Bayesian parameter estimation for phosphate dynamics during hemodialysis

Katrine O. Bangsgaard; Morten Andersen; James G. Heaf; Johnny T. Ottesen; Katrine O. Bangsgaard; Morten Andersen; James G. Heaf; Johnny T. Ottesen

doi:10.3934/mbe.2023207

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 4455-4492. doi: 10.3934/mbe.2023207

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Research article

Bayesian parameter estimation for phosphate dynamics during hemodialysis

1.
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Richard Petersens Plads, Building 324, 2800 Kongens Lyngby, Denmark
2.
Centre for Mathematical Modeling – Human Health and Disease, Department of Science and Mathematics, Roskilde University, 4000 Roskilde, Denmark
3.
Department of Medicine, Zealand University Hospital, 4000 Roskilde, Denmark

Received: 08 September 2022 Revised: 13 December 2022 Accepted: 19 December 2022 Published: 26 December 2022

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.
- hemodialysis,
- phosphate kinetics,
- mathematical modeling,
- parameter estimation,
- uncertainty quantification
Citation: Katrine O. Bangsgaard, Morten Andersen, James G. Heaf, Johnny T. Ottesen. Bayesian parameter estimation for phosphate dynamics during hemodialysis[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 4455-4492. doi: 10.3934/mbe.2023207

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Abstract

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.

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