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).

[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.

[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.

[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).

[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.

[6]

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

[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.

[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.

[9]

ILSI, Physiological Parameter Values for PBPK Models,, International Life 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. 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. 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.

[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.

[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.

[16]

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

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[24]

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

[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.

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).

[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.

[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.

[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).

[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.

[6]

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

[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.

[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.

[9]

ILSI, Physiological Parameter Values for PBPK Models,, International Life 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. 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. 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.

[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.

[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.

[16]

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

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[24]

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

[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.

[1]

Hayden Schaeffer, John Garnett, Luminita A. Vese. A texture model based on a concentration of measure. Inverse Problems & Imaging, 2013, 7 (3) : 927-946. doi: 10.3934/ipi.2013.7.927

[2]

Magali Tournus, Aurélie Edwards, Nicolas Seguin, Benoît Perthame. Analysis of a simplified model of the urine concentration mechanism. Networks & Heterogeneous Media, 2012, 7 (4) : 989-1018. doi: 10.3934/nhm.2012.7.989

[3]

Guoyuan Chen, Youquan Zheng. Concentration phenomenon for fractional nonlinear Schrödinger equations. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2359-2376. doi: 10.3934/cpaa.2014.13.2359

[4]

Xu Zhang. On the concentration of semiclassical states for nonlinear Dirac equations. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5389-5413. doi: 10.3934/dcds.2018238

[5]

Jun Yang. Coexistence phenomenon of concentration and transition of an inhomogeneous phase transition model on surfaces. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 965-994. doi: 10.3934/dcds.2011.30.965

[6]

D. Bartolucci, L. Orsina. Uniformly elliptic Liouville type equations: concentration compactness and a priori estimates. Communications on Pure & Applied Analysis, 2005, 4 (3) : 499-522. doi: 10.3934/cpaa.2005.4.499

[7]

Yi-hsin Cheng, Tsung-Fang Wu. Multiplicity and concentration of positive solutions for semilinear elliptic equations with steep potential. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2457-2473. doi: 10.3934/cpaa.2016044

[8]

Yu Chen, Yanheng Ding, Suhong Li. Existence and concentration for Kirchhoff type equations around topologically critical points of the potential. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1641-1671. doi: 10.3934/cpaa.2017079

[9]

Song Peng, Aliang Xia. Multiplicity and concentration of solutions for nonlinear fractional elliptic equations with steep potential. Communications on Pure & Applied Analysis, 2018, 17 (3) : 1201-1217. doi: 10.3934/cpaa.2018058

[10]

Daniele Cassani, João Marcos do Ó, Abbas Moameni. Existence and concentration of solitary waves for a class of quasilinear Schrödinger equations. Communications on Pure & Applied Analysis, 2010, 9 (2) : 281-306. doi: 10.3934/cpaa.2010.9.281

[11]

Dengfeng Lü. Existence and concentration behavior of ground state solutions for magnetic nonlinear Choquard equations. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1781-1795. doi: 10.3934/cpaa.2016014

[12]

Teresa D'Aprile. Some existence and concentration results for nonlinear Schrödinger equations. Communications on Pure & Applied Analysis, 2002, 1 (4) : 457-474. doi: 10.3934/cpaa.2002.1.457

[13]

Bernard Dacorogna, Alessandro Ferriero. Regularity and selecting principles for implicit ordinary differential equations. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 87-101. doi: 10.3934/dcdsb.2009.11.87

[14]

Zvi Artstein. Averaging of ordinary differential equations with slowly varying averages. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 353-365. doi: 10.3934/dcdsb.2010.14.353

[15]

Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences. Inverse Problems & Imaging, 2016, 10 (4) : 869-898. doi: 10.3934/ipi.2016025

[16]

Zhongyuan Liu. Concentration of solutions for the fractional Nirenberg problem. Communications on Pure & Applied Analysis, 2016, 15 (2) : 563-576. doi: 10.3934/cpaa.2016.15.563

[17]

Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 73-88. doi: 10.3934/dcdss.2016.9.73

[18]

Shuangjie Peng, Jing Zhou. Concentration of solutions for a Paneitz type problem. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 1055-1072. doi: 10.3934/dcds.2010.26.1055

[19]

Zheng Dai, I.G. Rosen, Chuming Wang, Nancy Barnett, Susan E. Luczak. Using drinking data and pharmacokinetic modeling to calibrate transport model and blind deconvolution based data analysis software for transdermal alcohol biosensors. Mathematical Biosciences & Engineering, 2016, 13 (5) : 911-934. doi: 10.3934/mbe.2016023

[20]

Myeongju Chae, Sunggeum Hong, Sanghyuk Lee. Mass concentration for the $L^2$-critical nonlinear Schrödinger equations of higher orders. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 909-928. doi: 10.3934/dcds.2011.29.909

2017 Impact Factor: 1.23

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (0)

[Back to Top]