Table of Contents Author Guidelines Submit a Manuscript
Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 654726, 11 pages
http://dx.doi.org/10.1155/2013/654726
Research Article

Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis

1AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Department of Electronics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
2Institute of Physiology, Center for Physiological Medicine, Medical University of Graz, Harrachgasse 21/5, 8010 Graz, Austria

Received 23 May 2013; Revised 5 August 2013; Accepted 26 August 2013

Academic Editor: Thierry Busso

Copyright © 2013 Przemysław Korohoda and Daniel Schneditz. 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. T. A. Depner, Prescribing Hemodialysis: A Guide to Urea Modeling, Kluwer Academic Publishers, Boston, Mass, USA, 1991.
  2. F. A. Gotch and M. L. Keen, “Kinetic modeling in hemodialysis,” in Clinical Dialysis, A. R. Nissenson and R. N. Fine, Eds., pp. 153–202, McGrraw-Hill, New York, NY, USA, 4th edition, 2005. View at Google Scholar
  3. J. Waniewski, M. Debowska, and B. Lindholm, “Theoretical and numerical analysis of different adequacy indices for hemodialysis and peritoneal dialysis,” Blood Purification, vol. 24, no. 4, pp. 355–366, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. P. Bugl, Differential Equations: Matrices and Models, Prentice Hall, Englewood Cliffs, NJ, USA, 1995.
  5. D. Schneditz and J. T. Daugirdas, “Formal analytical solution to a regional blood flow and diffusion based urea kinetic model,” ASAIO Journal, vol. 40, no. 3, pp. M667–M673, 1994. View at Google Scholar · View at Scopus
  6. F. Grandi, G. Avanzolini, and A. Cappello, “Analytic solution of the variable-volume double-pool urea kinetics model applied to parameter estimation in hemodialysis,” Computers in Biology and Medicine, vol. 25, no. 6, pp. 505–518, 1995. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Eloot, A. Torremans, R. De Smet et al., “Complex compartmental behavior of small water-soluble uremic retention solutes: evaluation by direct measurements in plasma and erythrocytes,” American Journal of Kidney Diseases, vol. 50, no. 2, pp. 279–288, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. D. Schneditz, Y. Yang, G. Christopoulos, and J. Kellner, “Rate of creatinine equilibration in whole blood,” Hemodialysis International, vol. 13, no. 2, pp. 215–221, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. F. Gotch, N. W. Levin, and P. Kotanko, “Calcium balance in dialysis is best managed by adjusting dialysate calcium guided by kinetic modeling of the interrelationship between calcium intake, dose of vitamin D analogues and the dialysate calcium concentration,” Blood Purification, vol. 29, no. 2, pp. 163–176, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. V. Maheshwari, L. Samavedham, and G. P. Rangaiah, “A regional blood flow model for β2-microglobulin kinetics and for simulating intra-dialytic exercise effect,” Annals of Biomedical Engineering, vol. 39, no. 12, pp. 2879–2890, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Schneditz, M. Galach, K. Thomaseth, and J. Waniewski, “A regional blood flow model for glucose and insulin kinetics during hemodialysis,” ASAIO Journal, vol. 59, no. 6, pp. 627–635, 2013. View at Google Scholar
  12. D. Schneditz, D. Platzer, and J. T. Daugirdas, “A diffusion-adjusted regional blood flow model to predict solute kinetics during haemodialysis,” Nephrology Dialysis Transplantation, vol. 24, no. 7, pp. 2218–2224, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley & Sons, Chichester, UK, 3rd edition, 2007.
  14. N. J. Higham, Functions of Matrices: Theory and Computation, SIAM, Philadephia, Pa, USA, 2008.
  15. S. L. Goldstein, J. M. Sorof, and E. D. Brewer, “Evaluation and prediction of urea rebound and equilibrated Kt/V in the pediatric hemodialysis population,” American Journal of Kidney Diseases, vol. 34, no. 1, pp. 49–54, 1999. View at Google Scholar · View at Scopus
  16. M. Debowska, B. Lindholm, and J. Waniewski, “Adequacy indices for dialysis in acute renal failure: kinetic modeling,” Artificial Organs, vol. 34, no. 5, pp. 412–419, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Jung, P. Korohoda, P. Krisper, and D. Schneditz, “Relationship between kinetics of albumin-bound bilirubin and water-soluble urea in extracorporeal blood purification,” Nephrology Dialysis Transplantation, vol. 27, no. 3, pp. 1200–1206, 2012. View at Google Scholar
  18. J. T. Daugirdas, T. A. Depner, T. Greene, and P. Silisteanu, “Solute-solver: a web-based tool for modeling urea kinetics for a broad range of hemodialysis schedules in multiple patients,” American Journal of Kidney Diseases, vol. 54, no. 5, pp. 798–809, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. G. Lillacci and M. Khammash, “Parameter estimation and model selection in computational biology,” PLoS Computational Biology, vol. 6, no. 3, Article ID e1000696, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. D. Schneditz, B. Fariyike, R. Osheroff, and N. W. Levin, “Is intercompartmental urea clearance during hemodialysis a perfusion term? A comparison of two pool urea kinetic models,” Journal of the American Society of Nephrology, vol. 6, no. 5, pp. 1360–1370, 1995. View at Google Scholar · View at Scopus
  21. D. Schneditz, J. C. Van Stone, and J. T. Daugirdas, “A regional blood circulation alternative to in-series two compartment urea kinetic modeling,” ASAIO Journal, vol. 39, no. 3, pp. M573–M577, 1993. View at Publisher · View at Google Scholar · View at Scopus
  22. S. F. F. Santos and A. J. Peixoto, “Revisiting the dialysate sodium prescription as a tool for better blood pressure and interdialytic weight gain management in hemodialysis patients,” Clinical Journal of the American Society of Nephrology, vol. 3, no. 2, pp. 522–530, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. F. Locatelli, A. Covic, C. Chazot, K. Leunissen, J. Luño, and M. Yaqoob, “Optimal composition of the dialysate, with emphasis on its influence on blood pressure,” Nephrology Dialysis Transplantation, vol. 19, no. 4, pp. 785–796, 2004. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Raimann, L. Liu, S. Tyagi, N. W. Levin, and P. Kotanko, “A fresh look at dry weight,” Hemodialysis International, vol. 12, no. 4, pp. 395–405, 2008. View at Publisher · View at Google Scholar · View at Scopus
  25. A. J. Peixoto, N. Gowda, C. R. Parikh, and S. F. F. Santos, “Long-term stability of serum sodium in hemodialysis patients,” Blood Purification, vol. 29, no. 3, pp. 264–267, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. S. W. Smye and E. J. Will, “A mathematical analysis of a two-compartment model of urea kinetics,” Physics in Medicine and Biology, vol. 40, no. 12, article 001, pp. 2005–2014, 1995. View at Publisher · View at Google Scholar · View at Scopus
  27. G. Cardano, Book Number One About the Great Art, or the Rules of Algebra, Nürnberg, Germany, 1545.
  28. J. P. Tignol, Galois' Theory of Algebraic Equations, World Scientific, London, UK, 2001.
  29. L. Ferrari, Book Number One About the Great Art, or the Rules of Algebra, G. Cardano, Ed., Nürnberg, Germany, 1545.
  30. http://www.galaxy.agh.edu.pl/~korohoda/applet_for_DA-RBF_model/MedCalApp.html.