Applications of variational data assimilation in computational hemodynamics

D’Elia, Marta; Mirabella, Lucia; Passerini, Tiziano; Perego, Mauro; Piccinelli, Marina; Vergara, Christian; Veneziani, Alessandro

doi:10.1007/978-88-470-1935-5_12

Cited by 32 publications

(54 citation statements)

References 75 publications

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“…The above constrained minimization approach resembles variational methods of Data Assimilation -see e.g. [20,47,48,197]. In this variational context, a further possibility consists of including in (25) some sparse measures available not only on the boundary but also inside the region of interest.…”

Section: A Control-based Approachmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

159

157

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This review paper addresses the so called geometric multiscale approach for the numerical simulation of blood flow problems, from its origin (that we can collocate in the second half of '90s) to our days. By this approach the blood fluid-dynamics in the whole circulatory system is described mathematically by means of heterogeneous featuring different degree of detail and different geometric dimension that interact together through appropriate interface coupling conditions.Our review starts with the introduction of the stand-alone problems, namely the 3D fluidstructure interaction problem, its reduced representation by means of 1D models, and the so-called lumped parameters (aka 0D) models, where only the dependence on time survives. We then address specific methods for stand-alone 3D models when the available boundary data are not enough to ensure the mathematical well posedness. These so-called "defective problems" naturally arise in practical applications of clinical relevance but also because of the interface coupling of heterogeneous problems that are generated by the geometric multiscale process. We also describe specific issues related to the boundary treatment of reduced models, particularly relevant to the geometric multiscale coupling. Next, we detail the most popular numerical algorithms for the solution of the coupled problems. Finally, we review some of the most representative works -from different research groups -which addressed the geometric multiscale approach in the past years.A proper treatment of the different scales relevant to the hemodynamics and their interplay is essential for the accuracy of numerical simulations and eventually for their clinical impact. This paper aims at providing a state-of-the-art picture of these topics, where the gap between theory and practice demands rigorous mathematical models to be reliably filled.

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Section: A Control-based Approachmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

159

157

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“…Furthermore, the relevance of lumen geometries of ruptured aneurysms may be lessened by thrombus formation or rapid changes in aneurysm geometry just before rupture. If wall motion is to be included in a study, either it is necessary to have clinical images of changes in wall position during the cardiac cycle, in which case wall motion can be prescribed, 5,6 or the heterogeneous material properties and thicknesses of the aneurysm wall must be known, so wall motion can be predicted. This level of information is rarely available to CFD researchers.…”

Section: Why Are There So Many Idealizations In Cfd Studies?mentioning

confidence: 99%

“…The recent application of methods of data assimilation to computational hemodynamics provides a promising approach for improving the reliability and accuracy of CFD studies using clinical data. 5 Dr Kallmes has raised timely and important questions for the field and has begun a beneficial and much needed exchange between clinicians and engineers. There is an irrefutable need to continue this frank dialogue in other forums, such as special sessions in conferences.…”

Section: Future Directionsmentioning

confidence: 99%

Computational Fluid Dynamics in Aneurysm Research: Critical Reflections, Future Directions

Robertson¹,

Watton²

2012

AJNR Am J Neuroradiol

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significant parameter that has yet to be fully evaluated.2 New technologies develop and evolve so as to both optimize their capabilities and expand the applications to which they may be applied. Such it was with x-rays, and such it is with CFD. New technologies are most often overvalued when first described; then, as they become disseminated, they sink below their true value, finally reaching a state of realistic value only when they have been widely tested and optimized. Potential applications of CFD have not been fully explored, optimization of computational techniques for assessing blood flow in and around IAs is ongoing, and the definition of the most meaningful output parameters are not at a stage where there can be any broad consensus. Thus, in our opinion, it is not realistic to make a value judgment regarding the ultimate value of CFDs, either as a means for investigating basic hemodynamic phenomena or as a tool that may be useful in a clinical environment. Next Step and Closing RemarksTo us, it seems implausible to expect that, in isolation, CFD studies may reveal singular keys to important questions about a biologic process such as the initiation, growth, and rupture of IAs. It does, however, seem quite plausible that the results from CFD studies on large populations could provide great help in categorizing aneurysms according any number of hemodynamic parameters. Perhaps, then, these categories, when correlated with other factors known to be important in vascular health-such as collagen mutations, smoking, family history, and so on-and then if further combined with information specific to individual patients-such as age, sex, and perianeurysmal environment-could give insights that might prove useful in predicting the risk of aneurysm rupture. We fully realize that correlations do not represent causation; however, in our experiences, as well as in those of others, they sometimes offer very significant hints. 3,4 As the ability to perform CFD in clinical environments on large numbers of patients increases, as more insight is gained into the regulation of arterial health (homeostasis) and remodeling, as more understanding is gained about the mechanics of the vascular wall, as the ability to image not only the vascular lumen but also the arterial wall increases, this additional information may send computational scientists back to broaden and refine their mathematic models, thereby leading to methods that would allow investigation and integration of other important and potentially clinically relevant parameters, such as collagen turnover, cross-linking, and so on (eg, fluid-structure-growth modeling).Believing in the great potential for the integration of observations and measurements made by clinicians with simulations, calculations, and models made by scientists, we feel that this is a time to be optimistic and proactive in collaborations that unite and optimize our ability to define just what value CFD adds to the ability to mitigate the death and misery currently associated with IAs.

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“…On the other hand, whenever some parameters are uncertain, we aim at inferring their values (and/or distributions) from indirect observations (and/or measures) by solving an inverse problem: given an observed output, can we deduce the value of the parameters that resulted in this output? Such problems are often encountered in cardiovascular mathematics as problems of parameter identification [7,70], variational data assimilation [13,50,63,66], or shape optimization [1,44,51,64]. Computational inverse problems are characterized by two main difficulties:…”

Section: Introductionmentioning

confidence: 99%

A reduced computational and geometrical framework for inverse problems in hemodynamics

Lassila

Manzoni

Quarteroni³

et al. 2013

Numer Methods Biomed Eng

104

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SUMMARYThe solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper we apply a domain parametrization technique to reduce both the geometrical and computational complexity of the forward problem, and replace the finite element solution of the incompressible NavierStokes equations by a computationally less expensive reduced basis approximation. This greatly reduces the cost of simulating the forward problem. We then consider the solution of inverse problems in both the deterministic sense, by solving a least-squares problem, and in the statistical sense, by using a Bayesian framework for quantifying uncertainty. Two inverse problems arising in haemodynamics modelling are considered: (i) a simplified fluid-structure interaction model problem in a portion of a stenosed artery for quantifying the risk of atherosclerosis by identifying the material parameters of the arterial wall based on pressure measurements; (ii) a simplified femoral bypass graft model for robust shape design under uncertain residual flow in the main arterial branch identified from pressure measurements.

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Applications of variational data assimilation in computational hemodynamics

Cited by 32 publications

References 75 publications

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Computational Fluid Dynamics in Aneurysm Research: Critical Reflections, Future Directions

A reduced computational and geometrical framework for inverse problems in hemodynamics

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