A deep learning approach for seizure detection in zebrafish model of epilepsy.

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University of Pisa

Department of Physics

Master’s degree thesis

A deep learning approach for seizure

detection in zebrafish model of epilepsy

Candidate Supervisors

Francesco Torre Prof. Gian Michele Ratto Prof. Nicola Belcari

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CHAPTER 1 Introduction

1.1 Zebrafish as model for human brain disorders

Zebrafish (Danio rerio, Figure 1.1) is a freshwater teleost fish used as a model organism in biology from the 1980 when Streisinger et al. developed a technique capable of re-producing clones of homozygous fishes from individual homozygotes [1]. This partic-ular model organism offers various advantages: low cost of maintenance, high rate of reproduction, easy genetic manipulation and availability of non-pigmented lines. If we combine these advantages with the crucial fact that its genome is 70% homologous to humans [2] it is easy to understand why it has become popular in biomedical research. Although the mammalian and the teleost central nervous system (CNS) display consider-able neuroanatomical differences, several fundamental principles of brain development and function are evolutionarily well conserved and reproduced in the characteristic tri-partite brain (visible in Figure 1.2) of zebrafish vertebrate model [3, 4]. Zebrafish larvae possess a compact nervous system containing ∼ 105neurons in less than half a cubic mil-limeter, nevertheless these fishes are capable of several behaviours and they represents an excellent compromise between system complexity and experimental accessibility, fea-tures that simplify the identification of potential therapeutic targets [5, 6]. Indeed, ze-brafish models reproduce several aspects of neurological disorders that can be exploited to explore the underlying molecular and genetic mechanisms of disease [7]. Transparency and external development of embryos and larvae allow non-invasive imaging by using fluorescent probes and reporter genes [8]. The increase of molecular tools available for high-resolution live-imaging has recently been expanded to include genetically encoded fluorescent calcium indicator GCaMP proteins, which can reveal the spatio-temporal ac-tivities of excitable cells such as neurons, in intact, living zebrafish [8, 9]. In addition, pharmacological studies can be performed just adding small compounds to the holding water of the fish. Therefore, they may represent an ideal species for medium and high-throughput screens for genetic mutations and putative therapeutic chemicals [10, 11]. All these characteristics motivated researchers to model human brain disorders using ze-brafish [12].

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Figure 1.1: Danio rerio larva, photo taken during our experiment. The glass electrode used for extracellular field recording is visible on the left.

1.2 Epilepsy

The International League Against Epilepsy (ILAE) defined a seizure as "a transient oc-currence of signs and/or symptoms due to abnormal excessive or synchronous neuronal activity in the brain." This definition has been used since the mid-nineteenth century. Epilepsy is one of the most common and disabling neurologic conditions, with an inci-dence rate as big as 61.44 per 100000 person-years [13]. Epilepsy is a pathological con-dition characterized by enduring predisposition to generate unprovoked seizure and by the neurobiological, cognitive, psychological consequences of this [14]. There are sev-eral causes of epilepsy but each one reflects an underlying brain dysfunction [15]. Dif-ferent forms of epilepsy can be distinguished according to their phenotypes by evalu-ating the similarity of seizure type(s), the onset age, the electroencephalogram (EEG) findings, the genetic background, the triggering factors and the response to antiepileptic drugs. Seizures are divided into three categories: generalized, focal and epileptic spasms [16]. The differences between the first two classes are based on the neuronal involvement within the brain. Focal seizures originate in neuronal network limited to part of one cere-bral hemisphere while generalized seizures begin in bilateral distributed neuronal net-works. Clinicians rely heavily on electroencephalographic patterns to identify, classify, quantify and localize seizures. Epileptiform EEG activity has been categorized according to its timing with respect to the seizure: ictal activity, if it begins during a seizure, postictal, if it happens after a seizure, and interictal if it is observed between seizures [17]. It is worth noting that, while seizures should be limited in time, it is often not clear how to distinguish between ictal, interictal and postictal activities. Moreover, we need a better

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understand-to find the precise electro-clinical correlations of sympunderstand-toms during seizures performed in animal models, in comparison to finer definitions in clinical epileptology, demonstrates the necessity to improve phenotyping in animal models of epilepsy. Furthermore, the condition of patients that show drug-resistant seizures, leading to the necessity of sur-gical treatment [18] requires the discovery of novel anticonvulsant compounds and the subsequent development of robust pre-clinical models.

1.3 EAST Syndrome model

The availability of a larval zebrafish model for Epilepsy, Ataxia, Sensorineural deafness and Tubulopathy (EAST) syndrome [19, 20], allow for a better understanding of the patho-genetic mechanisms underlying this disorder. This syndrome is caused by mutation of kcnj10 gene expressing an inwardly-rectifying potassium channel called Kir4.1. Recent experiments [21, 22] using an antisense morpholino to knockdown kcnj10 function in ze-brafish revealed that morphant larvae recapitulated many features of the human disease, including several aspects of the seizure phenotype, excessive spontaneous tail movements and abnormally long bursts of locomotion during free-swimming that were followed by a loss of posture mimicking the human convulsions. Subsequent EEG recordings demon-strated that this zebrafish model responded positively to pentobarbitone but not to di-azepam [23], thus illustrating the relevance of these studies to understanding epilepsy mechanisms and identifying specific treatments.

1.4 Hemi-neglect and hemisphere rivalry

The cerebral hemispheres are anatomically and neurophysiologically asymmetrical. The evolutionary basis for these differences remains uncertain. There are, however, highly consistent differences between the hemispheres. The fact that the brain, an organ which exists precisely to make connections, has a deeply divided structure has remained largely unexplained and even unexamined; to date, many important authors in the field [24– 27] accept that there is something manifestly important here that requires explanation. The fact that hemispheric asymmetries exist at every level of description suggests that the interhemispheric distribution of neuropsychological functions is unlikely to be random. Such asymmetries exist at the gross anatomical level in the size, weight, and conformation of either hemisphere as a whole but as well as differing in the size and shape of a number of defined brain areas, the hemispheres differ in the number of neurones, neuronal size, and the extent of dendritic branching within areas. Neurochemically the hemispheres differ in their sensitivity to hormones and to pharmacological agents, and there are sig-nificant differences in the ratio of dopaminergic to noradrenergic neurotransmission [28]. Structural and functional asymmetries in the nervous system are found throughout the animal kingdom. Lateralization is not a purely human characteristic, many studies now suggest that most vertebrate species, including monkeys [29–31], rodents [32–34],

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inantly in the left hemisphere. Brain lateralization is thought to increase cognitive perfor-mance, whereby specialization of one hemisphere leaves the other free to perform differ-ent tasks. Compromised brain asymmetries have been linked to several neuropatholo-gies including schizophrenia, autism, and neuronal degenerative diseases [45–47]. Yet, despite their prevalence and importance, both the role and changes of nervous system asymmetries in pathology are far from being clarified. Lateralization of brain and behav-ior is the apparent predisposition towards side bias, often manifested in terms of mo-tor output, such as handedness. Laterality has been extensively studied in humans, with functional laterality of different brain regions known to be an important aspect in lan-guage and cognition [48, 49]. Research has revealed that motor functions may also be under the control of lateralized mechanisms which, in humans, may manifest as prefer-ence for one side over the other for handedness, footedness and eyedness [50]. Behav-ioral asymmetries have been related to high escape performance [41], social responses [51] and even accelerated learning responses [52] in both fish and mammals. Zebrafish, as a versatile vertebrate model system widely used in translational neuropsychiatric re-search [7, 53], is a powerful instrument to understand the mechanisms underlying lat-eralization [40, 54–57]. Indeed, larval zebrafish have an increased use of left-eye when interacting with their own reflection [57]. Studies also showed that zebrafish initially use the right hemifield predominantly when interacting with novel object, but as the object becomes familiar, they switch to the left hemifield [58]. In a mutant zebrafish strain that shows strong laterality bias, asymmetry of diencephalic structures correlates with differ-ent behavior patterns such as boldness responses, with left-bias fish showing increased latency to interact with a novel object than right-bias fish [56]. It’s our interest to investi-gate whether the phenomenon of lateralization arises in the epileptic model under exam-ination and whether it characterizes it.

1.5 Detection of epileptic activity in Zebrafish: status of art

Locomotion and electrophysiological activities represented the main readout of the epilep-tic phenotype in zebrafish. The quantification of swimming behaviour changes of larvae can rely on automated locomotion-tracking technology performed on multi-well plates for high-throughput screening [59], providing information on seizure severity and on the outcome of administered drugs. The recording of the local field potential (LFP), which allows monitoring the brain activity in intact larvae [60–62], may complement the loco-motion study, helping to screen the mutant phenotypes and the effects of antiepileptic drugs. Recent multi-electrode systems have been implemented to monitor multiple ze-brafish through non-invasive recording [63, 64]. The electrophysiological recordings re-quire, however, algorithms for the unbiased identification and classification of epilepti-form events and physiological events such as eye or tail movement [64]. By applying deep learning classifiers [65], the detection is bound to an a priori hypothesis of seizure fea-tures, and to the completeness of the training dataset. A high-throughput LFP recording platform has recently analysed high-order statistical moments for an unsupervised

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detec-Figure 1.2: Neuroanatomy of the zebrafish brain. Lateral (a) and dorsal (b) views of the adult brain [74], in blue box the field of our observations.

by motion artefacts. Furthermore, from a single LFP signal, it is impossible to reconstruct the sources and the spatial dynamics of the genesis and propagation of electrophysiolog-ical activity, and the qualitative analysis of the LFP transients makes it difficult to distin-guish seizures from physiological events such as energetic tail flicks.

A complementary window on brain function is provided by imaging techniques ap-plied to the fluorescence of genetically encoded fluorescent calcium indicators (GECIs). Indeed, the zebrafish is a perfect model for monitoring brain activity given the small size of the larval brain and the availability of non-pigmented lines expressing a calcium sensor. Current imaging approaches allow brain-wide imaging both in head-fixed animals [67, 68] and in freely swimming fish [69, 70]. Calcium imaging provides information about neu-ronal activation at low temporal frequency compared to LFP recordings but with a very high spatial resolution [71]. Recently, wide-field imaging has been combined with elec-trophysiological and behavioural assays on a zebrafish transgenic line with pan-neuronal expression of the genetically-encoded calcium indicator GCaMP6s. In this study, the Ca2+ signal that originates from the surface of the brain provided a qualitative investigation of seizures and activity mapped at brain region level [72]. A very recent work raises the is-sue about the understanding of different network properties of epileptic-like activity in zebrafish exploiting traditional approaches of operator definition of ROI (Region of inter-est) and operator-assisted definition of electrophysiological epileptic events [73].

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by the Nobel Prize in Physics Maria Göppert-Mayer in her doctoral dissertation, in 1931. The units of two-photon absorption (TPA) cross-section (GM) are named in her honor (1 GM = 10−50 cm4· s · photon−1). Two-photon absorption is the absorption of two pho-tons of identical or different frequencies in order to excite a molecule from one state to a higher energy one, most commonly an excited electronic state. The energy difference between the involved lower and upper states of the molecule is equal to the sum of the photon energies of the two photons absorbed.

The greatest impediment to fluorescence imaging deep in tissues is light scattering, which weakens the beam exciting the specimen and thus reduces the fluorescence exci-tation. The scattering of light in tissues is largely due to the presence of objects like cell bodies and cell components that are larger than the wavelength of light, a phenomenon that increases exponentially with increasing specimen thickness. In confocal microscopy using visible light, scattering is so severe that imaging is usually limited to specimens less than 10µm to 50 µm thick. Two-photon microscopy with near-IR illumination solves some of these problems. Firstly, certain tissues like neural tissue are relatively transparent to near IR wavelengths, so that only about half of the incident excitation photons are scat-tered for every 50µm to 100 µm of tissue thickness. IR light is also absorbed less in tissues and produces less autofluorescence than does visible light [75], which further improves the efficiency of penetration and excitation. In addition, photon damage is avoided be-cause of the pulsed nature of light delivery with a mode-locked laser, and bebe-cause flu-orescence excitation is highly localized, see Figure 1.3. As a result, it is possible to use two-photon microscopy to image structures in samples of brain tissue that are in excess of 1 m m thick.

In one-photon fluorescence excitation (standard fluorescence imaging), a molecule is excited by a wavelength within its excitation spectrum and then emits a photon (Equation 1.1). A fluorophore existing in the ground state (S0) can absorb a single photon that excites

the fluorophore to a higher energy state (S1, an excited state). After a short period of

time in the excited state, the fluorophore relaxes back to its ground state by emitting a photon of light. To efficiently excite the fluorophore, the excitation photon should have a wavelength (λ1p ) that corresponds to an energy which matches the energy of the excited

state of the fluorophore (ES1). In this case, molecular excitations show a linear response to

illumination intensity and are not excited by longer or shorter wavelengths outside their excitation spectra.

ES1− ES0=

hc λ1p

(1.1) In a two-photon process, two photons, usually of the same wavelength and each with half the energy required to excite a fluorescent molecule, are absorbed simultaneously and have the same effect as a single photon of half the wavelength and twice the frequency and energy (Equation 1.2). The result is emission of a single fluorescent photon (Figure 1.4 [77]).

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Figure 1.3: Light scattering limits fluorescence imaging. (a) In confocal imaging, scattering re-duces excitation of the specimen and diverts confocal fluorescent rays (green arrows) from the pinhole, cutting signal strength. (b) In contrast, for two-photon imaging with near-IR rays, scat-tering of excitation rays is reduced, and fluorescence emission from the focal plane (green arrows) is efficiently collected on a wide area PMT. The improvement by two-photon imaging of deep tis-sue imaging is substantial [76].

This process is described by a time-dependent Schroedinger equation, in which the Hamiltonian contains an electric dipole interaction term: ~E_γ·~r , where ~E_γ is the electric field vector of the photons and~r is the position operator. This equation can be solved by perturbation theory, the first order solution corresponds on the one-photon excitation, the multiphoton transitions are represented by higher order solutions. In the case of two-photons the transition probability between the molecular initial state |i 〉 and the final state | f 〉 is given by Equation 1.3:

P ∼ ¯ ¯ ¯ ¯ ¯ X m 〈 f |~E_γ·~r |m〉〈m|~E_γ·~r |i 〉 ²γ− ²m ¯ ¯ ¯ ¯ ¯ 2 (1.3) where²_γis the photonic energy associated with the electric field vector ~E_γ , the sum-mation is over all intermediate states m and²mis the energy difference between the state

m and the ground state. Note that the dipole operator has odd parity (and absorbing

one photon changes the parity of the state), and the one-photon transition moment ~E_γ·~r

dictates that the initial and the final states have opposite parity. The two-photon moment 〈 f |~E_γ·~r |m〉〈m|~E_γ·~r |i 〉 enables transition in witch the two states have the same parity [75].

It seems implausible that long wavelengths, completely ineffective in one-photon stim-ulation, are exactly what are needed for two-photon excitation. Since two-photon

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excita-Figure 1.4: A Jablonski diagram showing one-and two-photon modes of fluorescence excitation. In one-photon excitation, fluorophores excited to the singlet excited state by absorption of a single photon of a specified energy (purple arrow) can return to the ground state through emission of a lower energy photon and vibrational energy (wavy blue arrow). In two-photon imaging with an IR laser, two photons, each with half the required energy, are absorbed simultaneously (red arrows), and the emitted fluorescent photon can have higher energy than the excitation photons (wavy blue arrow) [76].

ear process . Thus, the emitted fluorescence is proportional to the square of the excitation power.

The most important property of two-photon microscopy that makes it valuable for deep tissue imaging is a feature called localization of excitation, the confining of all flu-orescence excitation to a tiny volume at the focal point. In fact, fluflu-orescence excitation is restricted to the volume of the central diffraction spot of the point-spread function of the focused beam. Due to the nonlinear effect of photon excitation (two-photon excita-tion diminishes with the 4t hpower of the distance from the focal plane) the light intensity is immediately too weak outside the focal plane, and there is no fluorescence. Because fluorescence is restricted to the focal plane, two-photon images have excellent contrast and definition, 3D images can be obtained from image stacks of through-focus series, and photodamage and photobleaching are greatly reduced. The effect of the nonlinear intensity-squared relationship, frequency doubling, and the localization of excitation is shown in Figure 1.5.

The question of how neuronal networks accomplish information processing is central for the understanding of higher brain functions. This question is difficult to answer, not only because of the immense number of computing elements, but also because of the difficulties of direct real-time monitoring of network activity. So far, the function of

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neu-Figure 1.5: Localization of excitation by a microscope objective in a fluorescent substrate. A confo-cal microscope (a) and a two-photon microscope (b) were used to photobleach an area of interest at the same depth of focus of a rhodamine-containing plastic substrate. The plastic block was scanned with a confocal microscope to produce an image stack through the bleached area and the stack displayed as an x,z plane perpendicular to the surface of the block. Two-photon exci-tation bleached a sharply defined line in the focal plane (b), whereas confocal imaging bleached the figure of two cones meeting in the focal plane (a) and indicating the numerical aperture of the objective [76].

nance imaging, positron-emission tomography, imaging of intrinsic optical signals, and voltage-sensitive dye-based imaging. A real-time analysis of neuronal networks in vivo is so far best achieved by using the powerful approach of voltage-sensitive dye-based imag-ing. Over the years these techniques have been used extensively for studying different as-pects of brain function and have led to the discovery of important macroscopic features of processing networks, however, many aspects of signal processing at the single-cell level as well as the temporal dynamics in processing neuronal networks have remained unclear. Fluorometric Ca2+imaging is another sensitive method for monitoring neuronal activity. It makes use of the fact that in living cells, most depolarizing electrical signals are associ-ated with Ca2+influx attributable to the activation of one or more of the numerous types of voltage-gated Ca2+channels, abundantly expressed in the nervous system. These sig-nals are often amplified further by Ca2+release from intracellular Ca2+stores. Such Ca2+ signals are essential for elementary forms of neuronal communication, such as chemical synaptic transmission. In addition, Ca2+ signaling is obligatory for complex processes, such as the induction of memory- and learning-related forms of neuronal plasticity. Fur-thermore, many aspects of development at the beginning of a neuron’s life, including gene expression, neuronal migration, and neurite outgrowth require transient intracellular ele-vations in Ca2+concentration, whereas, paradoxically, Ca2+transients are also involved in neuronal cell death. The advantage of Ca2+imaging is dual: it allows for real-time analy-ses of individual cells and even subcellular compartments, while permitting simultaneous recordings from many individual cells. Further, it has been used successfully in numerous

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the cortical surface, has become possible [79].

1.7 LFP electrophysiology

The Local Field Potential (LFP) is the electric potential recorded in the extracellular space in brain tissue, typically using microelectrodes (metal, silicon or glass micropipettes). LFPs differ from the EEG, which is recorded at the surface of the scalp, and with macro-electrodes. It also differs from the electrocorticogram (EcoG), which are recorded from the surface of the brain using large subdural electrodes, while LFPs are recorded in depth, from within the cortical tissue (or other deep brain structures). Besides their invasive as-pect, LFPs also sample relatively localized populations of neurons, as these signals can be very different for electrodes separated by 1 mm [80] or by a few hundred microns [81]. In contrast, the EEG samples much larger populations of neurons [82]. The difference is due to the fact that the EEG signals must propagate through various media, such as cere-brospinal fluid, dura matter, cranium, muscle and skin, and are therefore much more sub-ject to filtering and diffusion phenomena across these media. However, even if recorded close to the neuronal sources, LFP signals are also filtered, because the recording elec-trode is separated from the sources by portions of cortical tissue. Besides these differ-ences, EEG and LFP signals display the same type of oscillations during wake and sleep states [83]. Early studies demonstrated that action potentials have a limited participation to the genesis of the EEG or LFPs. The initial theory about the genesis of the EEG and LFP oscillations, the "circus movement theory", postulated that the frequency of oscillations was due to travelling pulses along loops of connected neurons [84, 85]. Bremer [86, 87] was an opponent to this theory and he was the first to propose that the EEG is not gener-ated by action potentials but rather by oscillations of the membrane potential of neurons. Eccles [88] proposed that LFP and EEG activities are generated by summated postsynap-tic potentials arising from the synchronized excitation of neurons. Intracellular record-ings from cortical neurons later demonstrated a close correspondence between EEG/LFP activity and synaptic potentials [89, 90]. The current view is that EEG and LFPs are gener-ated by synchronized synaptic currents arising on cortical neurons, possibly through the formation of dipoles [82, 91].

One of the possible explanation for the fact that action potentials have a limited partic-ipation to EEG and LFP activities is that the cortical tissue exerts strong frequency-filtering properties. High frequencies (greater than ' 100 Hz ), such as that one produced by action potentials, are subject to steep attenuation, while low-frequency events, such as synaptic potentials, attenuate more gradually with distance. Consequently, the extracellular im-age of action potentials is visible only for electrodes immediately adjacent to the recorded cell [92], while synaptic events may propagate over large distances in extracellular space and can be recordable as far as on the surface of the scalp, where they participate to the genesis of the EEG. This frequency-dependent behavior is a property routinely seen in ex-tracellular recordings of neuronal units: the amplitude of exex-tracellularly-recorded spikes is very sensitive to the position of the electrode, presumably because action potentials

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rons, and thus are more stable to small changes of electrode position. This property is fundamental to allow the resolution of single units from extracellular recordings.

The relationship between LFP and the firing of neurons depends on the brain state, as illustrated in Figure 1.6. During wakefulness, the low-amplitude fast-frequency LFP was associated with sustained and very irregular firing activity in the units (Figure 1.6(A),(B) Wake). There was no apparent relation between units and LFP by visual inspection, al-though a statistical analysis revealed that the depth-negative deflections were on average related to an increase of firing activity in the units (Figure 1.6(C), Wake; see details in [80]). During slow-wave sleep, the ensemble activity was surprisingly similar to wakefulness, although more bursty (Figure 1.6(A), SWS). However, at closer scrutiny (Figure 1.6(B)), it appears that synchronous "silences" in all the units occur systematically and simulta-neously with the depth-positive part of the slow-wave (Figure 1.6(B), SWS; blue shaded area). This type of synchronized silence is often referred as "Down-state", and was also visible in the human recordings. This modulation of firing by the slow wave is also visi-ble when computing the statistical relation between units and slow-waves (Figure 1.6(C), SWS). The tight relation between slow waves and Up and Down states in single neurons was firmly demonstrated using intracellular recordings in natural slow-wave sleep in cats [83, 93]. The human and cat recordings display essentially the same features of the rela-tion between LFPs and neuronal units.

The LFP is generated by electric currents and charges in brain cells, including neurons and glial cells. In particular, all ionic currents in neurons can potentially contribute to the LFP. The main contribution to LFPs is believed to be the synaptic currents in neurons, although intrinsic voltage-dependent currents and spikes can also contribute. Today’s prevalent model is that EEG and LFPs are generated by synchronized synaptic currents arising on cortical pyramidal neurons, possibly through the formation of dipoles [82, 91]. The LFP also interacts with the extracellular medium, trough several mechanisms, such as capacitive effects, polarization, or ionic diffusion. These types of interaction confer specific frequency dependence of the extracellular electric potential, and thus are impor-tant for correctly interpreting the LFP. The simplest model for LFP generation assumes that the LFP is generated by transmembrane currents and that neurons are embedded in a perfectly resistive medium (also called Ohmic medium, such as salted water, with no capacitive or other component. This is equivalent to assume that the electric conductiv-ityσ and permittivity ² of the extracellular medium are constant everywhere and do not depend on frequency. In this case, one first considers the electric potential generated by a punctual current source. Combining Ohm’s law with the charge conservation law, and considering a spherical symmetry, we obtain:

V (r ) = 1

4πσ

I0

|r − r0|

, (1.4)

where V (r ) is the extracellular potential at a position r in extracellular space, I0is the

current source, and |r − r0| is the absolute distance between r and the position of the

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∇2V = 0. (1.5) Since the principle of linear superposition applies, the potential resulting from a set of current sources is given by:

V (r ) = 1 4πσ X j Ij |r − rj| . (1.6)

This equation will be referred to as the "standard model". This expression can be used to calculate the LFP resulting from complex morphologies, or from networks of neurons. This model is widely used to model extracellular potentials, from early models [94] to today’s models of extracellular activity [91, 92, 95–98].

Electric currents from all excitable membranes contribute to the extracellular voltage. These currents emerge mainly from synaptic activity but often with substantial contri-butions from Ca2+ spikes and other voltage dependent intrinsic events, as well as from action potentials and spike after potentials. The two most important factors contributing to the LFP are the cellular synaptic architectural organization of network and the syn-chrony of the current sources. The extracellular potential can be reconstructed from si-multaneous monitoring of several current source generators across the neuronal mem-brane, provided that sufficient details are known about the contributing sources and the extracellular milieu. This forward reconstruction is theoretically possible since the phys-ical processes underlying the generation of V are mostly understood. The forward re-construction of the LFP is accelerated by advancements in microelectrode technology and other new methods, and developments in computational modelling. Reconstruc-tion of the LFP signal from the measured current sources and sinks can, in turn, provide insights into resolving the inverse problem, that is, the deduction of the microscopic pro-cesses from the macroscopic LFP measurements. A practically important application of the forward-inverse relationship would be the reconstruction of cell assembly sequences from the constellation of the LFP recordings. Cell assemblies can be defined as a temporal coalition of neurons, the collective action of which can lead to the discharge of a down-stream "reader" neuron. Such assemblies (or "neural letters") are organized into assembly sequences (or "neural words") by the slower rhythms. Although the temporal organiza-tion of neuronal dynamics can be effectively inferred from the cross frequency coupling of the various brain rhythms, additional steps are required to reveal the spiking content of the LFP patterns. In the intact brain, spiking neurons are embedded in interconnected networks and may be influenced by the local electric field through direct electrical con-nections. Therefore, the output spikes of the cell assemblies within and across networks are transformed into spatially distributed transmembrane events through synaptic ac-tivity ("synapsembles"). Of course, these transmembane events are responsible for the generation of the LFP. Buzsaki, Anastassiou, Costas and Koch [99] suggest that as the com-position of spiking assemblies varies over time, the spike patterns induce unique patterns of LFPs, which vary from moment to moment. Recording the LFP from a sufficiently large and representative neuronal volume with sufficiently high spatial density may therefore

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about the encoded information as the spiking cell assemblies themselves. In support of this idea, it has been shown that during cognitive tasks, the spatial distribution of spec-tral power varies in a task-relevant manner [100–104]. It is expected that the spatially resolved, wideband LFP signal, which contains information about both afferent patterns and assembly outputs, may turn out to be the most useful signal for understanding neu-ronal computations [105, 106].

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Figure 1.6: Relation between LFP and single unit activity in different brain states in cats. (A) Left: During wakefulness, the low-amplitude fast-frequency LFP activity is associated with highly ir-regular firing activity of a 8 multi-units recorded simultaneously. Right: During slow-wave sleep (SWS), the activity is similar as wakefulness, except that synchronized "silences" of firing activ-ity occur in all cells simultaneously, and in relation to the slow waves. (B) Same activactiv-ity as in A at 20 times higher temporal resolution. The blue shaded area indicates the synchronized silence ("Down state") simultaneous in all cells, and occurring in parallel with slow waves. (C) Wave-triggered averages of spiking activity. During wakefulness, the LFP negative peaks were correlated with an increased firing activity in the units. During SWS, the negative peak of the slow wave was correlated with a strong decrease of firing in the units (Down state), followed by a rebound a sus-tained activity (Up state). [92]

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1.8 Aim of the thesis

The aim of the work can be summarized in two parts:

1. Seizures individuation and characterization

The aim of the first part of the work described in this thesis is to qualitatively eval-uate the activity and recruitment of neuronal populations through two-photon cal-cium imaging, by exploiting the availability of a non-pigmented zebrafish express-ing the calcium indicator GCaMP6f in neurons. For this purpose, we chose to use unsupervised machine learning tools [107] to implement an automated workflow aimed at extraction of significant information from the calcium imaging dataset. Clinically, the various types of epilepsy are classified starting from motor, psycho-logical, psychic and electrophysiological symptoms. Our goal is to find and char-acterize the seizures in the kcnj10a zebrafish model by two-photon calcium imag-ing and LFP records, in order to confirm and expand the current knowledge on the physiopathology of epileptic-like events.

2. LFP classification

Secondly we focused on the attempt to develop an innovative method for the elec-trophysiological recording characterization, based on imaging analysis informa-tion. Using the newest tools in the field of supervised learning [108] we try to build a convolutional neural network (CNN) designed to interpret the electrophysiological recording associating it with the neuronal recruitment emerged from the calcium imaging with the underlying idea of understand whether it is possible to train a neuronal network that allows to predict the extent of the brain recruitment (i.e., the extent of the high Ca2+territories) on the basis of the LFP recordings. This should allow us to investigate the nature of local field potential and question about lim-its and solidity of the widely used analysis based on electrophysiological recording only.

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CHAPTER 2 Materials and Methods

2.1 The experimental setup

All the larvae subject of our experiment belong to a genetic line expressing the sensor GCaAMP6f. GCaMP is a genetically encoded calcium indicator (GECI), initially developed by Junichi Nakai [109]. GECIs are designed to show the calcium ion status of a tissue or medium and are either transfected into cell lines or via transgenic crosses. GCaMP is cre-ated from the M13 fragment of the chicken Mylk gene (which contains the target sequence for calmodulin binding), fused to the N terminus of a circularly permutated form of EGFP. The C terminus of cpEGFP is fused to the rat calmodulin gene (CaM). When Ca2+binds to CaM, the interaction between Ca2+CaMM13 induces a conformational change in cpEGFP which causes a subsequent change in fluorescence intensity. The control group is com-posed of wild type animals (WT) and the experimental group of larvae, referred as mor-phants (MO), which have been treated with a morpholino antisense oligo to temporarily knock down expression of a targeted gene. A morpholino, is a type of oligomer molecule used in molecular biology to modify gene expression. Its molecular structure has DNA bases attached to a backbone of methylenemorpholine rings linked through phospho-rodiamidate groups. Morpholinos block access of other molecules to small (∼ 25 base) specific sequences of the base-pairing surfaces of ribonucleic acid (RNA). Morpholinos are used as research tools for reverse genetics by knocking down gene function, in our case we have employed morphants of kcnj10a as a model of spontaneous seizures [110].

Figure 2.1 shows the experimental setup: a zebrafish larva (120 h post-fertilization) is restrained in low melting point agar and the electrode is placed along the midline as indi-cated in the figure. Imaging was performed at a depth of 140 − 160 µm under the surface, thus providing an optical section that includes neuronal populations belonging to optic tectum, cerebellum and hindbrain. For each group, after attaining a stable electrophysio-logical (EP) signal, the LFP was recorded for at least 30 minutes. However, the records we used in our work are a subset of all experimental data: for only four morphants and one wild type it was possible to record simultaneously LFP signal and Imaging, Table 2.1.

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Table 2.1: Indexing of used recordings

Figure 2.1: Experimental model. (a) Five days old zebrafish larvae expressing the Ca2+ sensor GCaAMP6f were embedded in low melting point agar before LFP recordings and two-photon imaging. Larvae developed pathological activity because of the reduced expression of the gene kcnj10a coding for a K+ inward rectifier channel. (b) Larvae were transferred under the two-photon microscope and the LFP was recorded with a glass microelectrode during Ca2+imaging. (c) The imaged plane includes most of the zebrafish brain showed in Figure 1.2 , including the Habenula (Hb), the Optic Tectum (OT), the Cerebellum (Cb) and the Medulla Oblungata in the back (MOb). The image field is 0.6 mm wide.[111]

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In our experiment in vivo two-photon calcium imaging was performed on a Prairie Ul-tima Multiphoton microscope equipped with a mode-locked Ti:Sapphire laser (Coherent Chameleon Ultra II) and the power of excitation on the sample was < 15 mW. Acquisitions were performed with spiral scanning at about 4 Hz by a water immersion lens (Olympus, 20x, 1.00 NA) at a resolution of 512 ×512 pixels, and at an excitation of 920 nm. The imag-ing field was circular the imagimag-ing field is circular (because of a spiral acquisition[112]) with a diameter of 600µm. Imaging data were analyzed with ImageJ and custom Matlab code, the reader can see a sample image obtained with two-photons calcium imaging, in our laboratories, in Figure 2.2.

Each 5 dpf larval zebrafish was placed in a 40µl of egg water in the recording chamber with a transfer pipette, and then 200µl of 1.2% low melting point agar in egg water. The chamber was transferred either only on the stage of a stereomicroscope for LFP record-ings, or on the stage of the two-photon microscope for the double recordrecord-ings, as shown in Figure 2.1. The Local Field Potential (LFP) was recorded by a glass microelectrode (1-2 MΩ resistance) back loaded with extracellular recording solution and Sulforhodamine 101 (0.1 mM diluted in 2 M NaCl) to allow for imaging of the electrode tip under the two-photon microscope. Electrophysiological signals were amplified 1000-fold (EXT-02F, NPI), band pass filtered (0.1-1000 Hz), and slightly oversampled at 5 kHz with 16 bit precision by a Na-tional Instruments (NI-usb6251) AD board controlled by custom made LabView software. Line frequency 50 Hz noise was removed by means of a linear noise eliminator (Humbug, Quest Scientific). The electrode tip was placed under visual guidance in the midline of the forebrain at about 250µm of depth, the reference electrode was placed in the egg water and grounded. At the end of the recording session, the position of the microelectrode was reconstructed together with the surrounding brain structures by means of two-photon imaging. A sample electrophysiological record is showed in Figure 2.3.

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Figure 2.2: A sample image obtained with two-photons calcium imaging, in our laboratories.

Figure 2.3: (a) Representative LFP recording from control zebrafish (WT) and in the kcnj10a mor-phants (MO). (b) Magnification of the LFP events indicated by the magenta bars in panel (a). The black traces show the full band data, while the blue traces show the data band passed in the 30-95 Hz range [111].

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2.2 Data preparation

2.2.1 Calcium imaging preparation

Imaging data were initially analyzed with custom Matlab code. The data were processed as follows. The mean dark signal was subtracted from each time lapse stack and after-wards was binned 4×4 to decrease the size of the array. Then, the fluorescence fluctuation ∆F /F0was computed for each pixel by the equation:

∆F (x, y,t)

F0

=F (x, y, t ) − 〈F (x, y)〉

〈F (x, y)〉 , (2.1) The∆F (x, y,t)/F0process has a mean value of 0 and it is normally distributed in absence

of significant Ca2+events. In presence of activity, a right tail emerges and the amount of Ca2+fluctuations can be described in terms of the skewness of the distribution. For each sample is tested the probability of belonging to the Gaussian distribution (3σ) of the entire recording representing the baseline: if the sample falls within the baseline distribution is set to zero otherwise is set to 1, doing so we got the binarized activation maps that form our dataset (Figure 2.4).

Figure 2.4: A representative binary map form the dataset.

2.2.2 LFP recording preparation

LFP recordings was filtered by the custom Matlab software ZebraExplorer in the 30-95 Hz band, the frequencies belonging to this band are called "gamma oscillations". This is a conventional choice in epilepsy-oriented LFP analysis for the mouse [113] and the human model [114], frequencies lower than this band are mainly related to slow events like, for example, the movement and above the upper limit frequency, in fact, the local field potential is dominated by its characteristic 1/ f noise [92].

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z =x − µ

σ . (2.2)

whereµ is the mean of the population, σ is the standard deviation of the population and the absolute value of z represents the distance between the raw score and the population mean in units of the standard deviation. z is negative when the raw score is below the mean, positive when above.

Finally, a sub-sampling of the signal was carried out in compliance with the Nyquist-Shannon sampling theorem, which states that, to correctly sample (without loss of infor-mation) a limited bandwidth signal, it is sufficient to sample it with a sampling frequency of at least twice the maximum signal frequency. In fact datas has been sub-sampled to the sampling frequency of 200 Hz through the Python algorithm scipy.signal.decimate [116] based on an order 8t h Chebyshev type I filter.

2.2.3 Combined data preparation

At this point the need to establish a criterion for the crossed analysis of imaging and LFP was presented. Taking into account that the order of magnitude on the time scale of the event type we’re looking for is ∼1 s, we have chosen to implement an overlapped Maxi-mum Intensity Projection (MIP) every 10 binary maps. Doing so, for example, for a trace of 1200 binary maps we got 1190 MIP maps. At this point it was intuitive to associate the corresponding slice (∼2.4 s) of time series to each MIP map, Figure 2.5. This choice involved two advantages: the data set has been smoothed and no data augmentation op-erations, usually common in the preparation of machine learning techniques, were nec-essary, thus limiting the risk of inserting human bias into our, not large, dataset. Finally, we were able to start the analysis on my definitive dataset consisting constituted as shown in the Table 2.2.

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Figure 2.5: Creating a dataset of M.I.P and time-correlated EP slices.

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2.3 Unsupervised learning

2.3.1 Clustering

With the precise aim of looking for hyper-synchronous neuronal activations, characteris-tic of epilepcharacteris-tic-like’s events, and using the features of the Python package scipy.ndimage, we filtered the MIP maps eliminating all those connected objects smaller than 10 pixels. This reduced the database variability by eliminating only objects of the size (or minor) of the single larva’s neuron (∼ 164 µm ).

In order to be able to proceed to proceed with clustering operations we had to put into practice another common procedure before any machine learning operation, that is the application of a PCA filter to the data set. We did it for two reasons, firstly, to reduce substantially the computational processing time of the clustering algorithm, secondly, to make the validation of number k of clusters much more consistent. In fact, in my experi-ence, the various number of cluster’s validation algorithms give truly unstable and volatile results without an adequate PCA data filtering [117]. Once the number of clusters is set, whichever it is, the results of clustering algorithm used, gives always consistent, intuitive and, above all, uniform results with respect to varying the initial conditions. In order to choose the number of components to be used in the PCA decomposition, we proceeded with a study of the percentage of variance explained (see Figure 2.6), for each sample we chose a number of components that described its variability at 90%, we did this by as-suring myself that the results of clustering were the same as those obtained using higher percentages.

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(a) MO2 (b) MO3

(c) MO4 (d) MO5

(e) WT

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The KMeans algorithm

Organizing data into sensible groupings is one of the most fundamental modes of under-standing and learning. As an example, a common scheme of scientific classification puts organisms into a system of ranked taxa: domain, kingdom, phylum, class, etc. Cluster analysis is the formal study of methods and algorithms for grouping, or clustering, ob-jects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class la-bels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is to find structure in data and is therefore exploratory in nature. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, K-means, was first published in 1956 [118]. In spite of the fact that K-means was proposed over 50 years ago and thousands of clustering algorithms have been published since then, K-means is still widely used. This highlights to the dif-ficulty in designing a general purpose clustering algorithm and the ill-posed problem of clustering [119]. The k-means algorithm divides a set of N samples X into disjoint clusters

C , each described by the meanµjof the samples in the cluster. The means are commonly

called the cluster centroids. The algorithm aims to choose centroids that minimise the in-ertia (Equation 2.3), or within-cluster sum-of-squares criterion. Inin-ertia can be recognized as a measure of how internally coherent clusters are, making the assumption clusters are compact, convex and isotropic [120].

n

X

i =0

mi n_µ_j_∈C(∥ xi− µi ∥2) (2.3)

K-means is often referred to as Lloyd’s algorithm, in basic terms, the algorithm has four steps. The first step chooses the initial centroids, with the most basic method being to choose samples from the dataset . After initialization, K-means consists of looping between the two other steps.

1. k initial "means" (in this case k = 3) are randomly generated within the data domain (shown in color).

2. k clusters are created by associating every observation with the nearest mean. The partitions here represent the Voronoi diagram generated by the means.

3. The centroid of each of the k clusters becomes the new mean. 4. Steps 2 and 3 are repeated until convergence has been reached.

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Figure 2.7: KMeans four steps

2.3.2 Clustering validation: Cali ´

nski Harabasz method

As previously mentioned, the too broad definition of what a "cluster" is causes implemen-tation problems. The problem touches in an almost epistemological way the investigation of the experimenter: the definition of classes of equivalence between objects and the rela-tive equivalence relations is evidently based on the bias expressed by the researcher when he decides which objects belong or not to the same cluster. This problem strongly af-fects the attempt to automate the choice of the number k of clusters, in fact the KMeans algorithm needs to be initialized on a number of clusters decided a priori. There are prin-cipally three methods to decide the optimal number of cluster, namely, the Silhouette score, the Elbow method, and the Cali `nski-Harabasz score [117]. The first two, more rudi-mentary, did not give solid results on our dataset and this is a fairly common behavior if the data are not very clustered. We consider a brief overview of the "Dendrite Method for Cluster Analysis" [122] proposed by Cali ński and Harabasz in their 1974 article: if the ground truth labels are not known, the Cali ński-Harabasz index, also known as the Vari-ance Ratio Criterion, can be used to evaluate the model, where a higher Cali ński-Harabasz score relates to a model with better defined clusters. For k clusters, the Cali ´nski-Harabasz score is given as the ratio of the between-clusters dispersion mean and the within-cluster dispersion:

s(k) = Bk Wk

×N − k

k − 1 (2.4)

where Bk is the between group dispersion and Wkis the within-cluster dispersion

de-fined by:

Wk= k

X X

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being N the number of points in our data, Cq the set of points in cluster q, cq the

center of cluster q, c the center of E , nq the number of points in cluster q. The score is

higher when clusters are dense and well separated, which relates to a standard concept of a cluster, it is fast to compute, and it is generally higher for convex clusters than other concepts of clusters [120].

2.3.3 Mutual information

An essential tool in our work is the concept of mutual information (MI). In probability theory and information theory, the mutual information of two random variables is a mea-sure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as Shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fun-damental notion in information theory that quantifies the expected "amount of informa-tion" held in a random variable.

Given the knowledge of the ground truth class assignments labels_true and our clus-tering algorithm assignments of the same samples labels_pred, the Mutual Information is a function that measures the agreement of the two assignments, ignoring permutations. We used Adjusted Mutual Information (AMI) that has been recently proposed [123], which corrects the effect of agreement due to pure chance between clusterings. An example fol-lows showing the limit outputs of the algorithm [120]:

adjusted_mutual_info_score ( [ 0 , 0 , 1 , 1 ] , [ 0 , 0 , 1 , 1 ] ) = 1 . 0 adjusted_mutual_info_score ( [ 0 , 0 , 1 , 1 ] , [ 1 , 1 , 0 , 0 ] ) = 1 . 0 adjusted_mutual_info_score ( [ 0 , 0 , 0 , 0 ] , [ 0 , 1 , 2 , 3 ] ) = 0 . 0

Mathematical formulation of AMI

Here we summarize the mathematical formulation that can be found in [120, 124]. As-sume two label assignments (of the same N objects), U and V , their entropy is the amount of uncertainty for a partition set, defined by:

H (U ) = − |U |

X

i =1

P (i ) log(P (i )) (2.7)

where P (i ) = |Ui|/N is the probability that an object picked at random from U falls into

class Ui. Likewise for V :

H (V ) = − |V |

X

j =1

P0( j ) log(P0( j )) (2.8) with P0( j ) = |Vj|/N . The mutual information (MI) between U and V is calculated by:

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where P (i , j ) = |Ui∩ Vj|/N is the probability that an object picked at random falls into

both classes Ui and Vj. It also can be expressed in set cardinality formulation:

MI(U ,V ) = |U | X i =1 |V | X j =1 |Ui∩ Vj| N log µ N |Ui∩ Vj| |Ui||Vj| ¶ (2.10)

The normalized mutual information is defined as: NMI(U ,V ) = MI(U ,V )

mean(H (U ), H (V )) (2.11) This value of the mutual information and also the normalized variant is not adjusted for chance and will tend to increase as the number of different labels (clusters) increases, re-gardless of the actual amount of "mutual information" between the label assignments. The expected value for the mutual information can be calculated using the following equation. E [MI(U ,V )] = |U | X i =1 |V | X j =1 min(ai,bj) X ni j=(ai+bj−N )+ ni j N log µ_{N .n} i j aibj ¶ _a i!bj!(N − ai)!(N − bj)! N !ni j!(ai− ni j)!(bj− ni j)!(N − ai− bj+ ni j)! (2.12)

In this equation, ai= |Ui| is the number of elements in Ui and bj = |Vj| is the number of

elements in Vj. Using the expected value, the adjusted mutual information can then be

calculated using:

AMI = MI − E[MI]

mean(H (U ), H (V )) − E[MI] (2.13) This metric is independent of the absolute values of the labels: a permutation of the class or cluster label values won’t change the score value in any way, being more sym-metric at the same time: switching label_true with label_pred will return the same score value.

2.4 Supervised learning

You can interpret a neural network as a very complex geometric

trasformation in high-dimensional space, implemented via a long series of small steps.

François Chollet

As we will see later, for the classification of electrophysiological slices (Table 2.2) we used a deep machine learning system, in particular a convolutional type. Deep learning

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Figure 2.8: Anatomy of a Neural Network

layers may identify edges, while higher layers may identify human-meaningful items such as digits or letters or faces.

We can schematize the anatomy of a Neural Network (NN) into four main parts (see Figure 2.8).

1 Input data and corrisponding labels. NN can be designed for various types of data:

videos, images, simple vectors or, as in our case, time series.

2 Layers, wich are combined into a model. Deep Learning is built upon the concept

of layers. Indeed, a model is nothing but a set of layers clipped together to form a data transformation pipeline. Inspired by the organic multi-layered (V1, V2, V3...) visual cortex of mammals, the cells that form a layer are called neurons, witch fires under certain conditions established by the activation function (Sigmoid and Rec-tified Linear Unit, the most popular).

3 Loss function, wich defines the feedback signal, calculates the loss of the Network

on the data provides a measure of the mismatch between predictions and labels.

4 Optimizer, defines how the network will be updated implementing a specific variant

of stochastic gradient descent [115].

In our work we used a specific, very modern network architecture: Convolutional neu-ral network (CNN) [126]. The fundamental difference between a densely connected layer and a convolution layer is the following: dense layers learn global patterns in their input feature space (for example, for a image, patterns involving all pixels), whereas convolution

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1 The patterns they learn are translation invariant. After learning a certain pattern in, say, the lower-right corner of a picture, a CNN can recognize it anywhere: for example, in the upper-left corner (Figure 2.9). A densely connected network would have to learn the pattern from scratch if it appeared at a new location. This makes convnets data efficient when processing images (because the visual world is funda-mentally translation invariant): they need fewer training samples to learn represen-tations that have generalization power.

2 They can learn spatial hierarchies of patterns. A first convolution layer will learn small local patterns such as edges, a second convolution layer will learn larger pat-terns made of the features of the first layers, and so on. This allows convnets to efficiently learn increasingly complex and abstract visual concepts (this is a feature of paramount importance, as visual world is fundamentally spatially hierarchical).

Figure 2.9: Image can be bro-ken into local pattern [115].

Convolutions are defined by two key parameters: size of the patches extracted from the inputs and depth of the out-put feature map (the number of filters comout-puted by the con-volution).

The path recognition characteristics just shown, make CNN the ideal candidate for pattern research within electro-physiological timeseries. The design of a performing archi-tecture is, to date, still a purely artisan work. There are some general criteria and, above all, the empirical knowledge of some particularly functional architecture. To easily imple-ment the attempts needed to optimize the network, we in-stalled the CUDA drivers [127], which allow the network to run on parallel processors of an NVIDIA graphics card. In do-ing so on a medium-range laptop the processdo-ing times were one-thirds than those obtainable on a good desktop CPU.

All the interface work with the open source machine learning library Tensorflow was done thanks to Keras [108] an open-source neural-network library written in Python. It is capable of running on top of TensorFlow, Microsoft Cog-nitive Toolkit, Theano, or PlaidML. Designed to enable fast

experimentation with deep neural networks, it focuses on being user-friendly, modular, and extensible.

ZebraNetwork architecture

We verified that CNN works well for identifying simple patterns within our data which will then be used to form more complex patterns within higher layers. A 1D CNN is very effec-tive when you expect to derive interesting features from shorter (fixed-length) segments of the overall data set and where the location of the feature within the segment is not of

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Figure 2.10: ZebraNetwork architecture

the functioning of its parts (Figure 2.10).

• The input data are E.P. slices (see Table 2.2) corresponding to one MIP labeled with the k-cluster to which the MIP belongs (see Figure 2.5). Each slice (sampled at 200 Hz) is made up of 486 points corresponding to the time domain on which is defined each MIP

• First Conv1D layer. The first layer defines a filter (or also called feature detector) of height 9 (also called kernel size). The definition of a single filter would allow the neural network to learn only one single feature in the first layer. This might not be sufficient, therefore we will define 68 filters. This allows us to train 68 different features on the first layer of the network. The output of the first neural network layer is a 486 × 68 neuron matrix. Each column of the output matrix holds the weights of one single filter.

• The result from the first CNN will be fed into the second CNN layer. We will again define 68 different filters to be trained on this level. Following the same logic as the first layer, the output matrix will be of size 478 × 68.

• Max pooling layer. A pooling layer is often used after a CNN layer in order to reduce the complexity of the output and prevent overfitting of the data. In our example we chose a size of three. This means that the size of the output matrix of this layer is only a third of the input matrix.

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Figure 2.11: ZebraNetwork parameters.

• Average pooling layer. One more pooling layer to further avoid overfitting. This time not the maximum value is taken but instead the average value of two weights within the neural network. The output matrix has a size of 1 × 128 neurons. Per feature detector there is only one weight remaining in the neural network on this layer.

• Dropout layer. The dropout layer will randomly assign 0 weights to the neurons in the network. Since we chose a rate of 0.2, 20% of the neurons will receive a zero weight. With this operation, the network becomes less sensitive to react to smaller variations in the data [115]. Therefore it should further increase our accuracy on unseen data. The output of this layer is still a 1 × 128 matrix of neurons.

• Fully connected layer with Softmax activation. The final layer will reduce the vector of height 128 to a vector of six since we have ten classes that we want to predict. This reduction is done by another matrix multiplication. Softmax is used as the activation function. It forces all ten outputs of the neural network to sum up to one. The output value will therefore represent the probability for each of the ten classes.

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CHAPTER 3 Results

3.1 Imaging clustering

As we discussed in Section 2.3.2, in order to proceed with clustering operations we had to decide, using the Cali ´nski Harabasz method, how many k clusters to divide each imaging data set, so we decided to set a minimum of six subsets in which to divide the samples space and then we chose the k-value with the maximum Cali `nski-Harabasz score (Figure 3.1).

The KMeans algorithm was selected also for its intrinsic characteristic of creating a representative element, not belonging to the samples space, for each cluster: the centroid. On the following pages we show how the centroids, the results of the clustering operations implemented on imaging dataset as described in the Section 2.3.1, will provide a way to summarize and make accessible the information of the large dataset of images. Each Fig-ure, 3.2, 3.3, 3.4, 3.5, 3.6, is organized in panels representing for each experimental case (MO2, MO3, MO4, MO5 and WT, see Tables 2.1 and 2.2), the 300 s samples analyzed by KMeans algorithm. On the left column (first and third rows), there are the graph showing the fluorescence variation respect to background, the cluster number (second and fifth rows) and the electrophysiological trace (third and sixth rows), while on the right it is rep-resented the cluster analysis of imaging with the different representative centroid of each cluster.

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(a) (b)

(c) (d)

(e)

Figure 3.1: Cali ´nski Harabasz score for MO2 (a), MO3 (b), MO4 (c) ,MO5 (d) ,WT (e) KMeans clus-tering.

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3 .2 : M O2 clu st er ing resul ts . In th e left colu mn , first and four th ro w s, fluctuat ion of the C a 2+ sen sor measu re on th e e n ti re br ai n ; second h ro w s, cen tr oid number of th e associat ed ima ging c lust e ri n g; th ir d an d si xt h ro w s, L FP measur ed in th e 3 5 − 90 Hz b and . In the righ t n, th e cent roids repr esen tat iv e o f each clu st er .

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3 .6: W T c lust e ri n g resul ts . In the left c ol umn, first an d fou rt h ro w s, fl u ct u a tion o f the C a 2+ sen sor measur e on the e n tir e br ain; secon d an d w s, c ent roid n u mber o f the associat ed imag in g clu st er ing ; th ir d an d si xth ro w s, LF P measu red in the 35 − 90 Hz ban d. In th e rig ht colu m n, tr o ids repr e se n ta tiv e of eac h cluster .

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3.2 Electrophysiology clustering

Once we got the information from the image dataset we tried to cross it with the elec-trophysiological data in our possession. In the same spirit of the first part of the work we proceeded with EP dataset clustering. we build a samples space were each EP slice was represented by this four classical electrophysiology (EP) features: RMS power, maxi-mum Voltage, the power gradient and the time for which the signal is above 5σ. we chose these four scalar parameters because they are the most common tools used by electro-physiologists to characterize time series of interest. This time as well we faced the prob-lem of choosing the number of clusters in which to divide the dataset, but we opted to implement a different automated approach, through the adjusted mutual information (AMI) presented in the paragraph 2.3.3. We produced several clustering results through KMeans and then we evaluated which labeling of electrophysiology better matches, at an informative level with the time-based corresponding imaging one. Therefore, for the electrophysiology clustering we chose the number of clusters that maximizes mutual in-formation between the EP and the imaging labeling. The study, varying the number of clusters, is showed in Figure 3.7. In Figure 3.8 are shown the centroids, in the space of the electrophysiology’s features, resulting from clustering operations implemented with

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(a) MO2 (b) MO3

(c) MO4 (d) MO5

(e) WT

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Figure 3.8: EP centroids for MO2 (a), MO3 (b), MO4 (c) ,MO5 (d) ,WT (e) clustering. Each centroid is defined as a point in the space of the four chosen features: RMS power, maximum Voltage, the power gradient and the time for which the signal is above 5σ.

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3.3 Combined LFP recording and imaging clustering

In this section we show the correlation between the two labeling systems we have im-plemented. In Figure 3.9, 3.10, 3.11, 3.12, 3.13 the independent EP and imaging cluster-ing are juxtaposed with the intent to show qualitatively when the former is able to map the results of the latter, based on a time correlation principle. The Figure 3.14 intuitively communicate a quantitative measure of how much the EP clustering allows to predict the topology of the associated activation domain (high Ca2+ domains). The tables, in facts, show how much (in percentage) an electrophysiological cluster corresponds temporally to an imaging cluster, allowing to understand how precisely electrophysiology clustering labels calcium events.

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Figure 3.9: MO2, from top to bottom, imaging labeling, EP labeling, rmsPower comparison.

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Figure 3.11: MO4, from top to bottom, imaging labeling, EP labeling, rmsPower comparison.

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(a) MO2

(b) MO3 (c) MO4