A Bayesian approach for the identification of patient-specific parameters in a dialysis kinetic model

Abstract

Hemodialysis is the most common therapy to treat renal insufficiency. However, notwithstanding the recent improvements, hemodialysis is still associated with a non-negligible rate of comorbidities, which could be reduced by customizing the treatment. Many differential compartment models have been developed to describe the mass balance of blood electrolytes and catabolites during hemodialysis, with the goal of improving and controlling hemodialysis sessions. However, these models often refer to an average uremic patient, while on the contrary the clinical need for customization requires patient-specific models. In this work, we assume that the customization can be obtained by means of patient-specific model parameters. We propose and validate a Bayesian approach to estimate the patientspecific parameters of a multi-compartment model, and to predict the single patient's response to the treatment, in order to prevent intra-dialysis complications. The likelihood function is obtained by means of a discretized version of the multi-compartment model, where the discretization is in terms of a Runge-Kutta method to guarantee convergence, and the posterior densities of model parameters are obtained through Markov Chain Monte Carlo simulation. Results show fair estimations and the applicability in the clinical practice.

Bayesian parameter estimation for phosphate dynamics during hemodialysis

“…If we consider the uncertainty in the correlation plot for the parameters in Figure 11 and Figure 10, we see a large 95% CI for the parameter estimates and relative standard deviation in Table B. 4 which is similar to the uncertainty associated with the estimate for the SP estimation in Section 4.1.…”

“…Considering the relative standard deviation for K s in Table B. 4, we find that it decreases from 20% to 5 % by considering the consecutive sessions compared to a single session. However, even in the case of a single session, our Bayesian approach has significantly smaller relative standard deviation compared to the estimates found by Debowska et al [5] and Agar et al [1], who report a relative standard deviation of 79% and 47%, respectively.…”

“…The Bayesian approach gives a complete image of the parameter estimation in terms of uncertainty quantification, i.e., posterior mean, credibility intervals and correlations. A Bayesian approach for patient-specific parameters for hemodialysis has been proposed by Bianchi et al [4] but does not consider the phosphate kinetics.…”