Inlet and Outlet Boundary Conditions and Uncertainty Quantification in Volumetric Lattice Boltzmann Method for Image-Based Computational Hemodynamics

Xin Fang,Alan P Sawchuk,Rou Chen,Monsurul Khan,Huidan Yu,Xiaoping Du,Jianyun Long,Hao Wu,Chunze Zhang

doi:10.3390/fluids7010030

Abstract

Inlet and outlet boundary conditions (BCs) play an important role in newly emerged image-based computational hemodynamics for blood flows in human arteries anatomically extracted from medical images. We developed physiological inlet and outlet BCs based on patients’ medical data and integrated them into the volumetric lattice Boltzmann method. The inlet BC is a pulsatile paraboloidal velocity profile, which fits the real arterial shape, constructed from the Doppler velocity waveform. The BC of each outlet is a pulsatile pressure calculated from the three-element Windkessel model, in which three physiological parameters are tuned by the corresponding Doppler velocity waveform. Both velocity and pressure BCs are introduced into the lattice Boltzmann equations through Guo’s non-equilibrium extrapolation scheme. Meanwhile, we performed uncertainty quantification for the impact of uncertainties on the computation results. An application study was conducted for six human aortorenal arterial systems. The computed pressure waveforms have good agreement with the medical measurement data. A systematic uncertainty quantification analysis demonstrates the reliability of the computed pressure with associated uncertainties in the Windkessel model. With the developed physiological BCs, the image-based computation hemodynamics is expected to provide a computation potential for the noninvasive evaluation of hemodynamic abnormalities in diseased human vessels.

Highlights

We have presented the physiological inlet and outlet boundary conditions (BCs) for image-based computational hemodynamics (ICHD) and integrated them into our in-house computational platform, InVascular
Using the unified LBM modeling for image segmentation and computational hemodynamics, InVascular seamlessly integrates the anatomical extraction of the interested arterial segment and quantification of pulsatile hemodynamics and achieves fast computation via GPU parallel computing
A paraboloidal velocity profile is constructed based on the Doppler ultrasound (DUS) velocity waveform, which fits the real shape of the arterial lumen

Summary

Introduction

With the recent advances in medical imaging, computational power, and mathematical algorithms, image-based computational hemodynamics (ICHD) has emerged [1,2,3,4,5,6,7] as a new capability giving rise to the potential for computation-aided diagnostics and therapeutics in a patient-specific environment for cardiovascular diseases. Based on radiological imaging data, such as computed tomography angiography (CTA) images and Doppler ultrasound (DUS) velocity waveforms, ICHD enables noninvasive and patient-specific quantification of pulsatile hemodynamics in human vessels. Such data, including velocity vector, pressure, vorticity vector, and wall-shear stress (WSS) in the entire artery segment with fine spatial and temporal resolutions, are not readily available from the current standard clinical measurements. Through further postprocessing of the pulsatile hemodynamic data, either the assessment of the true hemodynamic abnormality or the prediction of potential therapeutic/surgical outcomes from an interventional treatment may aid in clinical decision-making for various cardiovascular diseases

Methods

Results

Conclusion