Nowadays, spectral analysis is one of the perspective trends of mathematics analysis of heart work. However, researchers face some problem. First of all it depends on the fact that tachogram are non-stationary, which is itself a serious obstacle for spectral methods.
This circumstance is discussed in the following article.
As an object of research we consider a sequence of intervals between heartbeats, where - a beat number in a row of beats. Choosing the formal model of the process for tachogram representing we considered all the proposals that had been discussed in literature. One of them is eventual with the use of delta-functions spectral presentation. The presentation of a tachogram as a sequence with unequal intervals is also among them. And the last one is an approximate presentation of the same sequence with equal intervals on the basis of preliminary interpolation of initial process with unequal intervals.
Summing it up in this work we used 2 versions of models according to the presentation of circulation system as a two-loop regulation system:
an additive model, for witch and , where - an interval mean , - trend variation (a low – frequency component) and - a quick component variation;
a multiplicative model, for which , where and correspondingly, relative trend and quick component variations. In the process of models are equal under the condition that certain accurateness is maintained.
The separation of general variation to their components – trend variation and quick variation must correspond certain requirements:
frequency of specter and separation must be equal to 0.04 Hz.
The separation is carried out with the assistance of slide filtration of the full tachogram by adapted finite impulse response filter , where - weighting coefficients, - number of coefficient, for which ; - filter size, and - integer ; - filter parameter, (for integers is the degree of fitting polynomial degree). The sequence is formed in the process of filtration . Then follows the sequence . The separation of the sequence to sequences and is an adaptive iteration numeral procedure with an argument . Then all the sequences , and will be objects of direct spectral transformation.
Standard methods of correlation theory lay in the basic of spectral estimation calculation. It is connected with the fact that autocorrelation functions got while calculation of spectral estimation realization let certain quantity and conclusions about the researched process be formed.
Combined autocorrelation and spectral functions analysis let us research the stationary of tachogram. In particular, according to the forms of the functions it is possible to choose such an interval of observation, that tachogram can be regarded as almost stationary. That is necessary for very application of spectral methods. Let’s stress that in many cases the length of tachogram permissible for such a processing is not 100-150 counts more.
Autocorrelation and spectral functions comparison also permit to speak about nonlinear phenomenon in a tachogram.
Summing up the results of the previous procedures application we may conclude the following:
Slow component of a tachogram – trend, remarkable for its sharp non-stationary, which distort the spectral analysis tachogram results. However, it is necessary to get an autocorrelation function of a trend.
Quick component can be highly stationary.
The removal of a trend from the initial tachogram gives possibility to edit tachograms to remove various artifacts. It also makes possible to apply spectral procedures to the quick component.
Trend calculation makes it possible to quantitatively evaluate various outward influences on the cardiorythm.