Global sensitivity analysis for assessing the parameters importance and setting a stopping criterion in a biomedical inverse problem

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.

Augmented patient-specific functional medical imaging by implicit manifold learning

This paper uses machine learning to enrich magnetic resonance angiography and magnetic resonance imaging acquisitions. A convolutional neural network is built and trained over a synthetic database linking geometrical parameters and mechanical characteristics of the arteries to blood flow rates and pressures in an arterial network. Once properly trained, the resulting neural network can be used in order to predict blood pressure in cerebral arteries noninvasively in nearly real-time. One challenge here is that not all input variables present in the synthetic database are known from patient-specific medical data. To overcome this challenge, a learning technique, which we refer to as implicit manifold learning, is employed: in this view, the input and output data of the neural network are selected based on their availability from medical measurements rather than being defined from the mechanical description of the arterial system. The results show the potential of the method and that machine learning is an alternative to costly ensemble based inversion involving sophisticated fluid structure models.

Backward sensitivity analysis and reduced-order covariance estimation in noninvasive parameter identification for cerebral arteries

Using a previously developed inversion platform for functional cerebral medical imaging with ensemble Kalman filters, this work analyzes the sensitivity of the results with respect to different parameters entering the physical model and inversion procedure, such as the inlet flow rate from the heart, the choice of the boundary conditions, and the nonsymmetry in the network terminations. It also proposes an alternative low complexity construction for the covariance matrix of the hemodynamic parameters of a network of arteries including the circle of Willis. The platform takes as input patient-specific blood flow rates extracted from magnetic resonance angiography and magnetic resonance imaging (dicom files) and is applied to several available patients data. The paper presents full analysis of the results for one of these patients, including a sensitivity study with respect to the proximal and distal boundary conditions. The results notably show that the uncertainties on the inlet flow rate led to uncertainties of the same order of magnitude in the estimated parameters (blood pressure and elastic parameters) and that three-lumped parameters boundary conditions are necessary for a correct retrieval of the target signals.