Quasi-steadiness approximation for the two-compartment solute kinetic model

We analytically solved the equation of the Variable volume, two-compartment solute kinetic model (TCSKM). From the solution, we constructed an expression of weekly concentration profiles developing in the patient's body by routine hemodialyses. Obtained formulas can be used to calculate Kt/V, solute reduction index (SRI), the solute generation rate (G) per unit distribution volume (V), and a mass transfer coefficient (MTC) between the two compartments. To estimate these parameters, the formulas only need three-point data during a dialysis, that is, pre-, one-hour, and post-dialysis solute concentrations instead of four that would otherwise be needed. A 48 hour data point is not required. The weekly concentration profiles can be easily calculated by the formulas. As examples of clinical applications, we calculated Kt/V, G/V, and SRI of urea, Cr, and uric acid using plasma data of 121 hemodialyzed patients. Then the results were compared with the single-compartment solute kinetic model (SCSKM). The obtained mean MTC/V values, that is, 1.08 (1/hr) for urea, 0.53 (1/hr) for Cr, and 1.11 (1/hr) for uric acid, were consistent with the previous works. SCSKM overestimated the mean G/V by 7.1%, 15.9%, and 10.0%, and the mean SRI by 6.7%, 18.6%, and 10.0%, for urea, Cr, and uric acid, respectively. The solute distribution volume ratio of TCSKM to SCSKM, (V)(TCSKM)/(V)(SCSKM), depended on the value of MTC/V and the hemodialysis duration. Using pedometers, we measured the total number of steps the patients took during a week. We found that the total number of steps in a week was significantly correlated with the Cr generation rate (r = 0.285, P < 0.03), but that it was not significantly correlated with the other generation rates (r = 0.204, P > 0.09 for urea, and r = 0.209, P > 0.08 for uric acid). These data suggest that the Cr generation rate is related to the patient's physical activity. We conclude that the formulas can estimate an adequate dialysis prescription for the hemodialyzed patient.