period doubling has been observed in ecg &# 39 ; s of experimental animals with high susceptibility to fibrillation as measured by the ventricular fibrillation threshold ( vft ) test . period doubling represents an excitation of a system at the first subharmonic of its fundamental frequency . in the context of the ecg it represents a modulation of the ecg waveform occurring on an every other beat basis &# 34 ; electrical alternans &# 34 ;. previous efforts at detecting doubling have utilized spectral techniques to measure the amount of waveform variability at the period doubling frequency . it has been recognized that the period doubling phenomena ( and other higher order periodicities may result from a nonliner autoregressive process which can also lead to chaotic aperiodic regimens ( feigenbaum , m . j ., &# 34 ; universal behavior in nonlinear systems &# 34 ;, los alamos science 1 : 4 , 1980 ). one simple nonlinear autoregressive operator which displays this behavior is x ( i )= 4λx ( i - 1 )[ 1 - x ( i - 1 )]. the parameter λ varies from 0 to unity and determines the strength of the coupling between x ( i - 1 ) and x ( i ) and also determines the periodicity of the behavior . in the method of this invention the linearly transformed sample points x ( i ) are fitted to the above equation and the strength of the coupling λ is determined . this measurement is much less sensitive to noise than is the case with spectral techniques . the expected periodicity could be effected by noise , yet λ could still be accurately determined . measurement of λ thus enables one to characterize the underlying beat - to - beat coupling which leads to both the periodic behavior and chaotic behavior . measurement of λ may provide an index of ecg waveform variability which may provide an improved correlation with susceptibility to ventricular fibrillation than previously available indices . the technique disclosed herein involves sampling an ecg or other physiologic waveform at corresponding fiducial locations for a series of cycles of the waveform . for example , when the ecg is the physiologic waveform , the ecg is sample at equal intervals after the peak of the qrs complex . it is to be understood that other portions of the ecg waveform may be utilized . the sampling operation generates a number for each beat in the ecg which represents the value of the ecg at the fiducial location . a scatter plot is made of the ith sample versus the ( i - 1 ) th sample . of course , it is not necessary to create an actual graph of the data points . what would be stored are the ordered pairs for the ith and ( i - 1 ) th samples . fig1 shows a representation scatter plot of the ith sample value versus the ( i - 1 ) th sample value . the exemplary data shown in fig1 are fitted to the equation x ( i )= 4λx (- 1 )[ 1 - x ( i - 1 )] using an iterative method to determine the value of λ which minimizes the sum of the total distances of the points to the curve . the single parameter λ is used to quantify the degree of alternation in the sampled waveform . the above equation has been much studied in the context of strange attractors and the transition to chaos of dynamical systems . for systems described by this equation , period doubling is observed for 0 . 75 & lt ; λ & lt ; 0 . 87 . as λ is increased further , a cascade of period doublings is observed . this cascade terminates in an aperiodic ( chaotic ) system for λ greater than 0 . 89 . it has been shown that many dynamic systems behave similarly to the above equation as the chaotic limit is approached . in this sense , λ can be used to measure how close a system is to chaos . fig2 shows a physical implementation of the present technique . the physiologic waveform , for example , an ecg is recorded , block 10 , and sample in the sampler 12 . as discussed above , sampling may be performed at equal intervals after the peak of the qrs complex of an ecg . the output of the sampler 12 is stored in a computer 14 which uses an iterative method to minimize the sum of the total distances of the sample points to the curve described by the above set forth equation . the output of the computer 14 is the parameter λ . as stated above , period doubling in an ecg is correlated with high susceptibility to fibrillation as measured by the ventricular fibrillation threshold test . the above set - forth equation exhibits period doubling when λ exceeds 0 . 75 . therefore , a value of λ exceeding 0 . 75 indicates high susceptibility to fibrillation . this technique may also be utilized with other physiologic waveforms such as blood pressure and respiration waveforms . it is recognized that modifications and variations of the present invention will be apparent to those skilled in the art and it is intended that all such modifications and variations be included within the scope of the appended claims .
myocardial electrical stability is assessed by sampling an ecg waveform at corresponding fiducial locations for a plurality of beats and creating a scatter plot of the i th sample versus the th sample . a parameter λ is determined which minimizes the sum of the total distances of the points of the scatter plot to an equation x = 4λx ]. the value of the parameter λ is related to the electrical stability of the heart .