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

Bayesian parameter estimation for phosphate dynamics during hemodialysis

Hyperphosphatemia in patients with renal failure is associated with increased vascular calcification and mortality. Hemodialysis is a conventional treatment for patients with hyperphosphatemia. Phosphate kinetics during hemodialysis may be described by a diffusion process and modeled by ordinary differential equations. We propose a Bayesian model approach for estimating patient-specific parameters for phosphate kinetics during hemodialysis. The Bayesian approach allows us to both analyze the full parameter space using uncertainty quantification and to compare two types of hemodialysis treatments, the conventional single-pass and the novel multiple-pass treatment. We validate and test our models on synthetic and real data. The results show limited identifiability of the model parameters when only single-pass data are available, and that the Bayesian model greatly reduces the relative standard deviation compared to existing estimates. Moreover, the analysis of the Bayesian models reveal improved estimates with reduced uncertainty when considering consecutive sessions and multiple-pass treatment compared to single-pass treatment.

Recent Advances and Future Perspectives in the Use of Machine Learning and Mathematical Models in Nephrology

We reviewed some of the latest advancements in the use of mathematical models in nephrology. We looked over 2 distinct categories of mathematical models that are widely used in biological research and pointed out some of their strengths and weaknesses when applied to health care, especially in the context of nephrology. A mechanistic dynamical system allows the representation of causal relations among the system variables but with a more complex and longer development/implementation phase. Artificial intelligence/machine learning provides predictive tools that allow identifying correlative patterns in large data sets, but they are usually harder-to-interpret black boxes. Chronic kidney disease (CKD), a major worldwide health problem, generates copious quantities of data that can be leveraged by choice of the appropriate model; also, there is a large number of dialysis parameters that need to be determined at every treatment session that can benefit from predictive mechanistic models. Following important steps in the use of mathematical methods in medical science might be in the intersection of seemingly antagonistic frameworks, by leveraging the strength of each to provide better care.