Fluid transport in peritoneal dialysis: A mathematical model and numerical solutions

Modeling and Simulation in Science, Engineering and Technology

Volumn 38, Issue , 2007, Pages 281-288

  Cherniha, Roman ^a   Dutka, Vasyl ^b   Stachowska Pietka, Joanna ^c   Waniewski, Jacek ^c  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

^b BAKUL INSTITUTE FOR SUPERHARD MATERIALS   (Ukraine)

^c INSTITUTE OF BIOCYBERNETICS AND BIOMEDICAL ENGINEERING   (Poland)

Author keywords

Distributed model; Glucose transport; Numerical solution; Peritoneal dialysis; Water transport

Indexed keywords

EID: 85027981584     PISSN: 21643679     EISSN: 21643725     Source Type: Book Series    
DOI: 10.1007/978-0-8176-4558-8_25     Document Type: Chapter

References (12)

1. Gokal, R., Nolph, K.D.: The textbook of peritoneal dialysis. Kluwer, Dordrecht (1994).
2. Seames, E.L., Moncrief, J.W., Popovich, R.P.: A distributed model of fluid and mass transfer in peritoneal dialysis. Am. J. Physiol., 258, R958–72 (1990).
3. Flessner, M.F.: Peritoneal transport physiology: insights from basic research. J. Am. Soc. Nephrol., 2, 122–135 (1991).
4. Flessner, M.F.: Transport of protein in the abdominal wall during intraperitoneal therapy. I. Theoretical approach. Am. J. Physiol. Gastrointest Liver Physiol., 281, G424–37 (2001).
5. Cherniha, R., Waniewski, J.: Exact solutions of a mathematical model for fluid transport in peritoneal dialysis. Ukrainian Math. J., 57, 1112–1119 (2005).
6. Zakaria, E.R., Lofthouse, J., Flessner, M.F.: In vivo effects of hydrostatic pressure on inter-stitium of abdominal wall muscle. Am. J. Physiol., 276, H517–529 (1999).
7. Waniewski, J.: Physiological interpretation of solute transport parameters for peritoneal dialysis. J. Theor. Med., 3, 177–190 (2001).
8. Waniewski, J.: A mathematical model of local stimulation of perfusion by vasoactive agent diffusing from tissue surface. Int. J. Cardiovas. Eng., 4, 115–123 (2004).
9. Imholz, A.L., Koomen, G.C., Voorn, W.J., Struijk, D.G., Arisz, L., Krediet, R.T.: Day-to-day variability of fluid and solute transport in upright and recumbent positions during CAPD. Nephrol. Dial. Transplant., 13, 146–153 (1998).
10. Stachowska-Pietka, J., Waniewski, J., Flessner, M.F., Lindholm, B.: A mathematical model of peritoneal fluid absorption. Am. J. Physiol. Heart Circ. Physiol., 291, 1862–1874 (2006).
11. Cherniha, R., Dutka, V.: Exact and numerical solutions of the generalized Fisher equation. Reports of Math.Phys., 47, 393–411 (2001).
12. Flessner, M.F.: Osmotic barrier of the parietal peritoneum. Am. J. Physiol., 267, F861–870 (1994).