Perivascular spaces include a variety of passageways around arterioles, capillaries and venules in the brain, along which a range of substances can move. Although perivascular spaces were first identified over 150 years ago, they have come to prominence recently owing to advances in knowledge of their roles in clearance of interstitial fluid and waste from the brain, particularly during sleep, and in the pathogenesis of small vessel disease, Alzheimer disease and other neurodegenerative and inflammatory disorders. Experimental advances have facilitated in vivo studies of perivascular space function in intact rodent models during wakefulness and sleep, and MRI in humans has enabled perivascular space morphology to be related to cognitive function, vascular risk factors, vascular and neurodegenerative brain lesions, sleep patterns and cerebral haemodynamics. Many questions about perivascular spaces remain, but what is now clear is that normal perivascular space function is important for maintaining brain health. Here, we review perivascular space anatomy, physiology and pathology, particularly as seen with MRI in humans, and consider translation from models to humans to highlight knowns, unknowns, controversies and clinical relevance.

Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks.

Late Gadolinium enhancement (LGE) cardiovascular magnetic resonance (CMR) imaging can be used to visualise regions of fibrosis and scarring in the left atrium (LA) myocardium. This can be important for treatment stratification of patients with atrial fibrillation (AF) and for assessment of treatment after radio frequency catheter ablation (RFCA). In this paper we present a standardised evaluation benchmarking framework for algorithms segmenting fibrosis and scar from LGE CMR images. The algorithms reported are the response to an open challenge that was put to the medical imaging community through an ISBI (IEEE International Symposium on Biomedical Imaging) workshop.

The glymphatic system (GS) hypothesis states that advective driven cerebrospinal fluid (CSF) influx from the perivascular spaces into the interstitial fluid space rapidly transport solutes and clear waste from brain. However, the presence of advection in neuropil is contested and solutes are claimed to be transported by diffusion only. To address this controversy, we implemented a regularized version of the optimal mass transport (rOMT) problem, wherein the advection/diffusion equation is the only a priori assumption required. rOMT analysis with a Lagrangian perspective of GS transport revealed that solute speed was faster in CSF compared to grey and white matter. Further, rOMT analysis also demonstrated 2-fold differences in regional solute speed within the brain. Collectively, these results imply that advective transport dominates in CSF while diffusion and advection both contribute to GS transport in parenchyma. In a rat model of cerebral small vessel disease (cSVD), solute transport in the perivascular spaces (PVS) and PVS-to-tissue transfer was slower compared to normal rats. Thus, the analytical framework of rOMT provides novel insights in the local dynamics of GS transport that may have implications for neurodegenerative diseases. Future studies should apply the rOMT analysis approach to confirm GS transport reductions in humans with cSVD.

We describe possible generalizations of the Wasserstein-2 metric, originally defined on the space of scalar probability densities, to the space of trace-one Hermitian matrices and to the space of matrix-valued probability densities. Our approach follows a control-theoretic optimization formulation of the Wasserstein-2 metric, having its roots in fluid dynamics, and utilizes a formalism from Quantum mechanics of open systems. Besides potential applications of our results to matrix-valued distributions (e.g., to matrix-valued power spectral analysis, diffusion tensor imaging, etc.), our framework has direct implications to key structures in Quantum mechanics. It induces a Wasserstein geometry to Quantum states and allows determining the gradient flows with respect to the newly defined Wasserstein metric(s). It allows expressing, in particular, the Lindblad equation of open Quantum systems as a gradient flow of the von Neumann Quantum entropy.