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

Abstract

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.

Augmented patient‐specific functional medical imaging by implicit manifold learning

“…So we are aware that more sophisticated physical models can be considered. However, to be able to make a fair comparison, we seek a supervised learning approach encapsulating the same physics as the one used in our previous studies with the objective to get the cerebral blood pressure in nearly real time. Again, this is why the same cardiovascular model and the same arterial network have been considered as with the EnKF procedure.…”

“…Figure presents the general flowchart for this work with the following main steps: Hemodynamic and morphological data extraction : first, from magnetic resonance angiography and magnetic resonance imaging acquisitions and segmentation of a 3D time of flight magnetic resonance angiography (3D‐TOF‐MRA)—dicom files provided by the Department of Neuroradiology of the Centre Hospitalier Régional Universitaire de Montpellier (CHRU), Montpellier, France ,—blood flow rates in ascending aorta (AA), right and left internal carotid arteries (R‐ICA and L‐ICA) have been extracted using the GTFlow sofware ( http://www.gyrotools.com/products/gt-flow.html/) together with the morphological data relevant to geometric measurements and the morphology of some arteries through the use of the RadiANT DICOM Viewer software ( http://www.radiantviewer.com/). Patient‐specific arterial network construction : on the basis of these images, a patient‐specific arterial network of 33 arteries as shown in Figure consisting of the aorta, vertebral, carotid, and brachial arteries together with the complete circle of Willis has been then constructed. For more details, the reader is referred to previous works Machine learning Database generation : the next step has consisted in generating synthetic data by performing a series of forward simulations of the blood flow model (ℳ) described in detail below in Section 2.2.…”

“…Compared with the method used in previous works, the novelty in the general framework proposed here is the use of ML method instead of EnKF‐based parameter estimation algorithm.…”

“…For a forward simulation using the blood flow model (ℳ) presented in Section 2.2, this data is interrelated in the sense that the variables r , h , l , E , R P , R D , C of the network associated with the variable q in , the inlet flow rate (the blood flow rate in AA), represent the input parameters of the model, which we refer to as model input parameters , and the variables q and P , the output parameters, which we refer to as model output parameters . As a reminder, the Young moduli E are given by where k 1 , k 2 , k 3 are model constants and the inlet flow rate q in is defined using two components α and τ as follows: where α = 302 mL/s and τ = 0.3 second are nominal values taken from Lal et al These will be randomly perturbated below following a Gaussian distribution with means equal to these nominal values and standard deviations σ , which will be specified later, to produce samples of q in . For more details, the reader is referred to Lal et al…”

“…In all these situations, analytic models or numerical simulations can fill the gap. In previous works, the use of an algorithm based on ensemble Kalman filter (EnKF) technique coupled to a 0D compartement network has allowed to noninvasively estimate patient‐specific blood pressure in cerebral arteries . However, this procedure, which requires inverse problem solving, is too long, expensive and difficult to integrate in a medical acquisition device.…”