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A Modified Two-Portion Absorption Model to Describe Double-Peak Absorption Profiles of Ranitidine

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Abstract

Background

The pharmacokinetics of oral drugs exhibiting double peaks cannot be adequately described by using conventional compartmental models.

Objective

To propose and evaluate a modified two-portion absorption model based on physiological and biopharmaceutical considerations to describe the double-peak concentration-time curve of ranitidine.

Model design

The proposed model assumes that oral ranitidine is absorbed sequentially in two portions due to delayed gastric emptying, and thus includes a gut compartment in addition to the central and peripheral compartments.

Methods

Validation of the model was performed with respect to structural identifiability, parameter estimability and model applicability. Using initial estimates of parameters obtained from previous intravenous data, the model was used to fit oral ranitidine data from six subjects who manifested clear double-peak concentration-time profiles as well as from six subjects who showed irregular but apparent single-peak concentration-time curves.

Results

Based on goodness-of-fit criteria, the model fitted well for both double-peak and single-peak concentration-time curves of ranitidine (for the two groups: weighted residual sum of squares, 0.044 ± 0.027 and 0.054 ± 0.036; correlation between observed and model predicted concentrations, 0.995 ± 0.003 and 0.995 ± 0.005). Simulation studies with concentrations generated with 10% normally distributed random error showed that all model fitted parameters had good accuracy and reasonable precision. The mean percentage bias ranged from −7.0 to 28.6%, and the coefficient of variance was within 30% for the majority of parameters compared with the theoretical values.

Conclusion

The modified two-portion absorption model may afford a useful approach to characterise the absorption phase and estimate pharmacokinetic parameters for drugs with two absorption peaks.

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Table I
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Notes

  1. Use of tradenames is for product identification only and does not imply endorsement.

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Acknowledgements

This project was partly supported by grant AF/193/98 from the Innovation and Technology Commission of the Government of Hong Kong SAR.

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Correspondence to Moses S. S. Chow.

Appendix

Appendix

Structural Identifiability Analysis by Similarity Transformation Approach

A linear compartment model can be described by the general form as (equation 18):

$$\matrix{ {{{{\rm{dx}}} \over {{\rm{dt}}}} = {\rm{A}}({\rm{p}}){\rm{x}} + {\rm{B}}({\rm{p}}){\rm{u}},} \& {{\rm{x}}({{\rm{t}}_0}) = {{\rm{x}}_0}({\rm{p}})} \cr } $$
$${\rm{y}} = {\rm{C}}({\rm{p}}){\rm{x}}$$

where A is the (n × n) system matrix, B is the input matrix, C is the output matrix, x0 represents the initial condition and pεP represents the unknown parameters in these matrices.

The model will be globally identifiable if the following three conditions are satisfied:

  1. (i)

    The system is controllable, i.e. a given input will affect all compartments.

  2. (ii)

    The system is observable, i.e. the drug can move from any compartment to a measured compartment.

  3. (iii)

    Let TεRn × n be a nonsingular n × n matrix. For pεP, determine all TεRn × n and qεP such that (equations 19–22): Equation 19:

    $${\rm{A}}({\rm{p}}){\rm{T}} = {\rm{TA}}({\rm{q}})$$

    Equation 20:

    $${\rm{B}}({\rm{p}}) = {\rm{TB}}({\rm{q}})$$

    Equation 21:

    $${\rm{C}}({\rm{p}}){\rm{T}} = {\rm{C}}({\rm{q}})$$

    Equation 22:

    $${{\rm{x}}_0}({\rm{p}}) = {\rm{T}}{{\rm{x}}_0}({\rm{q}})$$

Solving this set of equations gives only one possible solution q = p and T = I (n × n identity matrix).

To test the structural identifiability of the proposed model described in figure 1, the following two cases were considered (after an initial check for the system controllability and observability).

Plasma Concentration Data from Both Intravenous and Oral Doses Are Available

In this case, the system matrix A, input matrix B and output matrix C for the proposed model are expressed as (equations 23–26): Equation 23:

$${\rm{A}} = \left( {\matrix{ {{{\rm{a}}_{11}}} \& 0 \& 0 \& 0 \& 0 \cr 0 \& {{{\rm{a}}_{22}}} \& 0 \& 0 \& 0 \cr {{{\rm{a}}_{31}}} \& {{{\rm{a}}_{32}}} \& {{{\rm{a}}_{33}}} \& 0 \& 0 \cr 0 \& 0 \& {{{\rm{a}}_{43}}} \& {{{\rm{a}}_{44}}} \& {{{\rm{a}}_{45}}} \cr 0 \& 0 \& 0 \& {{{\rm{a}}_{54}}} \& {{{\rm{a}}_{55}}} \cr } } \right)$$

Equation 24:

$${\rm{B}} = \left( {\matrix{ 1 \& 0 \& 0 \cr 0 \& 1 \& 0 \cr 0 \& 0 \& 0 \cr 0 \& 0 \& 1 \cr 0 \& 0 \& 0 \cr } } \right)$$

Equation 25:

$${\rm{C}}(\matrix{ 0 \& 0 \& 0 \& {{{\rm{c}}_1}} \& 0 \cr } )$$

Equation 26:

$${{\rm{X}}_0} = \left( {\matrix{ {{{\rm{X}}_1}} \cr {{{\rm{X}}_2}} \cr 0 \cr 0 \cr 0 \cr } } \right)$$

where a11 = −k1, a22 = −k2, a31 = k1, a32 = k2, a33 = −ka, a43 = ka, a44 = −k10−k12, a45 = k21, a54 = k12, a55 = −k21, c1 = 1/Vc, x1 = f1 • D and x2 = (1−f1) • D.

The vector of unknown parameters is:

$${\rm{p}} = {({{\rm{k}}_1}\;{{\rm{k}}_2}\;{{\rm{k}}_a}\;{{\rm{k}}_{10}}\;{{\rm{k}}_{12}}\;{{\rm{k}}_{21}}\;{{\rm{V}}_{\rm{c}}}\;{{\rm{f}}_1})^{\rm{T}}}$$

By substituting A, B, C and x0 into the equations in condition (iii), and solving this set of equations, the solution (p, T) = (q, I) is obtained. Thus, when plasma data are obtained from both intravenous and oral doses in this proposed model, the model parameters k1, k2, ka, k10, k12, k21, Vc and f1 will be globally identifiable.

Only Plasma Concentration Data From an Oral Dose Are Available

In this case, the input matrix B is expressed differently as shown below, whereas the other matrices A, C and x0 remain the same (equation 27):

$$B = \left( {\matrix{ 1 \& 0 \cr 0 \& 1 \cr 0 \& 0 \cr 0 \& 0 \cr 0 \& 0 \cr } } \right)$$

The test of structural identifiability under this condition is performed using a similar approach to that above. Summarising the results, only f1 and k21 are uniquely identifiable when only plasma data from oral administration are obtained. If Vc, k10 and k12 are known a priori (i.e. from a previous intravenous study), all other parameters will be globally identifiable.

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Yin, O.Q.P., Tomlinson, B., Chow, A.H.L. et al. A Modified Two-Portion Absorption Model to Describe Double-Peak Absorption Profiles of Ranitidine. Clin Pharmacokinet 42, 179–192 (2003). https://doi.org/10.2165/00003088-200342020-00005

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