Modelling the time-series of cerebrovascular pressure transmission variation in head injured patients

Cerebral autoregulation is the process by which blood ow is maintained over a changing cerebral perfusion pressure. Clinically autoregulation is an important topic because it directly effects overall patient management strategy. However accurately predicting autoregulatory state or even modelling the underlying general physiological processes is a complex task. There are a number of models published within the literature but there has been no active attempt to compare and classify these models. Starting with the hypothesis that a physiologically based model would be a better predictor of autoregulatory state than a purely statistically based one has led us to investigate approaches to model comparison. Using three different models: a new mathematical arrangement of a physiological model by Ursino, the Highest Model Frequency (HMF) model by Daley and the Pressure reactivity index (PRx) statistical model by Czosnyka, a general comparison was carried out using the Matthews correlation coecient against a known autoregulatory state. This showed that the Ursino model was approximately three times as predictive as both the HMF model and the PRx model. However, in general, all of the models predictive accuracies were relatively poor so a number of optimisation strategies were then assessed. These optimisation strategies ultimately were formed into a generalised modelling framework. This framework draws on the ideas of mathematical topology to underpin and explain any change or optimisation to a model. Within the framework different optimisations can be grouped into four categories, each of which are explored in the text of this thesis: 1) Model Comparison. This is the simplest technique to apply where the number of models under examination are reduced based on the predictive accuracy. 2) Parameter restriction. A classical form of optimisation by constraining a model parameter to cause a better predictive accuracy. In the case of both the HMF and PRx we showed between a two hundred and six hundred percent increase in predictive accuracy over the initial assessment. 3) Parameter alteration. This change allows for related parameters to be substituted into a model. Four different alterations are explored as a surrogate measure for arterial-arteriolar blood volume the most clinically applicable of which is a transcranial impedance technique. This latter technique has the potential to be a non invasive measure correlated with both mean ICP and ICP pulse amplitude. 4) Model alteration. Allows for larger changes to the underlying structure of the model. Two examples are presented: firstly a new asymmetric sigmoid curve to overcome computational issues in the Ursino model and secondly a novel use of fractal characterisation which is applied in a wavelet noise reduction technique. The framework also gives an overview of the autoregulatory research domain as a whole as a result of its abstract nature. This helps to highlight some general issues in the domain including a more standardised way to record autoregulatory status. Finally concluding with research addressing the requirement for easier access to data and the need for the research community to cohesively start to address these issues.