A model of the hemodynamic response and oxygen delivery to brain

A recent nonlinear system by Friston et al. (2000. NeuroImage 12: 466–477) links the changes in BOLD response to changes in neural activity. The system consists of five subsystems, linking: (1) neural activity to flow changes; (2) flow changes to oxygen delivery to tissue; (3) flow changes to changes in blood volume and venous outflow; (4) changes in flow, volume, and oxygen extraction fraction to deoxyhemoglobin changes; and finally (5) volume and deoxyhemoglobin changes to the BOLD response. Friston et al. exploit, in subsystem 2, a model by Buxton and Frank coupling flow changes to changes in oxygen metabolism which assumes tissue oxygen concentration to be close to zero. We describe below a model of the coupling between flow and oxygen delivery which takes into account the modulatory effect of changes in tissue oxygen concentration. The major development has been to extend the original Buxton and Frank model for oxygen transport to a full dynamic capillary model making the model applicable to both transient and steady state conditions. Furthermore our modification enables us to determine the time series of CMRO2 changes under different conditions, including CO2 challenges. We compare the differences in the performance of the “Friston system” using the original model of Buxton and Frank and that of our model. We also compare the data predicted by our model (with appropriate parameters) to data from a series of OIS studies. The qualitative differences in the behaviour of the models are exposed by different experimental simulations and by comparison with the results of OIS data from brief and extended stimulation protocols and from experiments using hypercapnia.

Impact of oceanic processes on the carbon cycle during the last termination

During the last termination (from ~18 000 years ago to ~9000 years ago), the climate significantly warmed and the ice sheets melted. Simultaneously, atmospheric CO2 increased from ~190 ppm to ~260 ppm. Although this CO2 rise plays an important role in the deglacial warming, the reasons for its evolution are difficult to explain. Only box models have been used to run transient simulations of this carbon cycle transition, but by forcing the model with data constrained scenarios of the evolution of temperature, sea level, sea ice, NADW formation, Southern Ocean vertical mixing and biological carbon pump. More complex models (including GCMs) have investigated some of these mechanisms but they have only been used to try and explain LGM versus present day steady-state climates. In this study we use a coupled climate-carbon model of intermediate complexity to explore the role of three oceanic processes in transient simulations: the sinking of brines, stratification-dependent diffusion and iron fertilization. Carbonate compensation is accounted for in these simulations. We show that neither iron fertilization nor the sinking of brines alone can account for the evolution of CO2, and that only the combination of the sinking of brines and interactive diffusion can simultaneously simulate the increase in deep Southern Ocean δ13C. The scenario that agrees best with the data takes into account all mechanisms and favours a rapid cessation of the sinking of brines around 18 000 years ago, when the Antarctic ice sheet extent was at its maximum. In this scenario, we make the hypothesis that sea ice formation was then shifted to the open ocean where the salty water is quickly mixed with fresher water, which prevents deep sinking of salty water and therefore breaks down the deep stratification and releases carbon from the abyss. Based on this scenario, it is possible to simulate both the amplitude and timing of the long-term CO2 increase during the last termination in agreement with ice core data. The atmospheric δ13C appears to be highly sensitive to changes in the terrestrial biosphere, underlining the need to better constrain the vegetation evolution during the termination.

Changes in reactive stratospheric gases due to a change in Brewer–Dobson circulation: results from a simple model

Amounts of source gases with stratospheric sinks (CFCs, N2O, CH4) are affected by changes in Brewer–Dobson circulation. Source gases and their degradation products are important for atmospheric chemistry and climate. With a simple model, we examine how amounts and lifetimes of source gases and products depend on speed of the circulation. Transient results differ from steady-state and stratospheric results differ from those for stratosphere plus troposphere. Increases in speed increase the stratospheric burden of source gases, but reduce products and reduce total burdens and lifetimes of source gases

Impact of atmospheric forcing on Antarctic continental shelf water masses

The Antarctic continental shelf seas feature a bimodal distribution of water mass temperature, with the Amundsen and Bellingshausen Seas flooded by Circumpolar Deep Water that is several degrees Celsius warmer than the cold shelf waters prevalent in the Weddell and Ross Seas. This bimodal distribution could be caused by differences in atmospheric forcing, ocean dynamics, ocean and ice feedbacks, or some combination of these factors. In this study, a highly simplified coupled sea ice–mixed layer model is developed to investigate the physical processes controlling this situation. Under regional atmospheric forcings and parameter choices the 10-yr simulations demonstrate a complete destratification of the Weddell Sea water column in winter, forming cold, relatively saline shelf waters, while the Amundsen Sea winter mixed layer remains shallower, allowing a layer of deep warm water to persist. Applying the Weddell atmospheric forcing to the Amundsen Sea model destratifies the water column after two years, and applying the Amundsen forcing to the Weddell Sea model results in a shallower steady-state winter mixed layer that no longer destratifies the water column. This suggests that the regional difference in atmospheric forcings alone is sufficient to account for the bimodal distribution in Antarctic shelf-sea temperatures. The model prediction of mixed layer depth is most sensitive to the air temperature forcing, but a switch in all forcings is required to prevent destratification of the Weddell Sea water column.

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in an hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main precursor of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homestasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.

Freshwater and heat transports from global ocean synthesis

[1] An eddy-permitting ¼° global ocean reanalysis based on the Operational Met Office FOAM data assimilation system has been run for 1989–2010 forced by ERA-Interim meteorology. Freshwater and heat transports are compared with published estimates globally and in each basin, with special focus on the Atlantic. The meridional transports agree with observations within errors at most locations, but where eddies are active the transports by the mean flow are nearly always in better agreement than the total transports. Eddy transports are down gradient and are enhanced relative to a free run. They may oppose or reinforce mean transports and provide 40–50% of the total transport near midlatitude fronts, where eddies with time scales <1 month provide up to 15%. Basin-scale freshwater convergences are calculated with the Arctic/Atlantic, Indian, and Pacific oceans north of 32°S, all implying net evaporation of 0.33 ± 0.04 Sv, 0.65 ± 0.07 Sv, and 0.09 ± 0.04 Sv, respectively, within the uncertainty of observations in the Atlantic and Pacific. The Indian is more evaporative and the Southern Ocean has more precipitation (1.07 Sv). Air-sea fluxes are modified by assimilation influencing turbulent heat fluxes and evaporation. Generally, surface and assimilation fluxes together match the meridional transports, indicating that the reanalysis is close to a steady state. Atlantic overturning and gyre transports are assessed with overturning freshwater transports southward at all latitudes. At 26°N eddy transports are negligible, overturning transport is 0.67 ± 0.19 Sv southward and gyre transport is 0.44 ± 0.17 Sv northward, with divergence between 26°N and the Bering Strait of 0.13 ± 0.23 Sv over 2004–2010.

Inhibition of the cardiac Na+ channel Nav1.5 by carbon monoxide

Sub-lethal carbon monoxide (CO) exposure is frequently associated with myocardial arrhythmias and our recent studies have demonstrated that these may be attributable to modulation of cardiac Na+ channels, causing an increase in the late current and an inhibition of the peak current. Using a recombinant expression system, we demonstrate that CO inhibits peak human Nav1.5 current amplitude without activation of the late Na+ current observed in native tissue. Inhibition was associated with a hyperpolarizing shift in the steady-state inactivation properties of the channels and was unaffected by modification of channel gating induced by anemone toxin (rATX-II). Systematic pharmacological assessment indicated that no recognised CO-sensitive intracellular signalling pathways appeared to mediate CO inhibition of Nav1.5. Inhibition was, however, markedly suppressed by inhibition of nitric oxide (NO) formation, but NO donors did not mimic or occlude channel inhibition by CO, indicating that NO alone did not account for the actions of CO. Exposure of cells to dithiothreitol immediately before CO exposure also dramatically reduced the magnitude of current inhibition. Similarly, L-cysteine and N-ethylmaleimide significantly attenuated the inhibition caused by CO. In the presence of DTT and the NO inhibitor L-NAME, the ability of CO to inhibit Nav1.5 was almost fully prevented. Our data indicate that inhibition of peak Na+ current (which can lead to Brugada-syndrome like arrhythmias) occurs via a mechanism distinct from induction of the late current, requires NO formation and is dependent on channel redox state.

Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

Intercomparison of general circulation models for hot extrasolar planets

We compare five general circulation models (GCMs) which have been recently used to study hot extrasolar planet atmospheres (BOB, CAM, IGCM, MITgcm, and PEQMOD), under three test cases useful for assessing model convergence and accuracy. Such a broad, detailed intercomparison has not been performed thus far for extrasolar planets study. The models considered all solve the traditional primitive equations, but employ di↵erent numerical algorithms or grids (e.g., pseudospectral and finite volume, with the latter separately in longitude-latitude and ‘cubed-sphere’ grids). The test cases are chosen to cleanly address specific aspects of the behaviors typically reported in hot extrasolar planet simulations: 1) steady-state, 2) nonlinearly evolving baroclinic wave, and 3) response to fast timescale thermal relaxation. When initialized with a steady jet, all models maintain the steadiness, as they should—except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in pseudospectral models (only). However, exact numerical convergence is still not achieved across the pseudospectral models: amplitudes and phases are observably di↵erent. When subject to a typical ‘hot-Jupiter’-like forcing, all five models show quantitatively di↵erent behavior—although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Hence, as have been advocated in several past studies, specific quantitative predictions (such as the location of large vortices and hot regions) by GCMs should be viewed with caution. Overall, in the tests considered here, pseudospectral models in pressure coordinate (PEBOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid performs the worst.

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of lactating dairy cows

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of the lactating dairy cow is constructed and solved in the steady state. The model contains four intracellular and four extracellular pools and conservation of mass principles are applied to generate the fundamental equations describing the behaviour of the system. The experimental measurements required for model solution are milk secretion and plasma flow rate across the gland in combination with phenylalanine and tyrosine concentrations and plateau isotopic enrichments in arterial and venous plasma and free and protein bound milk during a constant infusion of [1-(13)C]phenylalanine and [2,3,5,6-(2)H]tyrosine tracer. If assumptions are made, model solution enables determination of steady state flows for phenylalanine and tyrosine inflow to the gland, outflow from it and bypass, and flows representing the synthesis and degradation of constitutive protein and hydroxylation. The model is effective in providing information about the fates of phenylalanine and tyrosine in the mammary gland and could be used as part of a more complex system describing amino acid metabolism in the whole ruminant.

Effects of a mid-latitude solar eclipse on the thermosphere and ionosphere: a modelling study

A modelling study is presented which investigates in-situ generated changes of the thermosphere and ionosphere during a solar eclipse. Neutral temperatures are expected to drop by up to 40 degrees K at 240 km height in the totality footprint, with neutral winds of up to 26 m/s responding to the change of pressure. Both temperatures and winds are found to respond with a time lag of 30 min after the passing of the Moon's shadow. A gravity wave is generated in the neutral atmosphere and propagates into the opposite hemisphere at around 300 m/s. The combined effects of thermal cooling and downwelling lead to an overall increase in [O], while [N(2)] initially rises and then for several hours after the eclipse is below the "steady state" level. An enhancement of [NmF2] is found and explained by the atmosphere's contraction during, and the reduced [O]/[N(2)] ratio after the eclipse.

An analysis of the accuracy of magnetopause reconnection rate variations deduced from cusp ion dispersion characteristics

We present an analysis of the accuracy of the method introduced by Lockwood et al. (1994) for the determination of the magnetopause reconnection rate from the dispersion of precipitating ions in the ionospheric cusp region. Tests are made by applying the method to synthesised data. The simulated cusp ion precipitation data are produced by an analytic model of the evolution of newly-opened field lines, along which magnetosheath ions are firstly injected across the magnetopause and then dispersed as they propagate into the ionosphere. The rate at which these newly opened field lines are generated by reconnection can be varied. The derived reconnection rate estimates are then compared with the input variation to the model and the accuracy of the method assessed. Results are presented for steady-state reconnection, for continuous reconnection showing a sine-wave variation in rate and for reconnection which only occurs in square wave pulses. It is found that the method always yields the total flux reconnected (per unit length of the open-closed field-line boundary) to within an accuracy of better than 5%, but that pulses tend to be smoothed so that the peak reconnection rate within the pulse is underestimated and the pulse length is overestimated. This smoothing is reduced if the separation between energy channels of the instrument is reduced; however this also acts to increase the experimental uncertainty in the estimates, an effect which can be countered by improving the time resolution of the observations. The limited time resolution of the data is shown to set a minimum reconnection rate below which the method gives spurious short-period oscillations about the true value. Various examples of reconnection rate variations derived from cusp observations are discussed in the light of this analysis.

Time-dependent flows in the coupled solar wind-magnetosphere-ionosphere system

Concepts of time-dependent flow in the coupled solar wind-magnetosphere-ionosphere system are discussed and compared with the frequently-adopted steady-state paradigm. Flows are viewed as resulting from departures of the system from equilibrium excited by dayside and nightside reconnection processes, with the flows then taking the system back towards a new equilibrium configuration. The response of the system to reconnection impulses, continuous but unbalanced reconnection and balanced steady-state reconnection are discussed in these terms. It is emphasized that in the time-dependent case the ionospheric and interplanetary electric fields are generally inductively decoupled from each other; a simple mapping of the interplanetary electric field along equipotential field lines into the ionosphere occurs only in the electrostatic steady-state case.

Large-scale fields and flows in the magnetosphere-ionosphere system

Advances in our understanding of the large-scale electric and magnetic fields in the coupled magnetosphere-ionosphere system are reviewed. The literature appearing in the period January 1991–June 1993 is sorted into 8 general areas of study. The phenomenon of substorms receives the most attention in this literature, with the location of onset being the single most discussed issue. However, if the magnetic topology in substorm phases was widely debated, less attention was paid to the relationship of convection to the substorm cycle. A significantly new consensus view of substorm expansion and recovery phases emerged, which was termed the ‘Kiruna Conjecture’ after the conference at which it gained widespread acceptance. The second largest area of interest was dayside transient events, both near the magnetopause and the ionosphere. It became apparent that these phenomena include at least two classes of events, probably due to transient reconnection bursts and sudden solar wind dynamic pressure changes. The contribution of both types of event to convection is controversial. The realisation that induction effects decouple electric fields in the magnetosphere and ionosphere, on time scales shorter than several substorm cycles, calls for broadening of the range of measurement techniques in both the ionosphere and at the magnetopause. Several new techniques were introduced including ionospheric observations which yield reconnection rate as a function of time. The magnetospheric and ionospheric behaviour due to various quasi-steady interplanetary conditions was studied using magnetic cloud events. For northward IMF conditions, reverse convection in the polar cap was found to be predominantly a summer hemisphere phenomenon and even for extremely rare prolonged southward IMF conditions, the magnetosphere was observed to oscillate through various substorm cycles rather than forming a steady-state convection bay.

Occurrence probability, width and number of steps of cusp precipitation for fully pulsed reconnection at the dayside magnetopause

We discuss the characteristics of magnetosheath plasma precipitation in the “cusp” ionosphere for when the reconnection at the dayside magnetopause takes place only in a series of pulses. It is shown that even in this special case, the low-altitude cusp precipitation is continuous, unless the intervals between the pulses are longer than observed intervals between magnetopause flux transfer event (FTE) signatures. We use FTE observation statistics to predict, for this case of entirely pulsed reconnection, the occurrence frequency, the distribution of latitudinal widths, and the number of ion dispersion steps of the cusp precipitation for a variety of locations of the reconnection site and a range of values of the local de-Hoffman Teller velocity. It is found that the cusp occurrence frequency is comparable with observed values for virtually all possible locations of the reconnection site. The distribution of cusp width is also comparable with observations and is shown to be largely dependent on the distribution of the mean reconnection rate, but pulsing the reconnection does very slightly increase the width of that distribution compared with the steady state case. We conclude that neither cusp occurrence probability nor width can be used to evaluate the relative occurrence of reconnection behaviors that are entirely pulsed, pulsed but continuous and quasi-steady. We show that the best test of the relative frequency of these three types of reconnection is to survey the distribution of steps in the cusp ion dispersion characteristics.