Pathogenic mechanisms in ischemic damage: a computational study

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.

On the Sensitivity Analysis of Porous Finite Element Models for Cerebral Perfusion Estimation

Computational physiological models are promising tools to enhance the design of clinical trials and to assist in decision making. Organ-scale haemodynamic models are gaining popularity to evaluate perfusion in a virtual environment both in healthy and diseased patients. Recently, the principles of verification, validation, and uncertainty quantification of such physiological models have been laid down to ensure safe applications of engineering software in the medical device industry. The present study sets out to establish guidelines for the usage of a three-dimensional steady state porous cerebral perfusion model of the human brain following principles detailed in the verification and validation (V&V 40) standard of the American Society of Mechanical Engineers. The model relies on the finite element method and has been developed specifically to estimate how brain perfusion is altered in ischaemic stroke patients before, during, and after treatments. Simulations are compared with exact analytical solutions and a thorough sensitivity analysis is presented covering every numerical and physiological model parameter. The results suggest that such porous models can approximate blood pressure and perfusion distributions reliably even on a coarse grid with first order elements. On the other hand, higher order elements are essential to mitigate errors in volumetric blood flow rate estimation through cortical surface regions. Matching the volumetric flow rate corresponding to major cerebral arteries is identified as a validation milestone. It is found that inlet velocity boundary conditions are hard to obtain and that constant pressure inlet boundary conditions are feasible alternatives. A one-dimensional model is presented which can serve as a computationally inexpensive replacement of the three-dimensional brain model to ease parameter optimisation, sensitivity analyses and uncertainty quantification. The findings of the present study can be generalised to organ-scale porous perfusion models. The results increase the applicability of computational tools regarding treatment development for stroke and other cerebrovascular conditions.

A porous circulation model of the human brain for in silico clinical trials in ischaemic stroke

The advancement of ischaemic stroke treatment relies on resource-intensive experiments and clinical trials. In order to improve ischaemic stroke treatments, such as thrombolysis and thrombectomy, we target the development of computational tools for in silico trials which can partially replace these animal and human experiments with fast simulations. This study proposes a model that will serve as part of a predictive unit within an in silico clinical trial estimating patient outcome as a function of treatment. In particular, the present work aims at the development and evaluation of an organ-scale microcirculation model of the human brain for perfusion prediction. The model relies on a three-compartment porous continuum approach. Firstly, a fast and robust method is established to compute the anisotropic permeability tensors representing arterioles and venules. Secondly, vessel encoded arterial spin labelling magnetic resonance imaging and clustering are employed to create an anatomically accurate mapping between the microcirculation and large arteries by identifying superficial perfusion territories. Thirdly, the parameter space of the problem is reduced by analysing the governing equations and experimental data. Fourthly, a parameter optimization is conducted. Finally, simulations are performed with the tuned model to obtain perfusion maps corresponding to an open and an occluded (ischaemic stroke) scenario. The perfusion map in the occluded vessel scenario shows promising qualitative agreement with computed tomography images of a patient with ischaemic stroke caused by large vessel occlusion. The results highlight that in the case of vessel occlusion (i) identifying perfusion territories is essential to capture the location and extent of underperfused regions and (ii) anisotropic permeability tensors are required to give quantitatively realistic estimation of perfusion change. In the future, the model will be thoroughly validated against experiments.

Sequential acquisition and processing of perfusion and diffusion MRI data for a porcine stroke model

An automated data processing pipeline, designed for handling a large throughput of sequentially acquired MRI brain data, is described. The system takes as input multiple diffusion weighted (DWI) and perfusion weighted imaging (PWI) volumes acquired at different temporal points, automatically segments and registers them, and ultimately outputs a database used to track various perfusion and diffusion parameters through time at individual brain voxels. This pipeline has been utilized to successfully process two pig brains from an induced stroke experiment.

Modeling brain energy metabolism and function: a multiparametric monitoring approach

Mathematical modeling of brain function is an important tool needed for a better understanding of experimental results and clinical situations. In the present study, we are constructing and testing a mathematical model capable of simulating changes in brain energy metabolism that develop in real time under various pathophysiological conditions. The model incorporates the following parameters: cerebral blood flow, partial oxygen pressure, mitochondrial NADH redox state, and extracellular potassium. Accordingly, all the model variables are only time dependent (;point-model' approach). Numerical runs demonstrate the ability of the model to mimic pathological conditions, such as complete and partial ischemia, cortical spreading depression under normoxic and partial ischemic conditions. They also show that, when properly tuned, a model of this type permits the monitoring of only one or two crucial variables and the computation of the remaining variables in real time during clinical or experimental procedures.

Simulation of the effect of Na+ and Cl- on the velocity of a spreading depression wave using a simplified electrochemical model of synaptic terminals

In the study of the spreading depression (SD) wave phenomenon and its dynamics, it is necessary to describe the ionic movements along the extracellular space, as well as between this and the intracellular space. In both cases, the ionic movement includes a double coupling involving the concentration and the potential gradients and hence must be described by electrodiffusion mechanisms. Based on this, the effects of the ionic composition on the characteristics of the wave propagation can be predicted. The influence of varying extracellular sodium and chloride concentrations on the velocity of propagation of the SD wave was investigated by simulation. The results achieved are close to the experimental measurement from the literature. These findings suggest the potentiality of the model proposed in supporting the interpretation of experimental data in neuronal tissues, particularly the SD.

Blockade of NMDA-receptors or calcium-channels attenuates the ischaemia-evoked efflux of glutamate and phosphoethanolamine and depression of neuronal activity in rat organotypic hippocampal slice cultures

We have investigated the effects of various insults on extracellular glutamate and phosphoethanolamine levels as well as electrical activity alterations in the early period following these insults in organotypic hippocampal slice cultures. Cultures prepared from 7-day-old rats were maintained in vitro for 7-14 days and then metabolic inhibition was induced: cultures were briefly exposed to potassium cyanide to induce chemical anoxia, 2-deoxyglucose with glucose removal to produce hypoglycaemia, or a combination of both to simulate ischaemia. Chemical anoxia induced a small increase in glutamate and a reversible decrease in evoked field potentials and these were greatly potentiated following simulated ischaemia: high, biphasic glutamate efflux and irreversible field potential abolition as well as increase in phosphoethanolamine levels were observed. We have characterised the effects of treatments using NMDA-receptor antagonists and the L-type calcium channel blocker diltiazem. Anoxia-induced glutamate accumulation was prevented by MK-801 and diltiazem D-AP5. Following simulated ischaemia, diltiazem totally prevented glutamate and phosphoethanolamine accumulations, whereas MK-801 did not block the first phase of glutamate accumulation and D-AP5 prevented none. We demonstrated that glutamate and phosphoethanolamine ischaemic-evoked efflux as well as the recovery of electrical activity in organotypic hippocampal slice cultures are sensitive to both NMDA-receptor and calcium-channel blockade. This model thus represents a useful in vitro system for the study of ischaemic neurodegeneration paralleling results reported using in vivo models.

Cortical spreading depression and the pathogenesis of brain disorders: a computational and neural network-based investigation

This paper reviews our recent studies of the role of cortical spreading depression (CSD) in the pathogenesis of brain disorders. Our investigation is a computational one, involving the development and utilization of a complex neuro-metabolic model of the interactions assumed to occur in the cortex during the passage of multiple CSD waves. Incorporating these neuro-metabolic changes of CSD within a neural network model of normoxic cortex produces cortical activation patterns during the passage of a CSD wave that, projected onto the visual fields, resemble the visual hallucinations observed during the migraine aura. When focal ischemia is simulated with the model, the evoked CSD waves are found to affect the expansion of the infarction into the ischemic penumbra. Our findings support the hypothesis that CSD does play an important pathogenic role in these and other neurological disorders, and suggest additional experimental studies that may further substantiate it.