Mechanics of swelling and damage in brain tissue: a theoretical approach

Thesis

Following trauma, such as an impact injury or stroke, brain tissue can swell. Swelling is the result of water accumulation in the tissue that is driven by pathological changes, such as increased permeability of the capillary walls and osmotic pressure changes within the tissue. Swelling causes increased intracranial pressure and mechanical deformation of the brain tissue, exacerbating the original injury. Furthermore, prolonged local swelling can lead to the spread of damage to the (initially undamaged) surrounding tissue, since compression and increased intracranial pressure may restrict blood flow in this tissue.

In this thesis, we develop mathematical models to examine the consequences of pathophysiological damage mechanisms on the swelling, and associated stress and strain, experienced by brain tissue. Mixture theory is used to represent brain tissue as a mixture of elastic solid, fluid and solutes. This modelling approach allows elastic deformations to be coupled with hydrodynamic pressure and osmotic gradients; the consequences of different mechanisms of damage may then be quantified.

We consider three particular problems motivated by experimental observations of swelling brain tissue. Firstly, we investigate the swelling of isolated, damaged, brain tissue slices; we show that mechanisms leading to an osmotic pressure difference between the tissue slice and its surroundings can explain experimental observations for swollen tissue slices. Secondly, we use our modelling approach to demonstrate that local changes in capillary permeability can cause significant stresses and strains in the surrounding tissue. Thirdly, we investigate the conditions under which a locally swollen, damaged, region can cause compression of the vasculature within the surrounding tissue, and potentially result in damage propagation. To do this, we propose a coupled model for the oxygen concentration within, and mechanical deformation of, brain tissue. We use our model to assess the impact of treatment strategies on damage propagation through the tissue, and show that performing a craniectomy reduces the extent of propagation.

Authors: Lang, G; Georgina E Lang

• Publication date: 2014
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: brain edema; soft tissue modelling; Biomechanics; mixture theory
• Subjects: Mathematical biology; Mechanics of deformable solids (mathematics)