American Institute of Mathematical Sciences

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February  2017, 37(2): 945-961. doi: 10.3934/dcds.2017039

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

Lambertus A. Peletier 1,, , Xi-Ling Jiang 2, , Snehal Samant 2, and  Stephan Schmidt 2,

1. 

Mathematical Institute, Leiden University, PB 9512,2300 RA Leiden, The Netherlands
2. 

Department of Pharmaceutics, Center for Pharmacometrics and Systems Pharmacology, University of Florida at Lake Nona (Orlando), 6550 Sanger Road, Office 467, Orlando, FL 32827, USA

* Corresponding author: Lambertus A. Peletier

Received  June 2015 Revised  February 2016 Published  November 2016

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.

Keywords: Clopidogrel, platelets, biotransformation, model reduction, dynamical systems analysis.
Mathematics Subject Classification: Primary:92C42, 92C45;Secondary:92C45.
Citation: Lambertus A. Peletier, Xi-Ling Jiang, Snehal Samant, Stephan Schmidt. Analysis of a complex physiology-directed model for inhibition of platelet aggregation by clopidogrel. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 945-961. doi: 10.3934/dcds.2017039
References:
[1]

R. Altman, A. J. Rivas and C. D. Gonzalez, Bleeding tendency in dual antiplatelet therapy with aspirin/clopidogrel: Rescue of the template bleeding time in a single-center prospective study, Thrombosis Journal, 10 (2012), 3pp. 

[2]

E. Amsterdam, N. K. Wenger and R. G. Brindis, AHA/ACC guideline for the management of patients with non-ST-elevation acute coronary syndromes: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines, Circulation, 130 (2014), e344-426. 

[3]

D. J. Angiolillo, A. Fernandez-Ortiz, E. Bernardo, F. Alfonso, C. Macaya, T. A. Bass and M. A. Costa, Variability in individual responsiveness to clopidogrel: Clinical implications, management, and future perspectives, Journal of the American College of Cardiology, 49 (2007), 1505-1516. 

[4]

N. L. Dayneka, V. Garg and W. J. Jusko, Comparison of four basic models of indirect pharmacodynamic responses, J. Pharmacokin. Biopharm, 21 (1993), 457-478. 

[5]

C. S. Ernest 2nd, D. S. Small, S. Rohatagi, D. E. Salazar, L. Wallentin, K. J. Winters and R. E. Wrishko, Population pharmacokinetics and pharmacodynamics of prasugrel and clopidogrel in aspirin-treated patients with stable coronary artery disease, J. Pharmacokinet. Pharmacodyn, 35 (2008), 593-618. 

[6]

FDA Drug Safety Communication: Reduced effectiveness of Plavix (clopidogrel) in patients who are poor metabolizers of the drug.

[7]

P. A. Gurbel and U. S. Tantry, Clopidogrel resistance?, Thromb. Res., 120 (2007), 311-321. 

[8]

K. Hagihara, M. Kazui, A. Kurihara, M. Yoshiike, K. Honda, O. Okazaki, N. A. Farid and T. Ikeda, A possible mechanism for the differences in efficiency and variability of active metabolite formation from thienopyridine antiplatelet agents, prasugrel and clopidogrel, Drug Metab. Dispos: the biological fate of chemicals, 37 (2009), 2145-2152. 

[9]

J. S. Hulot, A. Bura, E. Villard, V. Remones and C. Goyenvalle, Cytochrome P450 2C19 loss-of-function poly-morphism is a major determinant of clopidogrel responsiveness in healthy subjects, Blood, 108 (2006), 2244-2247. 

[10]

X. L. Jiang, R. B. Horenstein, A. R. Shuldiner, L. M. Yerges-Armstrong, S. Samant, L. J. Lesko and S. Schmidt, Development of a minimal physiologically-based pharmacokinetic and pharmacodynamics model for characterizing the impact of genetic and demographic factors on clopidogrel treatment response in healthy adults, presented at the 42nd Annual Meeting of the American College of Clinical Pharmacology (ACCP), Bethesda, September 23,2013.

[11]

X. L. Jiang, S. Samant, L. J. Lesko and S. Schmidt, Clinical pharmacokinetics and pharmacodynamics of clopidogrel, Clinical Pharmacokinetics, 54 (2015), 147-166. 

[12]

X. L. Jiang, S. Samant, J. P. Lewis, R. B. Horenstein, A. R. Shuldiner, L. M. Yerges-Armstrong, L. A. Peletier, L. J. Lesko and S. Schmidt, Development of a physiology-directed population pharmacokinetic and pharmacodynamic model for characterizing the impact of genetic and demographic factors on clopidogrel response in healthy adults, Eur. J. Pharm. Sci., 82 (2016), 64-78. 

[13]

M. Kazui, Y. Nishiya, T. Ishizuka, H. Katsunobu, A. F. Nagy, O. Osamu, I. Toshihiko and K. Atsushi, Identification of the human cytochrome P450 enzymes involved in the two oxidative steps in the bioactivation of clopidogrel to its pharmacologically active metabolite, Drug metabolism and disposition: The biological fate of chemicals, 38 (2010), 92-99. 

[14]

J. L. Mega, S. L. Close, S. D. Wiviott, L. Shen, R. D. Hockett, J. T. Brandt, J. R. Walker, E. M. Antman, W. Macias, E. Braunwald and M. S. Sabatine, Cytochrome p-450 polymorphisms and response to clopidogrel, N. Engl. J. Med., 360 (2009), 354-362. 

[15]

D. Mozaffarian, E. J. Benjamin and A. S. Go, Heart disease and stroke statistics-2015 update: A report from the American Heart Association, Circulation, 131 (2015), e29-e322.  doi: 10.1161/CIR.0000000000000152.

[16]

K. Ogungbenro and L. Aarons, Physiologically based pharmacokinetic modelling of methotrexate and 6-mercaptopurine in adults and children. Part 1: Methotrexate, J. Pharmacokinet. Pharmacodyn, 41 (2014), 159-217. 

[17]

K. S. Pang, A. D. Rodrigues and R. M. Peter eds, Enzyme-and Transporter-Based Drug-Drug Interactions: Progress and Future Challenges, Springer, New York, 2010.

[18]

K. S. Pang, S. Huadong and E. C. Y. Chow, Impact of physiological determinants: Flow, binding, transporters and enzymes on organ and total body clearances. In Enzyme-and transporter-based drug-drug interactions: Progress and future challenges, K. S. Pang, A. D. Rodrigues, R. M. Peter eds. Springer, New York, (2010), 107–147.

[19]

T. M. Post, J. I. Freijer, J. DeJongh and M. Danhof, Disease systems analysis: Basic disease progression models in degenerative disease, Pharm. Res., 22 (2005), 1038-1049.  doi: 10.1007/s11095-005-5641-5.

[20]

S. Samant, Identifying Clinically Relevant Sources of Variability: The Clopidogrel Challenge, Clinical Pharmacology & Therapeutics 11 OCT 2016.

[21]

Sanofi-Aventis. Prescribing information: Plavix Clopidogrel 75 and 300 mg Tablets, Manufacturer's Standard, 2011, http://products.sanofi.us/plavix/plavix.html.

[22]

P. Savi and J. M. Herbert, Clopidogrel and ticlopidine: P2Y12 adenosine diphosphate-receptor antagonists for the prevention of atherothrombosis, Seminars in Thrombosis and Hemostasis, 31 (2005), 174-183. 

[23]

R. M. Savic, D. M. Jonker, T. Kerbusch and M. O. Karlsson, Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies, J. Pharmacikin. Pharmacodyn, 34 (2007), 711-726.  doi: 10.1007/s10928-007-9066-0.

[24]

S. Schmidt, T. M. Post, M. Boroujerdi, C. van Kesteren, B. A. Ploeger, O. E. Della Pasqua and M. Danhof, Disease progression analysis: Towards mechanism-based models, in Clinical Trial Simulations -Applications and Trends, (eds. H. Kimko and C. Peck), Springer, 1 (2010), 433–455.

[25]

S. Schmidt, T. M. Post, L. A. Peletier, M. A. Boroujerdi and M. Danhof, Coping with time scales in disease systems analysis: Application to bone remodelling, J. Pharmacokinet. Pharmacodyn, 38 (2011), 873-900.  doi: 10.1007/s10928-011-9224-2.

[26]

A. R. Shuldiner, J. R. O'Connell, K. P. Bliden, A. Gandhi, K. Ryan, R. B. Horenstein, C. M. Damcott, R. Pakyz, U. S. Tantry, Q. Gibson, T. I. Pollin, W. Post, A. Parsa, B. D. Mitchell, N. Faraday, W. Herzog and P. A. Gurbel, Association of cytochrome P450 2C19 genotype with the antiplatelet effect and clinical efficacy of clopidogrel therapy, JAMA, 302 (2009), 849-857.  doi: 10.1001/jama.2009.1232.

[27]

World Health Organization, Cardiovascular diseases (CVDs) fact sheet No. 317, March 2013, http://www.who.int/mediacentre/factsheets/fs317/en/. Accessed March 09,2015.

[28]

J. Yang, M. Jamei, K. R. Yeo, A. Rostami-Hodjegan and G. T. Tucker, Misuse of the well-stirred model of hepatic drug clearance, Drug Metab. Dispos., 35 (2007), 501-502.  doi: 10.1124/dmd.106.013359.

[29]

A. M. Yousef, M. Melhem, B. Xue, T. Arafat, D. K. Reynolds and S. A. van Wart, Population pharmacokinetic analysis of clopidogrel in healthy Jordanian subjects with emphasis optimal sampling strategy, Biopharm. & emphDrug Dispos., 34 (2013), 215-226.  doi: 10.1002/bdd.1839.

[30]

H. J. Zhu, X. Wang, B. E. Gawronski, B. J. Brinda, D. J. Angiolillo and J. S. Markowitz, Carboxylesterase 1 as a determinant of clopidogrel metabolism and activation, J. Pharm. Exper. Therapeut. (JPET), 344 (2013), 665-672.  doi: 10.1124/jpet.112.201640.

show all references

References:
[1]

R. Altman, A. J. Rivas and C. D. Gonzalez, Bleeding tendency in dual antiplatelet therapy with aspirin/clopidogrel: Rescue of the template bleeding time in a single-center prospective study, Thrombosis Journal, 10 (2012), 3pp. 

[2]

E. Amsterdam, N. K. Wenger and R. G. Brindis, AHA/ACC guideline for the management of patients with non-ST-elevation acute coronary syndromes: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines, Circulation, 130 (2014), e344-426. 

[3]

D. J. Angiolillo, A. Fernandez-Ortiz, E. Bernardo, F. Alfonso, C. Macaya, T. A. Bass and M. A. Costa, Variability in individual responsiveness to clopidogrel: Clinical implications, management, and future perspectives, Journal of the American College of Cardiology, 49 (2007), 1505-1516. 

[4]

N. L. Dayneka, V. Garg and W. J. Jusko, Comparison of four basic models of indirect pharmacodynamic responses, J. Pharmacokin. Biopharm, 21 (1993), 457-478. 

[5]

C. S. Ernest 2nd, D. S. Small, S. Rohatagi, D. E. Salazar, L. Wallentin, K. J. Winters and R. E. Wrishko, Population pharmacokinetics and pharmacodynamics of prasugrel and clopidogrel in aspirin-treated patients with stable coronary artery disease, J. Pharmacokinet. Pharmacodyn, 35 (2008), 593-618. 

[6]

FDA Drug Safety Communication: Reduced effectiveness of Plavix (clopidogrel) in patients who are poor metabolizers of the drug.

[7]

P. A. Gurbel and U. S. Tantry, Clopidogrel resistance?, Thromb. Res., 120 (2007), 311-321. 

[8]

K. Hagihara, M. Kazui, A. Kurihara, M. Yoshiike, K. Honda, O. Okazaki, N. A. Farid and T. Ikeda, A possible mechanism for the differences in efficiency and variability of active metabolite formation from thienopyridine antiplatelet agents, prasugrel and clopidogrel, Drug Metab. Dispos: the biological fate of chemicals, 37 (2009), 2145-2152. 

[9]

J. S. Hulot, A. Bura, E. Villard, V. Remones and C. Goyenvalle, Cytochrome P450 2C19 loss-of-function poly-morphism is a major determinant of clopidogrel responsiveness in healthy subjects, Blood, 108 (2006), 2244-2247. 

[10]

X. L. Jiang, R. B. Horenstein, A. R. Shuldiner, L. M. Yerges-Armstrong, S. Samant, L. J. Lesko and S. Schmidt, Development of a minimal physiologically-based pharmacokinetic and pharmacodynamics model for characterizing the impact of genetic and demographic factors on clopidogrel treatment response in healthy adults, presented at the 42nd Annual Meeting of the American College of Clinical Pharmacology (ACCP), Bethesda, September 23,2013.

[11]

X. L. Jiang, S. Samant, L. J. Lesko and S. Schmidt, Clinical pharmacokinetics and pharmacodynamics of clopidogrel, Clinical Pharmacokinetics, 54 (2015), 147-166. 

[12]

X. L. Jiang, S. Samant, J. P. Lewis, R. B. Horenstein, A. R. Shuldiner, L. M. Yerges-Armstrong, L. A. Peletier, L. J. Lesko and S. Schmidt, Development of a physiology-directed population pharmacokinetic and pharmacodynamic model for characterizing the impact of genetic and demographic factors on clopidogrel response in healthy adults, Eur. J. Pharm. Sci., 82 (2016), 64-78. 

[13]

M. Kazui, Y. Nishiya, T. Ishizuka, H. Katsunobu, A. F. Nagy, O. Osamu, I. Toshihiko and K. Atsushi, Identification of the human cytochrome P450 enzymes involved in the two oxidative steps in the bioactivation of clopidogrel to its pharmacologically active metabolite, Drug metabolism and disposition: The biological fate of chemicals, 38 (2010), 92-99. 

[14]

J. L. Mega, S. L. Close, S. D. Wiviott, L. Shen, R. D. Hockett, J. T. Brandt, J. R. Walker, E. M. Antman, W. Macias, E. Braunwald and M. S. Sabatine, Cytochrome p-450 polymorphisms and response to clopidogrel, N. Engl. J. Med., 360 (2009), 354-362. 

[15]

D. Mozaffarian, E. J. Benjamin and A. S. Go, Heart disease and stroke statistics-2015 update: A report from the American Heart Association, Circulation, 131 (2015), e29-e322.  doi: 10.1161/CIR.0000000000000152.

[16]

K. Ogungbenro and L. Aarons, Physiologically based pharmacokinetic modelling of methotrexate and 6-mercaptopurine in adults and children. Part 1: Methotrexate, J. Pharmacokinet. Pharmacodyn, 41 (2014), 159-217. 

[17]

K. S. Pang, A. D. Rodrigues and R. M. Peter eds, Enzyme-and Transporter-Based Drug-Drug Interactions: Progress and Future Challenges, Springer, New York, 2010.

[18]

K. S. Pang, S. Huadong and E. C. Y. Chow, Impact of physiological determinants: Flow, binding, transporters and enzymes on organ and total body clearances. In Enzyme-and transporter-based drug-drug interactions: Progress and future challenges, K. S. Pang, A. D. Rodrigues, R. M. Peter eds. Springer, New York, (2010), 107–147.

[19]

T. M. Post, J. I. Freijer, J. DeJongh and M. Danhof, Disease systems analysis: Basic disease progression models in degenerative disease, Pharm. Res., 22 (2005), 1038-1049.  doi: 10.1007/s11095-005-5641-5.

[20]

S. Samant, Identifying Clinically Relevant Sources of Variability: The Clopidogrel Challenge, Clinical Pharmacology & Therapeutics 11 OCT 2016.

[21]

Sanofi-Aventis. Prescribing information: Plavix Clopidogrel 75 and 300 mg Tablets, Manufacturer's Standard, 2011, http://products.sanofi.us/plavix/plavix.html.

[22]

P. Savi and J. M. Herbert, Clopidogrel and ticlopidine: P2Y12 adenosine diphosphate-receptor antagonists for the prevention of atherothrombosis, Seminars in Thrombosis and Hemostasis, 31 (2005), 174-183. 

[23]

R. M. Savic, D. M. Jonker, T. Kerbusch and M. O. Karlsson, Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies, J. Pharmacikin. Pharmacodyn, 34 (2007), 711-726.  doi: 10.1007/s10928-007-9066-0.

[24]

S. Schmidt, T. M. Post, M. Boroujerdi, C. van Kesteren, B. A. Ploeger, O. E. Della Pasqua and M. Danhof, Disease progression analysis: Towards mechanism-based models, in Clinical Trial Simulations -Applications and Trends, (eds. H. Kimko and C. Peck), Springer, 1 (2010), 433–455.

[25]

S. Schmidt, T. M. Post, L. A. Peletier, M. A. Boroujerdi and M. Danhof, Coping with time scales in disease systems analysis: Application to bone remodelling, J. Pharmacokinet. Pharmacodyn, 38 (2011), 873-900.  doi: 10.1007/s10928-011-9224-2.

[26]

A. R. Shuldiner, J. R. O'Connell, K. P. Bliden, A. Gandhi, K. Ryan, R. B. Horenstein, C. M. Damcott, R. Pakyz, U. S. Tantry, Q. Gibson, T. I. Pollin, W. Post, A. Parsa, B. D. Mitchell, N. Faraday, W. Herzog and P. A. Gurbel, Association of cytochrome P450 2C19 genotype with the antiplatelet effect and clinical efficacy of clopidogrel therapy, JAMA, 302 (2009), 849-857.  doi: 10.1001/jama.2009.1232.

[27]

World Health Organization, Cardiovascular diseases (CVDs) fact sheet No. 317, March 2013, http://www.who.int/mediacentre/factsheets/fs317/en/. Accessed March 09,2015.

[28]

J. Yang, M. Jamei, K. R. Yeo, A. Rostami-Hodjegan and G. T. Tucker, Misuse of the well-stirred model of hepatic drug clearance, Drug Metab. Dispos., 35 (2007), 501-502.  doi: 10.1124/dmd.106.013359.

[29]

A. M. Yousef, M. Melhem, B. Xue, T. Arafat, D. K. Reynolds and S. A. van Wart, Population pharmacokinetic analysis of clopidogrel in healthy Jordanian subjects with emphasis optimal sampling strategy, Biopharm. & emphDrug Dispos., 34 (2013), 215-226.  doi: 10.1002/bdd.1839.

[30]

H. J. Zhu, X. Wang, B. E. Gawronski, B. J. Brinda, D. J. Angiolillo and J. S. Markowitz, Carboxylesterase 1 as a determinant of clopidogrel metabolism and activation, J. Pharm. Exper. Therapeut. (JPET), 344 (2013), 665-672.  doi: 10.1124/jpet.112.201640.

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 $P$
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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
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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
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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
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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
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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
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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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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)
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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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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