Geometry

The geometry of the entire simplified brain was created initially, but the unaffected hemisphere was deleted from the geometry before further input in order to expedite both coding and running the individual simulations. Structures such as the ventricles, meninges, skull and scalp were omitted for the same reason (see below for justification). The brain was modelled as a series of concentric hemispheres, consisting of an inner layer of grey matter 28mm in diameter (representing the basal ganglia) surrounded by a layer of white matter 39mm thick, which in turn was surrounded by another layer of grey matter 18mm thick (representing the cortex). These dimensions were derived from MRI measurements performed on a random healthy volunteers scanned as part of the experiment described in Chapter 3.2. Each concentric hemisphere was modelled from the same centre coordinate, so that the basal ganglia hemisphere was in the exact centre of both of the spheres representing the white matter and the cortex.

The ischaemic region was modelled as a series of concentric spheres effectively carved out of the existing brain structure. This region consisted of the infarct sphere 10mm in

diameter, the penumbra sphere 15mm in diameter and the oligaemia sphere 20mm in diameter. As with the hemispheres representing the overall brain structure, the 3 spheres representing the ischaemia region were modelled from the same centre-point (although this was offset from the centre-point used for the hemispheres representing the basal ganglia, white matter and cortex). Thus, the infarct was situated exactly in the centre of the penumbra, and the infarct and penumbra were exactly in the centre of the oligaemia.

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Figure 2.2.2 below illustrates the outline of the final geometry. The ischaemic region was situated so that all 3 spheres overlapped both white matter and cortex.

The scalp, skull, meninges and cerebrospinal fluid (including the ventricles) were all

disregarded from the geometry of this model. The CSF could be reasonably expected to be very close to the surrounding brain tissue (in particular the choroids plexus) in temperature it was thus judged unlikely to play a significant role in heat exchange except in cases where interventions are directed specifically at the CSF temperature. The level of conduction across the meninges, skull and scalp has previously been shown to be very small [191] so the effects of this conduction were ignored, with all surfaces of the model being treated as adiabatic. The inclusion of the lateral ventricles, CSF, meninges, skull and scalp increased the time needed to run a simulation from 10-15 minutes to 6-8 hours, and increased the volume of output data created to such a point (several tens of gigabytes per simulation) that the computer available could only store the results of one simulation at any one time, and these results would have to be deleted before another simulation could be run. Given the role these structures are believed to play in heat exchange is mostly limited to

providing insulation from the outside world[80, 85, 86, 192], it was decided to eliminate them from the model for the purposes of this thesis.

No attempt was made to model the brain-stem or cerebellum, as the only validation data available for comparison at the time of writing were from the cerebral hemispheres. Thus, it was decided to conduct verification and validation analysis focusing on the cerebral hemispheres, and build upon the complexity of the geometry of the model at a later date if these early experiments were successful. For the purposes of this thesis, the model was further reduced to a single cerebral hemisphere, thus the contralateral hemisphere (not affected by the simulated stroke) was not simulated. The aim of this was to further reduce the simulation times and the volume of data that needed to be stored after each

simulation.

Physical parameters and baseline perfusion and metabolism levels are outlined in Table 2.2.1 and are drawn primarily from Zhu and Diao [83]. Initial brain temperature was assumed to be 37°C, and initial blood temperature was assumed to be 36.7°C as this would produce a steady-state tissue temperature of 37°C under baseline perfusion and

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The use of an adiabatic (i.e. zero energy transfer) boundary condition on external surfaces is justified by the fact that conduction of heat across the skull and scalp is minimal, especially in comparison to heat exchange between the blood and brain tissue[86, 157, 166, 169].

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Figure 2.2.2 A (Top) The original, more complex geometry developed for Ansys simulations B (Bottom) The more simplified geometry developed in APDL.

The Ischaemic region is modelled as a central region of infarct (I)10mm in diameter surrounded by a region of penumbra (P) 15mm in diameter which in turn was surrounded by a region of oligaemia (O) 20mm in diameter all of which include both cortex (grey matter) and white matter Note that the more simplified geometry omits the entire contralateral (non-affected) hemisphere of the brain as well as structures such as the meninges, skull and scalp as the thermal effect of conduction across these structures is minimal with comparison to the thermal effect of perfusion. The surfaces of the hemisphere were therefore treated as adiabatic with the only heat sink being the arterial blood For technical reasons the more simplified version was used for Chapters 5.1 and 5.2.