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From inverse problems in mathematical physiology to quantitative differential diagnoses

Zenker, S and Rubin, J and Clermont, G (2007) From inverse problems in mathematical physiology to quantitative differential diagnoses. PLoS Computational Biology, 3 (11). 2072 - 2086. ISSN 1553-734X

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Abstract

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement today's evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information. © 2007 Zenker et al.


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Details

Item Type: Article
Status: Published
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Zenker, S
Rubin, Jjonrubin@pitt.eduJONRUBIN
Clermont, Gcler@pitt.eduCLER
Contributors:
ContributionContributors NameEmailPitt UsernameORCID
EditorTucker-Kellogg, GregUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Date: 1 November 2007
Date Type: Publication
Journal or Publication Title: PLoS Computational Biology
Volume: 3
Number: 11
Page Range: 2072 - 2086
DOI or Unique Handle: 10.1371/journal.pcbi.0030204
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
School of Medicine > Critical Care Medicine
Refereed: Yes
ISSN: 1553-734X
PubMed ID: 17997590
Date Deposited: 18 Jul 2012 21:04
Last Modified: 02 Feb 2019 16:58
URI: http://d-scholarship.pitt.edu/id/eprint/12922

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