Abstract :
The bio-electric potentials arising in the Purkinje fibres of the heart may by suitable apparatus be displayed and recorded. The resulting trace, known as an electrocardiogram, has characteristics designated by the letters P, Q, R, S, T, as indicated on Fig. 1. Both P and T ?waves? are seen to be rounded as compared with the QRS ?complex.? The latter is comparatively rich in ?high? frequencies (say, greater than 50 c/s), but to what extent, and as to which frequencies, can only be accurately assessed by Fourier analysis. Experimentally, using a Wave Analyser, this is a relatively simple matter, but to make a Fourier analysis of the electrocardiogram would be prohibitively time-consuming if carried out for individual patients. There is, however, an advantage in studying mathematically some of the more outstanding types of QRS impulse (or simple approximations thereto), as in this way theoretical support can be adduced for the contention that the results of experimental wave analysis really do refer, at least mainly, to impulses arising in the Purkinje fibres of the human heart and not to potentials having their origin in the general body muscles. The latter appear as a sort of roughness superposed on the trace, and when analysed definitely cause effects at the higher frequencies. Mathematical analysis of the kind given in the present paper helps in separating out the various bio-electric phenomena. An initial account in terms of elementary Fourier Analysis (leading to the well-known line spectrum of harmonic components) helps to establish the somewhat surprising fact that the impulses from the human heart do not require this form of treatment. The experimental frequency analysis corresponds, on the contrary, to isolated impulses, successive ?kicks? of the needle varying somewhat according to the variation in shape from impulse to impulse. The mathematical development proceeds with this fact in mind, and a large number of variants is provided with continuous ?spectra,- ? by application of Fourier´s Integral Theorem. In cases of patients giving particularly large P or T waves it may be necessary to take them into account, particularly at the lower frequencies. Suitable analyses are given. Experimentally, a technique is always available for separate study of P and T waves.
