Segmentation and mathematical modelling of cerebrospinal fluid in the vertebral column

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Segmentation and mathematical modelling of cerebrospinal fluid in the vertebral column

Group Industrial and Applied Mathematics

In the human body, the spinal cord, transmitting bi-directional information between brain and body, is found within the bony vertebral column. It is contained inside a membranous sac, the dura, and bathed in cerebrospinal fluid (CSF), which circulates throughout the central nervous system in the subarachnoid space between dura and cord. Blood vessels and nerves enter and exit through the walls of the dural sac along its length. During each cardiac cycle a cyclic flow and pressure change has been observed within the CSF having the same period as the cardiac cycle. However, little is known about the precise nature or mechanism of this “CSF circulation”, including how the geometry of the subarachnoid space may affect the pressure of the CSF and its flow pattern. This knowledge would further our understanding of several pathological conditions of the central nervous system.

With this in mind, the objective of this project is to understand the dynamics of the CSF, contained within the subarachnoid space of the spinal column, throughout a cardiac cycle. To achieve this goal the student will use 4D phase-contrast MR images, which are capable of detecting the velocity field of the CSF. In the beginning stages the focus will be on developing segmentation methods capable of creating a three-dimensional model of the subarachnoid space allowing visualization of the changes throughout a cycle. This segmentation is difficult due to the complicated geometry of the subarachnoid space including vasculature and exiting nerves. Once this first stage is complete the student will use the resulting segmentation to produce a computational model for the flow of CSF throughout the cardiac cycle. The goal of this modeling will be to measure local relative pressure changes of the CSF, as well as to understand the interaction between the CSF pressure and the geometry of the subarachnoid space.

Though based in the school of mathematics, this project will also involve close collaboration with researchers at the Royal Preston Hospital’s Neurosurgery and Neuroradiology departments who will be providing the MR images, produced as part of an ongoing study into CSF circulation in health and disease. 

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