# American Institute of Mathematical Sciences

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:
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##### References:
 [1] H. T. Banks, S. Hu and W. C. Thompson, Modeling and Inverse Problems in the Presence of Uncertainty, CRC Press, Boca Raton, Fl, 2014. [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), 52-61. doi: 10.1016/j.cmpb.2007.07.002. [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), Wiley-Interscience, John Wiley & Sons, Inc., 2008, 1167-1127. [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), R7-R24. [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), 1837-1843. doi: 10.1161/01.CIR.95.7.1837. [6] N. C. for Biotechnology Information, Ertapenem, http://pubchem.ncbi.nlm.nih.gov/summary/summary.cgi?cid=150610#x27. [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), 924-926. doi: 10.1128/AAC.00836-09. [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), 1915-1918. doi: 10.1128/AAC.45.6.1915-1918.2001. [9] ILSI, Physiological Parameter Values for PBPK Models, International Life Sciences Institute, Risk Sciences Institute, 1994. [10] M. C. Inc., Highlights of prescribing information, Invanz® (ertapenem for injection), 2012. [11] W. Jusko, Pharmacokinetics of capacity-limited systems, Journal of Clinical Pharmacology, 29 (1989), 488-493. doi: 10.1002/j.1552-4604.1989.tb03369.x. [12] G. M. Keating and C. M. Perry, Ertapenem: A review of its use in the treatment of bacterial infections, Drugs, 65 (2005), 2151-2178. doi: 10.2165/00003495-200565150-00013. [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), 1351-1361. [14] D. M. Livermore, A. M. Sefton and G. M. Scott, Properties and potential of ertapenem, J. Antimicrob. Chemoth., 52 (2003), 331-344. doi: 10.1093/jac/dkg375. [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), 3506-3511. doi: 10.1128/AAC.46.11.3506-3511.2002. [16] MATLAB, version 7.13.0.564 (R2011b), The MathWorks Inc., Natick, Massachusetts, 2011. [17] D. Nix, A. Majumdar and M. DiNubile, Pharmacokinetics and pharmacodynamics of ertapenem: An overview for clinicians, J. Antimicrob. Chemoth., 53 (2004), ii23-ii28. doi: 10.1093/jac/dkh205. [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), 365-405. doi: 10.1007/s10928-010-9165-1. [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), 60-78. doi: 10.1093/toxsci/69.1.60. [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), 117-129. [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), 273-280. [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), 469-503. [23] P. M. Shah and R. D. Isaacs, Ertapenem, the first of a new group of carbapenems, J. Antimicrob. Chemoth., 52 (2003), 538-542. doi: 10.1093/jac/dkg404. [24] B. Tummers, Datathief iii, http://datathief.org/. [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), 515-524. doi: 10.1016/j.metabol.2005.11.004.
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