Modelling brain temperatures in healthy patients and those with induced hypothermia
Blowers, Stephen John
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Hypothermia has been shown to provide protective benefits to the brain after head trauma. Current treatment methods employ full body hypothermia which can lead to further associated complications, such as a compromised immune system. Alternatively, cooling the brain individually can provide the same benefits whilst minimising the risks associated. Unfortunately, the feasibility of this is still uncertain due to the invasiveness of measuring cerebral temperatures directly and the unavailability of brain temperature maps. Mathematical modelling provides an important alternative avenue for predicting the outcome of hypothermic procedures, such as scalp cooling. However, these tend to rely on Pennes Bioheat Equation which simplifies the blood flow within the system as a single perfusion term. This removes any directional thermal advection which could play an important part in biological heat transfer. In this thesis, an alternative method is developed, tested, and proposed where the full cerebral circulatory system is modelled using vascular channels embedded in a porous tissue simulating the blood vessels and capillaries, respectively. This is dubbed the vascular porous (VaPor) method. This dissertation tests and discusses the feasibility of inducing hypothermia by cooling the scalp using the VaPor model. Initially, the blood vessels were modelled in 3D to fully capture the effects of flow, however, this was deemed computationally inefficient and difficult to manipulate so was subsequently replaced with a system of 1-Dimensional line segments. Temperatures produced from this method conform to expected ranges of values and agree with available data from studies in rat brains. It was observed that core brain temperatures can be impacted by scalp cooling but only with a large number of generated vessels. This is due to the tortuous nature of the vasculature which is not captured by the porous media alone. Various input parameters are also tested to ensure the validity of results from this model. One tested parameter that did not agree with in-vivo results was the measurement of tissue perfusion which appeared to be grossly exaggerated by the VaPor model, although conservation of mass was conserved at each stage. This was investigated further by simulating tracer transport in the cerebral domain in the same manner that in-vivo measurements use. While in-vivo measurements and the predictions by tracer transport produce perfusion values of the same order of magnitude, a full quantitative match cannot be expected because of the differences in the measurement techniques used. Various approximations that can be imposed to resolve this are discussed. The versatility of the VaPor model was explored by simulating a variety of applications relevant to cerebral cooling. The inclusion of counter-current flow within the porous domain showed similar results to trials performed with dense vascular trees. Trials on the scale of a neonatal brain showed that hypothermia could be achieved from scalp cooling alone contrary to previous models. The transient response of scalp cooling was explored as well as the thermal response after simulating an ischemic stroke. All results demonstrated that, due to the inclusion of directional flow, scalp cooling has a larger impact on cerebral temperatures than seen with previous bioheat models.