The authors carried out the study of the state of systemic and cerebral hemodynamics in normal conditions and in various neurosurgical pathologies using modern signal processing methods. The results characterize the condition for the mechanisms of cerebral circulation Institute of Computer Science and Control, Higher School of Cyber-Physical Systems and Control regulation, which allows for finding a solution to fundamental and specific clinical problems for the effective treatment of patients with various pathologies. The proposed method is based on the continuous wavelet transform of systemic arterial pressure and blood flow velocity signals in the middle cerebral artery recorded by non-invasive methods of photoplethysmography and transcranial doppler ultrasonography. The study of these signals in real-time in the frequency range of Mayer waves makes it possible to determine the cerebral autoregulation state in certain diseases before and after surgical interventions. The proposed method uses a cross-wavelet spectrum, which helps obtain wavelet coherence and a phase shift between the wavelet coefficients of systemic arterial pressure signals and blood flow velocity in the Mayer wave range. The obtained results enable comparing the proposed method with that based on the short-time Fourier transform. The comparison showed that the proposed method has higher sensitivity to changes in cerebral autoregulation and better localization of changes in time and frequency.
This work is devoted to the description and comparative study of some methods of mathematical modeling. We consider methods that can be applied for building cyber-physical systems and digital twins. These application areas add to the usual accuracy requirements for a model the need to be adaptable to new data and the small computational complexity allows it to be used in embedded systems. First, we regard the finite element method as one of the “pure” physics-based modeling methods and the general neural network approach as a variant of machine learning modeling with physics-based regularization (or physics-informed neural networks) and their combination. A physics-based network architecture model class has been developed by us on the basis of a modification of classical numerical methods for solving ordinary differential equations. The model problem has a parameter at some values for which the phenomenon of stiffness is observed. We consider a fixed parameter value problem statement and a case when a parameter is one of the input variables. Thus, we obtain a solution for a set of parameter values. The resulting model allows predicting the behavior of an object when its parameters change and identifying its parameters based on observational data.
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