Mathematical Modelling of Brain Haemodynamics and Pressure-Volume Compensation
Traumatic brain injury (TBI) is a major global health issue with diverse demographics and a dynamic clinical profile. Modern care of a pathology with such variabilities involves individualised treatment, which requires an accurate understanding of pressure-volume interactions inside the cranium. This thesis used a hydrodynamic model representing the circulation of cerebral fluids to investigate the relationships between intracranial pressure (ICP) and cerebral blood volume (CBV) changes. The effects of these relationships on the performance of indices describing vascular dynamics were also examined. The background of this project is discussed in Chapters 1 to 4 of this thesis. Chapter 1 provides a description of the anatomical and physiological aspects of the cerebrospinal space, including the circulation of cerebral fluids and the pressure-volume interactions among different compartments within the cranium. Chapter 2 introduces the pathophysiology of cerebral hydrodynamics in patients with TBI, and the important role of neuro-monitoring in its management. Chapter 3 specifies the aims and hypotheses of this project, while Chapter 4 includes a literature review of previous modelling work in cerebral blood flow (CBF) and cerebrospinal fluid (CSF) dynamics. In this project, a computer programme was written to create an implementation of the electrical equivalence of the hydrodynamic model. With a set of model parameters and imported data, the programme was used to simulate the pressures and flows of fluids in different intracranial compartments. Details of the programme were specified in Chapter 5, while experiments with the model were included in Chapters 6 to 9. In Chapter 6, the validity of an existing model was tested with a series of experiments simulating various clinical phenomena. The simulations include pathophysiological features caused by dynamic variations in cerebrovascular properties, as well as prolonged changes in CBV. In Chapter 7, the existing model was modified to include a compartment representing the bulk flow of cerebral interstitial fluid (ISF), coupled with the cerebrovascular compartment. The new model was tested using the same sets of experiments in the previous chapter, with its results compared to the original model. In Chapter 8, the modified model was used to assess the performance of common autoregulation indices in response to changing strength of cerebral autoregulation (CA), thus identifying the physiological factors determining the reliability of CA assessments. In Chapter 9, the modified model was used to explore the interplay between brain compliances and vascular reactivity, and its influence on pressure reactivity indices. The ability of the model to replicate clinical features observed in TBI patients was also investigated. In conclusion, the model has proved to be a robust tool to study the pressure-volume interactions among various intracranial compartments, as well as the performance of CA and pressure reactivity indices in different scenarios. The work in this thesis has laid the foundation of creating a ‘digital twin’ of cerebral hydrodynamics, with the potential of improving the individualisation of treatments in neuro-intensive care, particularly in dynamic pathologies such as TBI.
Cerebral Haemodynamics, Mathematical Modelling, Traumatic Brain Injury
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