ABSTRACT 77

AN ORIGINAL MATHEMATICAL FORMULA FOR COMPUTERIZED GENERATION OF DIFFERENT ELECTROCARDIOGRAMS:  A NEAR VIEW TO PERFECT MATHEMATICAL MAPPING OF NORMAL AND ABNORMAL ELECTROCARDIOGRAMS

Vahid Reza Abbasi (abbasi@sums.ac.ir)
Shiraz University of Medical Sciences, Shiraz, Iran

Introduction:  The generation and automated interpretation of normal and abnormal electrocardiograms through mathematical methods have been major areas of research for several decades.  If we consider the electrocardiograph to be a Cartesian plane, the data from each lead can be represented by a cyclic mathematical function correlating voltage to the independent variable of time:  Voltage = f (time).  The ECG strip, then, is simply a two-dimensional plot of the heart’s electrical activity along the axis of time.  This paper presents a new mathematical function (Pahlavi University formula), which, for the first time, is capable of generating normal 12-lead ECG’s and nearly all patterns of abnormal electrocardiograms.

Materials and Methods:  Using the Quick-Basic programming language on the personal computer, the mathematical function most closely approximating the morphology of electrocardiograms was found through trial and error.  When the crude features of the formula were worked out, the coefficients were refined based on the known parameters of each lead that  composed the 12-lead ECG.  Using these parameters, the coefficients for generating normal 12-lead ECGs, and some known patterns of abnormal ECG’s, were calculated.

Results and Conclusions:  The twenty-eight coefficients of the formula for generating a normal 12-lead ECG’s are present in a 12.28 matrix.  A similar, but larger, matrix has been partially completed representing patterns of electrical abnormality common to some cardiac diseases – hopefully, this project will be complete in the near future.

The basic function is flexible enough to incorporate multiple abnormalities in a single electrocardiogram.  The parametrical approach of the function allows for near-perfect replication of the electric signatures of cardiovascular disease.  By correlating a patient’s electrocardiograph with the function, the resultant equation can be compared with known equations of disease and a diagnosis made by an automated system.

While the technology is very promising, the complexity of the real world of electrocardiography, may be difficult to simulate in the ideal language of mathematics.  The efficacy and accuracy of this system in the clinical settings still requires much more research and testing to reliably serve our healthcare providers.