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Analysis of a complex physiology-directed model for inhibition of platelet aggregation by clopidogrel

  • Author Bio: E-mail address: peletier@math.leidenuniv.nl; E-mail address: xiling.jiang@gmail.com; E-mail address: ssamant@ufl.edu; E-mail address: SSchmidt@cop.ufl.edu
  • * Corresponding author: Lambertus A. Peletier

    * Corresponding author: Lambertus A. Peletier 
Abstract Full Text(HTML) Figure(6) / Table(2) Related Papers Cited by
  • Clopidogrel is an anti-platelet compound that is widely used with aspirin to reduce the risk of cardiovascular incidents.In itself it is inactive; only after a biotransformation into its active metabolite clop-AM, does it inhibit platelet aggregation.Recently a system-pharmacological model has been proposed for the network of processes leading to reduced platelet aggregation.In this paper we present a mathematical analysis of this model and demonstrate how the complex pharmacokinetic modelcan be reduced to two simple coupled models, one for clopidogrel and one for clop-AM, yielding insight into the dynamicsof clop-AM and the impact of inter-individual differences on the level of inhibition.

    Mathematics Subject Classification: Primary:92C42, 92C45;Secondary:92C450.


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  • Figure 1.  Schematic model of clopidogrel action on platelet aggregation: clopidogrel travels from the gut to the liver, where one fraction ($E_{CES1}$) is hydrolysed into an inactive metabolite, one fraction ($E_{CYP}$) is transformed into the active metabolite clop-AM and one fraction $F_H$ goes into systemic circulation. Clop-AM also goes into systemic circulation where it binds to receptors situated on the platelets and thus inhibits platelet aggregation. The compartments are numbered 1 to 6; the amounts of clopidogrel in the gut, the liver and plasma are denoted by, respectively, $A_1, A_2$ and $A_3$ and the amounts of clop-AM in the liver and in plasma by $A_4$ and $A_5$. The platelet reactivity in compartment 6 is denoted by $P$

    Figure 2.  Graph of the clop-AM concentration in plasma ($C_5$) versus the clopidogrel concentration in the liver ($C_2$) based on equation (15) and parameter values given in Table 1

    Figure 4.  Temporal behaviour of $A_1(t),\dots, A_5(t)$ according to the PK model with parameter values given by Table 1 after an iv bolus dose of 300 mg i.e., 931 $\mu$mol. In the left two panels values of $A_1-A_5$ are given on a linear scale, and in the right panel they are given on a logarithmic scale

    Figure 3.  Graph of the response $P_{\rm ss}$ versus the clop-AM concentration in plasma ($C_5$) based on equation (18) and parameter values given in Table 2

    Figure 5.  The relative maximal platelet aggregation $P(t)$ versus time according to equation (17), together with clop-AM concentration $C_5$ in blood plasma on two time scales: on the same scale of the PK graphs shown in Figure 4 and one on a time scale which is much larger. PK and PD parameters are taken from, respectively, Table 1 and Table 2, and the iv dose was 300 mg, i.e., 931 $\mu$mol

    Figure 6.  Orbit in the $(x_4,x_5)$-plane (red) together with the null clines $\Gamma_4$ (blue) and $\Gamma_5$ (green) for PK parameter values from Table 1 and an iv bolus dose of 300 mg i.e., 931 $\mu$mol

    Table 1.  PK parameter estimates

    Parameter Unit Estimate CV %
    $Q_H$ L/h 50 0 (fixed)
    $V_H$ L 1.5 0 (fixed)
    $F_a$ - 0.5 0 (fixed)
    $k_{a}$ 1/h 9.28 7.63
    $V_3$ L 61.3 24.3
    $V_{max:CYP}$ $\mu$mol/h 314 23.2
    $K_{m:CYP}$ $\mu$M 4.95 27.7
    $CL_{int:CES1}$ L/h 19400 19.5
    $CL_{50}$ L/h 3.86 11.5
    $V_5$ L 3 0 (fixed)
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    Table 2.  PD parameter estimates

    Parameter Unit Estimate CV %
    $k_{\rm in}$ 1/h 0.00783 5.54
    $k_{\rm out}$ 1/h 0.00783 5.54
    $k_{\rm irre}$ 1/$\mu$M/h 4.06 4.14
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