BB20: Modelling solid-fluid interactions in the brain

Background

Following a stroke or impact injury, brain tissue suffers from a lack of blood flow, triggering a sequence of events that leads to brain swelling – or oedema. Brain oedema occurs in two phases: a shift of water from the extracellular space to cells (cytotoxic oedema) resulting in swelling of individual cells, and tissue swelling due to water moving from capillaries into the extracellular space (ionic and vasogenic oedema). The consequences of oedema include increased intracranial pressure, localised deformation of brain tissue and nervous system damage. Therefore, it is important to understand the process by which swelling occurs.

Techniques and Challenges

The progression of oedema acts across several scales. Oedema is caused by ion movement and alterations in membrane permeability at the subcellular level, which results in swelling of both individual cells and regions of tissue. There has been little modelling work on brain tissue swelling, and a crucial challenge is to translate the understanding into a physically relevant model that can be used to address quantitative questions.

Results

We have developed a simple two-compartment model comprising the extracellular space and a cell to understand cytotoxic oedema. This compartment model allows us to gain insight into the effect that parameters such as cell membrane permeability and the diffusion rate of ions have on the rate of cell swelling due to ion dysregulation. We are also investigating the use of poroelastic models for soft tissue modelling, allowing us to couple the electrochemical effects to the deformation of a region of tissue.

The Future

In the future, we plan to extend our compartment model to include an additional compartment representing a capillary. This will allow us to capture the ionic and vasogenic phases of oedema, where liquid and ions from the capillary move into the brain tissue. We then aim to couple volume changes caused by subcellular level electrochemical movements to the mechanical deformation of a small region of tissue, developing quadraphasic poroelastic models to capture this process. 

References

Kimelberg H.K.: Current concepts of brain oedema: Review of laboratory investigations, J Neurosurg 83:1051–1059, 1995

Kahle K.T., Simard J.M., Staley K.J., Nahed B.V., Jones P.S., Sun D.: Molecular Mechanisms of Ischemic Cerebral Oedema: Role of Electroneutral Ion Transport, Physiology 24(4):257-265, 2009

Detournay, E., Cheng A.H-D.: Fundamentals of poroelasticity, Chapter 5, Comprehensive Rock Engrg. (J. Hudson, ed.), Vol. II, Pergamon Press, 113-169, 1993