| Popis: |
Samo-organizirana kritičnost in kritična dinamika sta lastnost različnih dinamičnih sistemov, ki so sestavljeni iz mnogih gradnikov in so nelinearni. Za te sisteme je značilno, da porazdelitev velikosti posameznih dogodkov sledi potenčni funkciji. Pojma zadnja leta pridobivata na veljavi na področju nevroznanosti, saj so plazovite nevronske aktivnosti, katerih porazdelitev velikosti sledi potenčni funkciji, opazili na različnih velikostnih skalah nevroloških sistemov, med njimi tudi v centralnem živčevju sesalcev. Kritična dinamika se povezuje z optimalnim delovanjem in v teoriji odraža obnašanje na območju faznega prehoda med redom in naključnostjo. Teoretične in numerične raziskave osnovnih modelov sklopljenih nevronov potrjujejo kritično dinamiko sistema zgolj za ozko območje izbranih parametrov, kar ni v skladu z realnimi biološkimi sistemi, ki so po naravi heterogeni. Zato v nalogi osnovni numerični model nadgradimo z vpeljavo različnih realnih mehanizmov in nevrobioloških determinant ter preverimo njihov vpliv na prostorsko-časovno aktivnost. V model vpeljemo heterogenost v ravneh vzdraženosti, kompleksno strukturo interakcij med nevroni, šibko zunanje periodično vzbujanje in heterogenost v sklopitvi. Izkaže se, da določene oblike prostorske heterogenosti, zunanjega vzbujanja in vpeljava kompleksnejše mreže interakcij znatno razširijo območje kritičnega delovanja, medtem ko statična heterogenost v sklopitvi nima velikega vpliva. Naše ugotovitve pripomorejo k razumevanju mehanizmov samo-organizacijskih principov v nevroloških sistemih. Self-organized criticality and critical dynamics are properties of various dynamical systems that are constituted by many elements and are essentially nonlinear. One of the main characteristics of these systems is that the size distribution of individual event sizes follows a power law. In recent years, these concepts have also been gaining attention in neuroscience, mainly due to the observation of avalanches in neuronal activity, whose size distribution follows a power law on different scales of neurological systems, including the central nervous system of mammals. Critical dynamics is associated with optimal performance and, in theory, reflects behavior in the phase transition between order and randomness. Theoretical and numerical studies of elemental models of coupled neurons confirm that the critical dynamics of the system occurs only in a narrow range of selected parameters, which is not in accordance with real biological systems that are heterogeneous in nature. Therefore, in the thesis, we upgrade the basic numerical model by introducing various realistic mechanisms and neurobiological determinants. We examine the impact of these on spatial-temporal neuronal activity. In the model, we introduce heterogeneity in the levels of excitability, a complex structure of interactions between neurons, a weak external periodic forcing and heterogeneity in coupling strength. It turns out that certain forms of spatial heterogeneity, external excitation, and the introduction of a more complex network of interactions considerably extends the critical dynamical regime, whereas static heterogeneity in the coupling does not have much influence on the neuronal activity. Our findings foster our understanding of the mechanisms related to self-organized criticality in neurological systems. |
