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Metrological Approach to Structural Complexity Estimation in Brain Biopotential Analysis System


L.G. Akulov, R.V. Litovkin

Article describes method for analysis structural complexity in measurement systems. As example we take bioinstrumental system for analysis brain electrical potentials. Such system formalized with signal graph of category. There are 12 vertexes in graph, what formalized determinate sources and chaotic sources and other measurement operations. As approach to estimation of structural complexity we can take any function with consideration number of vertex and relations between them. As relations we can take metrological characteristics, what make it easy to analysis system. In that approach every vertex may vary in number of classical states such as hypothetical state, ideal state and real state. Every state we can code with accordance as “0”, “1” and “2”. There are 15 ways in graph from sources to point of signal analysis and interpretation. As equivalent states of system we take states with same numbers of derivation from state with “0” derivation. If system has several ways from sources to interpretation point, we take way with maximum derivation.  Next step is computing all possible states of system with posterior assignment them to one of the equivalent classes. Knowledge of class distribution can provide probability of system statement in one of the equal classes. As integral function of structural complexity we can take entropy function, what depends on probability and have additive property. For described system we computed entropy with several approaches to distribution. It is shown that entropy increase with increasing complexity of computing method
May 29, 2020

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