Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis
Roman CHERNIHA, Jacek Waniewski

Last modified: 2014-03-31


Peritoneal dialysis is a life saving treatment for chronic patients with end stage renal disease. The peritoneal cavity, an empty space that separates bowels, abdominal muscles and other organs in the abdominal cavity, is applied as a container for dialysis fluid, which is infused there through a permanent catheter and left in the cavity for a few hours. During this time  small metabolites (urea, creatinine) and other uremic toxins diffuse from blood that perfuses the tissue layers close to the peritoneal cavity to the dialysis fluid, and finally are removed together with the drained fluid. The treatment cycle (infusion, dwell, drainage) is repeated several times every day. The peritoneal transport occurs between dialysis fluid in the peritoneal  cavity and blood passing down the capillaries in tissue surrounding the peritoneal cavity.An important objective of peritoneal dialysis is to remove excess water from the patient.    Typical values of the water  ultrafiltration measured  during  peritoneal dialysis  are  10 - 20 mL/min. This is achieved  by inducing osmotic pressure in the dialysis fluid by adding a solute (called osmotic agent) in high concentration. The most frequently  used osmotic agent is glucose. This medical application of high osmotic pressure is unique for peritoneal dialysis. The flow of water from blood across the tissue to the dialysis fluid in the peritoneal cavity carries solutes of different size, including large macromolecules (e.g., albumin), and adds a convective component to their diffusive transport.Mathematical description of fluid and solute transport between blood and dialysis fluid in the peritoneal cavity has not yet been fully formulated, in spite of the well-known basic physical laws for such transport. We have constructed  a  mathematical model for fluid and solute transport  in peritoneal dialysis. The model is based on a three-component nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model  ultrafiltration  of  water combined with inflow of glucose to the tissue and  removal  of albumin  from the body during dialysis,  by finding the spatial distributions of glucose and albumin concentrations and hydrostatic pressure. The model  is developed in   one spatial dimension  approximation and a governing equation for each of the variables is derived from physical principles. Under some assumptions the model  can be   simplified to obtain  exact formulae for spatially non-uniform steady-state solutions.  As the result, the exact formulae for the  fluid fluxes from blood to tissue and  across the tissue are constructed together with two linear autonomous ordinary differential equations for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin  transport  during peritoneal dialysis.The talk will be  based on the results obtained in  [1]—[2] and some unpublished results.[1] R. Cherniha,  J. Stachowska-Pietka,  and  J. Waniewski. arXiv:1310.5876v1  22 Oct 2013.[2] Cherniha R, Dutka V, Stachowska-Pietka J and Waniewski J In: Mathematical Modeling of Biological Systems, Vol.I. Ed. by A.Deutsch et al., Birkhaeuser, pp.291-298 (2007)

Acknowledgments: This work was done within  the project "Mathematical modeling transport processes in tissue during peritoneal dialysis" between Polish AS and NAS of Ukraine and was also supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme.


transport in peritoneal dialysis; fluid transport; nonlinear differential equation