Analytical solution of multicompartment solute kinetics for hemodialysis

Rapid prototyping of multi-compartment models for urea kinetics in hemodialysis: a System Dynamics approach

Models of urea kinetics facilitate a mechanistic understanding of urea transfer and provide a tool for optimizing dialysis efficacy. Dual-compartment models have largely replaced single-compartment models as they are able to accommodate the urea rebound on the cessation of dialysis. Modeling the kinetics of urea and other molecular species is frequently regarded as a rarefied academic exercise with little relevance at the bedside. We demonstrate the utility of System Dynamics in creating multi-compartment models of urea kinetics by developing a dual-compartment model that is efficient, intuitive, and widely accessible to a range of practitioners. Notwithstanding its simplicity, we show that the System Dynamics model compares favorably with the performance of a more complex volume-average model in terms of calibration to clinical data and parameter estimation. Its intuitive nature, ease of development/modification, and excellent performance with real-world data may make System Dynamics an invaluable tool in widening the accessibility of hemodialysis modeling.

Analytical Solutions of a Two-Compartment Model Based on the Volume-Average Theory for Blood Toxin Concentration during and after Dialysis

Accurate prediction of blood toxin concentration during and after dialysis will greatly contribute to the determination of dialysis treatment conditions. Conventional models, namely single-compartment model and two-compartment model, have advantages and disadvantages in terms of accuracy and practical application. In this study, we attempted to derive the mathematical model that predicts blood toxin concentrations during and after dialysis, which has both accuracy and practicality. To propose the accurate model, a new two-compartment model was mathematically derived by adapting volume-averaging theory to the mass transfer around peripheral tissues. Subsequently, to propose a practical model for predicting the blood toxin concentration during dialysis, an analytical solution expressed as algebraic expression was derived by adopting variable transformation. Furthermore, the other analytical solution that predicts rebound phenomena after dialysis was also derived through similar steps. The comparisons with the clinical data revealed that the proposed analytical solutions can reproduce the behavior of the measured blood urea concentration during and after dialysis. The analytical solutions proposed as algebraic expressions will allow a doctor to estimate the blood toxin concentration of a patient during and after dialysis. The proposed analytical solutions may be useful to consider the treatment conditions for dialysis, including the rebound phenomenon.

A unidimensional diffusion model applied to uremic toxin kinetics in haemodiafiltration treatments

Kinetic modelling in haemodialysis is usually based upon the resolution of volume-defined compartment models. The interaction among these compartments is described by purely diffusive processes. In this paper we present an alternative kinetic model for uremic toxins in post-dilutional haemodiafiltration treatments by means of a unidimensional diffusion equation. A wide range of solutes such as urea, creatinine, $\beta _{2}$-microglobulin, myoglobin and prolactin were studied by imposing appropriate boundary and initial conditions in a virtual [0,1] domain. The diffusivity along the domain and the extraction rate at the dialyser are the kinetic parameters which were fitted by least-squares for every studied solute. The accuracy of the presented volumeless model as well as the behavior of the proposed kinetic parameters could be an alternative to the compartment description for a variety of molecular weight uremic toxins undergoing different treatment configurations.

Mathematical Representation of Standard Kt/V Including Ultrafiltration and Residual Renal Function

A new formula for calculating standard Kt/V from clinical data has been derived mathematically. It is based on using the relation between eKt/V and the pre- and postdialysis concentrations in order to find the steady state concentrations. The resulting expression for standard Kt/V depends on the treatment schedule (number, length, and spacing of treatments), residual renal function, and eKt/V and relative ultrafiltration volume of each individual treatment. These results include the effects of ultrafiltration and residual renal function also in the case with unequal treatments that may be arbitrarily distributed over the week. The new formula is found to agree, within small fractions of a percentage, with standard Kt/V from simulations of 3 and 5 days per week schedules. Several approximations are also suggested and their accuracies analyzed. It is shown that the use of the midweek eKt/V and ultrafiltration for all treatments of the week is an acceptable approximation. In the presence of residual renal function, the timing of the treatments is an important factor, and particularly in this case, the new formula shows improved accuracy over previously published formulas.