Modelling midline shift and ventricle collapse in cerebral oedema following acute ischaemic stroke.

In ischaemic stroke, a large reduction in blood supply can lead to the breakdown of the blood-brain barrier and to cerebral oedema after reperfusion therapy. The resulting fluid accumulation in the brain may contribute to a significant rise in intracranial pressure (ICP) and tissue deformation. Changes in the level of ICP are essential for clinical decision-making and therapeutic strategies. However, the measurement of ICP is constrained by clinical techniques and obtaining the exact values of the ICP has proven challenging. In this study, we propose the first computational model for the simulation of cerebral oedema following acute ischaemic stroke for the investigation of ICP and midline shift (MLS) relationship. The model consists of three components for the simulation of healthy blood flow, occluded blood flow and oedema, respectively. The healthy and occluded blood flow components are utilized to obtain oedema core geometry and then imported into the oedema model for the simulation of oedema growth. The simulation results of the model are compared with clinical data from 97 traumatic brain injury patients for the validation of major model parameters. Midline shift has been widely used for the diagnosis, clinical decision-making, and prognosis of oedema patients. Therefore, we focus on quantifying the relationship between ICP and midline shift (MLS) and identify the factors that can affect the ICP-MLS relationship. Three major factors are investigated, including the brain geometry, blood-brain barrier damage severity and the types of oedema (including rare types of oedema). Meanwhile, the two major types (stress and tension/compression) of mechanical brain damage are also presented and the differences in the stress, tension, and compression between the intraparenchymal and periventricular regions are discussed. This work helps to predict ICP precisely and therefore provides improved clinical guidance for the treatment of brain oedema.

Computational modelling of cerebral oedema and osmotherapy following ischaemic stroke.

In ischaemic stroke, a large reduction in blood supply can lead to the breakdown of the blood brain barrier and to cerebral oedema after reperfusion therapy. Cerebral oedema is marked by elevated intracranial pressure (ICP), tissue herniation and reduced cerebral perfusion pressure. In clinical settings, osmotherapy has been a common practice to decrease ICP. However, there are no guidelines on the choice of administration protocol parameters such as injection doses, infusion time and retention time. Most importantly, the effects of osmotherapy have been proven controversial since the infusion of osmotic agents can lead to a range of side effects. Here, a new Finite Element model of brain oedema and osmotherapy is thus proposed to predict treatment outcome. The model consists of three components that simulate blood perfusion, oedema, and osmotherapy, respectively. In the perfusion model (comprising arteriolar, venous, and capillary blood compartments), an anatomically accurate brain geometry is used to identify regions with a perfusion reduction and potential oedema occurrence in stroke. The oedema model is then used to predict ICP using a porous circulation model with four fluid compartments (arteriolar blood, venular blood, capillary blood, and interstitial fluid). In the osmotherapy model, the osmotic pressure is varied and the changes in ICP during different osmotherapy episodes are quantified. The simulation results of the model show excellent agreement with available clinical data and the model is employed to study osmotherapy under various parameters. Consequently, it is demonstrated how therapeutic strategies can be proposed for patients with different pathological parameters based on simulations.

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.

Quantification of hypoxic regions distant from occlusions in cerebral penetrating arteriole trees.

The microvasculature plays a key role in oxygen transport in the mammalian brain. Despite the close coupling between cerebral vascular geometry and local oxygen demand, recent experiments have reported that microvascular occlusions can lead to unexpected distant tissue hypoxia and infarction. To better understand the spatial correlation between the hypoxic regions and the occlusion sites, we used both in vivo experiments and in silico simulations to investigate the effects of occlusions in cerebral penetrating arteriole trees on tissue hypoxia. In a rat model of microembolisation, 25 µm microspheres were injected through the carotid artery to occlude penetrating arterioles. In representative models of human cortical columns, the penetrating arterioles were occluded by simulating the transport of microspheres of the same size and the oxygen transport was simulated using a Green's function method. The locations of microspheres and hypoxic regions were segmented, and two novel distance analyses were implemented to study their spatial correlation. The distant hypoxic regions were found to be present in both experiments and simulations, and mainly due to the hypoperfusion in the region downstream of the occlusion site. Furthermore, a reasonable agreement for the spatial correlation between hypoxic regions and occlusion sites is shown between experiments and simulations, which indicates the good applicability of in silico models in understanding the response of cerebral blood flow and oxygen transport to microemboli.

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.

Modelling the effects of cerebral microthrombi on tissue oxygenation and cell death.

Thrombectomy, the mechanical removal of a clot, is the most common way to treat ischaemic stroke with large vessel occlusions. However, perfusion cannot always be restored after such an intervention. It has been hypothesised that the absence of reperfusion is at least partially due to the clot fragments that block the downstream vessels. In this paper, we present a new way of quantifying the effects of cerebral microthrombi on oxygen transport to tissue in terms of hypoxia and ischaemia. The oxygen transport was simulated with the Green's function method on physiologically representative microvascular cubes, which was found independent of both microvascular geometry and length scale. The microthrombi occlusions were then simulated in the microvasculature, which were extravasated over time with a new thrombus extravasation model. The tissue hypoxic fraction was fitted as a sigmoidal function of vessel blockage fraction, which was then taken to be a function of time after the formation of microthrombi occlusions. A novel hypoxia-based 3-state cell death model was finally proposed to simulate the hypoxic tissue damage over time. Using the cell death model, the impact of a certain degree of microthrombi occlusions on tissue viability and microinfarct volume can be predicted over time. Quantifying the impact of microthrombi on oxygen transport and tissue death will play an important role in full brain models of ischaemic stroke and thrombectomy.

Modelling the leptomeningeal collateral circulation during acute ischaemic stroke.

A novel model of the leptomeningeal collateral circulation is created by combining data from multiple sources with statistical scaling laws. The extent of the collateral circulation is varied by defining a collateral vessel probability. Blood flow and pressure are simulated using a one-dimensional steady state blood flow model. The leptomeningeal collateral vessels provide significant flow during a stroke. The pressure drop over an occlusion predicted by the model ranges between 60 and 85 mmHg depending on the extent of the collateral circulation. The linear transport of contrast material was simulated in the circulatory network. The time delay of peak contrast over an occlusion is 3.3 s in the model, and 2.1 s (IQR 0.8-4.0 s) when measured in dynamic CTA data of acute ischaemic stroke patients. Modelling the leptomeningeal collateral circulation could lead to better estimates of infarct volume and patient outcome.

Modelling the impact of clot fragmentation on the microcirculation after thrombectomy.

Many ischaemic stroke patients who have a mechanical removal of their clot (thrombectomy) do not get reperfusion of tissue despite the thrombus being removed. One hypothesis for this 'no-reperfusion' phenomenon is micro-emboli fragmenting off the large clot during thrombectomy and occluding smaller blood vessels downstream of the clot location. This is impossible to observe in-vivo and so we here develop an in-silico model based on in-vitro experiments to model the effect of micro-emboli on brain tissue. Through in-vitro experiments we obtain, under a variety of clot consistencies and thrombectomy techniques, micro-emboli distributions post-thrombectomy. Blood flow through the microcirculation is modelled for statistically accurate voxels of brain microvasculature including penetrating arterioles and capillary beds. A novel micro-emboli algorithm, informed by the experimental data, is used to simulate the impact of micro-emboli successively entering the penetrating arterioles and the capillary bed. Scaled-up blood flow parameters-permeability and coupling coefficients-are calculated under various conditions. We find that capillary beds are more susceptible to occlusions than the penetrating arterioles with a 4x greater drop in permeability per volume of vessel occluded. Individual microvascular geometries determine robustness to micro-emboli. Hard clot fragmentation leads to larger micro-emboli and larger drops in blood flow for a given number of micro-emboli. Thrombectomy technique has a large impact on clot fragmentation and hence occlusions in the microvasculature. As such, in-silico modelling of mechanical thrombectomy predicts that clot specific factors, interventional technique, and microvascular geometry strongly influence reperfusion of the brain. Micro-emboli are likely contributory to the phenomenon of no-reperfusion following successful removal of a major clot.

Coupling one-dimensional arterial blood flow to three-dimensional tissue perfusion models for in silico trials of acute ischaemic stroke.

An acute ischaemic stroke is due to the sudden blockage of an intracranial blood vessel by an embolized thrombus. In the context of setting up in silico trials for the treatment of acute ischaemic stroke, the effect of a stroke on perfusion and metabolism of brain tissue should be modelled to predict final infarcted brain tissue. This requires coupling of blood flow and tissue perfusion models. A one-dimensional intracranial blood flow model and a method to couple this to a brain tissue perfusion model for patient-specific simulations is presented. Image-based patient-specific data on the anatomy of the circle of Willis are combined with literature data and models for vessel anatomy not visible in the images, to create an extended model for each patient from the larger vessels down to the pial surface. The coupling between arterial blood flow and tissue perfusion occurs at the pial surface through the estimation of perfusion territories. The coupling method is able to accurately estimate perfusion territories. Finally, we argue that blood flow can be approximated as steady-state flow at the interface between arterial blood flow and tissue perfusion to reduce the cost of organ-scale simulations.