Journal of Applied Nonlinear Dynamics
Prediction of Ventricular Hypertrophy of Heart Using Fractional Calculus
Journal of Applied Nonlinear Dynamics 9(2) (2020) 287305  DOI:10.5890/JAND.2020.06.010
Srijan Sengupta$^{1}$, Uttam Ghosh$^{1}$, Susmita Sarkar$^{1}$, Shantanu Das$^{2}$
$^{1}$ Department of Applied Mathematics, University of Calcutta, Kolkata,
$^{2}$ Reactor Control System and Design Section (E and I Group), Bhabha Atomic Research Center, Mumbai, India
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Abstract
In this paper we have studied Left and Right ventricular hypertrophy of heart from ECGs using fractional calculus. An ECG is a rough or unreachable curve which is continuous everywhere but nondifferentiable at some points or all points where classical calculus fails.
Our purpose of this paper is to find left and right fractional derivatives at those nondifferentiable points and then predict LVH and RVH by calculating the phase transition values (absolute difference of left and right fractional derivatives). Our investigation shows that for LVH patients the phase transition values at the nondifferentiable points of V1, V2, V5 and V6 leads are higher than those for normal ECG. For RVH ECG the phase transition values at S are smaller than those of R in V1 leads which are just opposite to the case of normal ECGs. Fractal dimension and Hurst Exponents of V1, V2, V5 and V6 leads of the ECGs have been calculated for both problematic and normal ECGs. All such measures may help doctors to diagnose LVH and RVH from ECG more accurately than the technique they use.
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