Relationship between therapeutic changes in blood pressure and outcomes in acute stroke: a metaregression

Both low and high blood pressure (BP) during the acute phase of stroke are associated independently with a poor outcome. Several small clinical trials have involved the alteration of BP and this study assessed the relationship between change in BP and functional outcome. Randomised controlled trials of interventions that would be expected, on pharmacological grounds, to alter BP in patients within one week of the onset of acute ischaemic or haemorrhagic stroke were sought using electronic searches. Data were collected on BP and clinical outcome. The relationship between the difference in on-treatment BP and odds ratios (OR) for outcomes was assessed using meta-regression. Thirty-seven trials involving 9,008 patients were included. A ‘U’ or ‘J’ shaped relationship were found between on-treatment BP difference and early death, death at the end of 90 day follow up, and combined death or dependency at the end of follow up. Although outcomes were not significantly reduced at any level of change in BP, the lowest odds occurred at: early death (OR 0.87, 95% confidence interval, CI 0.54 to 1.23) - 8.1 mmHg; death at end of follow up (OR 0.96, 95% CI 0.31 to 1.65) - 14.4 mmHg; and combined death or dependency at end of follow up (OR 0.95, 95% CI 0.11 to 1.72) - 14.6 mmHg. Although large falls or increases in BP are associated with a worse outcome, modest reductions may reduce death, and combined death or dependency, although the confidence intervals are wide and compatible with overall benefit or hazard.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level. This work focuses on planar piece-wise linear models that can mimic the firing response of several different cell types. Under constant current injection the periodic response and phase response curve (PRC) is calculated in closed form. A simple formula for the stability of a periodic orbit is found using Floquet theory. From the calculated PRC and the periodic orbit a phase interaction function is constructed that allows the investigation of phase-locked network states using the theory of weakly coupled oscillators. For large networks with global gap junction connectivity we develop a theory of strong coupling instabilities of the homogeneous, synchronous and splay state. For a piece-wise linear caricature of the Morris-Lecar model, with oscillations arising from a homoclinic bifurcation, we show that large amplitude oscillations in the mean membrane potential are organized around such unstable orbits.

Gap junctions and emergent rhythms

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network.