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The Projects and Studies.

• Sum(QX) - sum of squares of least distances from graph nodes before axis ó. (Heart rate graph is inserted in square with side to equal variational range (VR): VR=RRmax-RRmin. The Axis ó is diagonal of square coming from left-lower corner. The Axis Y is diagonal coming from right-lower corner.)
• Sum(QY) - sum of squares of least distances from graph nodes before axis Y.

According to Table 1, sum of squares of least distances from graph nodes before axis ó has very high correlations with tone of parasympathetic nervous system indexes - RMSSD and HF (correlation between lnRMSSD and lnHF is 0.9631). At the same time, sum of squares of least distances from graph nodes before axis Y has very high correlations with the general heart rate variability indexes - SD and PW (correlation between SD^2 and PW is 0.9938, between lnSum(QY) and ln(lnSD) is 0.9920).
The high correlation of relation Sum(QX)/Sum(QY) with HFn (HFn=100*HF/PW) and LF/HF (LF-power of spectrum of heart rate in low-frequency range) indexes logistical was expect. The correlation analysis has confirmed this. The results are presented in Table 2 (PXY=Sum(QX)/Sum(QY)). The high values of correlation for DFA (Detrended Fluctuation Analysis) are presented in addition.

On the following step we have calculated the values of PXY index for harmonic fluctuation since different period and amplitude. The analysis has shown presence of relationship PXY with frequency of harmonic fluctuations. The fluctuations since odd periods (for example, 5, 15 sec.) have formed exception that follows from nature of graph (asymmetry of graph comparatively axises X and Y are appeared).
But real heart rate contains the ensemble of dynamic changing fluctuations of different frequency and amplitudes. Following hypothesis was formulated: PXY-index reflects leading (central) fluctuation frequency, having most influence upon heart rate. Spectrograms of RR-intervals were analyzed, frequencies of peaks with maximum spectral density were determined and were compared with PXY for ground of this hypothesis . Correlation between PXY and frequency a pica with maximum spectral density (fmax) though was enough high (r=0.7035, p=0.00), but has required the more detailed analysis of real rhythmograms. This has allowed selecting three variants of relations between PXY and fmax.
1) Exists very high coincidence of PXY and fmax values (for instance, fmax=0.082, PXY=0.080). It is characterized of active rest state (readiness to execution of activity). In this state the high influence of autonomic nervous system (ANS) on heart rate regulation can expect.
2) Growing PXY vastly overtakes the growing fmax (for instance, fmax=0.301, PXY=1.082). Given process is typical for condition of deep relaxation. This is accompanied the reduction role of ANS in heart rate regulation and growing of chaotic nature of process. PXY values strive to 1.0. Exactly such values were received at modeling "white noise".
3) Reduction fmax is accompanied the growing PXY (for instance, fmax=0.016, SD=3257 msec2, PXY=0.328 - chronic overstrain, registration in rest state). Given process is typical for high psychic strain and different pathological processes. It is probably in this case normal regulation of heart rate through ANS becomes impossible, that it is also accompanied the growing of chaotic nature of process, but with very low amplitude (the denominated stabilization of rhythm).
To consider the events, when spectrogram contains the significant peaks in different ranges of frequencies. In this case PXY index presents itself resulting frequencies two fluctuations. For instance, at presence of peaks of spectral density with frequency 0.102 Hz (LF-range, SD=337420 msec2) and 0.207 Hz (HF-range, SD=31345 msec2), PXY value was 0.132 Hz. Note also that PXY index is most sensitive to fluctuations in ranges LF and HF.
For four groups of man: 1 - normal state, 2 - neurotic excitement, 3 - functional fatigue, 4 - psychic overstrain were calculated average values of analyzed graph indexes on each group (Table 3, Nv - number of samples, Sum(QX) and Sum(QY) values are given in msec2).

Either as was expected, maximum Sum(QX) value (the indicator to activities of parasympathetic nervous system) was received for first group ("Norma"), and minimum - for fourth group ("Overstrain"). Maximum Sum(QY) value (the factor of general heart rate variability) is characteristic of neurotic excitement (the influence of corticolimbic brain structures systems, note the significant reduction PXY index of leading (resulting) of frequency of fluctuations of heart rate). High PXY value for group "Overstrain" reflects earlier considered dynamic of increasing PXY at reduction fmax for events of rhythm stabilizations.
Use the SumQX, SumQY and PXY indexes in discriminate analysis have allowed greatly to raise accuracy of differential diagnostics presented above functional states.
In conclusion we will afford to return to fact of difference medium of variational range and RRav-RRmin. There are three possible variants:
1) VR/2-(RRav-RRmin)>0 - it is characteristic of for connecting process: fluent (long-time) change one functional state others, firm emotional excitement.
2) VR/2-(RRav-RRmin)<0 - it is characteristic of for violation of heart rate regulation: sharp (short time) change one functional state others, sharp wave of emotional excitement.
3) VR/2-(RRav-RRmin)=0 - it is characteristic of for stationary process.
For validation this hypothesis we have compared own results with standard estimations of stationarity (through checking the constancy of mean and dispersion). The difference between VR/2 and (RRav-RRmin) have expressed in percent from (RRav-RRmin): Dvm=100*(VR/2-(RRav-RRmin))/(RRav-RRmin). For estimation of relations between two categorical variables on criterion Pearson Chi-square we used the registration of RR-intervals in rest state (N=10036). We have calculated stationarity on Dvm when difference did not exceed 1, 2 and 3 percent (Table 4).

According to results are presented in Table 4, Dvm index really can serve the estimation of stationarity time series. The analysis of real rhythmogram has shown that choice Dvm=1% brings about more exact diagnostics stationarity than in the event of standard estimation. Certainly, following studies must confirm or refuse our hypothesis.

According to table 1, complexity level of system (both on number nodes, and on number ribs) is most high in calm state (norm) and decreases at growing of tensity. The indexes of entropy (the level to uncertainties) and relative organization of system (both on number nodes, and on number ribs) are minimum for first group and maximum for tensity state.
In addition the index ND/NRib was calculated. Correlation analysis has revealled the interesting regularity between this index and number of nodes. If for first three groups the values of r (Pearson coefficient of correlation) indicated to high positive coorelation between ND and ND/NRib (0.98, 0.94 and 0.87, accordingly), then for tensity state r=-0.75. This possible comment as follows: in usual conditions a growing or reduction of ND is accompanied the identical growing or reduction of NRib. In tensity state, reduction of ND is accompanied comparatively more denominated reduction of NRib.In the future is planned to continue the studies of heart rate graph indexes by means of discriminant analysis.

From tables 1 is seen that reduction of tensity is connected with a decrease of alfa (to 0.5). In tensity state alfa approaches to 1.00. In neurotic state alfa exceeds 1.00.
The values of alfa and VLFn have a high positive correlation (the increase of VLFn-values are connected with growing of alfa) for all groups, except fourth. In tensity state a correlation between alfa and VLFn sharply falls (the dependency between variables becomes not obvious). Curiously enough note that alfa has negative correlation (but more denominated) with HFn (HFn = 100*HF/TP).
According to ANOVA analysis (on four groups) for alfa F=2214, for NRib F=4468, for ND F=3814.
Hereinafter the studies of possibility of using DFA on short samples for differential diagnostics of different functional conditions is planned to continue.