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Every time you move your hand, see a picture or remember a face, an amazing chain of events is triggered in your body. Brain cells send electrical signals to each other; trying to understand what you have seen or felt and issuing instructions for what to do next. To make these signals, the cells need extra energy provided by oxygen in the blood flowing through the brain. Therefore, they also send other signals asking for extra blood. To meet this increased need for energy, the blood vessels bringing blood to the cells expand to allow the blood to flow faster. The aim of my research is to investigate the different links in this chain and how they interact: Which groups of cells are making the instructions? How much energy is needed to produce the electrical signals? How does the blood flow change to meet this extra demand? The answers to these questions are crucial to our understanding both of how the healthy brain works and of what causes many brain illnesses.To answer these questions we have to be able to see inside the brain while it is working. Fortunately, we have a tool which lets us do exactly that. By combining radio waves and magnetic fields, Magnetic Resonance Imaging (MRI) machines can take measurements from thousands of places inside the brain and build these measurements into an image. Amongst other things, we can use these measurements to tell us about blood flow, and how it changes when different parts of the brain are busy. Importantly, the MRI techniques I will use are non-invasive; this means that we can take lots of images of the brain in a live human being, with no ill-effects.Unfortunately, it is far from easy to find these changes in blood flow from the MR images. This is not only because of the limited quality of the images, but also because we have a poor understanding of the way in which the brain is working, the energy it demands, and the way in which the blood flows in response to this demand. Techniques for extracting information about blood flow changes from the MRI pictures are severely limited. The research I am proposing is aimed at advancing these techniques, to extract more useful information from MRI. For this, mathematical models are used to predict the MR images we would get if a certain brain activity and blood flow response occurred. An important part of my research will be to improve on these models, to incorporate our knowledge of brain physiology and of how the MRI machines work. However, in practice we actually need to do the opposite of what the mathematical model tells us, that is we need to estimate the brain activity and blood flow response from the MR measurements we take. This is effectively done by solving the equations in the mathematical models. This will form the other part of the research, to use techniques from the field of applied probability to improve the way in which solve the mathematical models to get superior information about what the brain is doing. Crucially, this includes the confidence we have in that information, which we need to know for its safe use in medical applications.An important aspect of the work is that I will extract and combine information from more than one type of MRI measurement. The types of measurements include how much oxygen there is in the blood, how much blood is arriving in a certain area, and the volume of blood that is in a certain area. Using applied probability techniques I will combine this information in the optimal way to get a more complete picture about blood flow changes. Importantly, this more complete picture means that not only can we detect when there is a change in blood flow in response to brain activity, but also how big these changes are. Direct comparison of these actual changes in size can then be made for a single person at two different times, or between different people. This can provide important information about how a disease progresses, how a person recovers from injury, or the effects of medication.
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