Patient-specific Blood Flow Simulations: Setting Dirichlet Boundary Conditions for Minimal Error with Respect to Measured Data

Variational data assimilation for transient blood flow simulations: Cerebral aneurysms as an illustrative example

“…A possible extension is therefore to take into account the deformation of the vessel wall,?tricerritricerri2015 to determined patient‐specific compliance parameters and to determine non‐Newtonian effects in terms of nonlinear rheology models. Furthermore, the geometry of the blood vessel can be treated as an unknown variable and recovered from the observations, for example, with the approach taken in Tiago et al or via shape optimisation techniques . Other improvements concern the variational set‐up itself.…”

“…The idea of applying data assimilating techniques to blood flow models has received significant attention in recent years (see Bertagna et al for an overview). In particular, variational data assimilation, which identifies unknown model parameters such that the difference between physical observations and model results is minimised, has been studied in the general setting for the optimal control of the Navier‐Stokes equations and in the specific case of blood flow simulations . The mathematical theory behind variational data assimilation is partially developed; in particular, the well‐possessedness of the (regularised) inverse minimisation problem for both flow and fluid‐structure interaction problem has been addressed in, eg, Guerra et al and Perego et al Alternatively, more advanced data assimilation strategies use reduced basis methods and/or Bayesian parameter estimating, cf, eg, previous studies .…”

“…In particular, variational data assimilation, which identifies unknown model parameters such that the difference between physical observations and model results is minimised, has been studied in the general setting for the optimal control of the Navier-Stokes equations [22][23][24] and in the specific case of blood flow simulations. [25][26][27][28][29] The mathematical theory behind variational data assimilation is partially developed; in particular, the well-possessedness of the (regularised) inverse minimisation problem for both flow and fluid-structure interaction problem has been addressed in, eg, Guerra et al 24 and Perego et al 30 Alternatively, more advanced data assimilation strategies use reduced basis methods and/or Bayesian parameter estimating, cf, eg, previous studies. [31][32][33][34] For bifurcation problems, more general strategies of setting boundary conditions have been developed in previous works, [35][36][37] in particular since the main problem in these cases is the determination of the flow division rather than a complete set of boundary conditions as long as flow extensions are appropriate.…”

Numerical simulations for the stabilization and estimation problem of a semilinear partial differential equation

“…Meanwhile, during the last two decades, fluid dynamics has also been intensively used in blood flow modeling [18,27]. Within this framework, it has been shown that a robust usage of boundary control may be important to build effective tools for medical training and prediction, which require individual-based simulations [14,21,36]. Also, it as been seen that the role of the geometry in the behavior of the blood flow is very important [19].…”

Uncertainty propagation of phase contrast-MRI derived inlet boundary conditions in computational hemodynamics models of thoracic aorta

“…The subject is part of the data-set analyzed in Morbiducci et al (2011a). models: reconstructed vessel geometry (Sankaran & Marsden 2011;Sankaran et al 2015Sankaran et al , 2016, input and output BCs (Sankaran & Marsden 2011;Morbiducci et al 2013;Tiago et al 2014;Valen-Sendstad et al 2015;Schiavazzi et al 2016;Tran et al 2017), vessel distensibility and motion (Jin et al 2003;Zhao et al 2000;Eck et al 2016;Javadzadegan et al 2016) and rheological properties of blood (Lee & Steinman 2007;Morbiducci et al 2011b). In a recent study, the Authors reported a numerical experiment in which different possible strategies of applying PC-MRI measured flow data as BCs in computational hemodynamic models of healthy human aorta were implemented (Morbiducci et al 2013).…”