Uncertainty quantification of wall shear stress in intracranial aneurysms using a data-driven statistical model of systemic blood flow variability

Sarrami‐Foroushani, Ali; Lassila, Toni; Gooya, Ali; Geers, Arjan J.; Frangi, Alejandro F.

doi:10.1016/j.jbiomech.2016.10.005

Cited by 25 publications

(28 citation statements)

References 42 publications

(1 reference statement)

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“…We previously modelled between‐subjects ICA flow variability in Sarrami‐Foroushani et al, where data from 17 healthy young adults were used to train a Gaussian process model. In that work, the time‐averaged mean flow rate was normalised for a given arterial diameter to achieve a time‐averaged WSS of 1.5 Pa at the level of the carotid sinus.…”

Section: Methodsmentioning

confidence: 99%

“…The mechanobiological growth and rupture process of IAs has been linked to changes in wall shear stress (WSS) patterns. A number of CFD studies have looked at the effect of cerebral blood flow (CBF) fluctuations in WSS patterns, but none to our knowledge have considered the effect of the CARS. Quantities of interest include time‐averaged WSS (TAWSS), oscillatory shear index (OSI), and transverse WSS (TransWSS):

\begin{matrix} right TAWSS (x) & left = \frac{1}{T_{period}} \int_{T_{0}}^{T_{0} + T_{period}} | τ_{w} (x, t) | d t; & right \\ right OSI (x) & left = \frac{1}{2} (1 - \frac{|\int_{T_{0}}^{T_{0} + T_{period}} τ_{w} (x, t) d t|}{\int_{T_{0}}^{T_{0} + T_{period}} |τ_{w} (x, t)| d t}); \\ right TransWSS (x) & left = \frac{1}{T_{period}} \int_{T_{0}}^{T_{0} + T_{period}} |τ_{w} (x, t) \cdot (\hat{p} \times \hat{n})| d t, \end{matrix}

where

\overset{n}{true}

is the surface normal, and the unit vector

\overset{p}{true}

in the direction of the time‐averaged WSS vector can be calculated as follows:

\overset{p}{true} false(x false) = true \int_{T_{0}}^{T_{0} +}

…”

Section: Methodsmentioning

confidence: 99%

“…This, in turn, will lead to overconfidence in vascular CFD uncertainty quantification. More recently, statistical models of carotid flow variability have been proposed in the literature and used to perform uncertainty quantification of vascular CFD. While between‐subjects flow variability is relatively straightforward to quantify by repeated measurements in a suitably selected cohort, a more informative measure would be within‐subject flow variability, ie, multiple flow measurements in the same subject but over a series of physiological states (eg, rest vs exercise).…”

Section: Introductionmentioning

confidence: 99%

“…Mean flow varies less within‐subject (<10%) due to the modulating effect of the cerebral autoregulation system, yet changes to the flow waveform can still be observed. In previous studies, it has been shown that changes in wall shear stress (WSS) induced by flow variability can significantly change the CFD‐based predictions of intracranial aneurysm rupture risk . We consider within‐subject flow variability induced by changes in systolic blood pressure (BP) and heart rate (HR) during physical exercise and study the corresponding changes in WSS indicators, such as time‐averaged WSS (TAWSS) or oscillatory shear index (OSI) in 54 subjects.…”

Section: Introductionmentioning

confidence: 99%

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Population‐specific modelling of between/within‐subject flow variability in the carotid arteries of the elderly

Lassila

Sarrami‐Foroushani

Hejazi

et al. 2019

Numer Methods Biomed Eng

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Computational fluid dynamics models are increasingly proposed for assisting the diagnosis and management of vascular diseases. Ideally, patient-specific flow measurements are used to impose flow boundary conditions. When patient-specific flow measurements are unavailable, mean values of flow measurements across small cohorts are used as normative values. In reality, both the between-subjects and within-subject flow variabilities are large. Consequently, neither one-shot flow measurements nor mean values across a cohort are truly indicative of the flow regime in a given person. We develop models for both the between-subjects and within-subject variability of internal carotid flow. A log-linear mixed effects model is combined with a Gaussian process to model the between-subjects flow variability, while a lumped parameter model of cerebral autoregulation is used to model the within-subject flow variability in response to heart rate and blood pressure changes. The model parameters are identified from carotid ultrasound measurements in a cohort of 103 elderly volunteers. We use the models to study intracranial aneurysm flow in 54 subjects under rest and exercise and conclude that OSI, a common wall shear-stress derived quantity in vascular CFD studies, may be too sensitive to flow fluctuations to be a reliable biomarker.KEYWORDS cerebrovascular disease, computational fluid dynamics, Gaussian process models, patient-specific models, uncertainty quantification Numerous computational fluid dynamics (CFD) models of human cardiovascular and cerebrovascular physiology are published every year, but few of them make any impact in clinical practice. This inconvenient truth has been blamed on the improper use of CFD solvers, 1 insufficient validation of biomechanics models, 2 and lack of understanding of the clinical decision-making process by the biomedical engineers building the models. 3 One additional explanation is that many "patient-specific" CFD models fail to consider the physiological variability of vascular flow, confounding interpretation of model results and producing overly confident predictions of flow quantities.Patient-specific modelling of vascular flow requires an accurate description of the lumen plus the definition of boundary conditions. The latter is done by measuring patient-specific flow waveforms using either phase contrast magnetic resonance imaging (pcMRI) or ultrasound-based flow measurement techniques. When patient-specific flow measurements are not available, cohort-averaged values of flow from the literature are often used. For example, the small-scale studies 4-6 Int J Numer Meth Biomed Engng. 2020;36:e3271.wileyonlinelibrary.com/journal/cnm

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Section: Methodsmentioning

confidence: 99%

\begin{matrix} right TAWSS (x) & left = \frac{1}{T_{period}} \int_{T_{0}}^{T_{0} + T_{period}} | τ_{w} (x, t) | d t; & right \\ right OSI (x) & left = \frac{1}{2} (1 - \frac{|\int_{T_{0}}^{T_{0} + T_{period}} τ_{w} (x, t) d t|}{\int_{T_{0}}^{T_{0} + T_{period}} |τ_{w} (x, t)| d t}); \\ right TransWSS (x) & left = \frac{1}{T_{period}} \int_{T_{0}}^{T_{0} + T_{period}} |τ_{w} (x, t) \cdot (\hat{p} \times \hat{n})| d t, \end{matrix}

where

\overset{n}{true}

is the surface normal, and the unit vector

\overset{p}{true}

in the direction of the time‐averaged WSS vector can be calculated as follows:

\overset{p}{true} false(x false) = true \int_{T_{0}}^{T_{0} +}

…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Population‐specific modelling of between/within‐subject flow variability in the carotid arteries of the elderly

Lassila

Sarrami‐Foroushani

Hejazi

et al. 2019

Numer Methods Biomed Eng

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show abstract

“…The corresponding RMSE of the one with LF basis (orange) are plotted for comparison.is expected on the test set a priori. We proposed an empirical approach in Section 2.2.4 to assess the model quality and estimate the prediction error of the BF surrogate, where two useful assessment metrics, model similarity R s (z)(12) and error component ratio R e (z)(12), are used. In this section, a priori error bound estimations in our three test cases of vascular flows will be discussed based on the proposed assessment method.…”

mentioning

confidence: 99%

A bi-fidelity surrogate modeling approach for uncertainty propagation in three-dimensional hemodynamic simulations

Gao

Zhu

Wang

2020

Computer Methods in Applied Mechanics and Engineering

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Image-based computational fluid dynamics (CFD) modeling enables derivation of hemodynamic information (e.g., flow field, wall shear stress, and pressure distribution), which has become a paradigm in cardiovascular research and healthcare. Nonetheless, the predictive accuracy largely depends on precisely specified boundary conditions and model parameters, which, however, are usually uncertain (or unknown) in most patient-specific cases. Quantifying the uncertainties in model predictions due to input randomness can provide predictive confidence and is critical to promote the transition of CFD modeling in clinical applications.In the meantime, forward propagation of input uncertainties often involves numerous expensive CFD simulations, which is computationally prohibitive in most practical scenarios. This paper presents an efficient bi-fidelity surrogate modeling framework for uncertainty quantification (UQ) in cardiovascular simulations, by leveraging the accuracy of high-fidelity models and efficiency of low-fidelity models. Contrary to most data-fit surrogate models with several scalar quantities of interest, this work aims to provide high-resolution, full-field predictions (e.g., velocity and pressure fields). Moreover, a novel empirical error bound estimation approach is introduced to evaluate the performance of the surrogate a priori.The proposed framework is tested on a number of vascular flows with both standardized and patient-specific vessel geometries, and different combinations of high-and low-fidelity models are investigated. The results show that the bi-fidelity approach can achieve high * Corresponding authors. jwang33@nd.edu (J.-X. Wang), xueyu-zhu@uiowa.edu (X. Zhu) predictive accuracy with a significant reduction of computational cost, exhibiting its merit and effectiveness. Particularly, the uncertainties from a high-dimensional input space can be accurately propagated to clinically relevant quantities of interest (e.g., wall shear stress) in the patient-specific case using only a limited number of high-fidelity simulations, suggesting a good potential in practical clinical applications.

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Reduced order modelling of intracranial aneurysm flow using proper orthogonal decomposition and neural networks

MacRaild,

Sarrami‐Foroushani,

Lassila

et al. 2024

Numer Methods Biomed Eng

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Reduced order modelling (ROMs) methods, such as proper orthogonal decomposition (POD), systematically reduce the dimensionality of high‐fidelity computational models and potentially achieve large gains in execution speed. Machine learning (ML) using neural networks has been used to overcome limitations of traditional ROM techniques when applied to nonlinear problems, which has led to the recent development of reduced order models augmented by machine learning (ML‐ROMs). However, the performance of ML‐ROMs is yet to be widely evaluated in realistic applications and questions remain regarding the optimal design of ML‐ROMs. In this study, we investigate the application of a non‐intrusive parametric ML‐ROM to a nonlinear, time‐dependent fluid dynamics problem in a complex 3D geometry. We construct the ML‐ROM using POD for dimensionality reduction and neural networks for interpolation of the ROM coefficients. We compare three different network designs in terms of approximation accuracy and performance. We test our ML‐ROM on a flow problem in intracranial aneurysms, where flow variability effects are important when evaluating rupture risk and simulating treatment outcomes. The best‐performing network design in our comparison used a two‐stage POD reduction, a technique rarely used in previous studies. The best‐performing ROM achieved mean test accuracies of 98.6% and 97.6% in the parent vessel and the aneurysm, respectively, while providing speed‐up factors of the order .

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Uncertainty quantification of wall shear stress in intracranial aneurysms using a data-driven statistical model of systemic blood flow variability

Cited by 25 publications

References 42 publications

Population‐specific modelling of between/within‐subject flow variability in the carotid arteries of the elderly

Population‐specific modelling of between/within‐subject flow variability in the carotid arteries of the elderly

A bi-fidelity surrogate modeling approach for uncertainty propagation in three-dimensional hemodynamic simulations

Reduced order modelling of intracranial aneurysm flow using proper orthogonal decomposition and neural networks

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