Problems in four-dimensional data assimilation

With the introduction of new observing systems based on asynoptic observations, the analysis problem has changed in character. In the near future we may expect that a considerable part of meteorological observations will be unevenly distributed in four dimensions, i.e. three dimensions in space and one in time. The term analysis, or objective analysis in meteorology, means the process of interpolating observed meteorological observations from unevenly distributed locations to a network of regularly spaced grid points. Necessitated by the requirement of numerical weather prediction models to solve the governing finite difference equations on such a grid lattice, the objective analysis is a three-dimensional (or mostly two-dimensional) interpolation technique. As a consequence of the structure of the conventional synoptic network with separated data-sparse and data-dense areas, four-dimensional analysis has in fact been intensively used for many years. Weather services have thus based their analysis not only on synoptic data at the time of the analysis and climatology, but also on the fields predicted from the previous observation hour and valid at the time of the analysis. The inclusion of the time dimension in objective analysis will be called four-dimensional data assimilation. From one point of view it seems possible to apply the conventional technique on the new data sources by simply reducing the time interval in the analysis-forecasting cycle. This could in fact be justified also for the conventional observations. We have a fairly good coverage of surface observations 8 times a day and several upper air stations are making radiosonde and radiowind observations 4 times a day. If we have a 3-hour step in the analysis-forecasting cycle instead of 12 hours, which is applied most often, we may without any difficulties treat all observations as synoptic. No observation would thus be more than 90 minutes off time and the observations even during strong transient motion would fall within a horizontal mesh of 500 km * 500 km.

Stability of stationary solutions of the forced Navier-Stokes equations on the two-torus

We study the linear and nonlinear stability of stationary solutions of the forced two-dimensional Navier-Stokes equations on the domain [0,2π]x[0,2π/α], where α ϵ(0,1], with doubly periodic boundary conditions. For the linear problem we employ the classical energy{enstrophy argument to derive some fundamental properties of unstable eigenmodes. From this it is shown that forces of pure χ2-modes having wavelengths greater than 2π do not give rise to linear instability of the corresponding primary stationary solutions. For the nonlinear problem, we prove the equivalence of nonlinear stability with respect to the energy and enstrophy norms. This equivalence is then applied to derive optimal conditions for nonlinear stability, including both the high-and low-Reynolds-number limits.

Negative blood oxygen level dependence in the rat: a model for investigating the role of suppression in neurovascular coupling

Modern neuroimaging techniques rely on neurovascular coupling to show regions of increased brain activation. However, little is known of the neurovascular coupling relationships that exist for inhibitory signals. To address this issue directly we developed a preparation to investigate the signal sources of one of these proposed inhibitory neurovascular signals, the negative blood oxygen level-dependent (BOLD) response (NBR), in rat somatosensory cortex. We found a reliable NBR measured in rat somatosensory cortex in response to unilateral electrical whisker stimulation, which was located in deeper cortical layers relative to the positive BOLD response. Separate optical measurements (two-dimensional optical imaging spectroscopy and laser Doppler flowmetry) revealed that the NBR was a result of decreased blood volume and flow and increased levels of deoxyhemoglobin. Neural activity in the NBR region, measured by multichannel electrodes, varied considerably as a function of cortical depth. There was a decrease in neuronal activity in deep cortical laminae. After cessation of whisker stimulation there was a large increase in neural activity above baseline. Both the decrease in neuronal activity and increase above baseline after stimulation cessation correlated well with the simultaneous measurement of blood flow suggesting that the NBR is related to decreases in neural activity in deep cortical layers. Interestingly, the magnitude of the neural decrease was largest in regions showing stimulus-evoked positive BOLD responses. Since a similar type of neural suppression in surround regions was associated with a negative BOLD signal, the increased levels of suppression in positive BOLD regions could importantly moderate the size of the observed BOLD response.

The resting-state neurovascular coupling relationship: rapid changes in spontaneous neural activity in the somatosensory cortex are associated with haemodynamic fluctuations that resemble stimulus-evoked haemodynamics

Although promise exists for patterns of resting-state blood oxygen level-dependent (BOLD) functional magnetic resonance imaging (fMRI) brain connectivity to be used as biomarkers of early brain pathology, a full understanding of the nature of the relationship between neural activity and spontaneous fMRI BOLD fluctuations is required before such data can be correctly interpreted. To investigate this issue, we combined electrophysiological recordings of rapid changes in multi-laminar local field potentials from the somatosensory cortex of anaesthetized rats with concurrent two-dimensional optical imaging spectroscopy measurements of resting-state haemodynamics that underlie fluctuations in the BOLD fMRI signal. After neural ‘events’ were identified, their time points served to indicate the start of an epoch in the accompanying haemodynamic fluctuations. Multiple epochs for both neural ‘events’ and the accompanying haemodynamic fluctuations were averaged. We found that the averaged epochs of resting-state haemodynamic fluctuations taken after neural ‘events’ closely resembled the temporal profile of stimulus-evoked cortical haemodynamics. Furthermore, we were able to demonstrate that averaged epochs of resting-state haemodynamic fluctuations resembling the temporal profile of stimulus-evoked haemodynamics could also be found after peaks in neural activity filtered into specific electroencephalographic frequency bands (theta, alpha, beta, and gamma). This technique allows investigation of resting-state neurovascular coupling using methodologies that are directly comparable to that developed for investigating stimulus-evoked neurovascular responses.

A metabolic system-wide characterisation of the pig: a model for human physiology

The pig is a single-stomached omnivorous mammal and is an important model of human disease and nutrition. As such, it is necessary to establish a metabolic framework from which pathology-based variation can be compared. Here, a combination of one and two-dimensional 1H and 13C nuclear magnetic resonance spectroscopy (NMR) and high-resolution magic angle spinning (HR-MAS) NMR was used to provide a systems overview of porcine metabolism via characterisation of the urine, serum, liver and kidney metabolomes. The metabolites observed in each of these biological compartments were found to be qualitatively comparable to the metabolic signature of the same biological matrices in humans and rodents. The data were modelled using a combination of principal components analysis and Venn diagram mapping. Urine represented the most metabolically distinct biological compartment studied, with a relatively greater number of NMR detectable metabolites present, many of which are implicated in gut-microbial co-metabolic processes. The major interspecies differences observed were in the phase II conjugation of extra-genomic metabolites; the pig was observed to conjugate p-cresol, a gut microbial metabolite of tyrosine, with glucuronide rather than sulfate as seen in man. These observations are important to note when considering the translatability of experimental data derived from porcine models.

Observing crosswind over urban terrain using scintillometer and Doppler lidar

In this study, the crosswind (wind component perpendicular to a path, U⊥) is measured by a scintillometer and estimated with Doppler lidar above the urban environment of Helsinki, Finland, for 15 days. The scintillometer allows acquisition of a path-averaged value of U⊥ (U⊥), while the lidar allows acquisition of path-resolved U⊥ (U⊥ (x), where x is the position along the path). The goal of this study is to evaluate the performance of scintillometer U⊥ estimates for conditions under which U⊥ (x) is variable. Two methods are applied to estimate U⊥ from the scintillometer signal: the cumulative-spectrum method (relies on scintillation spectra) and the look-up-table method (relies on time-lagged correlation functions). The values of U⊥ of both methods compare well with the lidar estimates, with root-mean-square deviations of 0.71 and 0.73 m s−1. This indicates that, given the data treatment applied in this study, both measurement technologies are able to obtain estimates of U⊥ in the complex urban environment. The detailed investigation of four cases indicates that the cumulative-spectrum method is less susceptible to a variable U⊥ (x) than the look-up-table method. However, the look-up-table method can be adjusted to improve its capabilities for estimating U⊥ under conditions under for which U⊥ (x) is variable.

Neuronal-glial populations form functional networks in a biocompatible 3D scaffold

Monolayers of neurons and glia have been employed for decades as tools for the study of cellular physiology and as the basis for a variety of standard toxicological assays. A variety of three dimensional (3D) culture techniques have been developed with the aim to produce cultures that recapitulate desirable features of intact. In this study, we investigated the effect of preparing primary mouse mixed neuron and glial cultures in the inert 3D scaffold, Alvetex. Using planar multielectrode arrays, we compared the spontaneous bioelectrical activity exhibited by neuroglial networks grown in the scaffold with that seen in the same cells prepared as conventional monolayer cultures. Two dimensional (monolayer; 2D) cultures exhibited a significantly higher spike firing rate than that seen in 3D cultures although no difference was seen in total signal power (<50 Hz) while pharmacological responsiveness of each culture type to antagonism of GABAAR, NMDAR and AMPAR was highly comparable. Interestingly, correlation of burst events, spike firing and total signal power (<50 Hz) revealed that local field potential events were associated with action potential driven bursts as was the case for 2D cultures. Moreover, glial morphology was more physiologically normal in 3D cultures. These results show that 3D culture in inert scaffolds represents a more physiologically normal preparation which has advantages for physiological, pharmacological, toxicological and drug development studies, particularly given the extensive use of such preparations in high throughput and high content systems.