Identification of patient-specific parameters in a kinetic model of fluid and mass transfer during dialysis

Hemodialysis (HD) is nowadays the most common therapy to treat renal insufficiency. However, despite the improvements made in the last years, HD is still associated with a non-negligible rate of co-morbidities, which could be reduced by means of an appropriate treatment customization. Many differential multi-compartment models have been developed to describe solute kinetics during HD, to optimize treatments, and to prevent intra-dialysis complications; however, they often refer to an average uremic patient. On the contrary, the clinical need for customization requires patient-specific models. In this work, assuming that the customization can be obtained by means of patient-specific model parameters, we propose 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 through a discretized version of a multi-compartment model, where the discretization is in terms of a Runge-Kutta method to guarantee the convergence, and the posterior densities of model parameters are obtained through Markov Chain Monte Carlo simulation.