Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick's Law Model of Diffusion.

To investigate the impact of experimental interventions on living biological tissue, ex vivo rodent brain slices are often used as a more controllable alternative to a live animal model. However, for meaningful results, the biological sample must be known to be healthy and viable. One of the gold-standard approaches to identifying tissue viability status is to measure the rate of tissue oxygen consumption under specific controlled conditions. Here, we work with thin (400 µm) slices of mouse cortical brain tissue which are sustained by a steady flow of oxygenated artificial cerebralspinal fluid (aCSF) at room temperature. To quantify tissue oxygen consumption (Q), we measure oxygen partial pressure (pO2) as a function of probe depth. The curvature of the obtained parabolic (or parabola-like) pO2 profiles can be used to extract Q, providing one knows the Krogh coefficient Kt, for the tissue. The oxygen trends are well described by a Fick's law diffusion-consumption model developed by Ivanova and Simeonov, and expressed in terms of ratio (Q/K), being the rate of oxygen consumption in tissue divided by the Krogh coefficient (oxygen diffusivity × oxygen solubility) for tissue. If the fluid immediately adjacent to the tissue can be assumed to be stationary (i.e., nonflowing), one may invoke conservation of oxygen flux K·(∂P/∂x) across the interface to deduce (Kt/Kf), the ratio of Krogh coefficients for tissue and fluid. Using published interpolation formulas for the effect of salt content and temperature on oxygen diffusivity and solubility for pure water, we estimate Kf, the Krogh coefficient for aCSF, and hence deduce the Kt coefficient for tissue. We distinguish experimental uncertainty from natural biological variability by using pairs of repeated profiles at the same tissue location. We report a dimensionless Krogh ratio (Kt/Kf)=0.562±0.088 (mean ± SD), corresponding to a Krogh coefficient Kt=(1.29±0.21)×10-14 mol/(m·s·Pa) for mouse cortical tissue at room temperature, but acknowledge the experimental limitation of being unable to verify that the fluid boundary layer is truly stationary. We compare our results with those reported in the literature, and comment on the challenges and ambiguities caused by the extensive use of 'biologically convenient' non-SI units for tissue Krogh coefficient.

Tissue oxygen partial pressure as a viability metric for ex vivo brain tissue slices.

BACKGROUND: Despite the prevalent use of the ex vivo brain slice preparation in neurophysiology research, a reliable method for judging tissue viability - and thus suitability of a slice for inclusion in an experiment - is lacking. The utility of indirect electrophysiological measures of tissue health is model-specific and needs to be used cautiously. In this study, we verify a more direct test of slice viability, based on tissue oxygen consumption rate. NEW METHOD: We hypothesised that the minimum intra-slice partial pressure of oxygen (pO2min) would correlate with tissue oxygen consumption rate, providing an accessible method for reliably assessing tissue viability status. Using mouse brain cortex slices, we measured tissue oxygen consumption rate using a Fick's law diffusion-consumption model applied to full intra-tissue pO2 profiles and compared this to pO2min and 2,3,5-triphenol tetrazolium chloride (TTC) viability staining. RESULTS: Tissue pO2min correlated strongly with oxygen consumption rate in both neurophysiological active and quiescent tissue (in "no-magnesium" and "normal" artificial cerebrospinal fluid, respectively) (R2 =49.7% and 42.1%, respectively). Both correlated with TTC viability stain. Oxygen consumption rate was positively related to the frequency of seizure-like event activity in no-magnesium artificial cerebrospinal fluid (R2 = 44.8%). COMPARISON WITH EXISTING METHODS: While measurement of tissue oxygen levels and oxygen consumption is not new, intra-tissue pO2min is a novel approach to assess brain slice viability. CONCLUSION: The results confirm that tissue oxygen minimum pO2min is a robust metric for estimating tissue viability status - the lower the pO2min, the healthier the tissue.

An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia.

We study the dynamics of the transition between the low- and high-firing states of the cortical slow oscillation by using intracellular recordings of the membrane potential from cortical neurons of rats. We investigate the evidence for a bistability in assemblies of cortical neurons playing a major role in the maintenance of this oscillation. We show that the trajectory of a typical transition takes an approximately exponential form, equivalent to the response of a resistor-capacitor circuit to a step-change in input. The time constant for the transition is negatively correlated with the membrane potential of the low-firing state, and values are broadly equivalent to neural time constants measured elsewhere. Overall, the results do not strongly support the hypothesis of a bistability in cortical neurons; rather, they suggest the cortical manifestation of the oscillation is a result of a step-change in input to the cortical neurons. Since there is evidence from previous work that a phase transition exists, we speculate that the step-change may be a result of a bistability within other brain areas, such as the thalamus, or a bistability among only a small subset of cortical neurons, or as a result of more complicated brain dynamics.

Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.

Growth of critical fluctuations prior to catastrophic state transition is generally regarded as a universal phenomenon, providing a valuable early warning signal in dynamical systems. Using an ecological fisheries model of three populations (juvenile prey J, adult prey A and predator P), a recent study has reported silent early warning signals obtained from P and A populations prior to saddle-node (SN) bifurcation, and thus concluded that early warning signals are not universal. By performing a full eigenvalue analysis of the same system we demonstrate that while J and P populations undergo SN bifurcation, A does not jump to a new state, so it is not expected to carry early warning signs. In contrast with the previous study, we capture a significant increase in the noise-induced fluctuations in the P population, but only on close approach to the bifurcation point; it is not clear why the P variance initially shows a decaying trend. Here we resolve this puzzle using observability measures from control theory. By computing the observability coefficient for the system from the recordings of each population considered one at a time, we are able to quantify their ability to describe changing internal dynamics. We demonstrate that precursor fluctuations are best observed using only the J variable, and also P variable if close to transition. Using observability analysis we are able to describe why a poorly observable variable (P) has poor forecasting capabilities although a full eigenvalue analysis shows that this variable undergoes a bifurcation. We conclude that observability analysis provides complementary information to identify the variables carrying early-warning signs about impending state transition.

Frontal-temporal synchronization of EEG signals quantified by order patterns cross recurrence analysis during propofol anesthesia.

Characterizing brain dynamics during anesthesia is a main current challenge in anesthesia study. Several single channel electroencephalogram (EEG)-based commercial monitors like the Bispectral index (BIS) have suggested to examine EEG signal. But, the BIS index has obtained numerous critiques. In this study, we evaluate the concentration-dependent effect of the propofol on long-range frontal-temporal synchronization of EEG signals collected from eight subjects during a controlled induction and recovery design. We used order patterns cross recurrence plot and provide an index named order pattern laminarity (OPL) to assess changes in neuronal synchronization as the mechanism forming the foundation of conscious perception. The prediction probability of 0.9 and 0.84 for OPL and BIS specified that the OPL index correlated more strongly with effect-site propofol concentration. Also, our new index makes faster reaction to transients in EEG recordings based on pharmacokinetic and pharmacodynamic model parameters and demonstrates less variability at the point of loss of consciousness (standard deviation of 0.04 for OPL compared with 0.09 for BIS index). The result show that the OPL index can estimate anesthetic state of patient more efficiently than the BIS index in lightly sedated state with more tolerant of artifacts.

Noise-induced precursors of state transitions in the stochastic Wilson-cowan model.

The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions-sudden qualitative changes in the state of a dynamical system emerging from a bifurcation-accessible to the Wilson-Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein-Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these early-warning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.

BACKGROUND: Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. RESULTS: As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. CONCLUSIONS: The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts.

Gap junctions modulate seizures in a mean-field model of general anesthesia for the cortex.

During slow-wave sleep, general anesthesia, and generalized seizures, there is an absence of consciousness. These states are characterized by low-frequency large-amplitude traveling waves in scalp electroencephalogram. Therefore the oscillatory state might be an indication of failure to form coherent neuronal assemblies necessary for consciousness. A generalized seizure event is a pathological brain state that is the clearest manifestation of waves of synchronized neuronal activity. Since gap junctions provide a direct electrical connection between adjoining neurons, thus enhancing synchronous behavior, reducing gap-junction conductance should suppress seizures; however there is no clear experimental evidence for this. Here we report theoretical predictions for a physiologically-based cortical model that describes the general anesthetic phase transition from consciousness to coma, and includes both chemical synaptic and direct electrotonic synapses. The model dynamics exhibits both Hopf (temporal) and Turing (spatial) instabilities; the Hopf instability corresponds to the slow (≲8 Hz) oscillatory states similar to those seen in slow-wave sleep, general anesthesia, and seizures. We argue that a delicately balanced interplay between Hopf and Turing modes provides a canonical mechanism for the default non-cognitive rest state of the brain. We show that the Turing mode, set by gap-junction diffusion, is generally protective against entering oscillatory modes; and that weakening the Turing mode by reducing gap conduction can release an uncontrolled Hopf oscillation and hence an increased propensity for seizure and simultaneously an increased sensitivity to GABAergic anesthesia.

Investigation into the effect of the general anaesthetics etomidate and ketamine on long-range coupling of population activity in the mouse neocortical slice.

General anaesthetics have been hypothesised to ablate consciousness by decoupling intracortical neural connectivity. We explored this by investigating the effect of etomidate and ketamine on coupling of neural population activity using the low magnesium neocortical slice model. Four extracellular electrodes (50 µm) were positioned in mouse neocortical slices (400 µm thick) with varying separation. The effect of etomidate (24 µM) and ketamine (16 µM) on the timing of population activity recorded between channels was analysed. No decoupling was observed at the closest electrode separation of 0.2 mm. At 4mm separation, decoupling was observed in 50% and 42% of slices during etomidate and ketamine delivery, respectively (P<0.0001 and P=0.002, compared to 0.2 mm separation). A lower rate of decoupling was observed with 1mm separation (21% and 8%, respectively, P<0.03 for etomidate compared to 0.2mm separation). The data support the hypothesis that mechanistically diverse general anaesthetics disrupt neuronal connectivity across widely distributed intracortical networks.

Connexin36 knockout mice display increased sensitivity to pentylenetetrazol-induced seizure-like behaviors.

OBJECTIVE: Large-scale synchronous firing of neurons during seizures is modulated by electrotonic coupling between neurons via gap junctions. To explore roles for connexin36 (Cx36) gap junctions in seizures, we examined the seizure threshold of connexin36 knockout (Cx36KO) mice using a pentylenetetrazol (PTZ) model. METHODS: Mice (2-3months old) with Cx36 wildtype (WT) or Cx36KO genotype were treated with vehicle or 10-40mg/kg of the convulsant PTZ by intraperitoneal injection. Seizure and seizure-like behaviors were scored by examination of video collected for 20min. Quantitative real-time PCR (QPCR) was performed to measure potential compensatory neuronal connexin (Cx30.2, Cx37, Cx43 and Cx45), pannexin (PANX1 and PANX2) and gamma-aminobutyric acid type A (GABA(A)) receptor α1 subunit gene expression. RESULTS: Cx36KO animals exhibited considerably more severe seizures; 40mg/kg of PTZ caused severe generalized (≥grade III) seizures in 78% of KO, but just 5% of WT mice. A lower dose of PTZ (20mg/kg) induced grade II seizure-like behaviors in 40% KO vs. 0% of WT animals. There was no significant difference in either connexin, pannexin or GABA(A) α1 gene expression between WT and KO animals. CONCLUSION: Increased sensitivity of Cx36KO animals to PTZ-induced seizure suggests that Cx36 gap junctional communication functions as a physiological anti-convulsant mechanism, and identifies the Cx36 gap junction as a potential therapeutic target in epilepsy.