Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model

Generalised epileptic seizures are frequently accompanied by sudden, reversible transitions from low amplitude, irregular background activity to high amplitude, regular spike-wave discharges (SWD) in the EEG. The underlying mechanisms responsible for SWD generation and for the apparently spontaneous transitions to SWD and back again are still not fully understood. Specifically, the role of spatial cortico-cortical interactions in ictogenesis is not well studied. We present a macroscopic, neural mass model of a cortical column which includes two distinct time scales of inhibition. This model can produce both an oscillatory background and a pathological SWD rhythm. We demonstrate that coupling two of these cortical columns can lead to a bistability between out-of-phase, low amplitude background dynamics and in-phase, high amplitude SWD activity. Stimuli can cause state-dependent transitions from background into SWD. In an extended local area of cortex, spatial heterogeneities in a model parameter can lead to spontaneous reversible transitions from a desynchronised background to synchronous SWD due to intermittency. The deterministic model is therefore capable of producing absence seizure-like events without any time dependent adjustment of model parameters. The emergence of such mechanisms due to spatial coupling demonstrates the importance of spatial interactions in modelling ictal dynamics, and in the study of ictogenesis.

Self-organised transients in a neural mass model of epileptogenic tissue dynamics

Stimulation of human epileptic tissue can induce rhythmic, self-terminating responses on the EEG or ECoG. These responses play a potentially important role in localising tissue involved in the generation of seizure activity, yet the underlying mechanisms are unknown. However, in vitro evidence suggests that self-terminating oscillations in nervous tissue are underpinned by non-trivial spatio-temporal dynamics in an excitable medium. In this study, we investigate this hypothesis in spatial extensions to a neural mass model for epileptiform dynamics. We demonstrate that spatial extensions to this model in one and two dimensions display propagating travelling waves but also more complex transient dynamics in response to local perturbations. The neural mass formulation with local excitatory and inhibitory circuits, allows the direct incorporation of spatially distributed, functional heterogeneities into the model. We show that such heterogeneities can lead to prolonged reverberating responses to a single pulse perturbation, depending upon the location at which the stimulus is delivered. This leads to the hypothesis that prolonged rhythmic responses to local stimulation in epileptogenic tissue result from repeated self-excitation of regions of tissue with diminished inhibitory capabilities. Combined with previous models of the dynamics of focal seizures this macroscopic framework is a first step towards an explicit spatial formulation of the concept of the epileptogenic zone. Ultimately, an improved understanding of the pathophysiologic mechanisms of the epileptogenic zone will help to improve diagnostic and therapeutic measures for treating epilepsy.

Retrospective analysis of a nonforecasted rain-on-snow flood in the Alps – a matter of model limitations or unpredictable nature?

A rain-on-snow flood occurred in the Bernese Alps, Switzerland, on 10 October 2011, and caused significant damage. As the flood peak was unpredicted by the flood forecast system, questions were raised concerning the causes and the predictability of the event. Here, we aimed to reconstruct the anatomy of this rain-on-snow flood in the Lötschen Valley (160 km2) by analyzing meteorological data from the synoptic to the local scale and by reproducing the flood peak with the hydrological model WaSiM-ETH (Water Flow and Balance Simulation Model). This in order to gain process understanding and to evaluate the predictability. The atmospheric drivers of this rain-on-snow flood were (i) sustained snowfall followed by (ii) the passage of an atmospheric river bringing warm and moist air towards the Alps. As a result, intensive rainfall (average of 100 mm day-1) was accompanied by a temperature increase that shifted the 0° line from 1500 to 3200 m a.s.l. (meters above sea level) in 24 h with a maximum increase of 9 K in 9 h. The south-facing slope of the valley received significantly more precipitation than the north-facing slope, leading to flooding only in tributaries along the south-facing slope. We hypothesized that the reason for this very local rainfall distribution was a cavity circulation combined with a seeder-feeder-cloud system enhancing local rainfall and snowmelt along the south-facing slope. By applying and considerably recalibrating the standard hydrological model setup, we proved that both latent and sensible heat fluxes were needed to reconstruct the snow cover dynamic, and that locally high-precipitation sums (160 mm in 12 h) were required to produce the estimated flood peak. However, to reproduce the rapid runoff responses during the event, we conceptually represent likely lateral flow dynamics within the snow cover causing the model to react "oversensitively" to meltwater. Driving the optimized model with COSMO (Consortium for Small-scale Modeling)-2 forecast data, we still failed to simulate the flood because COSMO-2 forecast data underestimated both the local precipitation peak and the temperature increase. Thus we conclude that this rain-on-snow flood was, in general, predictable, but requires a special hydrological model setup and extensive and locally precise meteorological input data. Although, this data quality may not be achieved with forecast data, an additional model with a specific rain-on-snow configuration can provide useful information when rain-on-snow events are likely to occur.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Glacier mass balance reconstruction by sublimation induced enrichment of chemical species on Cerro Tapado (Chilean Andes)

A 36 m long ice core down to bedrock from the Cerro Tapado glacier (5536 m a.s.l, 30°08' S, 69°55' W) was analyzed to reconstruct past climatic conditions for Northern Chile. Because of the marked seasonality in the precipitation (short wet winter and extended dry summer periods) in this region, major snow ablation and related post-depositional processes occur on the glacier surface during summer periods. They include predominantly sublimation and dry deposition. Assuming that, like measured during the field campaign, the enrichment of chloride was always related to sublimation, the chemical record along the ice core may be applied to reconstruct the history of such secondary processes linked to the past climatic conditions over northern Chile. For the time period 1962–1999, a mean annual net accumulation of 316 mm water equivalent (weq) and 327 mm weq loss by sublimation was deduced by this method. This corresponds to an initial total annual accumulation of 539 mm weq. The annual variability of the accumulation and sublimation is related with the Southern Oscillation Index (SOI): higher net-accumulation during El-Niño years and more sublimation during La Niña years. The deepest part of the ice record shows a time discontinuity; with an ice body deposited under different climatic conditions: 290 mm higher precipitation but with reduced seasonal distribution (+470 mm in winter and –180 mm in summer) and –3°C lower mean annual temperature. Unfortunately, its age is unknown. The comparison with regional proxy data however let us conclude that the glacier buildup did most likely occur after the dry mid-Holocene.

Evaluation of 41calcium as a new approach to assess changes in bone metabolism: effect of a bisphosphonate intervention in postmenopausal women with low bone mass

A new technique was evaluated to identify changes in bone metabolism directly at high sensitivity through isotopic labeling of bone Ca. Six women with low BMD were labeled with 41Ca up to 700 days and treated for 6 mo with risedronate. Effect of treatment on bone could be identified using 41Ca after 4-8 wk in each individual. INTRODUCTION: Isotopic labeling of bone using 41Ca, a long-living radiotracer, has been proposed as an alternative approach for measuring changes in bone metabolism to overcome current limitations of available techniques. After isotopic labeling of bone, changes in urinary 41Ca excretion reflect changes in bone Ca balance. The aim of this study was to validate this new technique against established measures. Changes in bone Ca balance were induced by giving a bisphosphonate. MATERIALS AND METHODS: Six postmenopausal women with diagnosed osteopenia/osteoporosis received a single oral dose of 100 nCi 41Ca for skeleton labeling. Urinary 41Ca/40Ca isotope ratios were monitored by accelerator mass spectrometry up to 700 days after the labeling process. Subjects received 35 mg risedronate per week for 6 mo. Effect of treatment was monitored using the 41Ca signal in urine and parallel measurements of BMD by DXA and biochemical markers of bone metabolism in urine and blood. RESULTS: Positive response to treatment was confirmed by BMD measurements, which increased for spine by +3.0% (p = 0.01) but not for hip. Bone formation markers decreased by -36% for bone alkaline phosphatase (BALP; p = 0.002) and -59% for procollagen type I propeptides (PINP; p = 0.001). Urinary deoxypyridinoline (DPD) and pyridinoline (PYD) were reduced by -21% (p = 0.019) and -23% (p = 0.009), respectively, whereas serum and urinary carboxy-terminal teleopeptides (CTXs) were reduced by -60% (p = 0.001) and -57.0% (p = 0.001), respectively. Changes in urinary 41Ca excretion paralleled findings for conventional techniques. The urinary 41Ca/40Ca isotope ratio was shifted by -47 +/- 10% by the intervention. Population pharmacokinetic analysis (NONMEM) of the 41Ca data using a linear three-compartment model showed that bisphosphonate treatment reduced Ca transfer rates between the slowly exchanging compartment (bone) and the intermediate fast exchanging compartment by 56% (95% CI: 45-58%). CONCLUSIONS: Isotopic labeling of bone using 41Ca can facilitate human trials in bone research by shortening of intervention periods, lowering subject numbers, and having easier conduct of cross-over studies compared with conventional techniques.