International Journal of Cardiovascular and Cerebrovascular Disease 1(1): 10-14, 2013 http://www.hrpub.org DOI: 10.13189/ijccd.2013.010102 A Mathematical Evaluation of Mitral Regurgitation Severity with EROA Kalpana Saini 1,* , M. L. Dewal 1, , Manojkumar Rohit 2 1 Department of Electrical Engineering, Indian Institute of Technology Roorkee, Uttarakhand, 247667, India 2 Adavnced Cardiac Center, Post Graduate Institute of Medical Education and Research, Chandigarh, India *Corresponding Author: kal_2312@rediffmail.com Copyright © 2013 Horizon Research Publishing All rights reserved. Abstract It is to be investigated and verified that vena contracta width (VCW) obtained from color Doppler images and effective regurgitant orifice area (EROA) obtained from the VCW is capable of quantifying the severity of mitral regurgitation (MR). A mathematical expression has been developed between VCW and EROA. Vena contracta width is an efficient method for grading the severity of MR, but it is very difficult to locate this narrowest part exactly in transthoracic echocardiography as well as in transesophageal echocardiography. So, indeed, there is a need to develop a method which is capable of finding out the vena contracta width. A comparison has also been made between the results obtained using the proposed computing method and the results obtained by the clinicians, manually. For this analysis have been done from the results obtained with automatic VCW finding method and with clinical data for severity grading. Keywords Vena Contracta Width, Effective Regurgitant Orifice Area, Mitral Regurgitation, Severity Grading, Transthoracic Echocardiography, Transesophageal Echocardiography 1. Introduction At present interest in color Doppler imaging for vena contracta for the assessment of mitral re gurgitation is increasing progressively [1], [2] and [3]. The vena contracta is the narrowest part of the regurgitant jet, which can also be called as ‘neck’ of the jet [4] and having location just downstream from the orifice and before the jet area [5]. The cross sectional area is directly related to the regurgitant orifice area. Due to the complex and the unpredictable shape, it is very difficult to measure the regurgitant orifice area. For such a measurement jet is to be imaged in the short axis plane. In clinical settings, it is very difficult to localize the narrowest area from the jet. So a correlation is measured between the VCW which is measured from the zoomed view of the parasternal long axis and the apical views, and the EROA, by quantitative Doppler [3]. Relationship between the EROA and the VCW given at many places in the literatures [6], [7] and [8]. This relationship shows good results even in eccentric MR [9]. The VCW is the one dimensional measurement whereas EROA is the two dimensional so there are some limitations also. But in [10] it shown that VCW is the much better tool for measurement of severity of MR. Such as VCW less than 0.3cm indicates the mild MR. If this value is in between 0.3 and 0.5 then it is the case of moderate MR. But if the VCW is more. than 0.5cm than it indicates the severe MR. In any view the localization of the VCW is very difficult. So an experienced clinician is required for the measurement of such a narrowest portion. This gets very time consuming also to locate the exact VC. Hence as discussion in our research paper [14] an automatic segmentation have been done of echocardiographic images to get VCW. In this paper, a mathematical solution is derived which gives a relation between VCW and EROA. 2. Mathematical Treatment for EROA Calculation Mathematically, blood flow can be described by Darcy's law (which can be viewed as the fluid equivalent of Ohm's law) and approximately by Hagen-Poiseuille equation: ' P Darcy slaw F R ∆ = (1) ( ) ( ) 4 8 L Hagen PoiseuilleEquation R r ν π − = (2) Where F is blood flow, P is pressure, R is resistance, ν is blood viscosity, L is length of tube, and r is radius of tube. Here we are trying to calculate the vena contracta width according to the explanation given in [11]. However they used their formulation for the fluid flow. Here motive is to find out the vena contract width formulation for the mitral regurgitation jet.