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Computational and Mathematical Methods in Medicine
Volume 11, Issue 1, Pages 27-47
Original Article

A Model for Liver Homeostasis Using Modified Mean-Reverting Ornstein–Uhlenbeck Process

1Translational and Molecular Medicine, Pfizer Global Research and Development, Groton, CT, USA
2Division of Nephrology, Department of Internal Medicine, The Ohio State University, Columbus, OH, USA
3Department of Mathematics, The Ohio State University, Columbus, USA

Received 14 August 2008; Accepted 13 November 2008

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Short of a liver biopsy, hepatic disease and drug-induced liver injury are diagnosed and classified from clinical findings, especially laboratory results. It was hypothesized that a healthy hepatic dynamic equilibrium might be modelled by an Ornstein–Uhlenbeck (OU) stochastic process, which might lead to more sensitive and specific diagnostic criteria. Using pooled data from healthy volunteers in pharmaceutical clinical trials, this model was applied using maximum likelihood (ML) methods. It was found that the exponent of the autocorrelation function was proportional to the square root of time rather than time itself, as predicted by the OU model. This finding suggests a stronger autocorrelation than expected and may have important implications regarding the use of laboratory testing in clinical diagnosis, in clinical trial design, and in monitoring drug safety. Besides rejecting the OU hypothesis for liver test homeostasis, this paper presents ML estimates for the multivariate Gaussian distribution for healthy adult males. This work forms the basis for a new approach to mathematical modelling to improve both the sensitivity and specificity of clinical measurements over time.