**Part 1**

**Modeling, Methods and Technique**

**1** 

*1Poland 2Sweden* 

**Kinetic Modeling and Adequacy of Dialysis** 

Malgorzata Debowska1, Bengt Lindholm2 and Jacek Waniewski1

*2Divisions of Baxter Novum and Renal Medicine, Karolinska Institutet, Stockholm,* 

The mathematical description of hemodialysis (HD) includes two parts: 1) explanation of the exchange between patient's blood and dialysate fluid across a semipermeable membrane of the dialyzer, and 2) characterization of the solute removal from the patient. The solute transport across the dialyzer membrane depends on the difference in hydrostatic pressure and solute concentration gradients between both sides of the membrane and also on the permeability of the membrane to the solute. The local equations for solute and fluid transport through the membrane are based on a phenomenological (thermodynamic) description according to the Staverman-Kedem-Katchalsky-Spiegler approach (Staverman, 1951; Kedem & Katchalsky, 1958; Katchalsky & Curran, 1965; Spiegler & Kedem, 1966). The two compartment model describes the functioning of the patient – dialyzer system, assuming that body fluid is divided into two parts: one directly (extracellular compartment) and one indirectly (intracellular compartment) accessible for dialysis (Schneditz & Daugirdas, 2001). The one compartment model of the solute distribution volume assumes that the solute is distributed in a single, homogenous pool. Solute kinetic modeling is based on a set of ordinary differential equations describing the changes of solute mass, concentration and distribution volume in body compartments and in the dialyzer. Using

The question concerning dialysis dosing has been debated and remains controversial since the beginning of the dialysis treatment era. Between 1976 and 1981, the National Cooperative Dialysis Study (NCDS) was performed in the United States to establish objective, quantitative criteria for the adequate dose of dialysis (Gotch & Sargent, 1985; Sargent & Gotch, 1989; Locatelli et al., 2005). The primary analysis showed that morbidity was less at lower levels of time average urea concentration. The secondary 'mechanistic' analysis of the NCDS data done by Gotch and Sargent launched the issue of urea KT/V

Single-pool KT/V overestimates the removed amount of urea because of the postdialysis urea rebound, i.e., a fast postdialysis increase in urea concentration in plasma, which is a compartmental effect; therefore, the equilibrated KT/V (eqKT/V), estimated by the Daugirdas formula, was introduced to clinical practice (Daugirdas et al., 2001). Equilibrated KT/V values can be also calculated using an alternative equation by Daugirdas and

solute kinetic modeling one is able to evaluate dialysis efficiency.

**1. Introduction** 

(Gotch & Sargent, 1985).

*1Institute of Biocybernetics and Biomedical Engineering,* 

*Polish Academy of Sciences, Warsaw,* 
