A data assimilation approach for non-Newtonian blood flow simulations in 3D geometries

Guerra, Telma; Catarino, Catarina; Mestre, Tânia; Santos, Sara; Tiago, Jorge; Sequeira, Adélia

doi:10.1016/j.amc.2017.10.029

Cited by 9 publications

(8 citation statements)

References 27 publications

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“…with̃= 1 − and N+1 u = 0. From (25), we observe that the adjoint system employs the same timestepping scheme as the forward discretisation but with a modified advective velocity. Further, the adjoint system enforces homogeneous velocity Dirichlet boundary conditions on the controlled surfaces using a Nitsche-like approach.…”

Section: Adjoint Equationsmentioning

confidence: 99%

“…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 .…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Funke

Nordaas

Evju

et al. 2018

Numer Methods Biomed Eng

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Several cardiovascular diseases are caused from localised abnormal blood flow such as in the case of stenosis or aneurysms. Prevailing theories propose that the development is caused by abnormal wall shear stress in focused areas. Computational fluid mechanics have arisen as a promising tool for a more precise and quantitative analysis, in particular because the anatomy is often readily available even by standard imaging techniques such as magnetic resonance and computed tomography angiography. However, computational fluid mechanics rely on accurate initial and boundary conditions, which are difficult to obtain. In this paper, we address the problem of recovering high-resolution information from noisy and low-resolution physical measurements of blood flow (for example, from phase-contrast magnetic resonance imaging [PC-MRI]) using variational data assimilation based on a transient Navier-Stokes model. Numerical experiments are performed in both 3D (2D space and time) and 4D (3D space and time) and with pulsatile flow relevant for physiological flow in cerebral aneurysms. The results demonstrate that, with suitable regularisation, the model accurately reconstructs flow, even in the presence of significant noise.

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Section: Adjoint Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Funke

Nordaas

Evju

et al. 2018

Numer Methods Biomed Eng

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show abstract

“…On the contrary, we do not have this problem with the second lesion as the branch is long enough beyond the sensor. is shows that these types of boundary conditions are not appropriate and not realistic to perform such calculation in the coronary arteries, though their widespread use (see [17]). Now, comparing Windkessel and mixed boundary conditions, we can see that the first lesion conserves the same FFR classification-hemodynamically non significant-while the second lesion moves from the non significant stenosis class to the significant one.…”

Section: Discussionmentioning

confidence: 99%

Virtual FFR Quantified with a Generalized Flow Model Using Windkessel Boundary Conditions

Chahour

Aboulaïch

Habbal

et al. 2020

Computational and Mathematical Methods in Medicine

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Fractional flow reserve (FFR) has proved its efficiency in improving patient diagnosis. In this paper, we consider a 2D reconstructed left coronary tree with two artificial lesions of different degrees. We use a generalized fluid model with a Carreau law and use a coupled multidomain method to implement Windkessel boundary conditions at the outlets. We introduce our methodology to quantify the virtual FFR and conduct several numerical experiments. We compare FFR results from the Navier–Stokes model versus generalized flow model and for Windkessel versus traction-free outlet boundary conditions or mixed outlet boundary conditions. We also investigate some sources of uncertainty that the FFR index might encounter during the invasive procedure, in particular, the arbitrary position of the distal sensor. The computational FFR results show that the degree of stenosis is not enough to classify a lesion, while there is a good agreement between the Navier–Stokes model and the non-Newtonian flow model adopted in classifying coronary lesions. Furthermore, we highlight that the lack of standardization while making FFR measurement might be misleading regarding the significance of stenosis.

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“…PC‐MRI and ultrasound) use data assimilation to match simulation data with measured data. Many of these approaches focus on finding the optimal boundary conditions to match a target velocity field, for example, a measured velocity field [DPV12, FNE*18, IAWW18, GCM*18]. They often consider the whole measurement to find the 2D in/out‐flow conditions that best match the measured data.…”

Section: Related Workmentioning

confidence: 99%

Data Assimilation for Full 4D PC‐MRI Measurements: Physics‐Based Denoising and Interpolation

Hoon

Jalba

Farag

et al. 2020

Computer Graphics Forum

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Phase‐Contrast Magnetic Resonance Imaging (PC‐MRI) surpasses all other imaging methods in quality and completeness for measuring time‐varying volumetric blood flows and has shown potential to improve both diagnosis and risk assessment of cardiovascular diseases. However, like any measurement of physical phenomena, the data are prone to noise, artefacts and has a limited resolution. Therefore, PC‐MRI data itself do not fulfil physics fluid laws making it difficult to distinguish important flow features. For data analysis, physically plausible and high‐resolution data are required. Computational fluid dynamics provides high‐resolution physically plausible flows. However, the flow is inherently coupled to the underlying anatomy and boundary conditions, which are difficult or sometimes even impossible to adequately model with current techniques. We present a novel methodology using data assimilation techniques for PC‐MRI noise and artefact removal, generating physically plausible flow close to the measured data. It also allows us to increase the spatial and temporal resolution. To avoid sensitivity to the anatomical model, we consider and update the full 3D velocity field. We demonstrate our approach using phantom data with various amounts of induced noise and show that we can improve the data while preserving important flow features, without the need of a highly detailed model of the anatomy.

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A data assimilation approach for non-Newtonian blood flow simulations in 3D geometries

Cited by 9 publications

References 27 publications

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

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

Virtual FFR Quantified with a Generalized Flow Model Using Windkessel Boundary Conditions

Data Assimilation for Full 4D PC‐MRI Measurements: Physics‐Based Denoising and Interpolation

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