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

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.

A Mock Circulation Loop to Characterize In Vitro Hemodynamics in Human Systemic Arteries with Stenosis

“…However, trans-stenotic pressure gradient (TSPG), defined as the difference between p a and p d , has been popularly used for assessing the hemodynamic severity of non-coronary stenoses. Evidence, including ours, has shown that TSPG is an indicator to determine the amount of blood flow blockage caused by renal [5][6][7], iliac and femoral [8][9][10], and carotid [11] stenoses and can help guide the proper decisionmaking of interventional treatment. Nevertheless, the clinical application of either FFR or TSPG is rather limited [12], as they rely on the invasive pressure measurement of the local pressure values, i.e., p d and p a , which may expose patients to surgical complications and medical costs.…”

“…Obtained from a purely anatomical, noninvasive dataset of coronary CTA images [18] by utilizing ICHD, the FFR determines the hemodynamic severity of the coronary stenosis and then guides the decision-making of the interventional treatment for it. We have recently developed a proprietary ICHD technique [19] for a new noninvasive and patient-specific hemodynamic index that can assess the hemodynamic severity of non-coronary arterial stenosis and applied it to renal stenosis [6,7]. In addition to the application of ICHD for arterial stenosis, many studies have demonstrated the feasibility and validity of ICHD for vascular diseases caused by aneurysms [20][21][22].…”

A new noninvasive and patient‐specific hemodynamic index for the severity of renal stenosis and outcome of interventional treatment

“…We introduce velocity and pressure boundary conditions at the inlet and outlets 40 of the aortorenal arterial system, respectively. A pulsatile paraboloidal velocity profile is constructed based on patient's DUS velocity waveform at the inlet to drive the blood into the arterial systems.…”

“…As shown in Figure 4, the WK3 adopts a Windkessel circuit to model one capacitor ( C ) that represents the vessel compliance, and two resistors ( r and R ), representing the proximal and distal flow resistances, respectively. The detail algorithms for the inlet and outlet boundary conditions are found in the reference [40].…”

“…We use InVascular to compute the TPI based on imaging data. The detailed methods of InVascular including image segmentation, VLBM solver, inlet and outlet boundary conditions, and GPU parallelization are referred to references [34,37,39,40]. Here we consolidate the major components for the completion of this presentation.…”