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 Matem. Mod., 2017, Volume 29, Number 12, Pages 147–156 (Mi mm3924)

Determination of instaneous cardiac rhythm parameters in multifractal dynamics model by regularized Newton's method

S. A. Mikheev, V. N. Ryzikov, V. P. Tsvetkov, I. V. Tsvetkov

Tver State University, Tver

Abstract: In this paper we present the system of nonlinear equations of multifractal dynamics (MFD) model which describes instantaneous cardiac rhythm (ICR) in the regular and jump areas. We present the numerical solution of this system of nonlinear equations obtained by Newton's method, and the ICR parameter values of MFD model based on the data of Holter monitoring (HM) of a patient of the Tver Cardiology Health Center. It was demonstrated that the necessary condition for ICR jump in the above case is the proximity of pre-jump ICR fractal dimension $D$ to the fractal dimension value in bifurcation point $D_b$ which was calculated in the MFD model.

Keywords: instantaneous heart rate, bifurcation catastrophes, multifractal dynamics model, instantaneous heart rate jumps, regularized Newton method.

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Citation: S. A. Mikheev, V. N. Ryzikov, V. P. Tsvetkov, I. V. Tsvetkov, “Determination of instaneous cardiac rhythm parameters in multifractal dynamics model by regularized Newton's method”, Matem. Mod., 29:12 (2017), 147–156

Citation in format AMSBIB
\Bibitem{MihRyzTsv17}
\by S.~A.~Mikheev, V.~N.~Ryzikov, V.~P.~Tsvetkov, I.~V.~Tsvetkov
\paper Determination of instaneous cardiac rhythm parameters in multifractal dynamics model by regularized Newton's method
\jour Matem. Mod.
\yr 2017
\vol 29
\issue 12
\pages 147--156
\mathnet{http://mi.mathnet.ru/mm3924}
\elib{https://elibrary.ru/item.asp?id=30674658}