Cortical spreading depression is a propagating wave of depolarization that plays important roles in migraine, stroke, subarachnoid haemorrhage and brain injury. Cortical spreading depression is associated with profound vascular changes that may be a significant factor in the clinical response to cortical spreading depression events. We used a combination of optical intrinsic signal imaging, electro-physiology, potassium sensitive electrodes and spectroscopy to investigate neurovascular changes associated with cortical spreading depression in the mouse. We identified two distinct phases of altered neurovascular function, one during the propagating cortical spreading depression wave and a second much longer phase after passage of the wave. The direct current shift associated with the cortical spreading depression wave was accompanied by marked arterial constriction and desaturation of cortical haemoglobin. After recovery from the initial cortical spreading depression wave, we observed a second phase of prolonged, negative direct current shift, arterial constriction and haemoglobin desaturation, lasting at least an hour. Persistent disruption of neurovascular coupling was demonstrated by a loss of coherence between electro-physiological activity and perfusion. Extracellular potassium concentration increased during the cortical spreading depression wave, but recovered and remained at baseline after passage of the wave, consistent with different mechanisms underlying the first and second phases of neurovascular dysfunction. These findings indicate that cortical spreading depression is associated with a multiphasic alteration in neurovascular function, including a novel second direct current shift accompanied by arterial constriction and decrease in tissue oxygen supply, that is temporally and mechanistically distinct from the initial propagated cortical spreading depression wave. Vascular/metabolic uncoupling with cortical spreading depression may have important clinical consequences, and the different phases of dysfunction may represent separate therapeutic targets in the disorders where cortical spreading depression occurs.

Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarizations, CSD also involves significant changes in perfusion and metabolism—aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium–ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates the qualitative and quantitative behavior of CSD—vasoconstriction, oxygen depletion, extracellular potassium elevation, prolonged depolarization—found in experimental studies. We predict faster, longer duration CSD in vivo than in vitro due to the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease.

Spreading depolarizations are implicated in a diverse set of neurologic diseases. They are unusual forms of nervous system activity in that they propagate very slowly and approximately concentrically, apparently not respecting the anatomic, synaptic, functional, or vascular architecture of the brain. However, there is evidence that spreading depolarizations are not truly concentric, isotropic, or homogeneous, either in space or in time. Here we present evidence from KCl-induced spreading depolarizations, in mouse and rat, in vivo and in vitro, showing the great variability that these depolarizations can exhibit. This variability can help inform the mechanistic understanding of spreading depolarizations, and it has implications for their phenomenology in neurologic disease.

Estimation of infectiousness and fatality of the SARS-CoV-2 virus in the COVID-19 global pandemic is complicated by ascertainment bias resulting from incomplete and non-representative samples of infected individuals. We developed a strategy for overcoming this bias to obtain more plausible estimates of the true values of key epidemiological variables. We fit mechanistic Bayesian latent-variable SIR models to confirmed COVID-19 cases, deaths, and recoveries, for all regions (countries and US states) independently. Bayesian averaging over models, we find that the raw infection incidence rate underestimates the true rate by a factor, the case ascertainment ratio CAR t that depends upon region and time. At the regional onset of COVID-19, the predicted global median was 13 infections unreported for each case confirmed (CAR t = 0.07 C.I. (0.02, 0.4)). As the infection spread, the median CAR t rose to 9 unreported cases for every one diagnosed as of April 15, 2020 (CAR t = 0.1 C.I. (0.02, 0.5)). We also estimate that the median global initial reproduction number R 0 is 3.3 (C.I (1.5, 8.3)) and the total infection fatality rate near the onset is 0.17% (C.I. (0.05%, 0.9%)). However the time-dependent reproduction number R t and infection fatality rate as of April 15 were 1.2 (C.I. (0.6, 2.5)) and 0.8% (C.I. (0.2%,4%)), respectively. We find that there is great variability between country-and state-level values. Our estimates are consistent with recent serological estimates of cumulative infections for the state of New York, but 1 for use under a CC0 license. : medRxiv preprint inconsistent with claims that very large fractions of the population have already been infected in most other regions. For most regions, our estimates imply a great deal of uncertainty about the current state and trajectory of the epidemic.2 for use under a CC0 license. : medRxiv preprint estimated that 1 in 8 cases are symptomatic (Sutton et al.) , which is consistent with a recent press report by New York state based on sampling grocery store customers (New York Times) . Debates continue on the adequacy of these tests.Here, we develop a set of Bayesian, mechanistic, latent-variable, SIR models (Kermack and McKendrick; Wo and Ag, "Contributions to the Mathematical Theory of Epidemics--II. The Problem of Endemicity.1932"; Wo and Ag, "Contributions to the Mathematical Theory of Epidemics--III. Further Studies of the Problem of Endemicity. 1933") that respect the uncertainty in the underlying data. We explore multiple specifications and find general consensus among the models. Our models try to account for the effects of mitigation (such as social distancing), the possibility that CAR t (either through changes in definition or in detection, for example via ramp-up of testing) can vary in time, excess variability due to reporting and heterogeneity in the regional population, and incomplete quarantine of reported active cases. A similar model assumed complete quarantine on the basis of debilitating effects of illness or strict adherence to policy (Pede...