Transport in the Brain Extracellular Space: Diffusion, but Which Kind?

The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the parenchyma, in contrast to the previous notion that diffusion is the main mechanism. However, when discussing the issue of "diffusion or non-diffusion", much less attention was given to the question that diffusion itself can have a different character. In our opinion, some of the recently published results do not fit into the traditional understanding of diffusion. In this regard, we outline the relevant new theoretical approaches on transport processes in complex random media such as concepts of diffusive diffusivity and time-dependent homogenization, which expands the understanding of the forms of transport of substances based on diffusion.

Modeling of Astrocyte Networks: Toward Realistic Topology and Dynamics.

Neuronal firing and neuron-to-neuron synaptic wiring are currently widely described as orchestrated by astrocytes-elaborately ramified glial cells tiling the cortical and hippocampal space into non-overlapping domains, each covering hundreds of individual dendrites and hundreds thousands synapses. A key component to astrocytic signaling is the dynamics of cytosolic Ca2+ which displays multiscale spatiotemporal patterns from short confined elemental Ca2+ events (puffs) to Ca2+ waves expanding through many cells. Here, we synthesize the current understanding of astrocyte morphology, coupling local synaptic activity to astrocytic Ca2+ in perisynaptic astrocytic processes and morphology-defined mechanisms of Ca2+ regulation in a distributed model. To this end, we build simplified realistic data-driven spatial network templates and compile model equations as defined by local cell morphology. The input to the model is spatially uncorrelated stochastic synaptic activity. The proposed modeling approach is validated by statistics of simulated Ca2+ transients at a single cell level. In multicellular templates we observe regular sequences of cell entrainment in Ca2+ waves, as a result of interplay between stochastic input and morphology variability between individual astrocytes. Our approach adds spatial dimension to the existing astrocyte models by employment of realistic morphology while retaining enough flexibility and scalability to be embedded in multiscale heterocellular models of neural tissue. We conclude that the proposed approach provides a useful description of neuron-driven Ca2+-activity in the astrocyte syncytium.

Gaussian sliding window for robust processing laser speckle contrast images.

The laser speckle contrast analysis (LASCA) is one of the most applicable tools in microcirculation studies. While the basic idea, as well as experimental setup for this method, are fairly simple, there is still the room for advancing of data processing algorithms. Specifically, the conventional realizations of LASCA method may limit the spatial and/or temporal resolution and thus fail in the detection of very small contrast objects since they based on the fixed-size rectangular sliding window function. We suggest an alternative data processing algorithm based on the usage of the Gaussian sliding filter for a sequential determination of both spatial and temporal parts of the speckle contrast. The suggested replacement of conventional box filter leads to the monotonic damping of high-frequency spectral components that results in a better elimination of ringing and aliasing effects in the spatio-temporal speckle contrast outputs. Additionally, we show that such sliding filtration increases robustness with respect to the processing of a sequence of nonstabilised images. We support this consideration with representative examples of processing both surrogate and real experimental data.

Sodium-Calcium Exchanger Can Account for Regenerative Ca2+ Entry in Thin Astrocyte Processes.

Calcium transients in thin astrocytic processes can be important in synaptic plasticity, but their mechanism is not completely understood. Clearance of synaptic glutamate leads to increase in astrocytic sodium. This can electrochemically favor the reverse mode of the Na/Ca-exchanger (NCX) and allow calcium into the cell, accounting for activity-dependent calcium transients in perisynaptic astrocytic processes. However, cytosolic sodium and calcium are also allosteric regulators of the NCX, thus adding kinetic constraints on the NCX-mediated fluxes and providing for complexity of the system dynamics. Our modeling indicates that the calcium-dependent activation and also calcium-dependent escape from the sodium-mediated inactive state of the NCX in astrocytes can form a positive feedback loop and lead to regenerative calcium influx. This can result in sodium-dependent amplification of calcium transients from nearby locations or other membrane mechanisms. Prolonged conditions of elevated sodium, for example in ischemia, can also lead to bistability in cytosolic calcium levels, where a delayed transition to the high-calcium state can be triggered by a short calcium transient. These theoretical predictions call for a dedicated experimental estimation of the kinetic parameters of the astrocytic Na/Ca-exchanger.

Modeling of Kidney Hemodynamics: Probability-Based Topology of an Arterial Network.

Through regulation of the extracellular fluid volume, the kidneys provide important long-term regulation of blood pressure. At the level of the individual functional unit (the nephron), pressure and flow control involves two different mechanisms that both produce oscillations. The nephrons are arranged in a complex branching structure that delivers blood to each nephron and, at the same time, provides a basis for an interaction between adjacent nephrons. The functional consequences of this interaction are not understood, and at present it is not possible to address this question experimentally. We provide experimental data and a new modeling approach to clarify this problem. To resolve details of microvascular structure, we collected 3D data from more than 150 afferent arterioles in an optically cleared rat kidney. Using these results together with published micro-computed tomography (µCT) data we develop an algorithm for generating the renal arterial network. We then introduce a mathematical model describing blood flow dynamics and nephron to nephron interaction in the network. The model includes an implementation of electrical signal propagation along a vascular wall. Simulation results show that the renal arterial architecture plays an important role in maintaining adequate pressure levels and the self-sustained dynamics of nephrons.

Noise controlled synchronization in potassium coupled neural models.

The paper applies biologically plausible models to investigate how noise input to small ensembles of neurons, coupled via the extracellular potassium concentration, can influence their firing patterns. Using the noise intensity and the volume of the extracellular space as control parameters, we show that potassium induced depolarization underlies the formation of noise-induced patterns such as delayed firing and synchronization. These phenomena are associated with the appearance of new time scales in the distribution of interspike intervals that may be significant for the spatio-temporal oscillations in neuronal ensembles.

Neural synchronization via potassium signaling.

Using a relatively simple model we examine how variations of the extracellular potassium concentration can give rise to synchronization of two nearby pacemaker cells. With the volume of the extracellular space and the rate of potassium diffusion as control parameters, the dual nature of this resource-mediated coupling is found to be responsible for the coexistence of competing patterns of in- and anti-phase synchronization between identical cells. Cell heterogeneity produces significant modifications of the dynamical regimes in the control parameter plane. By comparison with conventional gap junctional coupling, potassium signaling gives rise to considerable changes of the cellular response to external stimuli.

Oscillator clustering in a resource distribution chain.

The paper investigates the special clustering phenomena that one can observe in systems of nonlinear oscillators that are coupled via a shared flow of primary resources (or a common power supply). This type of coupling, which appears to be quite frequent in nature, implies that one can no longer separate the inherent dynamics of the individual oscillator from the properties of the coupling network. Illustrated by examples from microbiological population dynamics, renal physiology, and electronic oscillator theory, we show how competition for primary resources in a resource distribution chain leads to a number of new generic phenomena, including partial synchronization, sliding of the synchronization region with the resource supply, and coupling-induced inhomogeneity.