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

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 patient-specific 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.