High fidelity blood flow in a patient-specific arteriovenous fistula

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.

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.

Simulation of the FDA nozzle benchmark: A lattice Boltzmann study

BACKGROUND AND OBJECTIVE

Contrary to flows in small intracranial vessels, many blood flow configurations such as those found in aortic vessels and aneurysms involve larger Reynolds numbers and, therefore, transitional or turbulent conditions. Dealing with such systems require both robust and efficient numerical methods.

METHODS

We assess here the performance of a lattice Boltzmann solver with full Hermite expansion of the equilibrium and central Hermite moments collision operator at higher Reynolds numbers, especially for under-resolved simulations. To that end the food and drug administration's benchmark nozzle is considered at three different Reynolds numbers covering all regimes: (1) laminar at a Reynolds number of 500, (2) transitional at a Reynolds number of 3500, and (3) low-level turbulence at a Reynolds number of 6500.

RESULTS

The lattice Boltzmann results are compared with previously published inter-laboratory experimental data obtained by particle image velocimetry. Our results show good agreement with the experimental measurements throughout the nozzle, demonstrating the good performance of the solver even in under-resolved simulations.

CONCLUSION

In this manner, fast but sufficiently accurate numerical predictions can be achieved for flow configurations of practical interest regarding medical applications.