Uncovering near-wall blood flow from sparse data with physics-informed neural networks

Amirhossein Arzani; Jian-Xun Wang; Roshan M. D'Souza

doi:10.1063/5.0055600

journal article Jul 01, 2021

Uncovering near-wall blood flow from sparse data with physics-informed neural networks

Amirhossein Arzani

Jian-Xun Wang

Roshan M. D'Souza

Physics of Fluids Vol. 33 No. 7 · AIP Publishing

View at Publisher Save 10.1063/5.0055600

Abstract

Near-wall blood flow and wall shear stress (WSS) regulate major forms of cardiovascular disease, yet they are challenging to quantify with high fidelity. Patient-specific computational and experimental measurement of WSS suffers from uncertainty, low resolution, and noise issues. Physics-informed neural networks (PINNs) provide a flexible deep learning framework to integrate mathematical equations governing blood flow with measurement data. By leveraging knowledge about the governing equations (herein, Navier–Stokes), PINN overcomes the large data requirement in deep learning. In this study, it was shown how PINN could be used to improve WSS quantification in diseased arterial flows. Specifically, blood flow problems where the inlet and outlet boundary conditions were not known were solved by assimilating very few measurement points. Uncertainty in boundary conditions is a common feature in patient-specific computational fluid dynamics models. It was shown that PINN could use sparse velocity measurements away from the wall to quantify WSS with very high accuracy even without full knowledge of the boundary conditions. Examples in idealized stenosis and aneurysm models were considered demonstrating how partial knowledge about the flow physics could be combined with partial measurements to obtain accurate near-wall blood flow data. The proposed hybrid data-driven and physics-based deep learning framework has high potential in transforming high-fidelity near-wall hemodynamics modeling in cardiovascular disease.

Topics

No keywords indexed for this article. Browse by subject →

References

67

[1]

"Application of physics-based flow models in cardiovascular medicine: Current practices and challenges" Biophys. Rev. (2021) 10.1063/5.0040315

[2]

"Lagrangian wall shear stress structures and near-wall transport in high-Schmidt-number aneurysmal flows" J. Fluid Mech. (2016) 10.1017/jfm.2016.6

[3]

"The story of wall shear stress in coronary artery atherosclerosis: Biochemical transport and mechanotransduction" J. Biomech. Eng. (2021) 10.1115/1.4049026

[4]

"Coronary artery wall shear stress is associated with progression and transformation of atherosclerotic plaque and arterial remodeling in patients with coronary artery disease" Circulation (2011) 10.1161/circulationaha.111.021824

[5]

"Comparison of statistical learning approaches for cerebral aneurysm rupture assessment" Int. J. Comput. Assisted Radiol. Surg. (2020) 10.1007/s11548-019-02065-2

[6]

"Characterization of the transport topology in patient-specific abdominal aortic aneurysm models" Phys. Fluids (2012) 10.1063/1.4744984

[7]

"Rethinking turbulence in blood" Biorheology (2009) 10.3233/bir-2009-0538

[8]

"Wall shear stress fixed points in cardiovascular fluid mechanics" J. Biomech. (2018) 10.1016/j.jbiomech.2018.03.034

[9]

"Characterizations and correlations of wall shear stress in aneurysmal flow" J. Biomech. Eng. (2016) 10.1115/1.4032056

[10]

"Wall shear stress topological skeleton analysis in cardiovascular flows: Methods and applications" Mathematics (2021) 10.3390/math9070720

[11]

(2018)

[12]

"Predicting the near-wall velocity of wall turbulence using a neural network for particle image velocimetry" Phys. Fluids (2020) 10.1063/5.0023786

[13]

"Data-driven cardiovascular flow modelling: Examples and opportunities" J. R. Soc. Interface (2021) 10.1098/rsif.2020.0802

[14]

"Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression" J. Biomech. (2017) 10.1016/j.jbiomech.2017.05.004

[15]

"Transient flow prediction in an idealized aneurysm geometry using data assimilation" Comput. Biol. Med. (2019) 10.1016/j.compbiomed.2019.103507

[16]

"Variational data assimilation for transient blood flow simulations: Cerebral aneurysms as an illustrative example" Int. J. Numer. Methods Biomed. Eng. (2019) 10.1002/cnm.3152

[17]

M. Habibi, R. M. D'Souza, S. Dawson, and A. Arzani, “Integrating multi-fidelity blood flow data with reduced-order data assimilation,” arXiv:2104.01971 (2021). 10.1016/j.compbiomed.2021.104566

[18]

"A bi-fidelity ensemble Kalman method for PDE-constrained inverse problems in computational mechanics" Comput. Mech. (2021) 10.1007/s00466-021-01979-6

[19]

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

M. Raissi, P. Perdikaris, G.E. Karniadakis

Journal of Computational Physics 2019 10.1016/j.jcp.2018.10.045

[20]

Multilayer feedforward networks are universal approximators

Kurt Hornik, Maxwell Stinchcombe, Halbert White

Neural Networks 1989 10.1016/0893-6080(89)90020-8

[21]

"Data-driven prediction of unsteady flow over a circular cylinder using deep learning" J. Fluid Mech. (2019) 10.1017/jfm.2019.700

[22]

The neural particle method – An updated Lagrangian physics informed neural network for computational fluid dynamics

Henning Wessels, Christian Weißenfels, Peter Wriggers

Computer Methods in Applied Mechanics and Engineer... 2020 10.1016/j.cma.2020.113127

[23]

Physics-informed machine learning: case studies for weather and climate modelling

K. Kashinath, M. Mustafa, A. Albert et al.

Philosophical Transactions of the Royal Society of... 2021 10.1098/rsta.2020.0093

[24]

D. Lucor, A. Agrawal, and A. Sergent, “Physics-aware deep neural networks for surrogate modeling of turbulent natural convection,” arXiv:2103.03565 (2021).

[25]

C. F. Gasmi and H. Tchelepi, “Physics informed deep learning for flow and transport in porous media,” arXiv:2104.02629 (2021).

[26]

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

Xiaowei Jin, Shengze Cai, Hui Li et al.

Journal of Computational Physics 2021 10.1016/j.jcp.2020.109951

[27]

DeepXDE: A Deep Learning Library for Solving Differential Equations

Lu Lu, Xuhui Meng, Zhiping Mao et al.

SIAM Review 2021 10.1137/19m1274067

[28]

O. Hennigh, S. Narasimhan, M. A. Nabian, A. Subramaniam, K. Tangsali, M. Rietmann et al., “Nvidia simnet™: An AI-accelerated multi-physics simulation framework,” arXiv:2012.07938 (2020). 10.1007/978-3-030-77977-1_36

[29]

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

Luning Sun, Han Gao, Shaowu Pan et al.

Computer Methods in Applied Mechanics and Engineer... 2020 10.1016/j.cma.2019.112732

[30]

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Maziar Raissi, Alireza Yazdani, George Em Karniadakis

Science 2020 10.1126/science.aaw4741

[31]

"Artificial intelligence velocimetry and microaneurysm-on-a-chip for three-dimensional analysis of blood flow in physiology and disease" Proc. Natl. Acad. Sci. (2021) 10.1073/pnas.2100697118

[32]

"Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks" Comput. Methods Appl. Mech. Eng. (2020) 10.1016/j.cma.2019.112623

[33]

B. Reyes, A. A. Howard, P. Perdikaris, and A. M. Tartakovsky, “Learning unknown physics of non-Newtonian fluids,” arXiv:2009.01658 (2020). 10.1103/physrevfluids.6.073301

[34]

"A generic physics-informed neural network-based constitutive model for soft biological tissues" Comput. Methods Appl. Mech. Eng. (2020) 10.1016/j.cma.2020.113402

[35]

"Personalising left-ventricular biophysical models of the heart using parametric physics-informed neural networks" Med. Image Anal. (2021) 10.1016/j.media.2021.102066

[36]

"Deep learning methods for super-resolution reconstruction of turbulent flows" Phys. Fluids (2020) 10.1063/1.5140772

[37]

A. Güemes, H. Tober, S. Discetti, A. Ianiro, B. Sirmacek, H. Azizpour, and R. Vinuesa, “From coarse wall measurements to turbulent velocity fields with deep learning,” arXiv:2103.07387 (2021). 10.1063/5.0058346

[38]

"Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows" J. Fluid Mech. (2021) 10.1017/jfm.2020.948

[39]

H. Gao, L. Sun, and J. X. Wang, “Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels,” arXiv:2011.02364 (2020). 10.1063/5.0054312

[40]

"Super-resolution and denoising of 4D-Flow MRI using physics-informed deep neural nets" Comput. Methods Programs Biomed. (2020) 10.1016/j.cmpb.2020.105729

[41]

"Prediction of wall-bounded turbulence from wall quantities using convolutional neural networks" J. Phys.: Conf. Ser. (2020) 10.1088/1742-6596/1522/1/012022

[42]

"Multiscale modeling meets machine learning: What can we learn?" Arch. Comput. Methods Eng. (2021) 10.1007/s11831-020-09405-5

[43]

P. Ramachandran, B. Zoph, and Q. V. Le, “Searching for activation functions,” arXiv:1710.05941 (2017).

[44]

(2012)

[45]

Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow

K. Leiderman, A. L. Fogelson

Mathematical Medicine and Biology: A Journal of th... 2011 10.1093/imammb/dqq005

[46]

"Finite element modeling of near-wall mass transport in cardiovascular flows" Int. J. Numer. Methods Biomed. Eng. (2019) 10.1002/cnm.3148

[47]

"Potential fluid mechanic pathways of platelet activation" Biomech. Model. Mechanobiol. (2013) 10.1007/s10237-012-0417-4

[48]

"Coronary artery plaque growth: A two-way coupled shear stress–driven model" Int. J. Numer. Methods Biomed. Eng. (2020) 10.1002/cnm.3293

[49]

Flow instability and wall shear stress variation in intracranial aneurysms

H. Baek, M. V. Jayaraman, P. D. Richardson et al.

Journal of The Royal Society Interface 2010 10.1098/rsif.2009.0476

[50]

"Association of hemodynamic characteristics and cerebral aneurysm rupture" Am. J. Neuroradiol. (2011) 10.3174/ajnr.a2274

Showing 50 of 67 references

Cited By

239

Machine-learning-based pressure reconstruction with moving boundaries

Hongping Wang, Fan Wu · 2025

Journal of Fluid Mechanics

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

Seohee Jang, Mohammad Jadidi · 2024

Machine Learning: Science and Techn...

Physics-informed neural networks for inversion of river flow and geometry with shallow water model

Y. Ohara, D. Moteki · 2024

Physics of Fluids

Stiff-PDEs and Physics-Informed Neural Networks

Prakhar Sharma, Llion Evans · 2023

Archives of Computational Methods i...

Metrics

239

Citations

67

References

Details

Published: Jul 01, 2021
Vol/Issue: 33(7)
License: View

Authors

A

Amirhossein Arzani

Department of Mechanical Engineering, Northern Arizona University 1 , Flagstaff, Arizona 86011, USA

J

Jian-Xun Wang

Department of Aerospace and Mechanical Engineering, University of Notre Dame 2 , Notre Dame, Indiana 46556, USA

R

Roshan M. D'Souza

Department of Mechanical Engineering, University of Wisconsin–Milwaukee 3 , Milwaukee, Wisconsin 53211, USA

Funding

National Science Foundation Award: CMMI-1934300

Cite This Article

Amirhossein Arzani, Jian-Xun Wang, Roshan M. D'Souza (2021). Uncovering near-wall blood flow from sparse data with physics-informed neural networks. Physics of Fluids, 33(7). https://doi.org/10.1063/5.0055600

Uncovering near-wall blood flow from sparse data with physics-informed neural networks

You May Also Like