American Institute of Mathematical Sciences

Advanced
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 & 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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[6]

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

[7]

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

[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.   Google Scholar

[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.   Google Scholar

[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. Google Scholar

[11]

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

[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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[20]

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

[21]

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

[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.   Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[6]

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

[7]

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

[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.   Google Scholar

[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.   Google Scholar

[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. Google Scholar

[11]

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

[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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[20]

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

[21]

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

[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.   Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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 Options

Download full-size image

Download as PowerPoint slide

Table 1">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 Options

Download full-size image

Download as PowerPoint slide

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 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 Options

Download full-size image

Download as PowerPoint slide

Table 2">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 Options

Download full-size image

Download as PowerPoint slide

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 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 Options

Download full-size image

Download as PowerPoint slide

Table 1 and an iv bolus dose of 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
Figure Options

Download full-size image

Download as PowerPoint slide

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)
Table Options

Download as excel

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
Table Options

Download as excel

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
[1]

Martin Redmann, Melina A. Freitag. Balanced model order reduction for linear random dynamical systems driven by Lévy noise. Journal of Computational Dynamics, 2018, 5 (1&2) : 33-59. doi: 10.3934/jcd.2018002
[2]

Loïs Boullu, Laurent Pujo-Menjouet, Jacques Bélair. Stability analysis of an equation with two delays and application to the production of platelets. Discrete & Continuous Dynamical Systems - S, 2020, 13 (11) : 3005-3027. doi: 10.3934/dcdss.2020131
[3]

Daniel Lear, David N. Reynolds, Roman Shvydkoy. Grassmannian reduction of cucker-smale systems and dynamical opinion games. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 5765-5787. doi: 10.3934/dcds.2021095
[4]

Boris Paneah. Noncommutative dynamical systems with two generators and their applications in analysis. Discrete & Continuous Dynamical Systems, 2003, 9 (6) : 1411-1422. doi: 10.3934/dcds.2003.9.1411
[5]

Oanh Chau, R. Oujja, Mohamed Rochdi. A mathematical analysis of a dynamical frictional contact model in thermoviscoelasticity. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 61-70. doi: 10.3934/dcdss.2008.1.61
[6]

Martin Redmann, Peter Benner. Approximation and model order reduction for second order systems with Levy-noise. Conference Publications, 2015, 2015 (special) : 945-953. doi: 10.3934/proc.2015.0945
[7]

Leonid A. Bunimovich. Dynamical systems and operations research: A basic model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 209-218. doi: 10.3934/dcdsb.2001.1.209
[8]

Hayato Chiba, Georgi S. Medvedev. The mean field analysis of the kuramoto model on graphs Ⅱ. asymptotic stability of the incoherent state, center manifold reduction, and bifurcations. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 3897-3921. doi: 10.3934/dcds.2019157
[9]

Georg Vossen, Stefan Volkwein. Model reduction techniques with a-posteriori error analysis for linear-quadratic optimal control problems. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 465-485. doi: 10.3934/naco.2012.2.465
[10]

Suxia Zhang, Hongbin Guo, Robert Smith?. Dynamical analysis for a hepatitis B transmission model with immigration and infection age. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1291-1313. doi: 10.3934/mbe.2018060
[11]

Salihu Sabiu Musa, Nafiu Hussaini, Shi Zhao, He Daihai. Dynamical analysis of chikungunya and dengue co-infection model. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1907-1933. doi: 10.3934/dcdsb.2020009
[12]

Juan Li, Yongzhong Song, Hui Wan, Huaiping Zhu. Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge. Mathematical Biosciences & Engineering, 2017, 14 (2) : 529-557. doi: 10.3934/mbe.2017032
[13]

Yu Yang, Lan Zou, Tonghua Zhang, Yancong Xu. Dynamical analysis of a diffusive SIRS model with general incidence rate. Discrete & Continuous Dynamical Systems - B, 2020, 25 (7) : 2433-2451. doi: 10.3934/dcdsb.2020017
[14]

Debora Amadori, Stefania Ferrari, Luca Formaggia. Derivation and analysis of a fluid-dynamical model in thin and long elastic vessels. Networks & Heterogeneous Media, 2007, 2 (1) : 99-125. doi: 10.3934/nhm.2007.2.99
[15]

Serena Brianzoni, Giovanni Campisi. Dynamical analysis of a banking duopoly model with capital regulation and asymmetric costs. Discrete & Continuous Dynamical Systems - B, 2021, 26 (11) : 5807-5825. doi: 10.3934/dcdsb.2021116
[16]

Peter Benner, Jens Saak, M. Monir Uddin. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 1-20. doi: 10.3934/naco.2016.6.1
[17]

Deepak Kumar, Ahmad Jazlan, Victor Sreeram, Roberto Togneri. Partial fraction expansion based frequency weighted model reduction for discrete-time systems. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 329-337. doi: 10.3934/naco.2016015
[18]

Mohammad-Sahadet Hossain. Projection-based model reduction for time-varying descriptor systems: New results. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 73-90. doi: 10.3934/naco.2016.6.73
[19]

Kazuyuki Yagasaki. Optimal control of the SIR epidemic model based on dynamical systems theory. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021144
[20]

Lianwen Wang, Zhijun Liu, Yong Li, Dashun Xu. Complete dynamical analysis for a nonlinear HTLV-I infection model with distributed delay, CTL response and immune impairment. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 917-933. doi: 10.3934/dcdsb.2019196

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (151)
  • HTML views (61)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy