Modelling the leptomeningeal collateral circulation during acute ischaemic stroke

Measuring global cerebrovascular pulsatility transmission using 4D flow MRI

Pulse wave encephalopathy (PWE) is hypothesised to initiate many forms of dementia, motivating its identification and risk assessment. As candidate pulsatility based biomarkers for PWE, pulsatility index and pulsatility damping have been studied and, currently, do not adequately stratify risk due to variability in pulsatility and spatial bias. Here, we propose a locus-independent pulsatility transmission coefficient computed by spatially tracking pulsatility along vessels to characterise the brain pulse dynamics at a whole-organ level. Our preliminary analyses in a cohort of 20 subjects indicate that this measurement agrees with clinical observations relating blood pulsatility with age, heart rate, and sex, making it a suitable candidate to study the risk of PWE. We identified transmission differences between vascular regions perfused by the basilar and internal carotid arteries attributed to the identified dependence on cerebral blood flow, and some participants presented differences between the internal carotid perfused regions that were not related to flow or pulsatility burden, suggesting underlying mechanical differences. Large populational studies would benefit from retrospective pulsatility transmission analyses, providing a new comprehensive arterial description of the hemodynamic state in the brain. We provide a publicly available implementation of our tools to derive this coefficient, built into pre-existing open-source software.

Modeling cerebrovascular responses to assess the impact of the collateral circulation following middle cerebral artery occlusion

OBJECTIVE

An improved understanding of the role of the leptomeningeal collateral circulation in blood flow compensation following middle cerebral artery (MCA) occlusion can contribute to more effective treatment development for ischemic stroke. The present study introduces a model of the cerebral circulation to predict cerebral blood flow and tissue oxygenation following MCA occlusion.

METHODS

The model incorporates flow regulation mechanisms based on changes in pressure, shear stress, and metabolic demand. Oxygen saturation in cerebral vessels and tissue is calculated using a Krogh cylinder model. The model is used to assess the effects of changes in oxygen demand and arterial pressure on cerebral blood flow and oxygenation after MCA occlusion.

RESULTS

An increase from five to 11 leptomeningeal collateral vessels was shown to increase the oxygen saturation in the region distal to the occlusion by nearly 100%. Post-occlusion, the model also predicted a loss of autoregulation and a decrease in flow to the ischemic territory as oxygen demand was increased; these results were consistent with data from experiments that induced cerebral ischemia.

CONCLUSIONS

This study highlights the importance of leptomeningeal collaterals following MCA occlusion and reinforces the idea that lower oxygen demand and higher arterial pressure improve conditions of flow and oxygenation.

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.

MRI-based parameter inference for cerebral perfusion modelling in health and ischaemic stroke

Cerebral perfusion modelling is a promising tool to predict the impact of acute ischaemic stroke treatments on the spatial distribution of cerebral blood flow (CBF) in the human brain. To estimate treatment efficacy based on CBF, perfusion simulations need to become suitable for group-level investigations and thus account for physiological variability between individuals. However, computational perfusion modelling to date has been restricted to a few patient-specific cases. This study set out to establish automated parameter inference for perfusion modelling based on neuroimaging data and thus enable CBF simulations of groups. Magnetic resonance imaging (MRI) data from 75 healthy senior adults were utilised. Brain geometries were computed from healthy reference subjects' T1-weighted MRI. Haemodynamic model parameters were determined from spatial CBF maps measured by arterial spin labelling (ASL) perfusion MRI. Thereafter, perfusion simulations were conducted in 75 healthy cases followed by 150 acute ischaemic stroke cases representing an occlusion and CBF cessation in the left and right middle cerebral arteries. The anatomical fitness of the brain geometries was evaluated by comparing the simulated grey (GM) and white matter (WM) volumes to measurements in healthy reference subjects. Strong positive correlations were found in both tissue types (GM: Pearson's r 0.74, P<0.001; WM: Pearson's r 0.84, P<0.001). Haemodynamic parameter tuning was verified by comparing the total volumetric blood flow rate to the brain in healthy reference subjects and simulations (Pearson's r 0.89, P<0.001). In acute ischaemic stroke cases, the simulated infarct volume using a perfusion-based estimate was 197±25 ml. Computational predictions were in agreement with anatomical and haemodynamic values from the literature concerning T1-weighted, T2-weighted, and phase-contrast MRI measurements in healthy scenarios and acute ischaemic stroke cases. The acute stroke simulations did not capture small infarcts (left tail of the distribution), which could be explained by neglected compensatory mechanisms, e.g. collaterals. The proposed parameter inference method provides a foundation for group-level CBF simulations and for in silico clinical stroke trials which could assist in medical device and drug development.

Computational modeling of multiscale collateral blood supply in a whole-brain-scale arterial network

The cerebral arterial network covering the brain cortex has multiscale anastomosis structures with sparse intermediate anastomoses (O[102] μm in diameter) and dense pial networks (O[101] μm in diameter). Recent studies indicate that collateral blood supply by cerebral arterial anastomoses has an essential role in the prognosis of acute ischemic stroke caused by large vessel occlusion. However, the physiological importance of these multiscale morphological properties-and especially of intermediate anastomoses-is poorly understood because of innate structural complexities. In this study, a computational model of multiscale anastomoses in whole-brain-scale cerebral arterial networks was developed and used to evaluate collateral blood supply by anastomoses during middle cerebral artery occlusion. Morphologically validated cerebral arterial networks were constructed by combining medical imaging data and mathematical modeling. Sparse intermediate anastomoses were assigned between adjacent main arterial branches; the pial arterial network was modeled as a dense network structure. Blood flow distributions in the arterial network during middle cerebral artery occlusion simulations were computed. Collateral blood supply by intermediate anastomoses increased sharply with increasing numbers of anastomoses and provided one-order-higher flow recoveries to the occluded region (15%-30%) compared with simulations using a pial network only, even with a small number of intermediate anastomoses (≤10). These findings demonstrate the importance of sparse intermediate anastomoses, which are generally considered redundant structures in cerebral infarction, and provide insights into the physiological significance of the multiscale properties of arterial anastomoses.

A multiscale computational framework to evaluate flow alterations during mechanical thrombectomy for treatment of ischaemic stroke

The treatment of ischaemic stroke increasingly relies upon endovascular procedures known as mechanical thrombectomy (MT), which consists in capturing and removing the clot with a catheter-guided stent while at the same time applying external aspiration with the aim of reducing haemodynamic loads during retrieval. However, uniform consensus on procedural parameters such as the use of balloon guide catheters (BGC) to provide proximal flow control, or the position of the aspiration catheter is still lacking. Ultimately the decision is left to the clinician performing the operation, and it is difficult to predict how these treatment options might influence clinical outcome. In this study we present a multiscale computational framework to simulate MT procedures. The developed framework can provide quantitative assessment of clinically relevant quantities such as flow in the retrieval path and can be used to find the optimal procedural parameters that are most likely to result in a favorable clinical outcome. The results show the advantage of using BGC during MT and indicate small differences between positioning the aspiration catheter in proximal or distal locations. The framework has significant potential for future expansions and applications to other surgical treatments.

Modelling collateral flow and thrombus permeability during acute ischaemic stroke

The presence of collaterals and high thrombus permeability are associated with good functional outcomes after an acute ischaemic stroke. We aim to understand the combined effect of the collaterals and thrombus permeability on cerebral blood flow during an acute ischaemic stroke. A cerebral blood flow model including the leptomeningeal collateral circulation is used to simulate cerebral blood flow during an acute ischaemic stroke. The collateral circulation is varied to capture the collateral scores: absent, poor, moderate and good. Measurements of the transit time, void fraction and thrombus length in acute ischaemic stroke patients are used to estimate thrombus permeability. Estimated thrombus permeability ranges between 10^-7 and 10^-4 mm². Measured flow rates through the thrombus are small and the effect of a permeable thrombus on brain perfusion during stroke is small compared with the effect of collaterals. Our simulations suggest that the collaterals are a dominant factor in the resulting infarct volume after a stroke.

Determining Clinically-Viable Biomarkers for Ischaemic Stroke Through a Mechanistic and Machine Learning Approach

Assessment of distal cerebral perfusion after ischaemic stroke is currently only possible through expensive and time-consuming imaging procedures which require the injection of a contrast medium. Alternative approaches that could indicate earlier the impact of blood flow occlusion on distal cerebral perfusion are currently lacking. The aim of this study was to identify novel biomarkers suitable for clinical implementation using less invasive diagnostic techniques such as Transcranial Doppler (TCD). We used 1D modelling to simulate pre- and post-stroke velocity and flow wave propagation in a typical arterial network, and Sobol’s sensitivity analysis, supported by the use of Gaussian process emulators, to identify biomarkers linked to cerebral perfusion. We showed that values of pulsatility index of the right anterior cerebral artery > 1.6 are associated with poor perfusion and may require immediate intervention. Three additional biomarkers with similar behaviour, all related to pulsatility indices, were identified. These results suggest that flow pulsatility measured at specific locations could be used to effectively estimate distal cerebral perfusion rates, and ultimately improve clinical diagnosis and management of ischaemic stroke.

In silico trials for treatment of acute ischemic stroke: Design and implementation

An in silico trial simulates a disease and its corresponding therapies on a cohort of virtual patients to support the development and evaluation of medical devices, drugs, and treatment. In silico trials have the potential to refine, reduce cost, and partially replace current in vivo studies, namely clinical trials and animal testing. We present the design and implementation of an in silico trial for treatment of acute ischemic stroke. We propose an event-based modelling approach for the simulation of a disease and injury, where changes to the state of the system (the events) are assumed to be instantaneous. Using this approach we are able to combine a diverse set of models, spanning multiple time scales, to model acute ischemic stroke, treatment, and resulting brain tissue injury. The in silico trial is designed to be modular to aid development and reproducibility. It provides a comprehensive framework for application to any potential in silico trial. A statistical population model is used to generate cohorts of virtual patients. Patient functional outcomes are also predicted with a statistical model, using treatment and injury results and the patient's clinical parameters. We demonstrate the functionality of the event-based modelling approach and trial framework by running proof of concept in silico trials. The proof of concept trials simulate the same cohort of patients twice: once with successful treatment (successful recanalisation) and once with unsuccessful treatment (unsuccessful treatment). Ways to overcome some of the challenges and difficulties in setting up such an in silico trial are discussed, such as validation and computational limitations.