Background Investigators use phase-contrast magnetic resonance (PC-MR) and computational fluid dynamics (CFD) to assess cerebrospinal fluid dynamics. We compared qualitative and quantitative results from the two methods. Methods Four volunteers were imaged with a heavily T2-weighted volume gradient echo scan of the brain and cervical spine at 3T and with PC-MR. Velocities were calculated from PC-MR for each phase in the cardiac cycle. Mean pressure gradients in the PC-MR acquisition through the cardiac cycle were calculated with the Navier-Stokes equations. Volumetric MR images of the brain and upper spine were segmented and converted to meshes. Models of the subarachnoid space were created from volume images with the Vascular Modeling Toolkit. CFD simulations were performed with a previously verified flow solver. The flow patterns, velocities and pressures were compared in PC-MR and CFD flow images. Results PC-MR images consistently revealed more inhomogeneous flow patterns than CFD, especially in the anterolateral subarachnoid space where spinal nerve roots are located. On average, peak systolic and diastolic velocities in PC-MR exceeded those in CFD by 31% and 41%, respectively. On average, systolic and diastolic pressure gradients calculated from PC-MR exceeded those of CFD by 11% and 39%, respectively. Conclusions PC-MR shows local flow disturbances that are not evident in typical CFD. The velocities and pressure gradients calculated from PC-MR are systematically larger than those calculated from CFD.

In this paper, we investigate the dynamics of a neuron-glia cell system and the underlying mechanism for the occurrence of seizures. For our mathematical and numerical investigation of the cell model we will use bifurcation analysis and some computational methods. It turns out that an increase of the potassium concentration in the reservoir is one trigger for seizures and is related to a torus bifurcation. In addition, we will study potassium dynamics of the model by considering a reduced version and we will show how both mechanisms are linked to each other. Moreover, the reduction of the potassium leak current will also induce seizures. Our study will show that an enhancement of the extracellular potassium concentration, which influences the Nernst potential of the potassium current, may lead to seizures. Furthermore, we will show that an external forcing term (e.g. electroshocks as unidirectional rectangular pulses also known as electroconvulsive therapy) will establish seizures similar to the unforced system with the increased extracellular potassium concentration. To this end, we describe the unidirectional rectangular pulses as an autonomous system of ordinary differential equations. These approaches will explain the appearance of seizures in the cellular model. Moreover, seizures, as they are measured by electroencephalography (EEG), spread on the macro-scale (cm). Therefore, we extend the cell model with a suitable homogenised monodomain model, propose a set of (numerical) experiment to complement the bifurcation analysis performed on the single-cell model. Based on these experiments, we introduce a bidomain model for a more realistic modelling of white and grey matter of the brain. Performing similar (numerical) experiment as for the monodomain model leads to a suitable comparison of both models. The individual cell model, with its seizures explained in terms of a torus bifurcation, extends directly to corresponding results in both the monodomain and bidomain models where the neural firing spreads almost synchronous through the domain as fast traveling waves, for physiologically relevant paramenters. Keywords Nonlinear dynamics • Bifurcation theory • Neuron-glia cell system • Monodomain and bidomain model • Seizure • Electroconvulsive therapy (ECT) JS was supported by RCN no.273077.

BackgroundElectroconvulsive therapy (ECT) is an effective treatment against severe depressive episodes, which has been shown to induce volume changes in the hippocampus. The power spectrum of the electroencephalogram (EEG) follows a characteristic power-law relation but its utility as a metric of ECT-induced seizures has not been explored.ObjectiveThis study aims to evaluate a novel metric based on the power spectrum of the EEG recordings from ECT-induced seizures; its association to volume changes in the hippocampus following ECT and improvement in depression rating scores.MethodsDepressed patients treated with ECT underwent brain MRI before- and after treatment and the EEG from each seizure was recorded (N=29). Hippocampal volume changes and EEG parameters were recorded in addition to clinician-rated and self-reported measures of depressive symptoms. The slope of the power-law in the power spectral density of the EEG was calculated. Multivariate linear models relating seizure parameters to volume change or clinical outcome was systematically and successively simplified. The best models were selected according to Akaike’s information criterion.ResultsThe slope of the power-law was steeper in the right than the left hemisphere (p < 0.001). EEG measures were included in the best models of volume change for both hippocampi as well as in the models explaining clinical outcome (p = 0.014, p = 0.004).ConclusionsA novel EEG measures was explored and contributed in models explaining the variation in volume change in the hippocampus and in clinical outcome following ECT.

Mathematical modeling of neurons is an essential tool to investigate neuronal activity alongside with experimental approaches. However, the conventional modeling framework to simulate neuronal dynamics and extracellular potentials makes several assumptions that might need to be revisited for some applications. In this chapter we apply the EMI model to investigate the ephaptic effect and the effect of the extracellular probes on the measured potential. Finally, we introduce reduced EMI models, which provide a more computationally efficient framework for simulating neurons with complex morphologies.

Epileptic seizures are due to excessive and synchronous neural activity. Extensive modelling of seizures has been done on the neuronal level, but it remains a challenge to scale these models up to whole brain models. Measurements of the brain’s activity over several spatiotemporal scales follow a power-law distribution in terms of frequency. During normal brain activity, the power-law exponent is often found to be around 2 for frequencies between a few Hz and up to 150 Hz, but is higher during seizures and for higher frequencies. The Bidomain model has been used with success in modelling the electrical activity of the heart, but has been explored far less in the context of the brain. This study extends previous models of epileptic seizures on the neuronal level to the whole brain using the Bidomain model. Our approach is evaluated in terms of power-law distributions. The electric potentials were simulated in 7 idealized two-dimensional models and 3 three-dimensional patient-specific models derived from magnetic resonance images (MRI). Computed electric potentials were found to follow power-law distributions with slopes ranging from 2 to 5 for frequencies greater than 10–30 Hz.