A parallel non-nested two-level domain decomposition method for simulating blood flows in cerebral artery of stroke patient

A computational study of the connection between coronary revascularization and cardio-cerebral hemodynamics

BACKGROUND AND OBJECTIVE

Some patients experience life-threatening strokes during coronary revascularization. Despite its clinical importance, few numerical studies have investigated the impact of coronary revascularization on cardio-cerebral hemodynamics. This study aims to address this gap by evaluating the effects of eliminating coronary stenosis on both coronary and cerebral blood flow using patient-specific simulations.

METHODS

A patient-specific cardio-cerebral arterial network with a 70% stenosis in the left main coronary artery was reconstructed, and computational fluid dynamics were employed to evaluate the effects of eliminating coronary stenosis. The three-dimensional time-dependent incompressible Navier-Stokes equations were discretized using a stabilized P1-P1 Galerkin finite element method and an implicit second-order backward differentiation formula. A regional blood flow distribution model, coupled with a lumped Windkessel model, was applied at the outlet boundaries. The 3D pulsatile blood flow was solved using a parallel solver based on a scalable Newton-Krylov-Schwarz algorithm, enabling fast and efficient simulations.

RESULTS

Coronary revascularization significantly improved myocardial blood flow, increasing the coronary fractional flow reserve from 0.742 to 0.904, indicating enhanced myocardial perfusion. However, cerebral hemodynamics were negatively affected, with a 2.49% reduction in blood flow through the main cerebral artery, suggesting an elevated risk of cerebral ischemia. The proposed computational framework demonstrated good parallel scalability across thousands of processor cores.

CONCLUSIONS

This study highlights the dual impact of coronary revascularization, improving myocardial perfusion while potentially elevating the risk of cerebral ischemic complications. The efficient computational approach provides a valuable tool for evaluating cardio-cerebral hemodynamics in patient-specific settings, making it suitable for complex and time-intensive simulations.

CT-FFR by expanding coronary tree with Newton-Krylov-Schwarz method to solve the governing equations of CFD

Aims

A new model of computational fluid dynamics (CFD)-based algorithm for coronary CT angiography (CCTA)-derived fractional flow reserve (FFR) (CT-FFR) analysis by expanding the coronary tree to smaller-diameter lumen (0.8 mm) using Newton-Krylov-Schwarz (NKS) method to solve the three-dimensional time-dependent incompressible Navier-Stokes equations has been developed; however, the diagnostic performance of this new method has not been sufficiently investigated. The aim of this study was to determine the diagnostic performance of a novel CT-FFR technique by expanding the coronary tree in the CFD domain.

Methods and results

Six centres enrolled 338 symptomatic patients with suspected or known coronary artery disease (CAD) who prospectively underwent CCTA and FFR. Stenosis assessment in CCTA and CT-FFR analysis were performed in independent core laboratories. Haemodynamically significant stenosis was defined by a CT-FFR and FFR ≤ 0.80, and anatomically obstructive CAD was defined as a CCTA with stenosis ≥ 50%. Diagnostic performance of CT-FFR was evaluated against invasive FFR using receiver operating characteristic (ROC) curve analysis. The correlation between CT-FFR and invasive FFR was analysed using the Spearman correlation coefficient and Bland-Altman analysis. Intra-observer and inter-observer agreements were evaluated utilizing the intraclass correlation coefficient (ICC). In this study, 338 patients with 422 targeted vessels were investigated, revealing haemodynamically significant stenosis in 31.1% (105/338) of patients and anatomically obstructive stenosis in 54.1% of patients. On a per-vessel basis, the area under the ROC curve for CT-FFR was 0.94 vs. 0.76 for CCTA (P < 0.001). Per-vessel accuracy, sensitivity, specificity, positive predictive value, and negative predictive value were 89.8%, 89.3%, 90.0%, 79.0%, and 99.2%, respectively, for CT-FFR and were 68.4%, 82.8%, 62.3%, 48.1%, and 89.6%, respectively, for CCTA stenosis. CT-FFR and FFR were well correlated (r = 0.775, P < 0.001) with a Bland-Altman bias of 0.0011, and limits of agreement from -0.1509 to 0.1531 (P = 0.770). The ICCs with CT-FFR for intro- and inter-observer agreements were 0.919 (95% CI: 0.866-0.952) and 0.909 (95% CI: 0.851-0.945), respectively. The average computation time for CT-FFR analysis was maintained at 11.7 min.

Conclusion

This novel CT-FFR model with the inclusion of smaller lumen provides high diagnostic accuracy in detecting haemodynamically significant CAD. Furthermore, the integration of the NKS method ensures that the computation time remains within an acceptable range for potential clinical applications in the future.

An aneurysm-specific preconditioning technique for the acceleration of Newton-Krylov method with application in the simulation of blood flows

In this paper, we develop an algorithm to simulate blood flows in aneurysmal arteries and focus on the construction of robust and efficient multilevel preconditioners to speed up the convergence of both linear and nonlinear solvers. The work is motivated by the observation that in the local aneurysmal region, the flow is often quite complicated with one or more vortices, but in the healthy section of the artery, the principal component of blood flows along the centerline of the artery. Based on this observation, we introduce a novel two-level additive Schwarz method with a mixed-dimensional coarse preconditioner. The key components of the preconditioner include (1) a three-dimensional coarse preconditioner covering the aneurysm; (2) a one-dimensional coarse preconditioner covering the central line of the healthy section of the artery; (3) a collection of three-dimensional overlapping subdomain preconditioners covering the fine meshes of the entire artery; (4) extension/restriction operators constructed by radial basis functions. The blood flow is modeled by the unsteady incompressible Navier-Stokes equations with resistance outflow boundary conditions discretized by a stabilized finite element method on fully unstructured meshes and the second-order backward differentiation formula in time. The resulting large nonlinear algebraic systems are solved by a Newton-Krylov algorithm accelerated by the new preconditioner in two ways: (1) the initial guess of Newton is obtained by solving a linear system defined by the coarse preconditioner; (2) the Krylov solver of the Jacobian system is preconditioned by the new preconditioner. Numerical experiments indicate that the proposed preconditioner is highly effective and robust for complex flows in a patient-specific artery with aneurysm, and it significantly reduces the numbers of linear and nonlinear iterations.

Blood flow CFD simulation on a cerebral artery of a stroke patient

Abstract

The purpose of this paper is to conduct a numerical simulation of the stroke patient's cerebral arteries and investigate the flow parameters due to the presence of stenosis. The computational fluid dynamics (CFD) simulations are based on simplified and realistic cerebral artery models. The seven simplified models (benchmarks) include straight cylindrical vessels with idealized stenosis with variable d/D (0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1). The realistic model of the cerebral artery is based on magnetic resonance imaging (MRI) for patient-specific cerebral arteries. The simulation for the realistic model of the cerebral artery is performed at boundary conditions measured by ultrasonography of the input and the output flow profiles (velocity and pressure). The obtained CFD results of the benchmarks are validated with actual data from the literature. Furthermore, a previous vascular contraction is assumed to be exist and the effect of this contraction area ratio on the blood flow regime is discussed and highlighted. Furthermore, CFD results show that a certain vascular contraction area critically affects the blood flow which shows increasing the wall shear stress WSS at the stenosis site. An increase in the blood velocity and vortex appears after the contraction zone, this lead to vessel occlusion and strokes.

Article highlights

High-resolution cerebral blood flow simulation with a domain decomposition method and verified by the TCD measurement

BACKGROUND

An efficient and accurate blood flow simulation can be useful for understanding many vascular diseases. Accurately resolving the blood flow velocity based on patient-specific geometries and model parameters is still a major challenge because of complex geomerty and turbulence issues. In addition, obtaining results in a short amount of computing time is important so that the simulation can be used in the clinical environment. In this work, we present a parallel scalable method for the patient-specific blood flow simulation with focuses on its parallel performance study and clinical verification.

METHODS

We adopt a fully implicit unstructured finite element method for a patient-specific simulation of blood flow in a full precerebral artery. The 3D artery is constructed from MRI images, and a parallel Newton-Krylov method preconditioned with a two-level domain decomposition method is adopted to solve the large nonlinear system discretized from the time-dependent 3D Navier-Stokes equations in the artery with an integral outlet boundary condition. The simulated results are verified using the clinical data measured by transcranial Doppler ultrasound, and the parallel performance of the algorithm is studied on a supercomputer.

RESULTS

The simulated velocity matches the clinical measured data well. Other simulated blood flow parameters, such as pressure and wall shear stress, are within reasonable ranges. The results show that the parallel algorithm scales up to 2160 processors with a 49% parallel efficiency for solving a problem with over 20 million unstructured elements on a supercomputer. For a standard cerebral blood flow simulation case with approximately 4 million finite elements, the calculation of one cardiac cycle can be finished within one hour with 1000 processors.

CONCLUSION

The proposed method is able to perform high-resolution 3D blood flow simulations in a patient-specific full precerebral artery within an acceptable time, and the simulated results are comparable with the clinical measured data, which demonstrates its high potential for clinical applications.

Efficient parallel simulation of hemodynamics in patient-specific abdominal aorta with aneurysm

Surgical planning for aortic aneurysm repair is a difficult task. In addition to the morphological features obtained from medical imaging, alternative features obtained with computational modeling may provide additional useful information. Though numerical studies are noninvasive, they are often time-consuming, especially when we need to study and compare multiple repair scenarios, because of the high computational complexity. In this paper, we present a highly parallel algorithm for the numerical simulation of unsteady blood flows in the patient-specific abdominal aorta before and after the aneurysmic repair. We model the blood flow with the unsteady incompressible Navier-Stokes equations with different outlet boundary conditions, and solve the discretized system with a highly scalable domain decomposition method. With this approach, a high resolution simulation of a full-size adult aorta can be obtained in less than an hour, instead of days with older methods and software. In addition, we show that the parallel efficiency of the proposed method is near 70% on a parallel computer with 2, 880 processor cores.

Expanding the coronary tree reconstruction to smaller arteries improves the accuracy of FFRCT

OBJECTIVES

We attempted to improve the accuracy of coronary CT angiography (CCTA)-derived fractional flow reserve (FFR) (FFR_CT) by expanding the coronary tree in the computational fluid dynamics (CFD) domain. An observational study was performed to evaluate the effects of extending the coronary tree analysis for FFR_CT from a minimal diameter of 1.2 to 0.8 mm.

METHODS

Patients who underwent CCTA and interventional FFR were enrolled retrospectively. Seventy-six patients qualified based on the inclusion criteria. The three-dimensional (3D) coronary artery tree was reconstructed to generate a finite element mesh for each subject with different lower limits of luminal diameter (1.2 mm and 0.8 mm). Outlet boundary conditions were defined according to Murray's law. The Newton-Krylov-Schwarz (NKS) method was applied to solve the governing equations of CFD to derive FFR_CT.

RESULTS

At the individual patient level, extending the minimal diameter of the coronary tree from 1.2 to 0.8 mm improved the sensitivity of FFR_CT by 16.7% (p = 0.022). This led to the conversion of four false-negative cases into true-positive cases. The AUC value of the ROC curve increased from 0.74 to 0.83. Moreover, the NKS method can solve the computational problem of extending the coronary tree to an 0.8-mm luminal diameter in 10.5 min with 2160 processor cores.

CONCLUSIONS

Extending the reconstructed coronary tree to a smaller luminal diameter can considerably improve the sensitivity of FFR_CT. The NKS method can achieve favorable computational times for future clinical applications.

KEY POINTS

• Extending the reconstructed coronary tree to a smaller luminal diameter can considerably improve the sensitivity of FFR_CT. • The NKS method applied in our study can effectively reduce the computational time of this process for future clinical applications.