Abstract
The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example) and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions) for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration) for a wide range of values of the model parameters.
Highlights
Peritoneal dialysis is a life saving treatment for chronic patients with end stage renal disease [1].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
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 aims are to compare the results with those obtained earlier and to check whether they are applicable for describing the fluid-glucose-albumin transport in peritoneal dialysis
Summary
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 large molecules (e.g., albumin) diffuse from blood that perfuses the tissue layers close to the peritoneal cavity to the dialysis fluid, and are removed together with the drained fluid. Many solutes are transported from blood to dialyzate, but some solutes such as for example an osmotic agent (glucose), which is present in a high concentration in dialysis fluid, are transported in the opposite direction, i.e., to the blood
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