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### Investigation of Left Ventricular Hypertrophy using Mean Deviation Function

#### Author(s)

Srijan Sengupta 1, Uttam Ghosh 1, Susmita Sarkar 1, Shantanu Das 2

#### Affiliation(s)

1 Department of Applied Mathematics, University of Calcutta, Kolkata, India
2 Reactor Control Systems Design Section E & I Group BARC Mumbai, India

Uttam Ghosh

#### ABSTRACT

In this paper we have projected a new methodology to characterize non-differentiable graphs. The continuous functions but non-differentiable at some points or every points may be characterized via mean deviation function. The mean deviation function is the deviation of the mean function from the original function. It is differentiable and approximates the given non-differentiable function. This is a new type of characterization of unreachable graphs. Since ECG graphs are continuous everywhere but non-differentiable at a few number of points thus in this paper we have used this new methodology to find some distinguishable measurements of left ventricular hypertrophy by comparing normal and problematic ECGs.

#### KEYWORDS

Mean function, Deviation function, non-differentiability of ECG graphs, Left Ventricular Hypertrophy.

#### CITE THIS PAPER

Srijan Sengupta, UttamGhosh, Susmita Sarkar, and Shantanu Das, Investigation of Left Ventricular Hypertrophy using Mean Deviation Function, Journal of Physics Through Computation (2019) Vol. 2: 41-46. DOI: http://dx.doi.org/10.23977/jptc.2019.21009.

#### REFERENCES

[1] S. Das(2011). Functional Fractional Calculus 2nd Edition, Springer-Verlag.
[2] S. Sengupta,U. Ghosh, S. Sarkar and S. Das(2018).A Mathematical Approach to Characterize Left Ventricular Hypertrophy from ECG Diagrams.Open Journal of Cardiology & Heart Diseases. Vol. 1; Issue No. 2.
[3] F. Ben Adda(2007). Mathematical Model for Fractal Manifold, International Journal of Pure and Applied Mathematics, vol.38 (2), 155-186.
[4] S. S. Ray, R.K. Bera(2005). An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method. Applied Mathematics and Computation. 167 561–571.
[5] V. S. Erturk and S. Momani(2008).Solving systems of fractional differential equations using differential transform method. Journal of Computational and Applied Mathematics 215 142 – 151
[6] S. Sengupta, U. Ghosh, S. Sarkar and S. Das(2018), "Application of fractional calculus to distinguish left ventricular hypertrophy with normal ECG," 4th International Conference on Recent Advances in Information Technology (RAIT), Dhanbad, 2018, pp. 1-6.
[7] G. Jumarie(2006), Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results, Computers and Mathematics with Applications, 51. 1367-1376.
[8] U. Ghosh, S. Sengupta, S. Sarkar and S. Das(2015). Characterization of non-differentiable points of a function by Fractional derivative of Jumarie type. European Journal of Academic Essays. 2(2): 70-86.
[9] R.P. Feynman, Quantum Electrodynamics, W.A. Benjamin, New York (1961)
[10] B. B. Mandelbrot, (1982). The Geometry of Nature. Freeman. San Francisco
[11] J. R. Hampton (2010). The ECG made easy. Eighth ed.
[12] ECGs are available from Internet (free Google Images).