**3.2 Cortico-limbocortical neuronal networks**

Theta activity in hippocampal networks (**Figure 8**) seems to represent a dynamic state emerging from engaging in the task of spatial navigation and memory retrieval processes. Larger theta activity has been seen in the left anterior hippocampus and parahippocampal cortex during goal-directed navigation compared to purposeless movements. Theta oscillations are also frequent during memory processing and more so during recall than learning tasks [60].

The major input to the Hippocampus is from the Entorhinal Cortex (EC) which is strongly and reciprocally connected with many cortical and subcortical structures. Different thalamic nuclei (anterior and midline groups), the medial septum (medial septal nucleus and diagonal band of Broca), the supramammillary nucleus of the hypothalamus, the raphe nuclei and locus coeruleus of the brainstem, are connected with the entorhinal cortex which serves as the interface between neocortical (e.g. parahippocampal gyrus and perirhinal cortex) and subcortical structures, and the hippocampus (**Figure 9**) [61].

The direct perforant pathway (axons from EC layer III) forms synapses on the very distal apical dendrites of CA1 neurons (monosynaptic circuit). The indirect perforant pathway (axons from EC layer II) reaches CA1 via the trisynaptic circuit: Granule cells in the Dentate Gyrus (first synapse), via the mossy fibers to pyramidal neurons in CA3 (second synapse), and via the Schaffer collaterals to pyramidal neurons in CA1 (third synapse). The major output of the Hippocampus is axons from CA1 projecting back directly and via the Subiculum to the Entorhinal Cortex, completing the trisynaptic circuit (**Figure 8**) [62]. The trisynaptic circuit of the hippocampus is organized transversely along the hippocampus. Association and commissural fibers are organized along the anteroposterior axis [63].

Hilar mossy cells and CA3 pyramidal cells give rise to ipsilateral hippocampal association fibers (to the dendrites of granule cells and GABAergic interneurons of the inner molecular layer of the dentate gyrus) and contralateral commissural fibers

#### **Figure 8.**

*By original: Santiago Ramón y Cajal (1852–1934) derivative = Looie496 - File:CajalHippocampus.jpeg from: Santiago Ramón y Cajal (1911) [1909] Histologie du Système nerveux de l&#039;Homme et des Vertébrés, Paris: A. Maloine, Public Domain, https://commons.wikimedia.org/w/index.php?curid=3908039.*

*Clinical Neurophysiology of Epileptogenic Networks DOI: http://dx.doi.org/10.5772/intechopen.104952*

#### **Figure 9.**

*The septal-hippocampal-thalamo-cortical axis. Overview of the complex interactive circuitry of excitatory, inhibitory and modulatory components, underlying some of the structural and functional connectivity of the limbocortical networks with clinical implications for the pharmacological and neurosurgical/neurostimulation treatment strategies of epilepsy.*

(terminating on principal cells and interneurons of CA3, CA2 and CA1 regions), passing through the dorsal and ventral hippocampal commissures to reach the contralateral hippocampus and dentate gyrus. Hippocampal commissural connections are mainly excitatory and seem to be less abundant and evolutionary declined in monkey and humans [64].

Schaffer collaterals are axon collaterals from the CA3 pyramidal cells of the ipsilateral and contralateral hippocampi and project information to the pyramidal neurons of the CA1 hippocampal area. The Schaffer collateral synapses represent excitatory (positive feedback) glutamatergic synapses that assist activity-dependent plasticity and development of memory processing and formation [65]. Basket cells in CA3 receive excitatory input from the pyramidal cells and provide inhibitory feedback to the pyramidal cells. This recurrent inhibition is a powerful feedback circuit that can dampen excitatory responses and shape up the oscillatory activity of the hippocampus [66]. The hippocampal trisynaptic loop with so extensive feedforward and feedback projections constitutes a fundamental mechanism of recurrent controlled excitation underpinning memory, learning and emotion in the limbocortical networks (Papez circuit) (**Figure 10**).

There are many brain structures that transmit information to and from the trisynaptic circuit and their activity can be directly or indirectly modulated by the activity of the trisynaptic loop. A major output goes via the fornix to the lateral septal area and to the mammillary body of the hypothalamus and additional output pathways go to other cortical areas including the anterior cingulate and prefrontal cortex.

#### **Figure 10.**

*Limbic system or circuit of Papez. Modified with permission from Weininger et al. [67]. OFC: orbitofrontal cortex, FP: frontopolar, PFC: prefrontal cortex, SSMA: supplementary sensorimotor area, PMC: primary motor cortex, PSSC: primary somatosensory cortex, PPC: posterior parietal cortex, PC: precuneus, C: cuneus.*

The crura of the fornix form connections through the corpus callosum and the hippocampal commissures with bilateral hippocampal formations. The CA3 is connected to the lateral and medial septum via the alveus and the fimbria fornix. The CA1 and the subiculum are connected to parahippocampal regions, the entorhinal cortex and nucleus accumbens, and project to septal nuclei, preoptic nuclei, ventral striatum, orbital cortex and anterior cingulate cortex (via the precommissural fornix) and to the anterior and lateral dorsal nuclei of the thalamus, the mammillary bodies, and ventromedial hypothalamus (via the postcommissural fornix) [68].

The mammillary bodies receive information from the hippocampal formation via the fornix and relay information to the anterior nuclei of the thalamus and the anterior cingulate cortex (Brodmann 24, 32, 33) via the mammillothalamic tract. The subiculum relays information to the posterior cingulate cortex (Brodmann 23). Via the cingulate gyrus and the thalamic nuclei primary sensory and association cortical areas can be reached which integrate information at a higher level attending to complex stimuli in the external and internal environments (**Figure 10**). The temporal association cortex identifies the nature of stimuli (perception), while the frontal association cortex plans responses to the stimuli (behaviour). The association cortex projects to other association cortical areas and to subcortical structures including the hippocampus, thalamus, basal ganglia, cerebellum and brainstem [33]. The hippocampus receives modulatory input from the serotoninergic, noradrenergic and dopaminergic systems, the amygdala, the nucleus reuniens of thalamus and the medial septum. The supramammillary nucleus of the hypothalamus is strongly connected via the medial forebrain bundle to the medial septum, diencephalon and brainstem. The medial septum (medial septal nucleus and diagonal band of Broca) sends cholinergic (65%) and GABAergic fibers to CA1 and glutamatergic fibers to all parts of the hippocampus (**Figure 9**) [34].

Theta (4–12 Hz) high amplitude oscillations of the hippocampal CA1 pyramidal cells emerge during active exploration, voluntary movements, rapid eye movement (REM) sleep and certain brain states related to arousal [69]. Type 1 (fast theta oscillations) associated with spatial navigation and movement are driven by atropineresistant inputs on the distal dendrites, whereas Type 2 (slow theta oscillations) associated with arousal and anxiety on sensory salience are driven by atropine-sensitive inputs on the somata, and chloride (Cl)-mediated inhibitory postsynaptic potentials

*Clinical Neurophysiology of Epileptogenic Networks DOI: http://dx.doi.org/10.5772/intechopen.104952*

on pyramidal cells. Although in vitro experiments suggest that theta oscillations can be intrinsically generated in the hippocampal excitatory—inhibitory networks, in vivo studies suggest that the supramammillary-septal-hippocampal loop is crucial for the generation and modulation of theta local-field potential oscillations in the hippocampus [70]. The hippocampus is a highly epileptogenic structure and part of an extensive network (limbic system) that involves all 4 neocortical lobes, the diencephalon/thalamus and the brainstem (**Figure 10**). The medial septum and the anterior nucleus of the thalamus could critically influence and/or allow propagation of seizures from and into the neocortex (**Figure 9**) and therefore have both been studied as a site of neurostimulation in human [71] and in animals with optogenetics [72].

#### **3.3 Neuronal network physiological dynamics**

We start by simulating a rudimental recurrent neuronal network of randomly connected 1000 neurons in real time (**Figure 11**). In the raster plots of network neurons, every excitatory neuron is represented by a black dot and every inhibitory neuron is represented by a red dot. The neuronal activity is manifested between 200 ms and 700 ms (within a 0.5 s interval). The graphs below the raster plots depict the cumulative spiking activity of all neurons (mV vs. ms) during the same time interval; the spikes of the excitatory neurons are depicted with blue and the spikes of the inhibitory neurons are depicted with red.

In our initial recurrent neuronal network (the first raster plot and cumulative spikogram below on the left of **Figure 12**), we omitted all inhibitory neuronal activity; this resulted in a very unstable network which rapidly went out of control, with all

#### **Figure 11.**

*Abstract state-space representation of the components of a recurrent neuronal network across different layers. The letters X, H, Z and Y represent sets of input [X], output [Y] and state variables [H, Z] in the form of state vectors related by differential or difference equations, whose values evolve over time depending on the values they have at any given time and the externally imposed values of input variables. The values of output variables depend on the state variables.*

#### **Figure 12.**

*Recurrent neuronal network without inhibition (on the left) and with inhibition (on the right). As soon as a tiny amount ( 1%) of recurrent inhibitory neurons were introduced into our random network, not only the spiking neuronal network gets effectively stabilized under such small inhibitory control, but starts also displaying quite complex rhythmical patterns and collective oscillatory behavior of self-organized neuronal assemblies. This is what we would describe as* order emerging out of chaos*. At the meso/macroscopic level, quasi-linear phenomena (oscillations of delta, theta, alpha, beta and gamma range and the harmonics thereof) can emerge on the large scale of neuronal networks despite the complex non-linear and stochastic dynamics that govern the behavior of single neurons at the microscopic level.*

excitatory neurons depolarising up to hundreds of millivolts: with such high voltages a small volume of cortex would literally thermocoagulate!

Biologically this is of course not plausible. In vivo when the membrane potential of any excitatory cell shoots up and remains above 25 mV without returning to its resting baseline level of 65 mV, the cell goes into a so-called *depolarization block* where Na<sup>+</sup> channels enter an inactivated state equivalent to the absolute refractory state of neurons (**Figure 3**). If there is sufficient Na-K-ATPase activity, energy supply and adequate time, allowing the electrochemical gradients to be restored over time, the neuron enters a relative refractory period and the Na+ channels resume an active state in which they can open up again upon critical fluctuations in the membrane potential that reach/surpass threshold level. Therefore, ongoing *repolarization* of excitatory pyramidal cells (facilitated by inhibitory interneurons) is essential in maintaining the critical membrane potential fluctuations that drive both physiological and epileptogenic network oscillations.

Motivated by the anatomy of the mammalian cortex [28], we choose the ratio of excitatory to inhibitory neurons to be 4 to 1, and we make the inhibitory synaptic connections stronger about 4 times. Besides the synaptic input, each neuron receives a noisy external (thalamic) input. In principle, one can use *Regular Spiking* (RS) cells to

#### *Clinical Neurophysiology of Epileptogenic Networks DOI: http://dx.doi.org/10.5772/intechopen.104952*

model all excitatory neurons and *Fast Spiking* (FS) cells to model all inhibitory neurons [37]. Based on the *Izhikevich* model, our neuronal spiking network exhibits rich cortical-like asynchronous spiking dynamics (**Figure 5**); neurons fire Poisson spiketrains with random firing rates varying from 0 to 25 Hz (similar to the firing-rate range of most cortical pyramidal neurons). Darker vertical linear areas emerge in our raster plots (on the right of **Figure 12**) that indicate that there are episodes of synchronized firing in the alpha and gamma frequency range (around 10 and 40 Hz, respectively). Although the network is connected randomly without any synaptic plasticity, the neurons, whether excitatory or inhibitory, when firing tend to selforganize into assemblies and exhibit rather collective rhythmical behavior across a wide range of frequencies corresponding to physiological rhythmical EEG activities (delta, theta, alpha, beta and gamma range) in the awake and sleep state of the mammalian cortex.

As the number of external input neurons varies from 1 to 500 (external drive increases), so does the number of oscillatory cycles (**Figures 13** and **14**). For example, for <10 neuron input no collective rhythmical activity is generated, for 10–25 input neurons a 2 Hz (slow delta) oscillatory activity is generated, for 25–50 input neurons a 2–4 Hz (delta) oscillatory activity is generated, for 50–100 input neurons a 4–6 Hz (slow theta) oscillatory activity is generated, for 100–150 input neurons a 6–8 Hz (fast theta) oscillatory activity is generated, for 150–250 input neurons a 8–10 Hz (lower alpha) oscillatory activity is generated, for 250–400 input neurons a 10-12 Hz (higher alpha) oscillatory activity is generated, for 350–500 input neurons a 12–18 Hz (fast/ beta) oscillatory activity is generated.

As we keep varying a few critical conditions in the continuous parameter space of our neuronal network model, a vast amount of variation can be introduced under scale transformation in the complex oscillatory behavior of the neuronal network. Our neuronal spiking network model can also simulate an allocortical septal-hippocampal network. The external driving input in a limbocortical neuronal network would be coming from the medial septum (integral part of the supramammillary-septal-hippocampal loop). Such a simulation requires a different ratio of excitatory to inhibitory neurons with perhaps stronger synaptic strengths, reflecting the strong perisomatic inhibition by parvalbumin-positive basket cells (generating Sharp-Wave Ripples and Gamma Oscillations in hippocampal models) [34, 49, 66, 68, 70].

#### **Figure 13.**

*Complex rhythmical patterns and collective oscillatory behaviour of self-organised neuronal assemblies (oscillations of delta, theta, and alpha range).*

**Figure 14.** *Complex rhythmical patterns and collective oscillatory behavior of self-organized neuronal assemblies (oscillations in the beta and low gamma frequency range).*

#### **3.4 Neuronal network epileptogenic dynamics**

While varying the aforementioned network parameters in our *local neocortical or allocortical* network simulation, the most interesting and unexpected behaviour of our network model was the emergence of erratic stochastic bursting of transient (spiking) neuronal activity outside the anticipated interval of 200-700 ms. This was initially an isolated event, quickly brought under control by a concomitant surge of local inhibitory activity (please see raster plot on the left and cumulative spikogram under in **Figure 15**). This stochastic type of bursting activity was reminiscent of an isolated and fairly limited paroxysmal depolarization [73] that died out as a result of sufficient or effective *local inhibitory control* [74]. On a macroscopic scale a *paroxysmal depolarization shift* could appear like an *interictal epileptiform discharge* on intracranial (iEEG) [74] and extracranial (scalp EEG) recordings [73].

At that stage the thalamic or septal input into our network was random noise or a Poisson train-like noise input. Slightly tuning the network further in the critical parameter space as follows: 200 *thalamo-cortical* or *septo-hippocampal* neuron input, overall synaptic weight/strength constant at 0.14, gamma probability distribution for the inhibition of scale-factor θ = 2.0 and shape-parameter k = 0.015, and intrinsic membrane excitability with resting membrane potential at 75 mV, sensitivity threshold at 65 mV and resting membrane recovery threshold at 15 mV, were sufficient to trigger the most remarkable and unpredictable behaviour observed in our neuronal network.

*Clinical Neurophysiology of Epileptogenic Networks DOI: http://dx.doi.org/10.5772/intechopen.104952*

**Figure 15.**

*Interictal and ictal paroxysmal depolarization shifts for critical parameters of our neuronal network (200 neuron input, overall synaptic weight/strength constant at 0.14, gamma probability distribution for the inhibition with scale-factor θ = 2.0 and shape-parameter k = 0.015, intrinsic membrane excitability with resting membrane potential at 75 mV, sensitivity threshold at 65 mV and resting membrane recovery threshold at 15 mV).*

This was the generation of sustained *pathological high frequency oscillatory activity* that emerged from stochastic or random noise like other previously described physiological high frequency (beta/gamma range) oscillatory activities [75]. This was amplified in amplitude and frequency beyond any limit. It could not be checked upon by the local inhibitory network and eventually went completely out of control in what could be the equivalent of a *seizure*. The model allows for incredible predictions of the underlying processes taking place during epileptogenesis/ictogenesis (the process of seizure generation and development).

As can be appreciated from the figure above (raster plot and cumulative spikograms at the bottom on the right of **Figure 15**) ictogenesis starts with a *hyperexcitation wave-front* through an initial process of *stochastic resonance* [75] similar to previously described high-frequency oscillatory generation processes [76]. This is immediately followed by a massive feedback burst of inhibitory activity (*phasic inhibition*) [77] that desynchronizes or brings the underlying unit oscillators to a transient halt, resulting on a network scale in transient attenuation/suppression of background rhythms (**Figure 16**). Depending then on the level of sustained or effective background inhibition (*tonic inhibition*) [78] a process of *synchronization* [35] starts and recurrent cycles of alternating excitation and inhibition go on to entrain larger and larger ensembles of unit oscillators into a common resonating high frequency [36]. This maximizes the amplitude of the oscillation and recruits a massive number of unit oscillators into excessive and hypersynchronous oscillatory activity.

#### **Figure 16.**

*Initial background rhythm attenuation (intermixed with muscle artefact on some channels) followed by rapid build-up of fast oscillatory activities. This is likely the result of widespread, initial phasic and then tonic inhibition through an extensive cortico-ganglio/thalamo-cortical (left > right) network. This focal-onset left mesial frontal/ sylvian tonic seizure manifested suddenly and evolved rapidly (secondary generalized).*

In both physiological and pathological high-frequency activities modelled, there was always a massive inhibitory response to the initial overexcitation wave front, something that is of note as it suggests that for any organized large-scale oscillatory activity to develop a critical level of *synchronization* of unit oscillators is required through recurrent cycles of excitation and inhibition [79]. This is achieved with the early excessive feedback wave of inhibition that follows the initial huge wave of excitation, resulting in an excessive hyperpolarization of the excitatory neurons. This is pivotal in uniformly suppressing or phase-resetting all unit oscillators and synchronously restarting them or coupling/forcing them into a *synchronization process* [78] that gradually entrains larger and larger neuronal ensembles. Excessive *afterhyperpolarization potentials* [80–82] are also crucial in shifting a huge number of inactivated sodium channels from the inactivated to the closed state, rendering them available again for repeated waves of overexcitation during a sustained *paroxysmal depolarization shift* [83, 84].

*Resonance* is an oscillation of maximal amplitude with all unit oscillators oscillating in a synchronous or synchronized manner, observed when the frequency of a periodically applied *depolarization force* (or a Fourier component of it) is equal or close to a natural frequency of the system. When a small oscillating or periodic *depolarization force* is applied near a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, nonresonant frequencies [35]. Obviously, the resonant frequencies of local neocortex or allocortex are defined by the critical combination of local structural and functional connectivity, periodic thalamic or septal input, synaptic weights, interaction of excitatory (recurrent excitatory synapses) and inhibitory (loss of inhibition or disinhibition) components and intrinsic neuronal excitability (endogenous bursting) [78, 79].

The inhibitory oscillatory components of our neuronal network manifest another interesting phenomenon. Driven by the initial overdepolarization of pyramidal cells, some of the inhibitory interneurons excessively 'depolarized' to hundreds of
