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Open Access Research article

Bayesian model selection validates a biokinetic model for zirconium processing in humans

Daniel Schmidl12, Sabine Hug12, Wei Bo Li3*, Matthias B Greiter3 and Fabian J Theis12*

Author Affiliations

1 Institute of Bioinformatics and Systems Biology, Helmholtz Zentrum München German Research Center for Environmental Health, Neuherberg, Germany

2 Institute for Mathematical Sciences, Technische Universität München, Garching, Germany

3 Research Unit Medical Radiation Physics and Diagnostics, Helmholtz Zentrum München German Research Center for Environmental Health, Neuherberg, Germany

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BMC Systems Biology 2012, 6:95  doi:10.1186/1752-0509-6-95

Published: 5 August 2012



In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection.


We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler.


In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.

Bayesian inference; Model selection; MCMC sampling; Compartmental model; Internal dosimetry; Systems biology