2016, 13(1): 119-133. doi: 10.3934/mbe.2016.13.119

A physiologically-based pharmacokinetic model for the antibiotic ertapenem

1. 

Department of Mathematics & Statistics, East Tennessee State University, Johnson City, TN, 37614, United States

2. 

Department of Mathematics and Computer Science, Meredith College, Raleigh, NC, 27607

3. 

Department of Mathematics & Computer Science, Meredith College, Raleigh, NC, 27607, United States, United States

Received  May 2015 Revised  August 2015 Published  October 2015

Ertapenem is an antibiotic commonly used to treat a broad spectrum of infections, which is part of a broader class of antibiotics called carbapenem. Unlike other carbapenems, ertapenem has a longer half-life and thus only has to be administered once a day. A physiologically-based pharmacokinetic (PBPK) model was developed to investigate the uptake, distribution, and elimination of ertapenem following a single one gram dose. PBPK modeling incorporates known physiological parameters such as body weight, organ volumes, and blood flow rates in particular tissues. Furthermore, ertapenem is highly bound in human blood plasma; therefore, nonlinear binding is incorporated in the model since only the free portion of the drug can saturate tissues and, hence, is the only portion of the drug considered to be medicinally effective. Parameters in the model were estimated using a least squares inverse problem formulation with published data for blood concentrations of ertapenem for normal height, normal weight males. Finally, an uncertainty analysis of the parameter estimation and model predictions is presented.
Citation: Michele L. Joyner, Cammey C. Manning, Whitney Forbes, Michelle Maiden, Ariel N. Nikas. A physiologically-based pharmacokinetic model for the antibiotic ertapenem. Mathematical Biosciences & Engineering, 2016, 13 (1) : 119-133. doi: 10.3934/mbe.2016.13.119
References:
[1]

H. T. Banks, S. Hu and W. C. Thompson, Modeling and Inverse Problems in the Presence of Uncertainty,, CRC Press, (2014). Google Scholar

[2]

G. Bellu, M. P. Saccomani, S. Audoly and L. D'Angio, Daisy: A new software tool to test global identifiability of biological and physiological systems,, Comput. Meth. Prog. Bio., 88 (2007), 52. doi: 10.1016/j.cmpb.2007.07.002. Google Scholar

[3]

H. J. Clewell III, M. B. Reddy, T. Lave and M. E. Andersen, Physiologically based pharmacokinetic modeling,, in Preclinical Development Handbook: ADME Biopharmaceutical Properties (ed. S. C. Gad), (2008), 1167. Google Scholar

[4]

C. Cobelli and J. J. DiStefano, Parameter and structural identifiability concepts and ambiguities: A critical review and analysis,, Am. J. Physiol. - Reg. I., 239 (1980). Google Scholar

[5]

G. de Simone, R. B. Devereux, S. R. Daniels, G. Mureddu, M. J. Roman, T. R. Kimball, R. Greco, S. Witt and F. Contaldo, Stroke volume and cardiac output in normotensive children and adults: assessment of relations with body size and impact of overweight,, Circulation, 95 (1997), 1837. doi: 10.1161/01.CIR.95.7.1837. Google Scholar

[6]

N. C. for Biotechnology Information, Ertapenem,, , (). Google Scholar

[7]

D. Frasca, S. Marchand, F. Petitpas, C. Dahyot-Fizelier, W. Couet and O. Mimoz, Pharmacokinetics of ertapenem following intravenous and subcutaneous infusions in patients,, Antimicrob. Agents Chemother., 54 (2010), 924. doi: 10.1128/AAC.00836-09. Google Scholar

[8]

P. C. Fuchs, A. L. Barry and S. D. Brown, In vitro activities of ertapenem (mk-0826) against clinical bacterial isolates from 11 north american medical centers,, Antimicrob. Agents Ch., 45 (2001), 1915. doi: 10.1128/AAC.45.6.1915-1918.2001. Google Scholar

[9]

ILSI, Physiological Parameter Values for PBPK Models,, International Life Sciences Institute, (1994). Google Scholar

[10]

M. C. Inc., Highlights of prescribing information,, Invanz® (ertapenem for injection), (2012). Google Scholar

[11]

W. Jusko, Pharmacokinetics of capacity-limited systems,, Journal of Clinical Pharmacology, 29 (1989), 488. doi: 10.1002/j.1552-4604.1989.tb03369.x. Google Scholar

[12]

G. M. Keating and C. M. Perry, Ertapenem: A review of its use in the treatment of bacterial infections,, Drugs, 65 (2005), 2151. doi: 10.2165/00003495-200565150-00013. Google Scholar

[13]

H. Kvist, B. Chowdhury, U. Grangård, U. Tylen and L. Sjöström, Total and visceral adipose-tissue volumes derived from measurements with computed tomography in adult men and women: predictive equations.,, Am. J. Clin. Nutr., 48 (1988), 1351. Google Scholar

[14]

D. M. Livermore, A. M. Sefton and G. M. Scott, Properties and potential of ertapenem,, J. Antimicrob. Chemoth., 52 (2003), 331. doi: 10.1093/jac/dkg375. Google Scholar

[15]

A. K. Majumdar, D. G. Musson, K. L. Birk, C. J. Kitchen, S. Holland, J. McCrea, G. Mistry, M. Hesney, L. Xi, S. X. Li, R. Haesen, R. A. Blum, R. L. Lins, H. Greenberg, S. Waldman, P. Deutsch and J. D. Rogers, Pharmacokinetics of ertapenem in healthy young volunteers,, American Society for Microbiology, 46 (2002), 3506. doi: 10.1128/AAC.46.11.3506-3511.2002. Google Scholar

[16]

MATLAB, version 7.13.0.564 (R2011b),, The MathWorks Inc., (2011). Google Scholar

[17]

D. Nix, A. Majumdar and M. DiNubile, Pharmacokinetics and pharmacodynamics of ertapenem: An overview for clinicians,, J. Antimicrob. Chemoth., 53 (2004). doi: 10.1093/jac/dkh205. Google Scholar

[18]

S. Pilari and W. Huisinga, Lumping of physiologically-based pharmacokinetic models and a mechanistic derivation of classical compartmental models,, J. Pharmacokinet. Phar., 37 (2010), 365. doi: 10.1007/s10928-010-9165-1. Google Scholar

[19]

D. Plowchalk and J. Teeguarden, Development of a physiologically based pharmacokinetic model for estradiol in rats and humans: A biologically motivated quantitative framework for evaluating responses to estradiol and other endocrine-active compounds,, Toxicol. Sci., 69 (2002), 60. doi: 10.1093/toxsci/69.1.60. Google Scholar

[20]

P. Poulin and K. Krishnan, An algorithm for predicting tissue:blood partition coefficients of organic chemicals from n-octanol:water partition coefficient data,, J. Toxicol. Env. Health, 46 (1995), 117. Google Scholar

[21]

P. Poulin and K. Krishnan, A biologically-based algorithm for predicting human tissue: Blood partition coefficients of organic chemicals,, Human and Experimental Toxicology, 14 (1995), 273. Google Scholar

[22]

P. Price, R. Conolly, C. Chaisson, E. Gross, J. Young, E. Mathis and D. Tedder, Modeling interindividual variation in physiological factors used in PBPK models of humans,, Crit. Rev. Toxicol., 33 (2003), 469. Google Scholar

[23]

P. M. Shah and R. D. Isaacs, Ertapenem, the first of a new group of carbapenems,, J. Antimicrob. Chemoth., 52 (2003), 538. doi: 10.1093/jac/dkg404. Google Scholar

[24]

B. Tummers, Datathief iii,, , (). Google Scholar

[25]

J. Verbraecken, P. van de Heyning, W. de Backer and L. van Gaal, Body surface area in normal-weight, overweight, and obese adults: A comparison study,, Metabolis., 55 (2006), 515. doi: 10.1016/j.metabol.2005.11.004. Google Scholar

show all references

References:
[1]

H. T. Banks, S. Hu and W. C. Thompson, Modeling and Inverse Problems in the Presence of Uncertainty,, CRC Press, (2014). Google Scholar

[2]

G. Bellu, M. P. Saccomani, S. Audoly and L. D'Angio, Daisy: A new software tool to test global identifiability of biological and physiological systems,, Comput. Meth. Prog. Bio., 88 (2007), 52. doi: 10.1016/j.cmpb.2007.07.002. Google Scholar

[3]

H. J. Clewell III, M. B. Reddy, T. Lave and M. E. Andersen, Physiologically based pharmacokinetic modeling,, in Preclinical Development Handbook: ADME Biopharmaceutical Properties (ed. S. C. Gad), (2008), 1167. Google Scholar

[4]

C. Cobelli and J. J. DiStefano, Parameter and structural identifiability concepts and ambiguities: A critical review and analysis,, Am. J. Physiol. - Reg. I., 239 (1980). Google Scholar

[5]

G. de Simone, R. B. Devereux, S. R. Daniels, G. Mureddu, M. J. Roman, T. R. Kimball, R. Greco, S. Witt and F. Contaldo, Stroke volume and cardiac output in normotensive children and adults: assessment of relations with body size and impact of overweight,, Circulation, 95 (1997), 1837. doi: 10.1161/01.CIR.95.7.1837. Google Scholar

[6]

N. C. for Biotechnology Information, Ertapenem,, , (). Google Scholar

[7]

D. Frasca, S. Marchand, F. Petitpas, C. Dahyot-Fizelier, W. Couet and O. Mimoz, Pharmacokinetics of ertapenem following intravenous and subcutaneous infusions in patients,, Antimicrob. Agents Chemother., 54 (2010), 924. doi: 10.1128/AAC.00836-09. Google Scholar

[8]

P. C. Fuchs, A. L. Barry and S. D. Brown, In vitro activities of ertapenem (mk-0826) against clinical bacterial isolates from 11 north american medical centers,, Antimicrob. Agents Ch., 45 (2001), 1915. doi: 10.1128/AAC.45.6.1915-1918.2001. Google Scholar

[9]

ILSI, Physiological Parameter Values for PBPK Models,, International Life Sciences Institute, (1994). Google Scholar

[10]

M. C. Inc., Highlights of prescribing information,, Invanz® (ertapenem for injection), (2012). Google Scholar

[11]

W. Jusko, Pharmacokinetics of capacity-limited systems,, Journal of Clinical Pharmacology, 29 (1989), 488. doi: 10.1002/j.1552-4604.1989.tb03369.x. Google Scholar

[12]

G. M. Keating and C. M. Perry, Ertapenem: A review of its use in the treatment of bacterial infections,, Drugs, 65 (2005), 2151. doi: 10.2165/00003495-200565150-00013. Google Scholar

[13]

H. Kvist, B. Chowdhury, U. Grangård, U. Tylen and L. Sjöström, Total and visceral adipose-tissue volumes derived from measurements with computed tomography in adult men and women: predictive equations.,, Am. J. Clin. Nutr., 48 (1988), 1351. Google Scholar

[14]

D. M. Livermore, A. M. Sefton and G. M. Scott, Properties and potential of ertapenem,, J. Antimicrob. Chemoth., 52 (2003), 331. doi: 10.1093/jac/dkg375. Google Scholar

[15]

A. K. Majumdar, D. G. Musson, K. L. Birk, C. J. Kitchen, S. Holland, J. McCrea, G. Mistry, M. Hesney, L. Xi, S. X. Li, R. Haesen, R. A. Blum, R. L. Lins, H. Greenberg, S. Waldman, P. Deutsch and J. D. Rogers, Pharmacokinetics of ertapenem in healthy young volunteers,, American Society for Microbiology, 46 (2002), 3506. doi: 10.1128/AAC.46.11.3506-3511.2002. Google Scholar

[16]

MATLAB, version 7.13.0.564 (R2011b),, The MathWorks Inc., (2011). Google Scholar

[17]

D. Nix, A. Majumdar and M. DiNubile, Pharmacokinetics and pharmacodynamics of ertapenem: An overview for clinicians,, J. Antimicrob. Chemoth., 53 (2004). doi: 10.1093/jac/dkh205. Google Scholar

[18]

S. Pilari and W. Huisinga, Lumping of physiologically-based pharmacokinetic models and a mechanistic derivation of classical compartmental models,, J. Pharmacokinet. Phar., 37 (2010), 365. doi: 10.1007/s10928-010-9165-1. Google Scholar

[19]

D. Plowchalk and J. Teeguarden, Development of a physiologically based pharmacokinetic model for estradiol in rats and humans: A biologically motivated quantitative framework for evaluating responses to estradiol and other endocrine-active compounds,, Toxicol. Sci., 69 (2002), 60. doi: 10.1093/toxsci/69.1.60. Google Scholar

[20]

P. Poulin and K. Krishnan, An algorithm for predicting tissue:blood partition coefficients of organic chemicals from n-octanol:water partition coefficient data,, J. Toxicol. Env. Health, 46 (1995), 117. Google Scholar

[21]

P. Poulin and K. Krishnan, A biologically-based algorithm for predicting human tissue: Blood partition coefficients of organic chemicals,, Human and Experimental Toxicology, 14 (1995), 273. Google Scholar

[22]

P. Price, R. Conolly, C. Chaisson, E. Gross, J. Young, E. Mathis and D. Tedder, Modeling interindividual variation in physiological factors used in PBPK models of humans,, Crit. Rev. Toxicol., 33 (2003), 469. Google Scholar

[23]

P. M. Shah and R. D. Isaacs, Ertapenem, the first of a new group of carbapenems,, J. Antimicrob. Chemoth., 52 (2003), 538. doi: 10.1093/jac/dkg404. Google Scholar

[24]

B. Tummers, Datathief iii,, , (). Google Scholar

[25]

J. Verbraecken, P. van de Heyning, W. de Backer and L. van Gaal, Body surface area in normal-weight, overweight, and obese adults: A comparison study,, Metabolis., 55 (2006), 515. doi: 10.1016/j.metabol.2005.11.004. Google Scholar

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