Abstract
The main aim of this study was the formula application of the superficial area of a truncated prolate spheroid (TPS) in Cartesian coordinates in obtaining a cardiac parameter that is not so much discussed in literature, related to the left ventricle (LV) surface area of the human heart, by age and sex. First we obtain a formula for the area of a TPS. Then a simple mathematical model of association of the axes measures of a TPS with the axes of the LV is built. Finally real values of the average dimensions of the humans LV are used to measure surface areas approximations of this heart chamber. As a result, the average superficial area of LV for normal patients is obtained and it is observed that the percentage differences of areas between men and women and their consecutive age groups are constant. A strong linear correlation between the obtained areas and the ventricular volumes normalized by the body areas was observed. The obtained results indicate that the superficial area of the LV, besides enabling a greater knowledge of the geometrical characteristics of the human LV, may be used as one of the normality cardiac verification criteria and be useful for medical and biological applications.
Highlights
The human heart possesses four chambers: right atrium, left atrium, right ventricle, and left ventricle (LV)
We developed a mathematical model that associates real data of the LV dimensions of normal patients with the dimensions of a truncated prolate spheroid (TPS) and, we have obtained approximations of the surface area of this cardiac chamber, so important for the functioning of the circulatory system
In this work the demonstration of the formula to obtain the surface area of a TPS in Cartesian coordinates has been done, in order to associate its parameters with dimensions of axes of human LV
Summary
The human heart possesses four chambers: right atrium, left atrium, right ventricle, and left ventricle (LV). Some of the main cardiac parameters for the LV, which allow verifying the normality of the heart function, are as follows: ventricular volume, ejection fraction, shortening fraction, and ventricular mass. They are based on the fact that this chamber possesses a similar geometry to the ellipsoid of revolution, or, still, to a truncated prolate spheroid (TPS), implying that two of its axle shafts must have equal measures [4,5,6,7,8,9]
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