Quantification of near-wall hemodynamic risk factors in large-scale cerebral arterial trees

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.

Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex

Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer’s disease.

Brain function critically depends on the maintenance of physiological blood supply and metabolism in the cortex. Disturbances to adequate perfusion have been linked to age-related neurodegeneration. However, the precise correlation between age-related hemodynamic changes and the resulting decline in oxygen delivery is not well understood and has not been quantified. Therefore, we introduce a new compact, and therefore highly scalable, computational method for predicting the physiological relationship between hemodynamics and cortical oxygen perfusion for large sections of the cortical microcirculation. We demonstrate the novel mesh generation-free (MGF), multi-scale simulation approach through realistic in vivo case studies of cortical microperfusion in the mouse brain. We further validate mechanistic correlations and a quantitative relationship between blood flow and brain oxygenation using experimental data from cohorts of young, middle aged and old mouse brains. Our computational approach overcomes size and performance limitations of previous unstructured meshing techniques to enable the prediction of oxygen tension with a spatial resolution of least two orders of magnitude higher than previously possible. Our simulation results support the hypothesis that structural changes in the microvasculature induce hypoxic pockets in the aged brain that are absent in the healthy, young mouse.

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

Numerical simulation of blood flows in patient-specific arteries can be useful for the understanding of vascular diseases, as well as for surgery planning. In this paper, we simulate blood flows in the full cerebral artery of stroke patients. To accurately resolve the flow in this rather complex geometry with stenosis is challenging and it is also important to obtain the results in a short amount of computing time so that the simulation can be used in pre- and/or post-surgery planning. For this purpose, we introduce a highly scalable, parallel non-nested two-level domain decomposition method for the three-dimensional unsteady incompressible Navier-Stokes equations with an impedance outlet boundary condition. The problem is discretized with a stabilized finite element method on unstructured meshes in space and a fully implicit method in time, and the large nonlinear systems are solved by a preconditioned parallel Newton-Krylov method with a two-level Schwarz method. The key component of the method is a non-nested coarse problem solved using a subset of processor cores and its solution is interpolated to the fine space using radial basis functions. To validate and verify the proposed algorithm and its highly parallel implementation, we consider a case with available clinical data and show that the computed result matches with the measured data. Further numerical experiments indicate that the proposed method works well for realistic geometry and parameters of a full size cerebral artery of an adult stroke patient on a supercomputers with thousands of processor cores.

Quantification of blood flow patterns in the cerebral arterial circulation of individual (human) subjects

There is a growing research interest in quantifying blood flow distribution for the entire cerebral circulation to sharpen diagnosis and improve treatment options for cerebrovascular disease of individual patients. We present a methodology to reconstruct subject-specific cerebral blood flow patterns in accordance with physiological and fluid mechanical principles and optimally informed by in vivo neuroimage data of cerebrovascular anatomy and arterial blood flow rates. We propose an inverse problem to infer blood flow distribution across the visible portion of the arterial network that best matches subject-specific anatomy and a given set of volumetric flow measurements. The optimization technique also mitigates the effect of uncertainties by reconciling incomplete flow data and by dissipating unavoidable acquisition errors associated with medical imaging data.

An efficient full space-time discretization method for subject-specific hemodynamic simulations of cerebral arterial blood flow with distensible wall mechanics

A computationally inexpensive mathematical solution approach using orthogonal collocations for space discretization with temporal Fourier series is proposed to compute subject-specific blood flow in distensible vessels of large cerebral arterial networks. Several models of wall biomechanics were considered to assess their impact on hemodynamic predictions. Simulations were validated against in vivo blood flow measurements in six human subjects. The average root-mean-square relative differences were found to be less than 4.3% for all subjects with a linear elastic wall model. This discrepancy decreased further in a viscoelastic Kelvin-Voigt biomechanical wall. The results provide support for the use of collocation-Fourier series approach to predict clinically relevant blood flow distribution and collateral blood supply in large portions of the cerebral circulation at reasonable computational costs. It thus opens the possibility of performing computationally inexpensive subject-specific simulations that are robust and fast enough to predict clinical results in real time on the same day.

Cerebral arteriovenous malformation venous stenosis is associated with hemodynamic changes at the draining vein-venous sinus junction

Cerebral arteriovenous malformations (AVMs) are an uncommon vascular anomaly that carry the risk of rupture and hemorrhage. Several factors have been implicated in the propensity of an AVM to bleed. One such factor is stenosis of AVM draining veins, as impairment of the AVM venous drainage system is associated with increased risk of intracranial hemorrhage. Currently, our understanding of the pathogenesis of AVM venous outflow stenosis is limited, as there is insufficient data on the blood flow patterns and local hemodynamic parameters of these draining veins. The angioarchitecture of AVMs features a nidus lacking a high resistance capillary network. Accordingly, our previous studies on AVM arterial feeders have demonstrated an abnormally high flow volume rate along with low pulsatility and resistance indices on quantitative magnetic resonance angiography. As such, AVM vessels endure high, non-physiologic levels of flow that may partially contribute to ectasia or stenosis depending on whether wall shear stress (WSS) is high or low, respectively. We hypothesize that AVM venous outflow stenosis occurs most commonly near the junction of the draining vein and the dural venous sinus. Increased flow volume rate through the AVM circuit coupled with the variation in compliance and rigidity between the walls of the draining vein and the dural venous sinus likely create turbulence of blood flow. The resulting flow separation, low WSS, and departure from axially aligned, unidirectional flow may create atherogenic conditions that can be implicated in venous intimal hyperplasia and outflow stenosis. We have previously found there to be a significant association between intimal hyperplasia risk factors and venous outflow stenosis. Additionally, we have found a significant association between age and likelihood as well as degree of stenosis, suggesting a progressive disease process. Similar conditions have been demonstrated in the pathophysiology of stenosis of the carotid artery and dialysis arteriovenous fistulas. In both of these conditions, the use of computational fluid dynamics (CFD) has been employed to characterize the local hemodynamic features that contribute to the pathogenesis of intimal hyperplasia and stenosis. We recommend the utilization of CFD to characterize the anatomic and hemodynamic features of AVM venous outflow stenosis. An improved understanding of the possible causative features of venous outflow stenosis may impact how clinicians choose to manage the treatment of patients with AVMs.

Validation of parametric mesh generation for subject-specific cerebroarterial trees using modified Hausdorff distance metrics

Accurate subject-specific vascular network reconstruction is a critical task for the hemodynamic analysis of cerebroarterial circulation. Vascular skeletonization and computational mesh generation for large sections of cerebrovascular trees from magnetic resonance angiography (MRA) is an error-prone, operator-dependent, and very time-consuming task. Validation of reconstructed computational models is essential to ascertain their accuracy and precision, which directly relates to the confidence of CFD computations performed on these meshes. The aim of this study is to generate an imaging segmentation pipeline to validate and quantify the spatial accuracy of computational models of subject-specific cerebral arterial trees. We used a recently introduced parametric structured mesh (PSM) generation method to automatically reconstruct six subject-specific cerebral arterial trees containing 1364 vessels and 571 bifurcations. By automatically extracting sampling frames for all vascular segments and bifurcations, we quantify the spatial accuracy of PSM against the original MRA images. Our comprehensive study correlates lumen area, pixel-based statistical analysis, area overlap and centerline accuracy measurements. In addition, we propose a new metric, the pointwise offset surface distance metric (PSD), to quantify the spatial alignment between dimensions of reconstructed arteries and bifurcations with in-vivo data with the ability to quantify the over- and under-approximation of the reconstructed models. Accurate reconstruction of vascular trees can a practical process tool for morphological analysis of large patient data banks, such as medical record files in hospitals, or subject-specific hemodynamic simulations of the cerebral arterial circulation.