Browsing by Author "Nolte, David"

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    Convergence analysis of pressure reconstruction methods from discrete velocities
    (2023) Araya, Rodolfo; Bertoglio, Cristobal; Carcamo, Cristian; Nolte, David; Uribe, Sergio
    Magnetic resonance imaging allows the measurement of the three-dimensional velocity field in blood flows. Therefore, several methods have been proposed to reconstruct the pressure field from such measurements using the incompressible Navier-Stokes equations, thereby avoiding the use of invasive technologies. However, those measurements are obtained at limited spatial resolution given by the voxel sizes in the image. In this paper, we propose a strategy for the convergence analysis of state-of-the-art pressure reconstruction methods. The methods analyzed are the so-called Pressure Poisson Estimator (PPE) and Stokes Estimator (STE). In both methods, the right-hand side corresponds to the terms that involving the field velocity in the Navier-Stokes equations, with a piecewise linear interpolation of the exact velocity. In the theoretical error analysis, we show that many terms of different order of convergence appear. These are certainly dominated by the lowest-order term, which in most cases stems from the interpolation of the velocity field. However, the numerical results in academic examples indicate that only the PPE may profit of increasing the polynomial order, and that the STE presents a higher accuracy than the PPE, but the interpolation order of the velocity field always prevails. Furthermore, we compare the pressure estimation methods on real MRI data, assessing the impact of different spatial resolutions and polynomial degrees on each method. Here, the results are consistent with the academic test cases in terms of sensitivity to polynomial order as well as the STE showing to be potentially more accurate when compared to reference pressure measurements.
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    Validation of 4D Flow based relative pressure maps in aortic flows
    (2021) Nolte, David; Urbina, Jesus; Sotelo, Julio; Sok, Leo; Montalba, Cristian; Valverde, Israel; Osses, Axel; Uribe, Sergio; Bertoglio, Cristobal
    While the clinical gold standard for pressure difference measurements is invasive catheterization, 4D Flow MRI is a promising tool for enabling a non-invasive quantification, by linking highly spatially resolved velocity measurements with pressure differences via the incompressible Navier-Stokes equations. In this work we provide a validation and comparison with phantom and clinical patient data of pressure difference maps estimators. We compare the classical Pressure Poisson Estimator (PPE) and the new Stokes Estimator (STE) against catheter pressure measurements under a variety of stenosis severities and flow intensities. Specifically, we use several 4D Flow data sets of realistic aortic phantoms with different anatomic and hemodynamic severities and two patients with aortic coarctation. The phantom data sets are enriched by subsampling to lower resolutions, modification of the segmentation and addition of synthetic noise, in order to study the sensitivity of the pressure difference estimators to these factors. Overall, the STE method yields more accurate results than the PPE method compared to catheterization data. The superiority of the STE becomes more evident at increasing Reynolds numbers with a better capacity of capturing pressure gradients in strongly convective flow regimes. The results indicate an improved robustness of the STE method with respect to variation in lumen segmentation. However, with heuristic removal of the wall-voxels, the PPE can reach a comparable accuracy for lower Reynolds' numbers. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )