Application of fractional calculus to distinguish left ventricular hypertrophy with normal ECG

Abstract

ECG graphs are the rough type of graphs which are continuous everywhere but non-differentiable at some points of PQRST complexes of each leads of ECG. These non-differentiable points cannot be interpreted by usual classical calculus but it can be characterized by fractional calculus. In this paper we have applied fractional calculus to distinguish Left Ventricular Hypertrophic ECG from Normal ECG. To interpret the non-differentiable points we have calculated modified left and right Riemann-Liouville fractional derivatives, corresponding Phase Transition(P.T.) values (i.e. difference between left and right modified R-L fractional derivative), mean and standard deviation of the P.T. values at the non-differentiable points of the considerable ECG leads. From the study we observe that the P.T. values are higher for Left Ventricular Hypertrophy cases compared to the normal ones. In addition for LVH patients mean and standard deviation of the P.T. values of considerable ECG leads are higher than those for normal ECGs. This may be a new approach to study any ECG via fractional calculus.