American Institute of Mathematical Sciences

2014, 11(6): 1449-1464. doi: 10.3934/mbe.2014.11.1449

A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis

 1 Department of Mathematics and Statistics, California State University, Holt Hall 181, Chico, CA 95929 2 Departments of Critical Care Medicine and Medicine, University of Pittsburgh and Pittsburgh Veterans Affairs Healthcare System, 644A Scaife Hall, 3550 Terrace Street, Pittsburgh, PA, 15261, United States 3 Departments of Critical Care Medicine and Medicine, University of Pittsburgh Pittsburgh Veterans Affairs Healthcare System, 644A Scaife Hall, 3550 Terrace Street, Pittsburgh, PA, 15261, United States

Received  November 2013 Revised  September 2014 Published  September 2014

A study of the process of pharmacokinetics-pharmacodynamics (PKPD) of antibiotics and their interaction with bacteria during peritoneal dialysis associated peritonitis (PDAP) is presented. We propose a mathematical model describing the evolution of bacteria population in the presence of antibiotics for different peritoneal dialysis regimens. Using the model along with experimental data, clinical parameters, and physiological values, we compute variations in PD fluid distributions, drug concentrations, and number of bacteria in peritoneal and extra-peritoneal cavities. Scheduling algorithms for the PD exchanges that minimize bacteria count are investigated.
Citation: Colette Calmelet, John Hotchkiss, Philip Crooke. A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1449-1464. doi: 10.3934/mbe.2014.11.1449
References:
 [1] M. Bouvier D’Yvoire and P. Maire, Dosage regimens of antibacterials: Implications of a pharmacokinetic/pharmacodynamic model, Clin. Drug. Invest., 11 (1996), 229-239. [2] E. M. C. D’Agata, Antimicrobial-resistant, gram positive bacteria among patients undergoing chronic hemodialysis, Clin. Infect. Dis., 15 (2002), 1212-1218. doi: 10.1086/344282. [3] J. T. Daugirdas, P. G. Blake and T. S. Ing, Physiology of Peritoneal Dialysis. Handbook of Dialysis, Lippincott Williams & Wilkins, 2011. [4] E. D. Hermsen, L. B. Hovde, J. R. Hotchkiss and J. C. Rotschafer, Increased killing of staphylococci and streptococci by daptomycin compared with cefazolin and vancomycin in an in vito peritoneal dialysate model, Antimicrobial Agents Chemotherapy, 47 (2003), 3764-3767. [5] S. Hota, P. S. Crooke and J. R. Hotchkiss, A Monte Carlo analysis of peritoneal antimicrobial pharmacokinetics, Adv. Exp. Med. Biol., 696 (2011), 401-410. doi: 10.1007/978-1-4419-7046-6_40. [6] J. R. Hotchkiss, E. D. Hermsen and L. B. Hovde, et al., Dynamic analysis of peritoneal dialysis associated peritonitis, ASAIO Journal, (2004), 568-576. doi: 10.1097/01.MAT.0000145238.98158.F0. [7] Q. Khairullah, R. Provenzano, J. Tayeb and A. Ahmad, et al., Comparison of vancomycin versus cefazolin as inititial therapy for peritonitis in peritoneal dialysis patients, Peritoneal Dialysis International, 22 (2002), 339-344. [8] J. K. Leypoldt and C. D. Mistry, Ultrafiltration in peritoneal dialysis, in The Textbook of Peritoneal Dialysis, Kluwer Academic Publishers, 1994, 135-160. [9] S. Millikin, G. Matzke and W. Keane, Antimicrobial treatment of peritonitis associated with continuous ambulatory peritoneal dialysis, Peritoneal Dialysis International, 11 (1991), 252-260. [10] E. Nielsen and L. Friberg, Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs, Pharmacol. Rev., 65 (2013), 1053-1090. doi: 10.1124/pr.111.005769. [11] R. R. Regoes, et al., Pharmacodynamic functions: A multiparameter approach to the design of antibiotic treatment regimens, Antimicrob. Agents & Chemo., 48 (2004), 3670-3676. [12] T. Tozer and M. Rowland, Introduction to Pharmacokinetics and Pharmacodynamics: The Quantitative Basis of Drug Therapy, Lippincott Williams & Wilkins, 2006. [13] J. Zhi, C. H. Nightingale and R. Quintiliani, A pharmacodynamic model for the activity of antibiotics against microorganisms under nonsaturable conditions, J. Pharm. Sci., 75 (1986), 1063-1067. doi: 10.1002/jps.2600751108.

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References:
 [1] M. Bouvier D’Yvoire and P. Maire, Dosage regimens of antibacterials: Implications of a pharmacokinetic/pharmacodynamic model, Clin. Drug. Invest., 11 (1996), 229-239. [2] E. M. C. D’Agata, Antimicrobial-resistant, gram positive bacteria among patients undergoing chronic hemodialysis, Clin. Infect. Dis., 15 (2002), 1212-1218. doi: 10.1086/344282. [3] J. T. Daugirdas, P. G. Blake and T. S. Ing, Physiology of Peritoneal Dialysis. Handbook of Dialysis, Lippincott Williams & Wilkins, 2011. [4] E. D. Hermsen, L. B. Hovde, J. R. Hotchkiss and J. C. Rotschafer, Increased killing of staphylococci and streptococci by daptomycin compared with cefazolin and vancomycin in an in vito peritoneal dialysate model, Antimicrobial Agents Chemotherapy, 47 (2003), 3764-3767. [5] S. Hota, P. S. Crooke and J. R. Hotchkiss, A Monte Carlo analysis of peritoneal antimicrobial pharmacokinetics, Adv. Exp. Med. Biol., 696 (2011), 401-410. doi: 10.1007/978-1-4419-7046-6_40. [6] J. R. Hotchkiss, E. D. Hermsen and L. B. Hovde, et al., Dynamic analysis of peritoneal dialysis associated peritonitis, ASAIO Journal, (2004), 568-576. doi: 10.1097/01.MAT.0000145238.98158.F0. [7] Q. Khairullah, R. Provenzano, J. Tayeb and A. Ahmad, et al., Comparison of vancomycin versus cefazolin as inititial therapy for peritonitis in peritoneal dialysis patients, Peritoneal Dialysis International, 22 (2002), 339-344. [8] J. K. Leypoldt and C. D. Mistry, Ultrafiltration in peritoneal dialysis, in The Textbook of Peritoneal Dialysis, Kluwer Academic Publishers, 1994, 135-160. [9] S. Millikin, G. Matzke and W. Keane, Antimicrobial treatment of peritonitis associated with continuous ambulatory peritoneal dialysis, Peritoneal Dialysis International, 11 (1991), 252-260. [10] E. Nielsen and L. Friberg, Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs, Pharmacol. Rev., 65 (2013), 1053-1090. doi: 10.1124/pr.111.005769. [11] R. R. Regoes, et al., Pharmacodynamic functions: A multiparameter approach to the design of antibiotic treatment regimens, Antimicrob. Agents & Chemo., 48 (2004), 3670-3676. [12] T. Tozer and M. Rowland, Introduction to Pharmacokinetics and Pharmacodynamics: The Quantitative Basis of Drug Therapy, Lippincott Williams & Wilkins, 2006. [13] J. Zhi, C. H. Nightingale and R. Quintiliani, A pharmacodynamic model for the activity of antibiotics against microorganisms under nonsaturable conditions, J. Pharm. Sci., 75 (1986), 1063-1067. doi: 10.1002/jps.2600751108.
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