Global sensitivity analysis for assessing the parameters importance and setting a stopping criterion in a biomedical inverse problem. (5th April 2021)

• Record Type: Journal Article
• Authors: Rapadamnaba, Robert; Ribatet, Mathieu; Mohammadi, Bijan
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 37:Number 6(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-04-05
• Subjects: convergence stopping criterion -- hemodynamic inverse problems -- parameter estimation -- sensitivity analysis -- Sobol' sensitivity indices -- uncertainty quantification; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.3458
• Languages: English
• ISSNs: 2040-7939

Abstract

Abstract: This paper shows how to obtain in addition to the standard deviations available after a data assimilation procedure based on the ensemble Kalman filter, an apportioning of the total uncertainty in the outputs of a patient‐specific blood flow model into small portions of uncertainty due to input parameters. Statistical indicators generally used for identifying the importance of numerical parameters, namely the Sobol' first order and total indices, are introduced and discussed. These allow the identification of the importance rank of the different input parameters for the patient‐specific blood flow model, as well as the influence of the interactions between these parameters on the model output variance. The results show that knowing the importance rank of the model input parameters during the assimilation procedure is useful to avoid unnecessary over‐solving and to find a suitable stopping criterion in clinical situations where faster diagnosis is always requested. Indeed, the work permits to reduce typically by a factor of six the time to solution and most importantly with very limited extra calculation using already available information. Abstract : Patient‐specific nonlinear and very complex blood flow model is linearized in order to perform global sensitivity analysis based on the Sobol' indices on a much simpler model. The technique used allows not only to identify and prioritize the important parameters of the blood flow model but also to explain the poor identifiability of the model parameters estimated using ensemble Kalman filtering. This provides, in addition to the filtering results, an indication of each model parameter importance and permits also to find when it is safe to stop the ensemble Kalman filter based parameter estimation algorithm used giving increasing confidence level on the outcome of the assimilation, and this even in situations where some parameters might have not fully converged to steady values. This stopping criterion setting is particularly useful in clinical situations where faster diagnosis is always requested.