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

Bateman, H. (1985). Higher Transcendental Functions, Vol. 2. Robert E. Krieger Publishing Company, Malabar, FL.Search in Google Scholar

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)90074-5Search in Google Scholar

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-KSearch in Google Scholar

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-TSearch in Google Scholar

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.0000026492.83560.81Search in Google Scholar

Cherniha, R., Dutka, V., Stachowska-Pietka, J. and Waniewski, J. (2007). Fluid transport in peritoneal dialysis: A mathematical model and numerical solutions, in A.Search in Google Scholar

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.Search in Google Scholar

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-ySearch in Google Scholar

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)90134-1Search in Google Scholar

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.x11119072Search in Google Scholar

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.Search in Google Scholar

Flessner, M.F. (1994). Osmotic barrier of the parietal peritoneum, American Journal of Physiology 267(5): F861-870.10.1152/ajprenal.1994.267.5.F8617977791Search in Google Scholar

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.G42411447023Search in Google Scholar

Flessner,M.F. (2006). Peritoneal ultrafiltration: Mechanisms and measures, Contributions to Nephrology 150: 28-36.10.1159/00009348216720988Search in Google Scholar

Flessner, M.F. (2009). Peritoneal ultrafiltration: Physiology and failure, Contributions to Nephrology 163: 7-14.10.1159/00022377319494589Search in Google Scholar

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.00062.200616684927Search in Google Scholar

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.R5976720931Search in Google Scholar

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.F4253919596Search in Google Scholar

Gokal, R. and Nolph, K.D. (1994). The Textbook of Peritoneal Dialysis, Kluwer, Dordrecht.10.1007/978-94-011-0814-0Search in Google Scholar

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.2011.00027352539822135316Search in Google Scholar

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:1016298906589Search in Google Scholar

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.1992.1961614047Search in Google Scholar

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/13.1.1469481731Search in Google Scholar

Katchalsky, A. and Curran, P.F. (1965). Nonequilibrium Thermodynamics in Biophysics, Harvard University Press, Cambridge.10.4159/harvard.9780674494121Search in Google Scholar

Landis, E.M. and Pappenheimer, J.R. (1963). Exchange of Substances Through the Capillary Walls. Handbook of Physiology. Circulation, American Physiological Society, Washington, DC.Search in Google Scholar

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.5001861Search in Google Scholar

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.1975.229.4.877Search in Google Scholar

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)90025-5Search in Google Scholar

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.x13942460Search in Google Scholar

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.1962.17.2.26814486600Search in Google Scholar

Polyanin, A.D. and Zaitsev, V.F. (2003). Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press Company, Boca Raton, FL.Search in Google Scholar

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.Search in Google Scholar

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.x15253742Search in Google Scholar

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.Search in Google Scholar

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.01320.200516714354Search in Google Scholar

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.Search in Google Scholar

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.00301.201122301624Search in Google Scholar

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.1968.214.5.11765647192Search in Google Scholar

Waniewski, J. (2001). Physiological interpretation of solute transport parameters for peritoneal dialysis, Computational and Mathematical Networks in Medicine 3(3): 177-190.10.1080/10273660108833073Search in Google Scholar

Waniewski, J. (2002). Distributed modeling of diffusive solute transport in peritoneal dialysis, Annals of Biomedical Engineering 30(9): 1181-1195.10.1114/1.151926412502229Search in Google Scholar

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): 37-49.10.1080/17486700701298293Search in Google Scholar

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/s10439-008-9544-618670881Search in Google Scholar

Waniewski, J.(2013). Peritoneal fluid transport: Mechanisms, pathways, methods of assessment, Archives of Medical Research 44(8): 576-583.10.1016/j.arcmed.2013.10.01024215786Search in Google Scholar

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.Search in Google Scholar

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): 455-466.10.1177/039139889601900806Search in Google Scholar

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.00121.200919329769Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

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.H5179950853Search in Google Scholar

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.F87510836975Search in Google Scholar