UCLA

After a traumatic brain injury, it is important for some patients’ intracranial pressure (ICP) to be measured while they are in intensive care. However, monitoring ICP first requires an invasive surgical procedure, an impediment that has prompted research on noninvasive ICP (NICP) estimation. This dissertation examines NICP estimation from the perspective of linear dynamical systems, and presents methods to address some of the challenges that have limited the success of NICP estimators. Examples of these challenges include the unreliability of corrupted signal data, and a large inter-patient variability that limits the ability to compare new patients to past patients.

Three sets of methods are presented in this dissertation. The first methods mitigate the effect of corruptions in cerebral blood flow velocity signals, which are strong predictors of ICP, but often contain artifacts or sections of missing data. These methods find completed approximations of these signals that produce low-order systems. The second family of methods provide an approach for clustering linear dynamical systems by their behavior. This framework can be used to determine a subset of past patients with similar signal dynamics to a new patient. The final methods are a novel approach to NICP estimation in which the partially-available data of a new patient is combined with information from past patients whose ICP was invasively measured.

The methods presented are flexible in two respects. First, they are developed for general linear dynamical systems, and so can be adapted to any new applications where these models are used. Second, they are posed as convex optimization problems, which can be easily extended to new scenarios through the use of new weights, constraints, and penalty functions. The methods are solved using proximal algorithms, a family of first-order convex optimization algorithms, which result in computationally tractable formulations.