A multiscale computational modeling for cerebral blood flow with aneurysms and/or stenoses

Using DFT on ultrasound measurements to determine patient-specific blood flow boundary conditions for computational hemodynamics of intracranial aneurysms

Boundary conditions (BCs) is one pivotal factor influencing the accuracy of hemodynamic predictions on intracranial aneurysms (IAs) using computational fluid dynamics (CFD) modeling. Unfortunately, a standard procedure to secure accurate BCs for hemodynamic modeling does not exist. To bridge such a knowledge gap, two representative patient-specific IA models (Case-I and Case-II) were reconstructed and their blood flow velocity waveforms in the internal carotid artery (ICA) were measured by ultrasonic techniques and modeled by discrete Fourier transform (DFT). Then, numerical investigations were conducted to explore the appropriate number of samples (N) for DFT modeling to secure the accurate BC by comparing a series of hemodynamic parameters using in-vitro validated CFD modeling. Subsequently, a comprehensive comparison in hemodynamic characteristics under patient-specific BCs and a generalized BC based on a one-dimensional (1D) model was conducted to reinforce the understanding that a patient-specific BC is pivotal for accurate hemodynamic risk evaluations on IA pathophysiology. In addition, the influence of the variance of heart rate/cardiac pulsatile period on hemodynamic characteristics in IA models was studied preliminarily. The results showed that N ≥ 16 for DFT model is a decent choice to secure the proper BC profile to calculate time-averaged hemodynamic parameters, while more data points such as N ≥ 36 can ensure the accuracy of instantaneous hemodynamic predictions. In addition, results revealed the generalized BC could overestimate or underestimate the hemodynamic risks on IAs significantly; thus, patient-specific BCs are highly recommended for hemodynamic modeling for IA risk evaluation. Furthermore, this study discovered the variance of heart rate has rare influences on hemodynamic characteristics in both instantaneous and time-averaged parameters under the assumption of an identical blood flow rate.

Pathophysiology of intracranial aneurysms in monozygotic twins: A rare case study from hemodynamic perspectives

Hemodynamic mechanisms of the formation and growth of intracranial aneurysms (IA) in monozygotic twins (MTs) are still under-reported. To partially fill such knowledge gap, this study employed an experimentally validated numerical model to compare hemodynamics in 3 anatomical and 5 ablation study neurovascular models from a rare pair of MTs in terms of 7 critical hemodynamic parameters. Numerical results showed significant differences in hemodynamics between the MTs, although they share the same genes, indicating that genetic mutation and environmental factors might affect neurovascular morphologies and cause hemodynamic changes. After virtual removals of IAs in the ablation study, the locations where the aneurysmal sac/bleb generated in bifurcated anterior cerebral arteries (ACAs) register a locally high instantaneous wall shear stress (IWSS) of 52.9 and 70.1 Pa at the systolic peak in twin A and twin B, respectively. Same scenario can be observed in the distribution of instantaneous wall shear stress gradient (IWSSG), with 571.1 Pa/mm for twin A and 301.3 Pa/mm for twin B due to aggressive blood impingements, leading to IA generation. The fenestrated complex approaching ACA bifurcations in twin A may assist IA growth and rupture, via. Causing abnormal IWSS of 116.3 Pa, IWSSG of 832.5 Pa/mm, and oscillatory shear index (OSI) of 0.49. The bleb in twin B has high risks of progression and possible rupture as the IA suffers relatively low IWSS and high OSI. Additionally, IA generation can change blood flow rates in each connected artery, then affecting blood supplies to associated tissues and organs.

Morphology and Hemodynamics of Cerebral Arteries and Aneurysms in a Rare Pair of Monozygotic Twins

In this preliminary study, the underlying pathophysiology mechanisms of cerebral aneurysms (CAs) in monozygotic twins (MTs) were investigated via a rare pair of MTs (twin A and twin B) involving four reconstructed arterial models using preclinical information. First, dimensions and configurated outlines of three-perspective geometries were compared. Adopting an in-vitro validated numerical CA model, hemodynamic characteristics were investigated in the MTs, respectively. Despite expected genetic similarities, morphological comparisons show that configurations of cerebral arteries exhibit significant differences between the twins. The ICA size of twin A is larger than that in twin B (2.23~25.86%), varying with specific locations, attributing to variations during embryological developments and environmental influences. Numerical modeling indicates the MTs have some hemodynamic similarities such as pressure distributions (~13,400 Pa) and their oscillatory shear index (OSI) (0~0.49), but present significant differences in local regions. Specifically, the difference in blood flow rate in the MTs is from 16% to 221%, varying with specifically compared arteries. The maximum time-averaged wall shear stress (53.6 Pa vs. 37.8 Pa) and different local OSI distributions were also observed between the MTs. The findings revealed that morphological variations in MTs could be generated by embryological and environmental factors, further influencing hemodynamic characteristics on CA pathophysiology.

Predicting brain temperature in humans using bioheat models: Progress and outlook

Brain temperature, regulated by the balance between blood circulation and metabolic heat generation, is an important parameter related to neural activity, cerebral hemodynamics, and neuroinflammation. A key challenge for integrating brain temperature into clinical practice is the lack of reliable and non-invasive brain thermometry. The recognized importance of brain temperature and thermoregulation in both health and disease, combined with limited availability of experimental methods, has motivated the development of computational thermal models using bioheat equations to predict brain temperature. In this mini-review, we describe progress and the current state-of-the-art in brain thermal modeling in humans and discuss potential avenues for clinical applications.

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.

Effects of Pulsatile Flow Rate and Shunt Ratio in Bifurcated Distal Arteries on Hemodynamic Characteristics Involved in Two Patient-Specific Internal Carotid Artery Sidewall Aneurysms: A Numerical Study

The pulsatile flow rate (PFR) in the cerebral artery system and shunt ratios in bifurcated arteries are two patient-specific parameters that may affect the hemodynamic characteristics in the pathobiology of cerebral aneurysms, which needs to be identified comprehensively. Accordingly, a systematic study was employed to study the effects of pulsatile flow rate (i.e., PFR−I, PFR−II, and PFR−III) and shunt ratio (i.e., 75:25 and 64:36) in bifurcated distal arteries, and transient cardiac pulsatile waveform on hemodynamic patterns in two internal carotid artery sidewall aneurysm models using computational fluid dynamics (CFD) modeling. Numerical results indicate that larger PFRs can cause higher wall shear stress (WSS) in some local regions of the aneurysmal dome that may increase the probability of small/secondary aneurysm generation than under smaller PFRs. The low WSS and relatively high oscillatory shear index (OSI) could appear under a smaller PFR, increasing the potential risk of aneurysmal sac growth and rupture. However, the variances in PFRs and bifurcated shunt ratios have rare impacts on the time-average pressure (TAP) distributions on the aneurysmal sac, although a higher PFR can contribute more to the pressure increase in the ICASA−1 dome due to the relatively stronger impingement by the redirected bloodstream than in ICASA−2. CFD simulations also show that the variances of shunt ratios in bifurcated distal arteries have rare impacts on the hemodynamic characteristics in the sacs, mainly because the bifurcated location is not close enough to the sac in present models. Furthermore, it has been found that the vortex location plays a major role in the temporal and spatial distribution of the WSS on the luminal wall, varying significantly with the cardiac period.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

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.

Cardiac and renal function interactions in heart failure with reduced ejection fraction: A mathematical modeling analysis

Congestive heart failure is characterized by suppressed cardiac output and arterial filling pressure, leading to renal retention of salt and water, contributing to further volume overload. Mathematical modeling provides a means to investigate the integrated function and dysfunction of heart and kidney in heart failure. This study updates our previously reported integrated model of cardiac and renal functions to account for the fluid exchange between the blood and interstitium across the capillary membrane, allowing the simulation of edema. A state of heart failure with reduced ejection fraction (HF-rEF) was then produced by altering cardiac parameters reflecting cardiac injury and cardiovascular disease, including heart contractility, myocyte hypertrophy, arterial stiffness, and systemic resistance. After matching baseline characteristics of the SOLVD clinical study, parameters governing rates of cardiac remodeling were calibrated to describe the progression of cardiac hemodynamic variables observed over one year in the placebo arm of the SOLVD clinical study. The model was then validated by reproducing improvements in cardiac function in the enalapril arm of SOLVD. The model was then applied to prospectively predict the response to the sodium-glucose co-transporter 2 (SGLT2) inhibitor dapagliflozin, which has been shown to reduce heart failure events in HF-rEF patients in the recent DAPAHF clinical trial by incompletely understood mechanisms. The simulations predict that dapagliflozin slows cardiac remodeling by reducing preload on the heart, and relieves congestion by clearing interstitial fluid without excessively reducing blood volume. This provides a quantitative mechanistic explanation for the observed benefits of SGLT2i in HF-rEF. The model also provides a tool for further investigation of heart failure drug therapies.

Patient-Specific Blood Flow Analysis for Cerebral Arteriovenous Malformation Based on Digital Subtraction Angiography Images

Real-time digital subtraction angiography (DSA) is capable of revealing the cerebral vascular morphology and blood flow perfusion patterns of arterial venous malformations (AVMs). In this study, we analyze the DSA images of a subject-specific left posterior AVM case and customize a generic electric analog model for cerebral circulation accordingly. The generic model consists of electronic components representing 49 major cerebral arteries and veins, and yields their blood pressure and flow rate profiles. The model was adapted by incorporating the supplying and draining patterns of the AVM to simulate some typical AVM features such as the blood "steal" syndrome, where the flow rate in the left posterior artery increases by almost three times (∼300 ml/min vs 100 ml/min) compared with the healthy case. Meanwhile, the flow rate to the right posterior artery is reduced to ∼30 ml/min from 100 ml/min despite the presence of an autoregulation mechanism in the model. In addition, the blood pressure in the draining veins is increased from 9 to 22 mmHg, and the blood pressure in the feeding arteries is reduced from 85 to 30 mmHg due to the fistula effects of the AVM. In summary, a first DSA-based AVM model has been developed. More subject-specific AVM cases are required to apply the presented in silico model, and in vivo data are used to validate the simulation results.

Numerical studies of hemodynamic alterations in pre- and post-stenting cerebral aneurysms using a multiscale modeling

The aim of this work was to use a multiscale modeling to study the influence of stent deployment, with generic stents, on flow distributions within the vascular network and the hemodynamic alterations within the cerebral aneurysms pre- and post-stenting. To achieve this goal, two image-based anatomical cerebral aneurysm models were reconstructed along with the respective aneurysms post-stenting models after deploying a 16- or 24-wire stent. The investigation results revealed that the stent may increase the local pressure resistance resulting in flow alterations. The hemodynamic parameters demonstrated stent placement can reduce the intra-aneurysmal pressure, decrease wall shear stress (WSS) at the neck region, and increase blood turnover time for aneurysm case I (sidewall aneurysm). These findings are consistent with the trends of hemodynamic changes reported previously. However, aneurysm case II (bifurcation aneurysm) showed gradually increased intra-aneurysmal pressure and the pressure at the neck region, decreased WSS over the sac surface, and enhanced flow vortices within the aneurysm. When simulating the hemodynamics of pre- and post-stenting aneurysms for a patient using measured flow waveforms, the flow alteration induced by the stent deployment may affect the hemodynamic predictions for the post-stenting aneurysm. Thus, the remeasurement of boundary conditions once the morphology of the aneurysm is deformed is needed in follow-up studies with a focus on aneurysm growth and stent deployment.

An In-Vitro Flow Study Using an Artificial Circle of Willis Model for Validation of an Existing One-Dimensional Numerical Model

A one-dimensional (1D) numerical model has been previously developed to investigate the hemodynamics of blood flow in the entire human vascular network. In the current work, an experimental study of water-glycerin mixture flow in a 3D-printed silicone model of an anatomically accurate, complete circle of Willis (CoW) was conducted to investigate the flow characteristics in comparison with the simulated results by the 1D numerical model. In the experiment, the transient flow and pressure waveforms were measured at 13 selected segments within the flow network for comparisons. In the 1D simulation, the initial parameters of the vessel network were obtained by a direct measurement of the tubes in the experimental setup. The results verified that the 1D numerical model is able to capture the main features of the experimental pressure and flow waveforms with good reliability. The mean flow rates measurement results agree with the predictions of the 1D model with an overall difference of less than 1%. Further experiment might be needed to validate the 1D model in capturing pressure waveforms.