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Neuronal Coding

The human brain contains more than ten thousand densely packed neurons that are connected to an intricate network. In every small volume of cortex, thousands of spikes are emitted each millisecond. What is the information contained in such a spatio-temporal pattern of pulses? What is the code used by the neurons to transmit that information? How might other neurons decode the signal? As external observers, can we read the code and understand the message of the neuronal activity pattern? These questions point to the problem of neuronal coding, one of the fundamental issues in neuroscience. At present, a definite answer to these questions is not known. Traditionally it has been thought that most, if not all, of the relevant information was contained in the mean firing rate of the neuron. The firing rate is usually defined by a temporal average. The experimentalist sets a time window of, say T = 100 ms or T = 500 ms and counts the number of spikes n(T) that occur in this time window. Division by the length of the time window gives the mean firing rate usually reported in units of Hz (Gerstner et al, 2002).


Figure 1. Spike rate per sample before and after training. Blue bars are spike rate before training and red ones represent the spike rate after the training (Lakymchuk et al, 2015).

Spike Timing

A single neuron in vertebrate cortex often connects to more than ten thousand postsynaptic neurons. Many of its axonal branches end in the direct neighbourhood of the neuron, but the axon can also stretch over several centimetres so as to reach to neurons in other areas of the brain (Caruso et al, 2018)



Figure 2. A. Single neuron in a drawing by Ramon y Cajal. Dendrite, soma, and axon can be clearly distinguished. The inset shows an example of a neuronal action potential (schematic). The action potential is a short voltage pulse of 1-2 ms duration and an amplitude of about 100 mV. B. Signal transmission from a presynaptic neuron j to a postsynaptic neuron i. The synapse is marked by the dashed circle. The axons at the lower right end lead to other neurons (schematic figure) (Caruso et al, 2018)

Single neurons may encode simultaneous stimuli by switching between activity patterns. The brain preserves information about multiple simultaneous items. Single neurons can represent multiple stimuli by interleaving signals across time (Caruso et al, 2018).

The non-linear properties of single neurons “amplify” the effect of small electric fields: when concurrent to supra-threshold synaptic input, small electric fields can have significant effects on spike timing. The effects of NeuroCes™ Cranial Electrotherapy Stimulator's  electric fields on spike timing are amplified with decreasing synaptic input slope and increased cell susceptibility. The mechanisms by which endogenous electric fields generated by the brain itself (e.g. delta, theta, gamma) could 'feed-back' unto the brain. Small electric fields will polarize neurons by only a small amount; for this reason small electric fields have previously been suggested to have no physiologically relevant effects. However, the hypothesis that small felds can affect brain function has garnered support from phenomenological studies applying low intensity electrical stimulation to brain slices, the latter indeed showing a causal effect on slow wave oscillations and declarative memory. While neurons often encode information in their firing rate, the timing of individual action potentials (temporal coding) has also been shown to carry significant information (Radman et al, 2007).

Electric field induced changes in spike timing would be particularly relevant for temporal coding during coherent (synchronous) network activity. An additional synchronizing effect may result during recurrent network activity when small changes in time add up over multiple cycles. More than an epiphenomenon, the results indicate a functional role for field potentials in modulating spike timing. Research results support the development of therapeutic NeuroCes™ Cranial Electrotherapy Stimulation technologies targeting neuronal timing; abnormal timing is indeed a hallmark of many neurological disorders and sub-threshold stimulation approaches may be readily adapted for non-invasive Cranial Electrotherapy Stimulation technologies (Radman et al, 2007). Accurate spike timing is emerging as an important concept in the encoding of sensory stimuli. NeuroCes™ Cranial Electrotherapy Stimulation can change the timing of the firing pattern.

Membrane potential dynamics of a single neuron with simplified membrane model.


Figure 3. After several incoming spikes, the membrane potential surpasses threshold and neuron fires a postsynaptic spike. For better visibility, neuron potential is increased twice for one TU after spiking. During refractory period, neuron does not change its potential. For visibility, neuron potential is shown with offset +100 (Lakymchuk et al, 2015).


Cerebrospinal Fluid and Plasma Neurochemicals

NeuroCes™ Cranial Electrotherapy Stimulator induces changes in neurohormones and neurotransmitters in various psychiatric diseases particularly in depression, and anxiety disorders. Cranial Electrotherapy Stimulation (CES) increases blood level of Beta-Endorphin and Serotonin immediately and may lead over a 2 week period to homeostasis of Serotonin in depressed patients (Shealy et al., 1989). 


Cerebrospinal fluid and plasma levels of five neurochemicals including serotonin, beta-endorphin, melatonin, norepinephrine and cholinesterase measured in five asymptomatic, normal subjects at rest and after 20 minutes of Cranial Electrotherapy Stimulation (CES) have been reported by Shealy et al,1989. Although cerebrospinal fluid levels of serotonin and beta-endorphin rise to a greater extent with CES, beta-endorphin, serotonin and melatonin appear to change significantly in plasma and provide observations of clinical interest. Plasma levels of norepinephrine appear to change moderately after CES. Hypothalamic modulation may explain the reported antidepressant effect of CES (Shealy et al, 1989). Figure 4 and Figure 5 show increased maximum level of neurochemicals in cerebrospinal and plasma in five asymptomatic, normal subjects.

Cranial Electrotherapy Stimulation of serotonergic neurons in the central nervous system (CNS) could act directly on the hypothalamus, causing release of hypothalamic releasing hormones (Liss S, Liss B, 1996).

Percentage Change of Neurochemicals in Plasma

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Figure 4. Percentage change of neurochemicals in plasma in asymptomatic, normal subjects after 20 minutes of CES (Shealy et al,1989).

Percentage Change of Neurochemicals in Cerebrospinal Fluid

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Figure 5. Percentage change of neurochemicals in cerebrospinal fluid in asymptomatic, normal subjects after 20 minutes of CES (Shealy et al,1989).

The difference in the levels of blood plasma serotonin, tryptophan, cortisol and ACTH following Cranial Electrotherapy Stimulation has been evaluated by Closson. Measurements of the serum concentration of each of the agents listed in Figure 6 were made before stimulation and 10 minutes after conclusion of a 20-minute treatment (Closson, Win. J. 1988).

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Figure 6. The difference in the levels of blood plasma biochemicals following 20 min. CES Stimulation.

Potential and Current Density Distributions

According to the study “Potential and Current Density Distributions of Cranial Electrotherapy Stimulation (CES) in a Four-Concentric-Spheres Model” conducted at the Biomedical Engineering Program of the University of Texas at Austin, based on the radial current density simulation, the maximum injected current density by the CES therapy, using a standard 1 mA stimulus, is about 5 µA/cm2 reaches the thalamic area at a radius of 13.30 mm of the model. This demonstrated that the CES electrical field as a facilitating stimulus could cause the release of neurotransmitters responsible for physiological effects (Ferdjallah et. al., 1996).


Figure 7. The four concentric spheres model of the human head representing the brain tissue, the cerebrospinal fluid, the skull, and the scalp.

Quantitative EEG and Low Resolution Tomography

The effects of cranial electrotherapy stimulation (CES) on human EEG and brain current density were evaluated by quantitative electroencephalography (qEEG) and low resolution brain electromagnetic tomography (LORETA) by Kennerly, 2006.


According to Kennerly’s study, changes in quantitative EEG and low resolution tomography following cranial electrotherapy stimulation, in 2006, the qEEG tests revealed that in 0.5 Hz frequency of CES there was a significant increase in alpha relative power (8 - 12 Hz) with concomitant decreases in delta (0 - 3.5 Hz) and beta relative power (12.5 - 30 Hz). The 0.5 Hz CES decreased a wide frequency range of delta activity. The changes found in qEEG relative power were consistent with the affective and cognitive effects of CES reported in the literature, such as increased relaxation and decreased anxiety.


Visual comparison of the relative power spectral display at baseline and after the stimulus revealed a consistent pattern of an increase in alpha activity with concomitant decreases in delta and beta activity (Figure 8.a and Figure 8.b). In some records a bimodal distribution appeared in the post CES spectral display that was not present in the baseline condition (Kennerly, 2006).

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Relative Pover (%)

Baseline Spectral EEG (0.5 Hz CES)

Frequench (Hz)

Figure 8.a. Relative power EEG spectra of a single individual before 0.5 Hz CES.

Relative power EEG spectra.png

Relative Pover (%)

Spectral EEG after 20 Minutes of 0.5 Hz CES

Frequench (Hz)

Figure 8.b. Relative power EEG spectra of a single individual after 0.5 Hz CES. There is an increase in alpha power with decreases in delta and beta Power. The bimodal distribution of the spectral EEG after CES is a response variant found in some individuals.

A Relative Power Topographical Map of activity shown in Figure 9 can represent the same information in a graphical manner that more clearly conveys the pattern of change by location (Kennerly, 2006):

FFT Relative Power Tomographical Map, 0.5 Hz CES

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Figure 9. Relative power p-value topographical map for 0.5 Hz CES. Statistically significant changes (0.05 or better) after 0.5 Hz CES are indicated by color; white indicates no significant change. The arrows indicate the direction of change. Statistically significant decreases were seen in delta and beta with statistically significant increases in alpha.

Functional Magnetic Resonance Imaging (fMRI)

The immediate effects of CES stimulation on patterns of brain activity in the resting state, and on functional connectivity within intrinsic connectivity networks using functional neuroimaging simultaneously with cranial stimulation have been determined by Feusner et al, 2012.

CES causes cortical brain deactivation in midline prefrontal and parietal regions. CES thus appears to result in similar cortical deactivation patterns for different frequencies but is associated with stronger alterations in functional connectivity for higher frequency. Cortical deactivation patterns differ from those associated with current intensity, suggesting that cortical deactivation may depend more on frequency than intensity of stimulation (Feusner et al, 2012).


Figure 10. Regions of decreased brain activity as a result of cranial electrotherapy stimulation (CES) for  0.5-Hz stimulation (blue), 100-Hz stimulation (yellow), and regions of overlap between the two frequencies (green).

NeuroCes™ stimulation may result in cortical deactivation, as well as altering brain connectivity in the default mode network (DMN) after 20 minutes of treatment.


Gerstner et al, 2002. Spiking Neuron Models. Single Neurons, Populations, Plasticity. Cambridge University Press, 2002.

Lakymchuk et al, 2018. Simplified spiking neural network architecture and STDP learning algorithm applied to image Classification. EURASIP Journal on Image and Video Processing (2015) 2015:4 DOI 10.1186/s13640-015-0059-4.


Caruso et al, 2018. Single neurons may encode simultaneous stimuli by switching between activity patterns. Nature Communications | (2018) 9:2715 | DOI: 10.1038/s41467-018-05121-8.


Radman et al, 2007 Spike timing amplifies the effect of electric fields on neurons: implications for endogenous field-effects. Department of Biomedical Engineering, City College of the City University of New York, New York, NY 10031. The Journal of Neuroscience, in press, 2007.


Shealy et al,1989. Depression: A Diagnostic, Neurochemicals Profile & Therapy with Cranial Electrotherapy Stimulation (CES). The Journal of Neurological & Orthopaedic Medicine & Surgery, 1989.


Liss S, Liss B., 1996. Physiological and therapeutic effects of high frequency electrical pulses. Integr Physiol Behav Sci 1996;31:88–96.

Closson, Win. J. 1988. Changes in Blood Biochemical Levels following Treatment with TENS Devices of Differing Frequency Composition, private experiment partially funded by Pain Suppression Labs Inc.

Ferdjallah et. al, 1996. Potential and current density distributions of cranial electrotherapy stimulation (CES) in a four concentric-spheres model. IEEE Trans Biomed Eng 1996;43:939–43.


Kennerly, Richard C, 2006. Changes in quantitative EEG and low resolution tomography following cranial electrotherapy stimulation. August 2006, 425 pp., 81 tables, 233 figures, 171 references.


Feusner JD, et al.,2012,  Effects of Cranial Electrotherapy Stimulation on resting state brain activity. Brain Behav 2012;2(3):211–20.

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