Submitted on February 4, 2009
Revised on March 12, 2009
Accepted on March 24, 2009
Distributed modeling of osmotically driven fluid transport in peritoneal dialysis: theoretical and computational investigations
Jacek Waniewski1*, Joanna Stachowska-Pietka2, and Michael Flessner3
1 Institute of Biocybernetics and Biomedical Engineering
2 Polish Academy of Sciences
3 University of Mississippi med center
* To whom correspondence should be addressed. E-mail: jacekwan{at}ibib.waw.pl.
Based on a distributed model of peritoneal transport, a mathematical theory is presented to explain how the osmotic agent in the peritoneal dialysis solution that penetrates tissue induces osmotically driven flux out of the tissue. The relationships between phenomenological transport parameters (hydraulic permeability, reflection coefficient) and the respective specific transport parameters for the tissue and the capillary wall are separately described. Closed formulas for steady state flux across the peritoneal surface and for hydrostatic pressure at the opposite surface are obtained using an approximate description of the concentration profile of the osmotic agent within the tissue by exponential function. A case of experimental study with mannitol as the osmotic agent in the rat abdominal wall is shown to be well described by our theory and computer simulations and to validate the applied approximations. Furthermore, clinical dialysis with glucose as the osmotic agent is analyzed and the effective transport rates and parameters are derived from the description of the tissue and capillary wall.
