A mathematical model of ephaptic interactions in neuronal fiber pathways: Could there be more than transmission along the tracts?

Multiple Neuronal Processes, Including the Mauthner Axon, Form a Multi-Axial Fiber Within a Common Myelin Sheath in the Central Nervous System of Adult Lungfishes, Protopterus annectens, Lepidosiren paradoxa, and Neoceratodus forsteri

Mauthner cells are found in most fish and amphibians. The prominence of their large fiber is commonly used as one criterion to identify the presence of these cells in fish and the largest of these fibers have been reported in lungfish. While some authors believe that Mauthner fibers in lungfish contain a single axon, others report that many processes join the Mauthner axon (M-axon) inside a common myelin sheath to form a "multi-axial fiber." To distinguish between these two possibilities, we have used light and transmission electron microscopy to determine whether multi-axial fibers exist in African, Protopterus annectens, Australian, Neoceratodus forsteri, and South American, Lepidosiren paradoxa, lungfish. Ultrastructural analysis provides evidence of a multi-axial fiber that contains a M-axon, non-M-axons and glial processes within a common myelin sheath. The glial processes form myelin and paranodal-like structures. Stacked desmosome-like structures have been identified that may be part of Schmidt-Lanterman incisures. We discuss how the electrical activity of a select group of axons may affect that of other axons within a common myelin sheath.

Metabolic implications of axonal demyelination and its consequences for synchronized network activity: An in silico and in vitro study

Myelination enhances the conduction velocity of action potentials (AP) and increases energy efficiency. Thick myelin sheaths are typically found on large-distance axonal connections or in fast-spiking interneurons, which are critical for synchronizing neuronal networks during gamma-band oscillations. Loss of myelin sheath is associated with multiple alterations in axonal architecture leading to impaired AP propagation. While numerous studies are devoted to the effects of demyelination on conduction velocity, the metabolic effects and the consequences for network synchronization have not been investigated. Here we present a unifying computational model for electrophysiology and metabolism of the myelinated axon. The computational model suggested that demyelination not only decreases the AP speed but AP propagation in demyelinated axons requires compensatory processes like mitochondrial mass increase and a switch from saltatory to continuous propagation to rescue axon functionality at the cost of reduced AP propagation speed and increased energy expenditure. Indeed, these predictions were proven to be true in a culture model of demyelination where the pharmacologically-induced loss of myelin was associated with increased oxygen consumption rates, and a significant broadening of bandwidth as well as a decrease in the power of gamma oscillations.

Organotopic organization of the porcine mid-cervical vagus nerve

Introduction

Despite detailed characterization of fascicular organization of somatic nerves, the functional anatomy of fascicles evident in human and large mammal cervical vagus nerve is unknown. The vagus nerve is a prime target for intervention in the field of electroceuticals due to its extensive distribution to the heart, larynx, lungs, and abdominal viscera. However, current practice of the approved vagus nerve stimulation (VNS) technique is to stimulate the entire nerve. This produces indiscriminate stimulation of non-targeted effectors and undesired side effects. Selective neuromodulation is now a possibility with a spatially-selective vagal nerve cuff. However, this requires the knowledge of the fascicular organization at the level of cuff placement to inform selectivity of only the desired target organ or function.

Methods and results

We imaged function over milliseconds with fast neural electrical impedance tomography and selective stimulation, and found consistent spatially separated regions within the nerve correlating with the three fascicular groups of interest, suggesting organotopy. This was independently verified with structural imaging by tracing anatomical connections from the end organ with microCT and the development of an anatomical map of the vagus nerve. This confirmed organotopic organization.

Discussion

Here we show, for the first time, localized fascicles in the porcine cervical vagus nerve which map to cardiac, pulmonary and recurrent laryngeal function (N = 4). These findings pave the way for improved outcomes in VNS as unwanted side effects could be reduced by targeted selective stimulation of identified organ-specific fiber-containing fascicles and the extension of this technique clinically beyond the currently approved disorders to treat heart failure, chronic inflammatory disorders, and more.

Improving the study of brain-behavior relationships by revisiting basic assumptions

Neuroimaging research has been at the forefront of concerns regarding the failure of experimental findings to replicate. In the study of brain-behavior relationships, past failures to find replicable and robust effects have been attributed to methodological shortcomings. Methodological rigor is important, but there are other overlooked possibilities: most published studies share three foundational assumptions, often implicitly, that may be faulty. In this paper, we consider the empirical evidence from human brain imaging and the study of non-human animals that calls each foundational assumption into question. We then consider the opportunities for a robust science of brain-behavior relationships that await if scientists ground their research efforts in revised assumptions supported by current empirical evidence.

Nine insights from internet engineering that help us understand brain network communication

Philosophers have long recognized the value of metaphor as a tool that opens new avenues of investigation. By seeing brains as having the goal of representation, the computer metaphor in its various guises has helped systems neuroscience approach a wide array of neuronal behaviors at small and large scales. Here I advocate a complementary metaphor, the internet. Adopting this metaphor shifts our focus from computing to communication, and from seeing neuronal signals as localized representational elements to seeing neuronal signals as traveling messages. In doing so, we can take advantage of a comparison with the internet's robust and efficient routing strategies to understand how the brain might meet the challenges of network communication. I lay out nine engineering strategies that help the internet solve routing challenges similar to those faced by brain networks. The internet metaphor helps us by reframing neuronal activity across the brain as, in part, a manifestation of routing, which may, in different parts of the system, resemble the internet more, less, or not at all. I describe suggestive evidence consistent with the brain's use of internet-like routing strategies and conclude that, even if empirical data do not directly implicate internet-like routing, the metaphor is valuable as a reference point for those investigating the difficult problem of network communication in the brain and in particular the problem of routing.

Angular gyrus: an anatomical case study for association cortex

The angular gyrus is associated with a spectrum of higher order cognitive functions. This mini-review undertakes a broad survey of putative neuroanatomical substrates, guided by the premise that area-specific specializations derive from a combination of extrinsic connections and intrinsic area properties. Three levels of spatial resolution are discussed: cellular, supracellular connectivity, and synaptic micro-scale, with examples necessarily drawn mainly from experimental work with nonhuman primates. A significant factor in the functional specialization of the human parietal cortex is the pronounced enlargement. In addition to "more" cells, synapses, and connections, however, the heterogeneity itself can be considered an important property. Multiple anatomical features support the idea of overlapping and temporally dynamic membership in several brain wide subnetworks, but how these features operate in the context of higher cognitive functions remains for continued investigations.

Knösche T. Modelling the effect of ephaptic coupling on spike propagation in peripheral nerve fibres

Experimental and theoretical studies have shown that ephaptic coupling leads to the synchronisation and slowing down of spikes propagating along the axons within peripheral nerve bundles. However, the main focus thus far has been on a small number of identical axons, whereas realistic peripheral nerve bundles contain numerous axons with different diameters. Here, we present a computationally efficient spike propagation model, which captures the essential features of propagating spikes and their ephaptic interaction, and facilitates the theoretical investigation of spike volleys in large, heterogeneous fibre bundles. We first lay out the theoretical basis to describe how the spike in an active axon changes the membrane potential of a passive axon. These insights are then incorporated into the spike propagation model, which is calibrated with a biophysically realistic model based on Hodgkin-Huxley dynamics. The fully calibrated model is then applied to fibre bundles with a large number of axons and different types of axon diameter distributions. One key insight of this study is that the heterogeneity of the axonal diameters has a dispersive effect, and that a higher level of heterogeneity requires stronger ephaptic coupling to achieve full synchronisation between spikes.

The Narrowed Internal Auditory Canal: A Distinct Etiology of Pediatric Vestibular Paroxysmia

Vestibular paroxysmia (VP) is a disorder encountered in the pediatric population that etiology has been attributed to neurovascular cross-compression syndrome (NVCC). The purpose of this study was to report a new probable pathological condition, the narrowed internal auditory canal (IAC), which appears to be involved in the development of a clinical picture of VP in the pediatric population. A retrospective descriptive comparative study was conducted to compare clinical, electrophysiological, radiological, and therapeutic outcomes in both etiologies. Overall, 16 pediatric patients suffering from VP were included and divided into two groups: patients with narrowed internal auditory (Group 1) were compared to those with NVCC syndrome (Group 2). Patients in both groups were similar in terms of auditory complaints, as well as hearing, vestibular, and electrophysiological status. A narrowed IAC was encountered in the adolescent age category and females, especially those with rapid growth. The diagnosis requires a careful analysis of the shape and diameters of the IAC. Radiologic measurements in the axial plane do not seem to be sufficient to confirm the diagnosis, and, therefore, an analysis of diameters in the coronal plane is required. Treatment with sodium-channel blockers drugs showed promising results not only by relieving vertigo but also by normalizing the electrophysiological findings. In conclusion, a narrowed IAC can be considered in patients suffering from VP.

Edges in brain networks: Contributions to models of structure and function

Network models describe the brain as sets of nodes and edges that represent its distributed organization. So far, most discoveries in network neuroscience have prioritized insights that highlight distinct groupings and specialized functional contributions of network nodes. Importantly, these functional contributions are determined and expressed by the web of their interrelationships, formed by network edges. Here, we underscore the important contributions made by brain network edges for understanding distributed brain organization. Different types of edges represent different types of relationships, including connectivity and similarity among nodes. Adopting a specific definition of edges can fundamentally alter how we analyze and interpret a brain network. Furthermore, edges can associate into collectives and higher order arrangements, describe time series, and form edge communities that provide insights into brain network topology complementary to the traditional node-centric perspective. Focusing on the edges, and the higher order or dynamic information they can provide, discloses previously underappreciated aspects of structural and functional network organization.

Dissecting whole-brain conduction delays through MRI microstructural measures

Network models based on structural connectivity have been increasingly used as the blueprint for large-scale simulations of the human brain. As the nodes of this network are distributed through the cortex and interconnected by white matter pathways with different characteristics, modeling the associated conduction delays becomes important. The goal of this study is to estimate and characterize these delays directly from the brain structure. To achieve this, we leveraged microstructural measures from a combination of advanced magnetic resonance imaging acquisitions and computed the main determinants of conduction velocity, namely axonal diameter and myelin content. Using the model proposed by Rushton, we used these measures to calculate the conduction velocity and estimated the associated delays using tractography. We observed that both the axonal diameter and conduction velocity distributions presented a rather constant trend across different connection lengths, with resulting delays that scale linearly with the connection length. Relying on insights from graph theory and Kuramoto simulations, our results support the approximation of constant conduction velocity but also show path- and region-specific differences.

Modeling seizures: From single neurons to networks

Dynamical system tools offer a complementary approach to detailed biophysical seizure modeling, with a high potential for clinical applications. This review describes the theoretical framework that provides a basis for theorizing certain properties of seizures and for their classification according to their dynamical properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. This narrative review provides an accessible overview of this field, including non-exhaustive examples of key recent works.

Ephaptic coupling in white matter fibre bundles modulates axonal transmission delays

Axonal connections are widely regarded as faithful transmitters of neuronal signals with fixed delays. The reasoning behind this is that extracellular potentials caused by spikes travelling along axons are too small to have an effect on other axons. Here we devise a computational framework that allows us to study the effect of extracellular potentials generated by spike volleys in axonal fibre bundles on axonal transmission delays. We demonstrate that, although the extracellular potentials generated by single spikes are of the order of microvolts, the collective extracellular potential generated by spike volleys can reach several millivolts. As a consequence, the resulting depolarisation of the axonal membranes increases the velocity of spikes, and therefore reduces axonal delays between brain areas. Driving a neural mass model with such spike volleys, we further demonstrate that only ephaptic coupling can explain the reduction of stimulus latencies with increased stimulus intensities, as observed in many psychological experiments.

Axonal fibre bundles that connect distant cortical areas contain millions of densely packed axons. When synchronous spike volleys travel through such fibre bundles, the extracellular potential within the bundles is perturbed. We use computer simulations to examine the magnitude and shape of this perturbation, and demonstrate that it is sufficiently strong to affect axonal transmission speeds. Since most spikes within a spike volley are positioned in an area where the extracellular potential is negative (relative to a distant reference), the resulting depolarisation of the axonal membranes accelerates the spike volley on average. This finding is in contrast to previous studies of ephaptic coupling effects between axons, where ephaptic coupling was found to slow down spike propagation. Our finding has consequences for information transmission and synchronisation between cortical areas.

The Continuum Between Temperament and Mental Illness as Dynamical Phases and Transitions

The full range of biopsychosocial complexity is mind-boggling, spanning a vast range of spatiotemporal scales with complicated vertical, horizontal, and diagonal feedback interactions between contributing systems. It is unlikely that such complexity can be dealt with by a single model. One approach is to focus on a narrower range of phenomena which involve fewer systems but still cover the range of spatiotemporal scales. The suggestion is to focus on the relationship between temperament in healthy individuals and mental illness, which have been conjectured to lie along a continuum of neurobehavioral regulation involving neurochemical regulatory systems (e.g., monoamine and acetylcholine, opiate receptors, neuropeptides, oxytocin), and cortical regulatory systems (e.g., prefrontal, limbic). Temperament and mental illness are quintessentially dynamical phenomena, and need to be addressed in dynamical terms. A meteorological metaphor suggests similarities between temperament and chronic mental illness and climate, between individual behaviors and weather, and acute mental illness and frontal weather events. The transition from normative temperament to chronic mental illness is analogous to climate change. This leads to the conjecture that temperament and chronic mental illness describe distinct, high level, dynamical phases. This suggests approaching biopsychosocial complexity through the study of dynamical phases, their order and control parameters, and their phase transitions. Unlike transitions in physical systems, these biopsychosocial phase transitions involve information and semiotics. The application of complex adaptive dynamical systems theory has led to a host of markers including geometrical markers (periodicity, intermittency, recurrence, chaos) and analytical markers such as fluctuation spectroscopy, scaling, entropy, recurrence time. Clinically accessible biomarkers, in particular heart rate variability and activity markers have been suggested to distinguish these dynamical phases and to signal the presence of transitional states. A particular formal model of these dynamical phases will be presented based upon the process algebra, which has been used to model information flow in complex systems. In particular it describes the dual influences of energy and information on the dynamics of complex systems. The process algebra model is well-suited for dealing with the particular dynamical features of the continuum, which include transience, contextuality, and emergence. These dynamical phases will be described using the process algebra model and implications for clinical practice will be discussed.