In-vitro Recordings of Neural Magnetic Activity From the Auditory Brainstem Using Color Centers in Diamond: A Simulation Study

Magnetometry based on nitrogen-vacancy (NV) centers in diamond is a novel technique capable of measuring magnetic fields with high sensitivity and high spatial resolution. With the further advancements of these sensors, they may open up novel approaches for the 2D imaging of neural signals in vitro. In the present study, we investigate the feasibility of NV-based imaging by numerically simulating the magnetic signal from the auditory pathway of a rodent brainstem slice (ventral cochlear nucleus, VCN, to the medial trapezoid body, MNTB) as stimulated by both electric and optic stimulation. The resulting signal from these two stimulation methods are evaluated and compared. A realistic pathway model was created based on published data of the neural morphologies and channel dynamics of the globular bushy cells in the VCN and their axonal projections to the principal cells in the MNTB. The pathway dynamics in response to optic and electric stimulation and the emitted magnetic fields were estimated using the cable equation. For simulating the optic stimulation, the light distribution in brain tissue was numerically estimated and used to model the optogenetic neural excitation based on a four state channelrhodopsin-2 (ChR2) model. The corresponding heating was also estimated, using the bio-heat equation and was found to be low (<2°C) even at excessively strong optic signals. A peak magnetic field strength of ∼0.5 and ∼0.1 nT was calculated from the auditory brainstem pathway after electrical and optical stimulation, respectively. By increasing the stimulating light intensity four-fold (far exceeding commonly used intensities) the peak magnetic signal strength only increased to 0.2 nT. Thus, while optogenetic stimulation would be favorable to avoid artefacts in the recordings, electric stimulation achieves higher peak fields. The present simulation study predicts that high-resolution magnetic imaging of the action potentials traveling along the auditory brainstem pathway will only be possible for next generation NV sensors. However, the existing sensors already have sufficient sensitivity to support the magnetic sensing of cumulated neural signals sampled from larger parts of the pathway, which might be a promising intermediate step toward further maturing this novel technology.

Physics and biophysics fundamentals of transcranial stimulation

Transcranial stimulation induces or modulates neural activity in the brain through basic physical and biophysical processes. Transcranial electrical stimulation and transcranial magnetic stimulation impose an exogenous electric field in the brain that is determined by the stimulation device and the geometric and electric parameters of the head. The imposed electric field drives an electric current through the brain tissue, which macroscopically behaves as a volume conductor. The electric field polarizes neuronal membranes as described by the cable equation, resulting in direct activation of individual neurons and neural networks or indirect modulation of intrinsic activity. Computational modeling can estimate the delivered electric field as well as the resultant responses of individual neurons. This dosimetric information can be used to optimize and individualize stimulation targeting. The field distributions of transcranial stimulation are well understood and characterized, whereas analysis and modeling of the neural responses require further investigation, especially at the network level.

The Impact of Anomalous Diffusion on Action Potentials in Myelinated Neurons

Action potentials in myelinated neurons happen only at specialized locations of the axons known as the nodes of Ranvier. The shapes, timings, and propagation speeds of these action potentials are controlled by biochemical interactions among neurons, glial cells, and the extracellular space. The complexity of brain structure and processes suggests that anomalous diffusion could affect the propagation of action potentials. In this paper, a spatio-temporal fractional cable equation for action potentials propagation in myelinated neurons is proposed. The impact of the ionic anomalous diffusion on the distribution of the membrane potential is investigated using numerical simulations. The results show spatially narrower action potentials at the nodes of Ranvier when using spatial derivatives of the fractional order only and delayed or lack of action potentials when adding a temporal derivative of the fractional order. These findings could reveal the pathological patterns of brain diseases such as epilepsy, multiple sclerosis, and Alzheimer’s disease, which have become more prevalent in the latest years.

Electro-physiology Models of Cells with Spherical Geometry with Non-conducting Center

We study the flow of electrical currents in spherical cells with a non-conducting core, so that current flow is restricted to a thin shell below the cell’s membrane. Examples of such cells are fat storing cells (adipocytes). We derive the relation between current and voltage in the passive regime and examine the conditions under which the cell is electro-tonically compact. We compare our results to the well-studied case of electrical current flow in cylinder structures, such as neurons, described by the cable equation. In contrast to the cable, we find that for the sphere geometry (1) the voltage profile across the cell depends critically on the electrode geometry, and (2) the charging and discharging can be much faster than the membrane time constant; however, (3) voltage clamp experiments will incur similar distortion as in the cable case. We discuss the relevance for adipocyte function and experimental electro-physiology.