The Study of the Function of AQP4 in Cerebral Ischaemia-Reperfusion Injury using Poroelastic Theory

Brain oedema is thought to form and to clear through the use of water-protein channels, aquaporin-4 (AQP4), which are found in the astrocyte endfeet. The model developed here is used to study the function of AQP4 in the formation and elimination of oedema fluid in ischaemia-reperfusion injury. The cerebral space is assumed to be made of four fluid compartments: astrocyte, neuron, ECS and blood microvessels, and a solid matrix for the tissue, and this is modelled using multiple-network poroelastic theory. AQP4 allows the movement of water between astrocyte and the ECS and the microvessels. It is found that the presence of AQP4 may help in reducing vasogenic oedema shown by a decrease in brain tissue extracellular pressure. However, the astrocyte pressure will increase to compensate for this decrease, which may lead to cytotoxic oedema. In addition, the swelling will also depend on the ionic concentrations in the astrocyte and extracellular space, which may change after ischaemic stroke. Understanding the role of AQP4 in oedema may thus help the development of a treatment plan in reducing brain swelling after ischaemia-reperfusion

Application of asymptotic expansion homogenization for vascularized poroelastic brain tissue

Brain oedema formation after ischaemia-reperfusion has been previously modelled by assuming that the blood vessels distribution in the brain as homogeneous. However, the blood vessels in the brain have variety of sizes and this assumption should be reconsidered. One of the ways to improve this assumption is by taking into account the microstructure of the blood vessels and their distribution by formulating the model using asymptotic expansion homogenization (AEH) technique. In this paper, AEH of the vascularized poroelastic model is carried out to obtain a set of new homogenized macroscale governing equations and their associated microscale cell problems. An example of solving the microscale cell problems using a simple cubic geometry with embedded 6-branch cylinders representing brain tissue and capillaries is shown to obtain four important tensors L;Q;K; and G, which will be used to solve the homogenized macroscale equations on a larger brain geometry. This method will be extended in the future to include statistically accurate capillary distribution of brain tissue

Investigation of the capillary effects toward brain tissue poroelastic properties using asymptotic expansion homogenization

Existing brain model to study brain oedema formation has an assumption of homogeneous brain capillary distribution, despite it is actually normally distributed. In this paper, the assumption is improved by applying asymptotic expansion homogenization (AEH) to a vascularized poroelastic model to obtain a new homogenized macroscale governing equations with 4 microscale cell problems. The cell problems are solved on a cube of brain tissue with capillary to obtain 4 tensors describing the mechanical and fluid transport properties of the brain. From the simulations, only the blood permeability and Biot’s parameter tensors are significantly affected by the capillary tortuosities

Age-based sensitivity analysis on cardiac hemodynamics using lumped-parameter modelling

Age is a major risk for heart failure, which is associated with the reduction in ventricular compliance, increase in arterial stiffening, and increase in systemic vascular resistance. In this study, a lumped-parameter model is used to investigate the effect of aging on the possibility of heart failure occurrence. Model parameters including the systemic and pulmonary arterial compliance and resistance, and the left ventricular elastance are calculated for different ages using a ratio-based method. These parameters are then used in the lumped-parameter model. Our findings show that as age increases, there is a leftward and a rightward shift in the left ventricle and right ventricle pressure-volume loops, respectively. For the left ventricle, there is a decrease in stroke volume and an increase in ventricular pressure as the age increases. This correlates with the occurrence of arterial hypertension in the older population. Meanwhile, the right ventricular pressure is maintained as the population gets older, despite the increase in the stroke volume. This is possibly due to the shift in intraventricular septum that causes an enlargement of the right ventricle as the age increases. This study provides understanding on the effect of age on the occurrence of heart failure.This study demonstrates the relationship of aging with cardiac hemodynamics, which provides the potential risk of heart failure occurrence. Although there are many risk factors that can cause heart failure, aging has been strongly associated with its occurrence. Understanding how age affects heart failure can help to differentiate them from other effects such as dietary, gender, and early cardiovascular diseases including arrhythmia and myocardial infarction

Simulation of decompressive craniectomy for ischaemic stroke treatment: A computational study

To evaluate the effectiveness of DC in treating brain tissue swelling using computational study based on capillary filtration and poroelastic theory

Simulation of decompressive craniectomy for ischaemic stroke treatment: A conceptual modeling study

Decompressive craniectomy is a treatment in which part of the skull is removed so as to reduce the intracranial pressure in the skull, especially during brain tissue swelling. Computational modeling studies may be used to understand the efficiency of this treatment in ischaemic stroke for advance clinical decision making. Thus, we performed a simulation using a mathematical model based on poroelastic theory and capillary filtration to see the effects of craniectomy in treating brain tissue swelling using 3D brain geometry. The results show that performing craniectomy can reduce intracranial pressure and reduce the effect of herniation. However, part of the brain is bulging out from the surgical hole and exerts a small amount of stress on the tissue by the surgical edge. This mathematical modeling framework can be used for further investigation of finding the suitable parameters for a decompressive craniectom

Multiscale Modelling of 3-Dimensional Brain Tissue Using Ideal Capillary Model

This project aims to investigate the effects of capillary size and shape toward the brain tissue poroelastic properties model using asymptotic expansion homogenization (AEH). Applying AEH to the existing poroelastic governing equations (GE) results in a new GE consists of 6 macroscale equations and 4 microscale cell problems. The cell problems are solved on a microstructure geometry of brain tissue with capillary embedded to obtain effective parametric tensors, namely the capillary and interstitial hydraulic conductivity (K and G ), capillary and interstitial homogenous Biot’s coefficient (αc and αt ), Young’s modulus (E) and Poisson’s ratio (v). By varying the tortuosity, the percentage difference of K is 97.98%, shows that it is highly affected by tortuosity. The percentage difference of G is 0.25% implying that tortuosity insignificantly affecting G. Meanwhile, αc and αt decreases and increases with tortuosity, respectively. The percentage difference of E and v are 0.14% and 0.03% respectively, implying that both parameters does not affected by tortuosity. Besides, K is exponentially increases with the increase of radius. On the other hand, G decreases as the radius increases. Meanwhile αc and αt increases and decreases, respectively as radius increases. The percentage differences of E and v are 18.26% and 14.55% respectively, suggesting that they are significantly affected by the radius. In conclusion, capillary shape and size have significant impact on the simulation of human brain. Thus, both characteristics should be precisely emphasized in the development of the geometry so that accurate parameters can be obtained to solve macroscale equations in future

Development of brain tissue swelling predictive tools for ischaemic stroke patient post-treatment

Ischaemic stroke is one of the causes of death worldwide. Treatments such as thrombolysis and catheterisation must be given within 3 hours after stroke onset, in which treatments beyond this time may pose risk of brain tissue swelling. Thus, a prediction system must be made to determine the suitability of a stroke treatment to avoid the risk of failure. In this report, a mathematical model based on poroelastic theory and asymptotic expansion homogenization has been developed to study the formation of brain tissue swelling after ischaemia-reperfusion treatment. Firstly, the mathematical model of brain tissue swelling after ischaemia-reperfusion treatment is investigated using an ideal 2D brain geometry. The objective here is to observe the effect of infarct size and location towards the formation and severity of brain herniation, which will form due to brain tissue swelling. However, this model assumed that the blood pressure is constant and homogeneous throughout the brain, while in fact, the blood capillaries vary in sizes and shapes. Therefore, asymptotic expansion homogenization technique is applied to allow for the inclusion of capillaries sizes into the initial model. This method transforms the initial model into two types of equations: (1) macroscale governing equations; and (2) microscale cell problems. In order to solve for the macroscale governing equations, the microscale cell problems must first be solved on a brain tissue geometry to calculate the effective parametric tensors, which later be used in the macroscale governing equations. Lastly, the mathematical model is solved in a realistic brain geometry to evcaluate the effect of different mechanical properties of the brain towards brain tissue swelling formation

Mathematical modelling of cerebral ischaemia-reperfusion injury

Restoring cerebral blood flow using reperfusion treatment is a common method in treating ischaemic stroke. Reperfusion treatment should be given within 4.5 hours from stroke onset. However, reperfusion beyond this time window poses the risk of reperfusion injuries such as intracranial haemorrhage and cerebral tissue swelling. The focus of this thesis is to study the effect of cerebral tissue swelling after reperfusion as it can occur in a few hours after the treatment. Cerebral tissue swelling may cause brain structure movement and cerebral microvessel compression; the latter may then lead to secondary ischaemia occurrence. In this thesis, two mathematical models are presented. The first model investigates the effect of ischaemia-reperfusion in the formation of cerebral tissue swelling. This model provides the understanding of suitable reperfusion conditions to reduce the effect of tissue swelling and also becomes the basis for the subsequent model. Meanwhile, the second model studies the role of a water-transporting protein, aquaporin-4 in ischaemia-reperfusion and its potential as part of treatments for cerebral tissue swelling. In addition, the ionic concentration may change during ischaemia which may be a factor contributing to cerebral tissue swelling. Thus, the effect of ionic concentration on the swelling formation is also investigated. Finally, validations of these models are achieved by developing patient-specific geometries from available ischaemic stroke patient MRI data and utilising finite element analysis. Comparison between the simulation results and the MRI data is done by quantifying the brain ventricles movement during cerebral tissue swelling.</p

Mathematical modelling of cerebral ischaemia-reperfusion injury

Restoring cerebral blood flow using reperfusion treatment is a common method in treating ischaemic stroke. Reperfusion treatment should be given within 4.5 hours from stroke onset. However, reperfusion beyond this time window poses the risk of reperfusion injuries such as intracranial haemorrhage and cerebral tissue swelling. The focus of this thesis is to study the effect of cerebral tissue swelling after reperfusion as it can occur in a few hours after the treatment. Cerebral tissue swelling may cause brain structure movement and cerebral microvessel compression; the latter may then lead to secondary ischaemia occurrence. In this thesis, two mathematical models are presented. The first model investigates the effect of ischaemia-reperfusion in the formation of cerebral tissue swelling. This model provides the understanding of suitable reperfusion conditions to reduce the effect of tissue swelling and also becomes the basis for the subsequent model. Meanwhile, the second model studies the role of a water-transporting protein, aquaporin-4 in ischaemia-reperfusion and its potential as part of treatments for cerebral tissue swelling. In addition, the ionic concentration may change during ischaemia which may be a factor contributing to cerebral tissue swelling. Thus, the effect of ionic concentration on the swelling formation is also investigated. Finally, validations of these models are achieved by developing patient-specific geometries from available ischaemic stroke patient MRI data and utilising finite element analysis. Comparison between the simulation results and the MRI data is done by quantifying the brain ventricles movement during cerebral tissue swelling