Table of Contents Author Guidelines Submit a Manuscript
Computational and Mathematical Methods in Medicine
Volume 2017, Article ID 7246286, 11 pages
https://doi.org/10.1155/2017/7246286
Research Article

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

1Department of Clinical Pharmacy, School of Pharmacy, University of California San Francisco, San Francisco, CA, USA
2Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, Kogle Alle 6, 2970 Hørsholm, Denmark
3Department of Civil and Environmental Engineering, James H. Clark Center, Stanford University, Rm E250, 318 Campus Drive, Stanford, CA 94305, USA

Correspondence should be addressed to Davide Verotta; ude.fscu@attorev.edivad

Received 10 August 2017; Revised 14 November 2017; Accepted 26 November 2017; Published 20 December 2017

Academic Editor: Michele Migliore

Copyright © 2017 Davide Verotta et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Hall-Stoodley, P. Stoodley, S. Kathju et al., “Towards diagnostic guidelines for biofilm-associated infections,” FEMS Immunology & Medical Microbiology, vol. 65, no. 2, pp. 127–145, 2012. View at Publisher · View at Google Scholar · View at Scopus
  2. N. Høiby, T. Bjarnsholt, M. Givskov, S. Molin, and O. Ciofu, “Antibiotic resistance of bacterial biofilms,” International Journal of Antimicrobial Agents, vol. 35, no. 4, pp. 322–332, 2010. View at Publisher · View at Google Scholar
  3. G. J. Tortora, B. R. Funke, and C. L. Case, Microbiology, Pearson/Benjamin Cummings, San Francisco, Calif, USA, 8th edition, 2004.
  4. M. R. Parsek and T. Tolker-Nielsen, “Pattern formation in Pseudomonas aeruginosa biofilms,” Current Opinion in Microbiology, vol. 11, no. 6, pp. 560–566, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Lipsitch and B. R. Levin, “The population dynamics of antimicrobial chemotherapy,” Antimicrobial Agents and Chemotherapy, vol. 41, no. 2, pp. 363–373, 1997. View at Google Scholar · View at Scopus
  6. M. A. Beaumont, “Estimation of population growth or decline in genetically monitored populations,” Genetics, vol. 164, no. 3, pp. 1139–1160, 2003. View at Google Scholar · View at Scopus
  7. J. J. Bull and C. O. Wilke, “Lethal mutagenesis of bacteria,” Genetics, vol. 180, no. 2, pp. 1061–1070, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. W. E. Olmstead and R. A. Handelsman, “Diffusion in a semi-infinite region with nonlinear surface dissipation,” SIAM Review, vol. 18, no. 2, pp. 275–291, 1976. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. N. G. Cogan, J. S. Gunn, and D. J. Wozniak, “Biofilms and infectious diseases: Biology to mathematics and back again,” FEMS Microbiology Letters, vol. 322, no. 1, pp. 1–7, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. I. Klapper and J. Dockery, “Mathematical description of microbial biofilms,” SIAM Review, vol. 52, no. 2, pp. 221–265, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. E. Ariens, “The mode of action of biologically active compounds,” in Molecular Pharmacology, G. De Stevens, Ed., pp. 136–148, Academic Press, New York, NY, USA, 1964. View at Google Scholar
  12. I. F. Troconiz, L. B. Sheiner, and D. Verotta, “Semiparametric models for antagonistic drug interactions,” Journal of Applied Physiology, vol. 76, no. 5, pp. 2224–2233, 1994. View at Google Scholar · View at Scopus
  13. C. Csajka and D. Verotta, “Pharmacokinetic-pharmacodynamic modelling: History and perspectives,” Journal of Pharmacokinetics and Pharmacodynamics, vol. 33, no. 3, pp. 227–279, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Heydorn, A. T. Nielsen, M. Hentzer et al., “Quantification of biofilm structures by the novel computer program COMSTAT,” Microbiology, vol. 146, no. 10, pp. 2395–2407, 2000. View at Publisher · View at Google Scholar · View at Scopus
  15. M. H. Zwietering, I. Jonenburger, F. M. Rombouts, and K. Van 'Triet, “Modeling of the bacterial growth curve,” Applied and Enviromental Microbiology, pp. 1875–1881, 1990. View at Google Scholar
  16. R. Xiong, G. Xie, A. S. Edmondson, R. H. Linton, and M. A. Sheard, “Comparison of the Baranyi model with the modified Gompertz equation for modelling thermal inactivation of Listeria monocytogenes Scott A,” Food Microbiology, vol. 16, no. 3, pp. 269–279, 1999. View at Publisher · View at Google Scholar · View at Scopus
  17. R. C. McKellar, “A heterogeneous population model for the analysis of bacterial growth kinetics,” International Journal of Food Microbiology, vol. 36, no. 2-3, pp. 179–186, 1997. View at Publisher · View at Google Scholar · View at Scopus
  18. J. Clairambault, “Modelling physiological and pharmacological control on cell proliferation to optimise cancer treatments,” Mathematical Modelling of Natural Phenomena, vol. 4, no. 3, pp. 12–67, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. B. Gompertz, “On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies,” Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, vol. 115, pp. 513–583, 1825. View at Publisher · View at Google Scholar
  20. L. Norton, “A Gompertzian model of human breast cancer growth,” Cancer Research, vol. 48, pp. 7067–7071, 1988. View at Google Scholar · View at Scopus
  21. F. Kozusko and Z. Bajzer, “Combining Gompertzian growth and cell population dynamics,” Mathematical Biosciences, vol. 185, no. 2, pp. 153–167, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  22. L. Von Bertalanffy, “Problems of organic growth,” Nature, vol. 163, no. 4135, pp. 156–158, 1949. View at Publisher · View at Google Scholar · View at Scopus
  23. S. M. Moskowitz, J. M. Foster, J. Emerson, and J. L. Burns, “Clinically feasible biofilm susceptibility assay for isolates of Pseudomonas aeruginosa from patients with cystic fibrosis,” Journal of Clinical Microbiology, vol. 42, no. 5, pp. 1915–1922, 2004. View at Publisher · View at Google Scholar · View at Scopus
  24. E. R. Carson, C. Cobelli, and L. Finkelstein, The Mathematical Modeling of Metabolic and Endocrine Systems, John Wiley & Sons, New York, NY, USA, 1983.
  25. L. Finkelstein and E. R. Carson, Mathematical Modeling of Dynamic and Biological Systems, Research Studies Press, London, UK, 1985.
  26. P. Craven and G. Wahba, “Smoothing noisy data with spline functions—estimating the correct degree of smoothing by the method of generalized cross-validation,” Numerische Mathematik, vol. 31, no. 4, pp. 377–403, 1978. View at Publisher · View at Google Scholar · View at Scopus
  27. M. J. Wade, J. Harmand, B. Benyahia et al., “Perspectives in mathematical modelling for microbial ecology,” Ecological Modelling, vol. 321, pp. 64–74, 2016. View at Publisher · View at Google Scholar · View at Scopus
  28. A. Juška, “Minimal models of growth and decline of microbial populations,” Journal of Theoretical Biology, vol. 269, pp. 195–200, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  29. J. B. Kaplan, “Biofilm dispersal: mechanisms, clinical implications, and potential therapeutic uses,” Journal of Dental Research, vol. 89, no. 3, pp. 205–218, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. L. Hall-Stoodley and P. Stoodley, “Biofilm formation and dispersal and the transmission of human pathogens,” Trends in Microbiology, vol. 13, no. 1, pp. 7–10, 2005. View at Publisher · View at Google Scholar · View at Scopus
  31. M. Davidian and D. M. Giltinan, Nonlinear Models for Repeated Measurement Data, Monographs on Statistics and Applied Probability, Chapman & Hall, 1995.
  32. A. J. Boeckmann, S. L. Beal, and L. B. Sheiner, NONMEM V Users Guide, Part VII; Conditional Estimation Methods, vol. 1, Division of Clinical Pharmacology, University of California, San Francisco, Calif, USA, 2016.
  33. M. J. Lindstrom and D. M. Bates, “Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data,” Journal of the American Statistical Association, vol. 83, no. 404, pp. 1014–1022, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  34. E. J. Hannan, “Rational transfer function approximation,” Statistical Science, vol. 2, pp. 1029–1054, 1987. View at Google Scholar
  35. H. Akaike, “A New Look at the Statistical Model Identification,” IEEE Transactions on Automatic Control, vol. 19, no. 6, pp. 716–723, 1974. View at Publisher · View at Google Scholar · View at Scopus
  36. J. A. J. Haagensen, D. Verotta, L. Huang, A. Spormann, and K. Yang, “New in vitro model to study the effect of human simulated antibiotic concentrations on bacterial biofilms,” Antimicrobial Agents and Chemotherapy, vol. 59, no. 7, pp. 4074–4081, 2015. View at Publisher · View at Google Scholar · View at Scopus
  37. J. A. J. Haagensen, M. Klausen, R. K. Ernst et al., “Differentiation and distribution of colistin- and sodium dodecyl sulfate-tolerant cells in Pseudomonas aeruginosa biofilms,” Journal of Bacteriology, vol. 189, no. 1, pp. 28–37, 2007. View at Publisher · View at Google Scholar · View at Scopus
  38. J. L. Kuti, P. K. Dandekar, C. H. Nightingale, and D. P. Nicolau, “Use of Monte Carlo simulation to design an optimized pharmacodynamic dosing strategy for meropenem,” Clinical Pharmacology and Therapeutics, vol. 43, no. 10, pp. 1116–1123, 2003. View at Publisher · View at Google Scholar · View at Scopus
  39. D. J. Touw, A. J. Knox, and A. Smyth, “Population pharmacokinetics of tobramycin administered thrice daily and once daily in children and adults with cystic fibrosis,” Journal of Cystic Fibrosis, vol. 6, no. 5, pp. 327–333, 2007. View at Publisher · View at Google Scholar · View at Scopus
  40. L. Huang, J. Haagensen, D. Verotta, P. Lizak, F. Aweeka, and K. Yang, “Determination of meropenem in bacterial media by LC-MS/MS,” Journal of Chromatography B: Analytical Technologies in the Biomedical and Life Sciences, vol. 961, pp. 71–76, 2014. View at Publisher · View at Google Scholar
  41. R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2016.