Quantification of free water transport in peritoneal dialysis

Abstract

The method applied here is the first direct quantification of free water transport, calculated from a single standard peritoneal function test. It offers a quick possibility to evaluate patients suffering from ultrafiltration failure. In these patients free water transport was impaired, but the origin of this impairment is still to be determined.

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

“…To obtain values of the ultrafiltration that correspond to those measured during peritoneal dialysis, we need to set σ T G ≥ 0.02. For example, setting σ T G = 0.02 and σ T G = 0.03, we obtain the ultrafiltration rates of 10 mL/min and 15 mL/min, which are close to those measured in clinical conditions for similar boundary concentration of glucose (Smit et al, 2004a;2004b;Waniewski et al, 1996a;2009;Stachowska et al, 2012). The initial values of ultrafiltration remain in agreement with those obtained by our group in clinical studies (Waniewski et al, 1996b;Waniewski, 2007).…”

“…The mathematical descriptions of these systems were obtained using partial differential equations based on the simplification that capillaries are homogeneously distributed within the tissue. Experimental evidence confirmed the good applicability of such models (see, for example, the papers of Waniewski et al (1996a;1996b;2007), Smit et al (2004a), Flessner (2006), Parikova et al (2006), Stachowska-Pietka et al (2012), Guest et al (2012) and the references therein).…”

“…Our aim is to check whether they are applicable for describing the fluid-glucose-albumin transport in peritoneal dialysis. The parameter values in these formulae were derived from experimental and clinical data and have been applied in previous mathematical studies ( Van Liew, 1968;Imholz et al, 1998;Zakaria et al, 1999;Flessner, 2001;Smit et al 2004a;2004b;Waniewski, 2001;Stachowska-Pietka et al, 2006;2007;Cherniha et al, 2007;Waniewski et al, 2009 ). Most of the parameters, especially those for water and glucose, were derived from experimental data or obtained by fitting the distributed model to clinical data, and are discussed in detail in a recent paper of Stachowska-Pietka et al (2012).…”

“…Nevertheless, the model covers all basic transport phenomena and provides a good background for further modifications. However, only numerical studies are available for such extended models (see Smit et al, 2004a;2004b;Stachowska-Pietka et al, 2006). Furthermore, those parameters without firmly established experimental values (i.e., Staverman reflection coefficients), were varied to check their impact on the results of modelling .…”

“…Typical values of water ultrafiltration measured during peritoneal dialysis are 10-20 mL/min (Heimbürger et al, 1992;Waniewski et al, 1996aWaniewski et al, , 1996bSmit et al, 2004a;2004b). This is achieved by inducing osmotic pressure in the dialysis fluid by adding a solute (called the osmotic agent) in high concentration.…”