Validation of Patient-Specific Cerebral Blood Flow Simulation Using Transcranial Doppler Measurements

Uncertainty quantification of the lattice Boltzmann method focussing on studies of human-scale vascular blood flow

Uncertainty quantification is becoming a key tool to ensure that numerical models can be sufficiently trusted to be used in domains such as medical device design. Demonstration of how input parameters impact the quantities of interest generated by any numerical model is essential to understanding the limits of its reliability. With the lattice Boltzmann method now a widely used approach for computational fluid dynamics, building greater understanding of its numerical uncertainty characteristics will support its further use in science and industry. In this study we apply an in-depth uncertainty quantification study of the lattice Boltzmann method in a canonical bifurcating geometry that is representative of the vascular junctions present in arterial and venous domains. These campaigns examine how quantities of interest-pressure and velocity along the central axes of the bifurcation-are influenced by the algorithmic parameters of the lattice Boltzmann method and the parameters controlling the values imposed at inlet velocity and outlet pressure boundary conditions. We also conduct a similar campaign on a set of personalised vessels to further illustrate the application of these techniques. Our work provides insights into how input parameters and boundary conditions impact the velocity and pressure distributions calculated in a simulation and can guide the choices of such values when applied to vascular studies of patient specific geometries. We observe that, from an algorithmic perspective, the number of time steps and the size of the grid spacing are the most influential parameters. When considering the influence of boundary conditions, we note that the magnitude of the inlet velocity and the mean pressure applied within sinusoidal pressure outlets have the greatest impact on output quantities of interest. We also observe that, when comparing the magnitude of variation imposed in the input parameters with that observed in the output quantities, this variability is particularly magnified when the input velocity is altered. This study also demonstrates how open-source toolkits for validation, verification and uncertainty quantification can be applied to numerical models deployed on high-performance computers without the need for modifying the simulation code itself. Such an ability is key to the more widespread adoption of the analysis of uncertainty in numerical models by significantly reducing the complexity of their execution and analysis.

Uncertainty quantification of the impact of peripheral arterial disease on abdominal aortic aneurysms in blood flow simulations

Peripheral arterial disease (PAD) and abdominal aortic aneurysms (AAAs) often coexist and pose significant risks of mortality, yet their mutual interactions remain largely unexplored. Here, we introduce a fluid mechanics model designed to simulate the haemodynamic impact of PAD on AAA-associated risk factors. Our focus lies on quantifying the uncertainty inherent in controlling the flow rates within PAD-affected vessels and predicting AAA risk factors derived from wall shear stress. We perform a sensitivity analysis on nine critical model parameters through simulations of three-dimensional blood flow within a comprehensive arterial geometry. Our results show effective control of the flow rates using two-element Windkessel models, although specific outlets need attention. Quantities of interest like endothelial cell activation potential (ECAP) and relative residence time are instructive for identifying high-risk regions, with ECAP showing greater reliability and adaptability. Our analysis reveals that the uncertainty in the quantities of interest is 187% of that of the input parameters. Notably, parameters governing the amplitude and frequency of the inlet velocity exert the strongest influence on the risk factors' variability and warrant precise determination. This study forms the foundation for patient-specific simulations involving PAD and AAAs which should ultimately improve patient outcomes and reduce associated mortality rates.

Comparison of computational fluid dynamics with transcranial Doppler ultrasound in response to physiological stimuli

Cerebrovascular haemodynamics are sensitive to multiple physiological stimuli that require synergistic response to maintain adequate perfusion. Understanding haemodynamic changes within cerebral arteries is important to inform how the brain regulates perfusion; however, methods for direct measurement of cerebral haemodynamics in these environments are challenging. The aim of this study was to assess velocity waveform metrics obtained using transcranial Doppler (TCD) with flow-conserving subject-specific three-dimensional (3D) simulations using computational fluid dynamics (CFD). Twelve healthy participants underwent head and neck imaging with 3 T magnetic resonance angiography. Velocity waveforms in the middle cerebral artery were measured with TCD ultrasound, while diameter and velocity were measured using duplex ultrasound in the internal carotid and vertebral arteries to calculate incoming cerebral flow at rest, during hypercapnia and exercise. CFD simulations were developed for each condition, with velocity waveform metrics extracted in the same insonation region as TCD. Exposure to stimuli induced significant changes in cardiorespiratory measures across all participants. Measured absolute TCD velocities were significantly higher than those calculated from CFD (P range < 0.001-0.004), and these data were not correlated across conditions (r range 0.030-0.377, P range 0.227-0.925). However, relative changes in systolic and time-averaged velocity from resting levels exhibited significant positive correlations when the distinct techniques were compared (r range 0.577-0.770, P range 0.003-0.049). Our data indicate that while absolute measures of cerebral velocity differ between TCD and 3D CFD simulation, physiological changes from resting levels in systolic and time-averaged velocity are significantly correlated between techniques.

High resolution simulation of basilar artery infarct and flow within the circle of Willis

On a global scale, cerebro- and cardiovascular diseases have long been one of the leading causes of death and disability and their prevalence appears to be increasing in recent times. Understanding potential biomarkers and risk factors will help to identify individuals potentially at risk of suffering an ischemic stroke. However, the widely variable construction of the cerebral vasculature makes it difficult to provide a specific assessment without the knowledge of a patient's physiology. In this paper we use the 3D blood flow simulator HemeLB to study flow within three common structural variations of the circle of Willis during and in the moments after a blockage of the basilar artery. This tool, based on the lattice Boltzmann method, allows the 3D flow entering the basilar artery to be finely controlled to replicate the cessation of blood feeding this particular vessel-we demonstrate this with several examples including a sudden halt to flow and a gradual loss of flow over three heartbeat cycles. In this work we start with an individualised 3D representation of a full circle of Willis and then construct two further domains by removing the left or right posterior communicating arteries from this geometry. Our results indicate how, and how quickly, the circle of Willis is able to redistribute flow following such a stroke. Due to the choice of infarct, the greatest reduction in flow was observed in the posterior cerebral arteries where flow was reduced by up to 70% in some cases. The high resolution domains used in this study permit the velocity magnitude and wall shear stress to be analysed at key points during and following the stroke. The model we present here indicates how personalised vessels are required to provide the best insight into stroke risk for a given individual.

Validation of a cerebral hemodynamic model with personalized calibration in patients with aneurysmal subarachnoid hemorrhage

This study aims to validate a numerical model developed for assessing personalized circle of Willis (CoW) hemodynamics under pathological conditions. Based on 66 computed tomography angiography images, investigations were obtained from 43 acute aneurysmal subarachnoid hemorrhage (aSAH) patients from a local neurovascular center. The mean flow velocity of each artery in the CoW measured using transcranial Doppler (TCD) and simulated by the numerical model was obtained for comparison. The intraclass correlation coefficient (ICC) over all cerebral arteries for TCD and the numerical model was 0.88 (N = 561; 95% CI 0.84-0.90). In a subgroup of patients who had developed delayed cerebral ischemia (DCI), the ICC had decreased to 0.72 but remained constant with respect to changes in blood pressure, Fisher grade, and location of ruptured aneurysm. Our numerical model showed good agreement with TCD in assessing the flow velocity in the CoW of patients with aSAH. In conclusion, the proposed model can satisfactorily reproduce the cerebral hemodynamics under aSAH conditions by personalizing the numerical model with TCD measurements. Clinical trial registration: [http://www.trialregister.nl/], identifier [NL8114].

Parametric analysis of an efficient boundary condition to control outlet flow rates in large arterial networks

Substantial effort is being invested in the creation of a virtual human-a model which will improve our understanding of human physiology and diseases and assist clinicians in the design of personalised medical treatments. A central challenge of achieving blood flow simulations at full-human scale is the development of an efficient and accurate approach to imposing boundary conditions on many outlets. A previous study proposed an efficient method for implementing the two-element Windkessel model to control the flow rate ratios at outlets. Here we clarify the general role of the resistance and capacitance in this approach and conduct a parametric sweep to examine how to choose their values for complex geometries. We show that the error of the flow rate ratios decreases exponentially as the resistance increases. The errors fall below 4% in a simple five-outlets model and 7% in a human artery model comprising ten outlets. Moreover, the flow rate ratios converge faster and suffer from weaker fluctuations as the capacitance decreases. Our findings also establish constraints on the parameters controlling the numerical stability of the simulations. The findings from this work are directly applicable to larger and more complex vascular domains encountered at full-human scale.

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

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.

An efficient, localised approach for the simulation of elastic blood vessels using the lattice Boltzmann method

Many numerical studies of blood flow impose a rigid wall assumption due to the simplicity of its implementation compared to a full coupling with a solid mechanics model. In this paper, we present a localised method for incorporating the effects of elastic walls into blood flow simulations using the lattice Boltzmann method implemented by the open-source code HemeLB. We demonstrate that our approach is able to more accurately capture the flow behaviour expected in elastic walled vessels than ones with rigid walls. Furthermore, we show that this can be achieved with no loss of computational performance and remains strongly scalable on high performance computers. We finally illustrate that our approach captures the same trends in wall shear stress distribution as those observed in studies using a rigorous coupling between fluid dynamics and solid mechanics models to solve flow in personalised vascular geometries. These results demonstrate that our model can be used to efficiently and effectively represent flows in elastic blood vessels.

High fidelity blood flow in a patient-specific arteriovenous fistula

An arteriovenous fistula, created by artificially connecting segments of a patient’s vasculature, is the preferred way to gain access to the bloodstream for kidney dialysis. The increasing power and availability of supercomputing infrastructure means that it is becoming more realistic to use simulations to help identify the best type and location of a fistula for a specific patient. We describe a 3D fistula model that uses the lattice Boltzmann method to simultaneously resolve blood flow in patient-specific arteries and veins. The simulations conducted here, comprising vasculatures of the whole forearm, demonstrate qualified validation against clinical data. Ongoing research to further encompass complex biophysics on realistic time scales will permit the use of human-scale physiological models for basic and clinical medicine.

Uncertainty quantification in classical molecular dynamics

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalizing experimental observations to producing apparently credible predictions for a number of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for molecular dynamics simulation designed to endow the method with better error estimates that will enable it to be used to report actionable results. The approach adopted is a standard one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large number of replicas are run concurrently, from which reliable statistics can be extracted. Indeed, because molecular dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estimation. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

Towards blood flow in the virtual human: efficient self-coupling of HemeLB

Many scientific and medical researchers are working towards the creation of a virtual human—a personalized digital copy of an individual—that will assist in a patient’s diagnosis, treatment and recovery. The complex nature of living systems means that the development of this remains a major challenge. We describe progress in enabling the HemeLB lattice Boltzmann code to simulate 3D macroscopic blood flow on a full human scale. Significant developments in memory management and load balancing allow near linear scaling performance of the code on hundreds of thousands of computer cores. Integral to the construction of a virtual human, we also outline the implementation of a self-coupling strategy for HemeLB. This allows simultaneous simulation of arterial and venous vascular trees based on human-specific geometries.

Study protocol of validating a numerical model to assess the blood flow in the circle of Willis

INTRODUCTION

We developed a zero-dimensional (0D) model to assess the patient-specific haemodynamics in the circle of Willis (CoW). Similar numerical models for simulating the cerebral blood flow (CBF) had only been validated qualitatively in healthy volunteers by magnetic resonance (MR) angiography and transcranial Doppler (TCD). This study aims to validate whether a numerical model can simulate patient-specific blood flow in the CoW under pathological conditions.

METHODS AND ANALYSIS

This study is a diagnostic accuracy study. We aim to collect data from a previously performed prospective study that involved patients with aneurysmal subarachnoid haemorrhage (aSAH) receiving both TCD and brain Computerd Tomography angiography (CTA) at the same day. The cerebral flow velocities are calculated by the 0D model, based on the vessel diameters measured on the CTA of each patient. In this study, TCD is considered the gold standard for measuring flow velocity in the CoW. The agreement will be analysed using Pearson correlation coefficients.

ETHICS AND DISSEMINATION

This study protocol has been approved by the Medical Ethics Review Board of the University Medical Center Groningen: METc2019/103. The results will be submitted to an international scientific journal for peer-reviewed publication.

TRIAL REGISTRATION NUMBER

NL8114.

Lattice-Boltzmann interactive blood flow simulation pipeline

PURPOSE

Cerebral aneurysms are one of the prevalent cerebrovascular disorders in adults worldwide and caused by a weakness in the brain artery. The most impressive treatment for a brain aneurysm is interventional radiology treatment, which is extremely dependent on the skill level of the radiologist. Hence, accurate detection and effective therapy for cerebral aneurysms still remain important clinical challenges. In this work, we have introduced a pipeline for cerebral blood flow simulation and real-time visualization incorporating all aspects from medical image acquisition to real-time visualization and steering.

METHODS

We have developed and employed an improved version of HemeLB as the main computational core of the pipeline. HemeLB is a massive parallel lattice-Boltzmann fluid solver optimized for sparse and complex geometries. The visualization component of this pipeline is based on the ray marching method implemented on CUDA capable GPU cores.

RESULTS

The proposed visualization engine is evaluated comprehensively and the reported results demonstrate that it achieves significantly higher scalability and sites updates per second, indicating higher update rate of geometry sites' values, in comparison with the original HemeLB. This proposed engine is more than two times faster and capable of 3D visualization of the results by processing more than 30 frames per second.

CONCLUSION

A reliable modeling and visualizing environment for measuring and displaying blood flow patterns in vivo, which can provide insight into the hemodynamic characteristics of cerebral aneurysms, is presented in this work. This pipeline increases the speed of visualization and maximizes the performance of the processing units to do the tasks by breaking them into smaller tasks and working with GPU to render the images. Hence, the proposed pipeline can be applied as part of clinical routines to provide the clinicians with the real-time cerebral blood flow-related information.

Relationship between middle cerebral parent artery asymmetry and middle cerebral artery aneurysm rupture risk factors

OBJECTIVE

The exact pathophysiological mechanisms underlying cerebral aneurysm formation remain unclear. Asymmetrical local vascular geometry may play a role in aneurysm formation and progression. The object of this study was to investigate the association between the geometric asymmetry of the middle cerebral artery (MCA) and the presence of MCA aneurysms and associated high-risk features.

METHODS

Using a retrospective case-control study design, the authors examined MCA anatomy in all patients who had been diagnosed with an MCA aneurysm in the period from 2008 to 2017 at the University Hospitals Cleveland Medical Center. Geometric features of the MCA ipsilateral to MCA aneurysms were compared with those of the unaffected contralateral side (secondary control group). Then, MCA geometry was compared between patients with MCA aneurysms and patients who had undergone CTA for suspected vascular pathology but were ultimately found to have normal intracranial vasculature (primary control group). Parent vessel and aneurysm morphological parameters were measured, calculated, and compared between case and control groups. Associations between geometric parameters and high-risk aneurysm features were identified.

RESULTS

The authors included 247 patients (158 cases and 89 controls) in the study. The aneurysm study group consisted of significantly more women and smokers than the primary control group. Patients with MCA bifurcation aneurysms had lower parent artery inflow angles (p = 0.01), lower parent artery tortuosity (p < 0.01), longer parent artery total length (p = 0.03), and a significantly greater length difference between ipsilateral and contralateral prebifurcation MCAs (p < 0.01) than those in primary controls. Type 2 MCA aneurysms (n = 89) were more likely to be associated with dome irregularity or a daughter sac and were more likely to have a higher cumulative total of high-risk features than type 1 MCA aneurysms (n = 69).

CONCLUSIONS

Data in this study demonstrated that a greater degree of parent artery asymmetry for MCA aneurysms is associated with high-risk features. The authors also found that the presence of a long and less tortuous parent artery upstream of an MCA aneurysm is a common phenotype that is associated with a higher risk profile. The aneurysm parameters are easily measurable and are novel radiographic biomarkers for aneurysm risk assessment.