Geodesic
Gradient descent method in computation of instantaneous cardiac rhythm multifractal model parameters
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2018), pp. 55-67

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In this paper we present the numerically solved system of nonlinear equations which determinates the parameters of multifractal dynamics model (MFD) of instantaneous cardiac rhythm (ICR) of one of the patients of Tver cardiology health center using a gradient descent method with step size optimization. We constructed the ICR change rate-fractal dimension relation. It follows that the ICR fractal dimension values in pre-jump time intervals are located in close proximity to the bifurcation point value while maximally deviating by just $0.04$. We showed that the ICR jump necessary condition is the proximity to the bifurcation point value of pre-jump ICR fractal dimension. We obtained the formula for evaluation of ICR jump area diameter, and on its basis we evaluated this diameter. We showed the proximity of the fractal dimension value in bifurcation point to the Gaussian value which was $1.5$. We wrote and implemented the software program to count the ICR jump frequency for the patient under examination. The average value was found to be $956.526$ hour$^{-1}$.
Keywords: instantaneous heart rate, multifractal dynamics model, instantaneous heart rate jumps, regularized Newton method.
Mots-clés : bifurcation catastrophes, gradient descent method 
@article{VTPMK_2018_1_a4,
     author = {E. V. Bespalko and V. A. Gubin and S. A. Miheev and V. P. Redchits and V. N. Ryzhikov},
     title = {Gradient descent method in computation of instantaneous cardiac rhythm multifractal model parameters},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {55--67},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2018_1_a4/}
}
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%A V. N. Ryzhikov
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E. V. Bespalko; V. A. Gubin; S. A. Miheev; V. P. Redchits; V. N. Ryzhikov. Gradient descent method in computation of instantaneous cardiac rhythm multifractal model parameters. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2018), pp. 55-67. http://geodesic.mathdoc.fr/item/VTPMK_2018_1_a4/