text{d}}t}} = {\text{QC}} \times (C_{{{\text{VLu}},{\text{AMD}}}} - C_{{{\text{A}},{\text{AMD}}}} )$$

(23)

$$C_{{{\text{A}},{\text{AMD}}}} = \frac{{A_{{{\text{AB}},{\text{AMD}}}} }}{{V_{\text{AB}} }}$$

(24)

Equation 23 describes the changing rate of AMD amount in arterial blood.

2. For AMD

$$\frac{{{\text{d}}A_{{{\text{AB}},{\text{DEA}}}} }}{{{\text{d}}t}} = {\text{QC}} \times (C_{{{\text{VLu}},{\text{DEA}}}} - C_{{{\text{A}},{\text{DEA}}}} )$$

(25)

$$C_{{{\text{A}},{\text{DEA}}}} = \frac{{A_{{{\text{AB}},{\text{DEA}}}} }}{{V_{\text{AB}} }}$$

(26)