"Control Theory for Brain Modelling and Analysis"

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This project aims to develop and analyse accurate computer models simulating epileptic seizures in the human brain, and apply control theory techniques to advise novel treatment strategies for epilepsy, as would be needed to implement direct closed-loop stimulation of the brain by a future implantable device.Epilepsy is a relatively common, life-limiting and sometimes life-threatening condition. First-line treatment is with medication, but this is not without side effects, and some cases can remain intractable. Some patients are willing to resort to surgical treatment in order to control their condition. This can be effective, but is not guaranteed to work, is invasive, and carries its own set of risks.Already there are a number of open-loop devices used in the treatment of severe neurological diseases, such as electrical deep brain stimulation for Parkinson's disease. Research is underway to apply closed-loop techniques to the treatment of epilepsy. The question then becomes about how an implementation in a medical device could effectively stimulate the brain in response to real time sensor data. As a general guiding principle of medicine, one should "first do no harm". Modelling and experimental work has previously suggested that closed-loop control, if applied with the wrong parameters, may be liable to cause, worsen or prolong the seizure activity it is intended to treat. Any form of stimulation has the potential to adversely affect normal brain function during and following its application. In particular, direct electrical stimulation may cause permanent damage to brain tissue. For these reasons there is a genuine interest both in minimising episodes of intervention overall and in ensuring that, when it is applied, it is both beneficial and safe to do so. Additionally, but not inconsequentially, there would also be practical engineering benefits from reducing the overall power consumption of any potential implantable device that might eventually arise from this line of research. In particular, it is intended that the project should ask: what techniques from control theory are suitable for analysing models of the human brain; how we can design effective stimulation strategies to control epilepsy with such techniques; how to make concepts and techniques from control theory applicable to large-scale models of the brain; and how to encode uncertainty in the brain's behaviour using mathematical models of the brain and answer the previous questions while analysing the effect of uncertainty.Candidate methods to be investigated for possible use include barrier certificates, Gaussian processes, stochastic optimal control, recurrent neural networks, model reduction, abstraction-based verification, and compositional synthesis methods.