Validation

The results of the simulations in healthy brain tissue (i.e., tissue receiving normal blood flow) were quite realistic in terms of the equilibrium temperature difference between the blood and the brain tissue. However, the results were less successful in ischaemic tissue. None of the simulations in Ansys or Simulink produced results that closely matched the experimental data (See Tables 5.1.3-5.1.9 above). Some of the differences may be explained by the choice of parameters used in this study, but some of the differences, in particular the scale of the temperature differences between the ischaemic tissue and healthy tissue were much greater in the experimental data than any of the simulation results. The key differences, and the factors that may have caused them, will be dealt with one by one, but first it is worth examining the results of the simulations in detail.

In scenario A, the peak temperature (37.09°C) was found to be in the penumbra, and the lowest temperature (36.95°C) was found in the infarct. The average temperature of each tissue segment followed a similar pattern, albeit with much smaller temperature variation (See Table 5.1.7). The Penumbra had the highest average temperature, followed by the oligaemia, then normal tissue, and the infarct had the coolest average temperature. Scenario B produced less straightforward results. Once again, the peak temperature (36.93°C) was found in the penumbra (although the adjacent oligaemia was just as warm) and the coolest temperature (36.85°C) was found in the infarct. However, the average temperature of the infarct was actually warmer than the average temperature of any other tissue segment, followed by the penumbra, oligaemia and normal tissue respectively. The

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maximum temperature and all of the temperature differentials were lower in scenario B compared to scenario A, which is unsurprising given the lower baseline brain temperature. The results of scenario C were significantly affected by the presence of residual metabolism in the infarct. Thus, the peak temperature occurred in the infarct, and the coolest

temperature occurred in normal tissue. The average temperature of each segment followed the same pattern as scenario B (albeit with greater temperature differentials), with the infarct being the warmest on average, followed by the penumbra, oligaemia and normal tissue respectively. Interestingly, in scenario C the ischaemic and oligaemic grey matter tended to be warmer than the equivalent white matter, whereas for scenarios A and B the reverse was true. This is likely because the 50% increase in metabolism

simulated in the penumbra for scenario C was much greater in absolute terms in the grey matter compared to the white matter, and this tended to dominate the results of the simulation.

In contrast, in the experimental data these simulations were being compared to, the penumbra was found to have the warmest average tissue temperature, followed by the infarct, then the oligaemia and the healthy tissue. Furthermore, the difference in

temperature between the penumbra and healthy tissue was 1.44°C, whereas none of the simulations that assumed normal physical properties generated temperature differences greater than 0.29°C. The differences in average tissue temperature for each of the

simulations were no greater than 0.24°C, and most were less than 0.1°C (See Table 5.1.7). As mentioned above, some of these differences can be attributed to the choice of

parameters used in the simulations. For example, the fact that the infarct was cooler than normal tissue in scenario A (which was the ‘most likely’ scenario) was probably due to the assumption that metabolism in the infarct instantly dropped to zero. It is quite conceivable that there would be some residual metabolic heat generation in the infarct core, especially during the first hour of ischaemia (which was when this temperature data was collected in the monkeys). Scenario C did assume that cerebral metabolism in the infarct merely dropped to 50% of the baseline value, rather than stopping entirely. In this scenario, the infarct was warmer than the penumbra (which also fails to match the in vivo experimental data). However, this could simply be because 50% of baseline metabolism was

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output somewhere between zero and 50% that would cause the infarct to be warmer than the normal tissue, but not as warm as the penumbra (which is what was found in the monkey experiment). The geometry of the ischaemic region could also contribute to this. A smaller infarct, effectively experiencing a greater surface area to volume ratio (referring to the surface area exposed to the penumbra) would have an average temperature closer to that of the penumbra because heat energy would be conducted from the penumbra throughout the infarct more efficiently. Thus, there should be an alternative geometry where the infarct would equilibrate at a temperature warmer than that of the healthy tissue but cooler than that of the penumbra.

The method used to measure temperature in the monkey experiment may also have affected the results. The authors used a magnetic resonance spectroscopic imaging (MRSI) method (See Chapter 1.3 for a more explanation of this technique and the associated advantages and disadvantages) that effectively produced a 6x6 grid of voxels across the volume of interest and a temperature estimate for each voxel. However, the temperature estimates for individual voxels produced by this technique are not accurate enough to be used alone. This is why the authors reported the average temperature of each tissue classification. Unfortunately, some of the voxels produce spectra that were so poor that temperature estimation cannot be performed at all, especially in ischaemic tissue. Thus, the number of voxels that are averaged together for each tissue segment can vary widely, with a corresponding variation in the confidence that should be attached to each average temperature. Furthermore, if only 1 or 2 voxels were available in the infarct of a given monkey, it is possible that these voxels did not accurately represent the average

temperature of the infarct (or any other tissue segment). The authors did not report the number of voxels they were forced to reject, nor the number of voxels available within each tissue segment. It is noteworthy that the temperatures reported for the infarct and oligaemia had larger confidence intervals than the temperatures reported for the

penumbra (0.19°C and 0.14°C compared to 0.08°C, respectively). This suggests that there were fewer voxels available in the infarct and oligaemia than there were in the penumbra. It is also possible that the many of the spectra from the ischaemic tissue were of slightly poorer quality without being poor enough for the authors to reject. This would cause less accurate temperature estimations (and hence greater confidence intervals) but would be expected to affect the penumbra more than the oligaemia. It is more likely therefore, that

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this source of error was simply unaccounted for by the authors and the number of voxels available in each tissue segment was the primary cause of the increased confidence intervals in the infarct and oligaemia. The confidence intervals reported by Sun et al refer to the variation in the temperature estimated across the individual monkeys in the study, and it is not known how these confidence intervals relate to the absolute temperature, or even the relative temperature of each tissue segment. This was always going to be an issue with using MR thermography data for validation, but unfortunately it was the best data-set available. The MR thermography experiments conducted for the purpose of this thesis indicated that the accuracy of temperature estimation from a single voxel was no better than ±1.25°C, and when using NAA as the sole chemical reference (as Sun et al did) the accuracy was ±1.68°C. Estimates based on single voxels from an MRSI scan are likely to be even worse (See Chapter 1.3 for an explanation of the problems associated with MRSI). The most glaring difference between the simulation results and the experimental data was the magnitude of the temperature differences. Whereas temperature differences of 1°C or more between tissue segments were found to be the norm in the experimental data, the Ansys simulations resulted in maximum temperature differences of the order of 0.1°C, and even smaller differences when the average temperature of each tissue segment (which more closely matched the method of data collection from the monkey experiments) was considered. While one could, in theory, find a combination of CBF and CMR that recreated the temperature elevations found in the monkey experiments, the simulation parameters would have to be well outside realistic limits. The 50% increase in metabolism simulated in the penumbra for scenario C was purely hypothetical, as what data are available suggest that metabolism in the penumbra decreases as a result of nutrient deficiencies [8, 212]. With all the problems and pitfalls associated with MR thermography, especially when using MRSI, it is possible that the experimental data that this study has relied on was simply wrong. However, it is just as likely (if not more so) that the fault lies in the model. If the physical characteristics of the tissue (such as density, specific heat capacity or conductivity) assumed in this study were incorrect, this would invalidate the model. This scenario is not unlikely. When it comes to the physical properties of the tissue, engineers publishing models of the brain tend to reference previous modelling papers, rather than the experiments that actually measured the physical properties directly. The most recent

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paper found in the literature search for this thesis that actually referenced such an experiment was published in 1988 [196] and the papers the authors referenced were published no later than 1982. Many of these original sources are no longer readily available to authors. Werner and Buse list physical characteristics of ‘cortex’ but did not differentiate between grey matter and white matter. Subsequent engineering models, including the one described in this study, have therefore assumed that grey matter and white matter have identical physical properties. However, white matter has a significantly higher lipid content compared to grey matter [213] and the fat content of tissue has been shown to have an effect on such physical properties as specific heat capacity [214]. Furthermore, it is likely that there are small differences in some of the physical properties between individuals, and even more likely that such differences exist between monkeys and humans. Therefore, experiments to update, or at least confirm the validity of the physical parameters being used by biomedical engineers would be extremely helpful, especially if the authors of such experiments were to measure tissue from more than one individual and publish confidence intervals for each parameter. That being said, previous studies have successfully modelled heat exchange in the human brain using the same physical parameters as this study [155, 156, 158, 167], which would suggest that the values used were at least plausible.

One of the most vulnerable assumptions made in this model is that blood reaches the small arterioles at core body temperature. One of the key reasons that this assumption may hold is that the high velocity of the blood and small surface area to volume ratio of the larger arterioles minimise the level of heat exchange between the blood and the surrounding tissue before the blood reaches the small arterioles. The realistic results obtained in healthy brain tissue suggest that this is a reasonable assumption under normal

circumstances. However, the changes in the cerebral blood flow during a stroke almost certainly extend beyond the mere reduction in the overall rate of blood flow, which may render this assumption implausible. Even a partial occlusion of a larger or medium-sized artery would reduce the velocity of the remaining blood flow through that artery. Furthermore, if the blood flowing to ischaemic tissue were reaching that tissue via

downstream anastomoses (See Chapter 1.4.4) it may first have to travel through the small arteries and arterioles of surrounding brain tissue. This would mean that the blood would

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have already warmed to the temperature of the surrounding brain tissue, which would significantly reduce the efficacy of the heat sink provided by the blood.