Uyarlamalı üstel tut&ateşle (AdExI&F) sinir hücresi modeline yönelik bir sinaptik bağlantı ve devre benzetimi
A synaptic coupling for the adaptive exponential integrate and fire (AdExI&F) neuron model with circuit simulations
Yazar: AYŞEN BAŞARGAN
Danışman: PROF. DR. İ. SERDAR ÖZOĞUZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı / Elektrik Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2013
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering
Dizin: Nörofizyoloji = Neurophysiology ; Nöron sistemleri = Neuron systems ; Nöronlar = Neurons ; Sinapslar = Synapses

Özet:
Bu yüksek lisans tezinde, daha önce Hindmarsh-Rose sinir hücresi modeli için kullanılmış olan sinaptik bir bağlantı, uyarlamalı üstel tut&ateşle modeli için uyarıcı ve kısıtlayıcı bağlantı şeklinde uygulanmış, düzenli ve patlamalı ateşleme için aynı fazlı ve zıt fazlı davranışlar görülmüştür. Daha sonra, sinir hücresi ve sinaptik bağlantı modellerinin düşük güçlü ve akım modlu olacak şekilde devre benzetimleri yapılmış ve sayısal analizle uyumlu sonuçlar elde edilmiştir.Hodgkin-Huxley sinir hücresi modeli gerçek sinir hücresini en iyi modelleyen, biyolojik olarak anlamlı ve ölçilebilir matematiksel bir sistemdir. Model dört eşitlik ve on parametreden oluşmaktadır. Bu nedenle Hodgkin-Huxley sinir hücresi modeli biyolojik olarak anlamlı olmasına rağmen, ifadesi karmaşık ve uygulaması maliyetlidir. Bu sorunu çözebilmek için literatürde son birkaç yılda hesaplaması basit, anlaşılması ve analizi kolay ayrıca gerçek sinir hücresi davranışlarını oluşturabilen Izhikevich sinir hücresi modeli, uyarlamalı üstel tut ve ateşle sinir hücresi modeli gibi modeller tanımlanmıştır. Uyarlamalı Üstel Tut&Ateşle (AdExI&F,2005) sinir hücresi modelinin parametreleri fizyolojik niceliklerle ilişkilendirilebilmekte, piramit tipi hücrelerin davranışlarını başarıyla kopyalayabilmekte ve piramit tipi hücrelerin biyofiziksel modeline uymaktadır. Bu modelin tercih edilmesinin en önemli nedeni, az parametre ile zengin ateşleme örüntüleri oluşturabilmeleridir.Canlıların ritmik hareketleri merkezi sinir düğümüne yerleşmiş ya da omuriliğe yerleşmiş merkezi örüntü üreteciyle (CPG) kontrol edilmektedir. CPG'ler ile hücrelerin periyodik davranışları arasında matematiksel bir ilişki tanımlanmıştır. Parmak tıklatma, el çırpma, alkışlama, dört ayak üzerinde hareket CPG'de üretilen örüntülere örnek olarak verilebilir. CPG'ler biyolojik nöronların lineer olmayan dinamik modellerine dayanan elektronik nöronlardan kurgulanabilmektedirler. Elektronik CPG tasarımlarında temel davranışlar olan kısıtlayıcı ve uyarıcı sinapsların her ikiside kullanılmaktadır. Hindmarsh-Rose sinir hücresi modeli için kullanılan sinaps modeli AdExI&F modeli için de kullanılmış, kısıtlayıcı ve uyarıcı bağlantı için düzenli ateşleme ve düzenli patlamalı ateşleme davranışları sayısal olarak analiz edilmiştir. Kısıtlayıcı bağlantı durumunda hem aynı fazlı davranış hem de zıt fazlı davranış elde edilebilmektedir. Bu durum faz farkı için başlangıç koşulları değiştirilerek elde edilmektedir. Uyarıcı bağlantı için ise sadece aynı fazlı eş zamanlıdavranış görülmektedir. Bir sonraki aşamada ise, sinir hücresi modeline ve sinaps modeline karşılık gelen düşük güçlü, akım modlu devre benzetimi yapılmış, elde edilen sonuçların daha önceki model ile elde edilen sonuçlara göre daha başarılı olduğu gözlemlenmiştir.

Abstract:
In this M.Sc. thesis, by using adaptive exponential integrate and fire model and synaptic connection, which was used with Hindmarsh-Rose neuron model, is observed anti-phase and in-phase locking for excitatory and inhibitory coupling for tonic spiking firing pattern and regular bursting firing pattern. Later, circuit, which is with low power and current mode, simulation of these models is realized and simulation results are identical which are numerically observed. First of all, a neuron is a nerve cell that is the basic building block of the nervous system. A typical neuron possesses a cell body, often called the soma, dendrites, and an axon. The soma contains a neuron cell and nucleolus. Dendrites are thin structures that arise from the cell body, often extending for hundreds of micrometres and branching multiple times, giving rise to a complex "dendritic tree". The dendrites are responsible for picking up information from neighboring neurons and transmitting this information to the cell body, also known as the soma. An axon also known as a nerve fibre; is a long, slender projection of a nerve cell, or neuron. The axon is the elongated fiber that extends from the cell body to the terminal endings and transmits the neural signal. From the soma, the information is passed on along the axon, another structure in the nerve cell, and the axon in turn transmits signals to the dendrites of neighboring neurons. A small gap at the end of a neuron is called synapse that allows information to pass from one neuron to the next. A neuron is an electrically excitable cell that processes and transmits information through electrical and chemical signals. A typical neuron receives inputs from more than 10.000 other neurons through the contacts on its dendritic tree called synapses. The inputs produce electrical transmembrane currents that change the membrane potential of the neuron. Synaptic currents produce changes, called postsynaptic potentials (PSPs). Small currents produce small PSPs, larger currents produce significant PSPs that can be amplified by the voltage-sensitive channels embedded in the neuronal membrane and lead to the generation of an action potential or spike, an abrupt and transient change of membrane voltage that propagates to other neurons via a long protrusion called an axon. In general, neurons do not fire on their own, they fire as a result of incoming spikes from other neurons. From the neuronal level we can go up to neuronal circuits, to cortical structures, to the whole brain, and finally to the behavior of the organism.The neurons split up two types. The first one of these neurons is described neurons as integrators with a threshold. Neurons sum incoming PSPs and compare the integrated PSP with a certain voltage value, called the firing threshold. If it is below thethreshold, the neuron remains quiescent; when it is above the threshold, the neuron fires an all-or-none spike. Integrators neurons prefer high-frequency input. The higher the frequency of the input, the sooner they fire. The other types are called resonator neurons. Resonators prefer oscillatory input with the same frequency as that of damped oscillations. Increasing the frequency may delay or even terminate xxiitheir response. It can be understood from this sample that neurons are mathematical systems. To understand how the brain works, it is needed to combine experimental studies of animal and human nervous systems with numerical simulation of largescale brain models. As it is developed such large-scale brain models consisting of spiking neurons, it must be found compromises between two seemingly mutually exclusive requirements. The model for a single neuron must be firstly computationally simple, yet capable of producing rich firing patterns exhibited by real biological neurons.One of the most important models in computational neuroscience is the HodgkinHuxley model of the squid giant axon. Using pioneering experimental techniques of that time, Hodgkin and Huxley (1952) determined that the squid axon carries three major currents: voltage-gated persistent K+ current with four activation gates,voltage gated transient Na+ current with three activation gates and one inactivation gate, and Ohmic leak current which is carried mostly by Clions.All living cells have an electrical voltage, or potential difference, between theirinside and outside. Since the cell's membrane is what separates the inside from the outside, this potential difference is referred to as the membrane potential. The resting potential refers to the potential across the membrane when the cell is at rest. A typical neuron has a resting potential of about -70mV and ions which enter and leave cell make neuron generate an action potential. An inward current corresponds to a positively charged ion, such as Na+, entering the cell. This raises the membrane potential; that is, it brings the membrane potential closer to zero. In this case, the cell is said to be depolarized. An outward current corresponds to a positively charged ion, such as K+, leaving the cell or a negatively charged ion, such as Cl-, entering the cell. In this case, the cell becomes hyperpolarized. There are two types of ion channels in the membrane, gated and non-gated. Non-gated channels are always open, whereas gated channels can open and close and the probability of opening often depends on the membrane potential; these are referred to as voltage-gated channels. Gated channels are typically selective for a single ion. Neurons at rest are permeable to Na+and Clin addition to K+. Because of their concentration differences, Na+and Clions move into the cell and K+ions move outward. The influx of Na+ions tends to depolarize the cell, whereas the efflux of K+and the influx of Clhave the opposite effect. The resting potential of the cell is the potential at which there is a balance between these fluxes. It depends on the concentrations of the ions both inside and outside the cell, as well as the permeability of the cell membrane to each of the ions. At rest, many more K+and Clchannels than Na+channels are open; hence, the cell's resting potential is determined primarily by the K+and Cl- Nernst potentials. For a cell to maintain a constant resting potential, the efflux of K+ions must balance the influx of Na+ions here Clions are ignored.The basic mechanisms underlying action potentials are; the following. At rest, most of the Na+channels are closed, so the membrane potential is determined primarily by the K+ Nernst potential. If the cell is depolarized above some threshold, then Na+channels open and this further depolarizes the cell. This allows even more Na+channels to open, allowing more Na+ ions to enter the cell and forcing the cell toward the Na+ Nernst potential. This is the upstroke of the action potential. The Na+channel is transient, so even when they are depolarized, the Na+channels eventually shut down. In the meantime, the depolarization opens K+channels and K+ions exit the cell. This hyperpolarizes the cell as the membrane potential moves toward the K+equilibrium potential. Until the voltage-gated K+channels close up again, the xxiiimembrane is refractory. During this time, pumps exchange excess Na+ions inside the cell with excess K+ions outside the cell. Only a very small change in the concentration of Na+ions is needed to generate an action potential.In general, scientists refer to all conductance-based models as being of the Hodgkin–Huxley-type. Such models are important not only because their parameters are biophysically meaningful and measurable, but also because they allow us to investigate questions related to synaptic integration, dendritic cable filtering, effects of dendritic morphology, the interplay between ionic currents, and other issues related to single cell dynamics. The model consists of four equations and tens of parameters, so although the model is biophysically meaningful, it is complicated and is extremely expensive to implement.In literature over the last few years, neuron models, which are computationally simple, easy to understand and analyze also capable of producing rich firing patterns exhibited by real biological neurons like Izhikevich neuron model and adaptive exponential integrate and fire neuron model, is described. The adaptive exponential integrate-and-fire model's (AdExI&F,2005) parameters can be easily related to physiological quantities, and the model has been successfully fit to a biophysical model of a regular spiking pyramidal cell and to real recordings of pyramidal cells.The most important reason for preferring this model is possible to arise rich firing patterns with least parameters. Tonic spiking, adaptation, initial burst, regular bursting, delayed accelerating, delayed regular bursting, transient spiking and irregular spiking can be given as an example of how the different firing patterns arise with simple adaptive exponential integrate-and-fire model.The Adaptive Exponential Integrate-and-Fire model (AdEx) describes the evolution of the membrane potential when a current is injected. It consists of a system of two differential equations and four parameters. When the current drives the potential beyond the threshold voltage, the exponential term actuates a positive feedback which leads to the upswing of the action potential. The exponential is related to the quasi-instantaneous reaction of the activation variable of the sodium channel in a Hodgkin–Huxley-type neuron model. The upswing is stopped at a reset threshold. The downswing of the action potential is replaced by the reset condition.Rhythmic motions of animals are controlled by central pattern generators (CPGs) resident in central ganglia or the spinal cord. We will consider three examples: finger tapping, hand clapping, and quadrupedal locomotion. CPGs can be constructed from electronic neurons based on non-linear dynamical models of biological neurons. It can be seen to implement an electronic neuron circuit, the Hindmarsh-Rose neuron model is used. For AdExI&F neuron model, the same synapse model is used and for excitatory and inhibitory coupling, tonic spiking firing pattern and regular bursting firing pattern is numerically analyzed. In case of inhibitory coupling, in-phase and anti-phase locking occurs which can be achieved for different initial conditions of the phase difference. When the coupling is excitatory, the in-phase locked state can be seen only.The next step is that low power current mode circuit is simulated for neuron and synapse model and simulation results is more successful than the other neuron model's simulation results which was analyzed before