Have a personal or library account? Click to login
A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis Cover

A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

Open Access
|Dec 2014

References

  1. Bateman, H. (1985). Higher Transcendental Functions, Vol. 2. Robert E. Krieger Publishing Company, Malabar, FL.
  2. Baxter, L.T. and Jain, R.K. (1989). Transport of fluid and macromolecules in tumors, I: Role of interstitial pressure and convection, Microvascular Research 37(1): 77-104.10.1016/0026-2862(89)90074-5
  3. Baxter, L.T. and Jain, R.K. (1990). Transport of fluid and macromolecules in tumors, II: Role of heterogeneous perfusion and lymphatics, Microvascular Research 40(2): 246-263.10.1016/0026-2862(90)90023-K
  4. Baxter, L.T. and Jain, R.K. (1991). Transport of fluid and macromolecules in tumors, III: Role of binding and metabolism, Microvascular Research 41(1): 5-23.10.1016/0026-2862(91)90003-T
  5. Chagnac, A., Herskovitz, P., Ori Y., Weinstein, T., Hirsh, J., Katz, M. and Gafter, U. (2002). Effect of increased dialysate volume on peritoneal surface area among peritoneal dialysis patients, Journal of the American Society of Nephrology 13(10): 2554-2559.10.1097/01.ASN.0000026492.83560.81
  6. Cherniha, R., Dutka, V., Stachowska-Pietka, J. and Waniewski, J. (2007). Fluid transport in peritoneal dialysis: A mathematical model and numerical solutions, in A.
  7. Deutsch, L. Brusch, H. Byrne, G. de Vries and H.P. Herzel (Eds.), Mathematical Modeling of Biological Systems, Vol. I, Birkhaeuser, Boston, MA, pp. 291-298.
  8. Cherniha, R. and Waniewski, J. (2005). Exact solutions of a mathematical model for fluid transport in peritoneal dialysis, Ukrainian Mathematical Journal 57(8): 1112-1119.10.1007/s11253-005-0263-y
  9. Collins, J.M. (1981). Inert gas exchange of subcutaneous and intraperitoneal gas pockets in piglets, Respiration Physiology 46(3): 391-404.10.1016/0034-5687(81)90134-1
  10. Czyzewska, K., Szary, B. and Waniewski, J. (2000). Transperitoneal transport of glucose in vitro, Artificial Organs 24(11): 857-863.10.1046/j.1525-1594.2000.06637.x11119072
  11. Dedrick, R.L., Flessner, M.F., Collins, J.M. and Schultz, J.S. (1982). Is the peritoneum a membrane? Journal of American Society for Artificial Internal Organs 5(1): 1-8.
  12. Flessner, M.F. (1994). Osmotic barrier of the parietal peritoneum, American Journal of Physiology 267(5): F861-870.10.1152/ajprenal.1994.267.5.F8617977791
  13. Flessner,M.F. (2001). Transport of protein in the abdominal wall during intraperitoneal therapy, I: Theoretical approach, American Journal of Physiology-Gastrointestinal and Liver Physiology 281(2): G424-437.10.1152/ajpgi.2001.281.2.G42411447023
  14. Flessner,M.F. (2006). Peritoneal ultrafiltration: Mechanisms and measures, Contributions to Nephrology 150: 28-36.10.1159/00009348216720988
  15. Flessner, M.F. (2009). Peritoneal ultrafiltration: Physiology and failure, Contributions to Nephrology 163: 7-14.10.1159/00022377319494589
  16. Flessner, M.F., Deverkadra, R., Smitherman, J., Li, X. and Credit, K. (2006). In vivo determination of diffusive transport parameters in a superfused tissue, American Journal of Physiology-Renal Physiology 291(5): F1096-1103.10.1152/ajprenal.00062.200616684927
  17. Flessner, M.F., Dedrick, R.L. and Schultz J.S. (1984). A distributed model of peritoneal-plasma transport: Theoretical considerations, American Journal of Physiology 246(4): R597-607.10.1152/ajpregu.1984.246.4.R5976720931
  18. Flessner, M. F., Fenstermacher, J.D., Dedrick, R.L. and Blasberg, R.G. (1985). A distributed model of peritoneal-plasma transport: Tissue concentration gradients, American Journal of Physiology 248(3): F425-435.10.1152/ajprenal.1985.248.3.F4253919596
  19. Gokal, R. and Nolph, K.D. (1994). The Textbook of Peritoneal Dialysis, Kluwer, Dordrecht.10.1007/978-94-011-0814-0
  20. Guest, S., Akonur, A., Ghaffari, A., Sloand, J. and Leypoldt, J. K. (2012). Intermittent peritoneal dialysis: Urea kinetic modeling and implication of residual kidney function, Peritoneal Dialysis International 32(2): 142-148.10.3747/pdi.2011.00027352539822135316
  21. Gupta, E., Wientjes, M.G. and Au, J.L. (1995). Penetration kinetics of 2’, 3’-dideoxyinosine in dermis is described by the distributed model, Pharmaceutical Research 12(1): 108-112.10.1023/A:1016298906589
  22. Heimbürger, O., Waniewski, J., Werynski, A. and Lindholm, B. (1992). A quantitative description of solute and fluid transport during peritoneal dialysis, Kidney International 41(5): 1320-1332.10.1038/ki.1992.1961614047
  23. Imholz, A.L., Koomen, G.C., Voorn, W.J., Struijk, D.G., Arisz, L. and Krediet, R.T. (1998). Day-to-day variability of fluid and solute transport in upright and recumbent positions during CAPD, Nephrology Dialysis Transplantation 13(1): 146-153.10.1093/ndt/13.1.1469481731
  24. Katchalsky, A. and Curran, P.F. (1965). Nonequilibrium Thermodynamics in Biophysics, Harvard University Press, Cambridge.10.4159/harvard.9780674494121
  25. Landis, E.M. and Pappenheimer, J.R. (1963). Exchange of Substances Through the Capillary Walls. Handbook of Physiology. Circulation, American Physiological Society, Washington, DC.
  26. Parikova, A., Smit, W., Struijk, D.G. and Krediet, R.T. (2006). Analysis of fluid transport pathways and their determinants in peritoneal dialysis patients with ultrafiltration failure, Kidney International 70(11): 1988-1994.10.1038/sj.ki.5001861
  27. Patlak, C.S. and Fenstermacher, J.D. (1975). Measurements of dog blood-brain transfer constants by ventriculocisternal perfusion, American Journal of Physiology 229(4): 877-884.10.1152/ajplegacy.1975.229.4.877
  28. Perl,W. (1962). Heat and matter distribution in body tissues and the determination of tissue blood flow by local clearance methods, Journal of Theoretical Biology 2(3): 201-235.10.1016/0022-5193(62)90025-5
  29. Perl, W. (1963). An extension of the diffusion equation to include clearance by capillary blood flow, Annals of the New York Academy of Sciences 108: 92-105.10.1111/j.1749-6632.1963.tb13366.x13942460
  30. Piiper, J., Canfield, R.E. and Rahn, H. (1962) Absorption of various inert gases from subcutaneous gas pockets in rats, Journal of Applied Physiology 17(2): 268-274.10.1152/jappl.1962.17.2.26814486600
  31. Polyanin, A.D. and Zaitsev, V.F. (2003). Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press Company, Boca Raton, FL.
  32. Rosengren, B.I., Carlsson, O., Venturoli, D., al Rayyes, O. and Rippe, B. (2004). Transvascular passage of macromolecules into the peritoneal cavity of normo- and hypothermic rats in vivo: Active or passive transport? Journal of Vascular Research 41(2): 123-130. Seames, E.L., Moncrief, J.W. and Popovich, R.P. (1990). A distributed model of fluid and mass transfer in peritoneal dialysis. American Journal of Physiology 258(4): R958-972.
  33. Smit, W., Struijk, D.G., Pannekeet, M.M. and Krediet, R.T. (2004a). Quantification of free water transport in peritoneal dialysis, Kidney International 66(2): 849-854.10.1111/j.1523-1755.2004.00815.x15253742
  34. Smit, W., van Esch, S., Struijk, D.G., Pannekeet, M.M. and Krediet, R.T. (2004b). Free water transport in patients starting with peritoneal dialysis: A comparison between diabetic and non diabetic patients, Advances in Peritoneal Dialysis 20: 13-17.
  35. Stachowska-Pietka, J., Waniewski, J., Flessner, M.F. and Lindholm, B. (2006). Distributed model of peritoneal fluid absorption, American Journal of Physiology-Heart and Circulatory Physiology 291(4): H1862-1874.10.1152/ajpheart.01320.200516714354
  36. Stachowska-Pietka, J., Waniewski, J., Flessner, M.F. and Lindholm, B. (2007). A distributed model of bidirectional protein transport during peritoneal fluid absorption, Advances in Peritoneal Dialysis 23: 23-27.
  37. Stachowska-Pietka, J., Waniewski, J., Flessner, M.F. and Lindholm, B. (2012). Computer simulations of osmotic ultrafiltration and small solute transport in peritoneal dialysis: A spatially distributed approach, American Journal of Physiology-Renal Physiology 302(10): F1331-1341.10.1152/ajprenal.00301.201122301624
  38. Van Liew, H.D. (1968). Coupling of diffusion and perfusion in gas exit from subcutaneous pocket in rats, American Journal of Physiology 214(5): 1176-1185.10.1152/ajplegacy.1968.214.5.11765647192
  39. Waniewski, J. (2001). Physiological interpretation of solute transport parameters for peritoneal dialysis, Computational and Mathematical Networks in Medicine 3(3): 177-190.10.1080/10273660108833073
  40. Waniewski, J. (2002). Distributed modeling of diffusive solute transport in peritoneal dialysis, Annals of Biomedical Engineering 30(9): 1181-1195.10.1114/1.151926412502229
  41. Waniewski, J. (2007). Mean transit time and mean residence time for linear diffusion-convection-reaction transport system, Computational and Mathematical Methods in Medicine 8(1): 37-49.10.1080/17486700701298293
  42. Waniewski, J.(2008). Transit time, residence time, and the rate of approach to steady state for solute transport during peritoneal dialysis, Annals of Biomedical Engineering 36: 1735-1743.10.1007/s10439-008-9544-618670881
  43. Waniewski, J.(2013). Peritoneal fluid transport: Mechanisms, pathways, methods of assessment, Archives of Medical Research 44(8): 576-583.10.1016/j.arcmed.2013.10.01024215786
  44. Waniewski, J., Dutka, V., Stachowska-Pietka, J. and Cherniha, R. (2007). Distributed modeling of glucose-induced osmotic flow, Advances in Peritoneal Dialysis 23: 2-6.
  45. Waniewski, J., Heimbürger, O., Werynski, A. and Lindholm, B. (1996a). Simple models for fluid transport during peritoneal dialysis, International Journal of Artificial Organs 19(8): 455-466.10.1177/039139889601900806
  46. Waniewski, J., Heimbürger, O., Werynski, A. and Lindholm, B. (1996b). Osmotic conductance of the peritoneum in CAPD patients with permanent loss of ultrafiltration capacity, Peritoneal Dialysis International 16(5): 488-496. Waniewski, J., Stachowska-Pietka, J. and Flessner, M.F. (2009). Distributed modeling of osmotically driven fluid transport in peritoneal dialysis: Theoretical and computational investigations, American Journal of Physiology-Heart and Circulatory Physiology 296(6): H1960-1968.10.1152/ajpheart.00121.200919329769
  47. Wientjes, M.G., Badalament, R.A., Wang, R.C., Hassan, F. and Au, J.L. (1993). Penetration of mitomycin C in human bladder, Cancer Research 53(14): 3314-3320.
  48. Wientjes, M.G., Dalton, J.T., Badalament, R.A., Drago, J.R. and Au, J.L. (1991). Bladder wall penetration of intravesical mitomycin C in dogs, Cancer Research 51(16): 4347-4354.
  49. Zakaria, E.R., Lofthouse, J. and Flessner, M.F. (1999). In vivo effects of hydrostatic pressure on interstitium of abdominal wall muscle, American Journal of Physiology 276(2): H517-529.10.1152/ajpheart.1999.276.2.H5179950853
  50. Zakaria, E.R., Lofthouse, J. and Flessner, M.F. (2000). Effect of intraperitoneal pressures on tissue water of the abdominal muscle, American Journal of Physiology-Renal Physiology 278(6): F875-885. 10.1152/ajprenal.2000.278.6.F87510836975
DOI: https://doi.org/10.2478/amcs-2014-0062 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 837 - 851
Submitted on: Oct 7, 2013
Published on: Dec 20, 2014
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2014 Roman Cherniha, Joanna Stachowska-Piętka, Jacek Waniewski, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.