This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.
Perfusion imaging is the most applied modality for the assessment of acute stroke. Parameters such as Cerebral Blood Flow (CBF), Cerebral Blood volume (CBV) and Mean Transit Time (MTT) are used to distinguish the tissue infarct core and ischemic penumbra. Due to lack of standardization these parameters vary significantly between vendors and software even when provided with the same data set. There is a critical need to standardize the systems and make them more reliable. We have designed a uniform phantom to test and verify the perfusion systems. We implemented a flow loop with different flow rates (250, 300, 350 ml/min) and injected the same amount of contrast. The images of the phantom were acquired using a Digital Angiographic system. Since this phantom is uniform, projection images obtained using DSA is sufficient for initial validation. To validate the phantom we measured the contrast concentration at three regions of interest (arterial input, venous output, perfused area) and derived time density curves (TDC). We then calculated the maximum slope, area under the TDCs and flow. The maximum slope calculations were linearly increasing with increase in flow rate, the area under the curve decreases with increase in flow rate. There was 25% error between the calculated flow and measured flow. The derived TDCs were clinically relevant and the calculated flow, maximum slope and areas under the curve were sensitive to the measured flow. We have created a systematic way to calibrate existing perfusion systems and assess their reliability.