**3. Spectral analysis**

Linear HRV can be assessed by frequency domains. For the frequency domain, a spectral analysis was performed by FFT applied to a single window after the subtraction of a linear trend, at the R-R intervals previously chosen. The power spectral components were obtained at low (LF: 0.04 to 0.15 Hz) and high (HF: 0.15 to 0.4 Hz) frequencies, in absolute units (ms2), and the normalized units (nu) were computed by dividing the absolute power of a given LF or HF component (ms2) by the total power minus very low frequency (0.003-0.04 Hz) power 170 Fourier Transform Applications

Given the importance of the autonomic nervous system to cardiovascular health, several analytical measures, grouped into linear and non-linear methods, can be used to assess HRV. The ECG is recorded with the subject in a steady state (when rhythms are stationary) for a sufficiently long period to determine events occurring within the frequencies of interest. R-R interval spectral power is calculated from this series of intervals using an autoregressive algorithm, which yields center frequencies and absolute power of component

Sympathovagal balance (in dimensionless units) is simply the ratio of absolute LF to absolute HF power, or the LF/HF ratio. The literature on sympathovagal balance is replete with disclaimers that spectral power reflects fluctuations, not absolute levels of autonomic nerve traffic (Akselrod 1995). If mathematical manipulation of R-R interval spectral power is to inspire confidence as a robust, reliable metric, it must be grounded solidly on physiological principles. It must stand on its own and calculations of sympathovagal balance may obscure rather than illuminate human physiology and pathophysiology

This chapter discusses the measurement and analysis of HRV, as well as results of data for women and the relationship between aging and hormonal changes (oral contraceptives and hormone replacement therapy), which contribute to modifications of the autonomic control

An electrocardiogram and HR data were obtained using a one-channel heart monitor (MINISCOPE II Instramed, Porto Alegre, RS, Brazil) and processed using a Lab. PC+ analogto-digital converter (Lab PC + / National Instruments, Co., Austin, TX, USA) acting as an interface between the heart rate monitor and a microcomputer. The ECG signal was recorded in real time after analog-to-digital conversion at a sampling rate of 500 Hz and the R-R intervals (ms) were calculated on a beat-to-beat basis using specific software (Silva et al., 1994). To evaluate the effect of body position on the HR response and its variability, R-R intervals were recorded over a 15-min period under resting conditions with the subjects in

HR and R-R intervals (RRI) can be obtained in real time, beat-by-beat, using the ECG and specific software (Silva et al., 1994). First, a visual inspection of RRI (ms) distribution obtained during 900s of collection at rest in the supine condition was carried out in order to eliminate the fragments containing spikes, which resulted in an interval with higher stability

Linear HRV can be assessed by frequency domains. For the frequency domain, a spectral analysis was performed by FFT applied to a single window after the subtraction of a linear trend, at the R-R intervals previously chosen. The power spectral components were obtained at low (LF: 0.04 to 0.15 Hz) and high (HF: 0.15 to 0.4 Hz) frequencies, in absolute units (ms2), and the normalized units (nu) were computed by dividing the absolute power of a given LF or HF component (ms2) by the total power minus very low frequency (0.003-0.04 Hz) power

of the heart. Each item will be discussed in a separate subitem of this chapter.

**2. Measurement of heart rate variability** 

the supine and sitting positions, respectively.

of ECG RRI tracing (Task Force, 1996).

**3. Spectral analysis** 

fluctuations (Task Force, 1996).

(Eckberg 1997).

and then multiplying this ratio by 100. Since the LF band is modulated by both sympathetic and parasympathetic activity and the HF band is correlated with vagal cardiac control, the LF/HF ratio was calculated to determine the sympathovagal balance (Task Force, 1996). Sympathovagal balance is the ratio between LF and respiratory-frequency powers. Based on this analysis, it is possible to determine the predominance of one component over the other and the relationship between them, reflecting the autonomic modulation of the heart in the control of heart rate.

Figure 1, which is based on an autoregressive model, illustrates the HRV power spectra at rest in the supine and sitting positions of a representative subject in different conditions.

Fig. 1. Power spectral density of heart rate variability of a representative subject from the groups of young women (A and B), and postmenopausal women undergoing (C and D) and not undergoing (E and F) estrogen therapy, obtained at rest in the supine and sitting positions, respectively. Spectral components are shown as LF (0.04 to 0.15 Hz), HF (0.15 to 0.4 Hz) and VLF (below 0.04 Hz). (adapted by Neves et al., 2007)

Spectral Analysis of Heart Rate Variability in Women 173

sound wave, electric current or any form of cyclic wave) occurs over time. Normally, the frequency unit employed is Hertz (Hz), which is equivalent to one cycle per second. Figure 3 shows the application of an autoregressive model to view the power spectrum of the analysis of heart rate variability corresponding to these values of a volunteer of this study. In long records (24 h), the total power is decomposed into four distinct bands: 1) high frequency band (HF), oscillating at a frequency of 0.15 a 0.40 Hz, i.e., 9-24 cycles/min, corresponding to the heart rate variations related to the respiratory cycle (respiratory sinus arrhythmia), which are typically modulated by parasympathetic activity; 2) low frequency or LF band (0.04 to 0.15 Hz or 2.4 to 9 cycles/min), modulated by both sympathetic and parasympathetic activities, with a predominance of sympathetic in some specific situations, and which reflects the oscillations of the baroreceptors system; 3) very low frequency or VLF band (0.003 to 0.04 Hz or 0.2 to 2.4 cycles/min), depending on the thermoregulatory mechanisms and the renin-angiotensin system, which is also regulated by sympathetic and parasympathetic activities; and 4) ultra low frequency or ULF band (< 0.003 Hz or < 0.2 cycles/min), which corresponds to most of the total variance, but whose physiological significance is not yet well defined. This band is influenced by the parasympathetic and sympathetic systems and is obviously absent from short duration records. It appears to be related with the neuroendocrine system, circadian rhythm, and other systems (Task Force,

A high frequency component equivalent to 0.25 Hz (15 cycles/min = 15 cycles/60 s = 0.25 cycles/s = 0.25 Hz), a low frequency component equivalent to 0.1 Hz (6 cycles/min) and a very low frequency component of 0.016 Hz (1 cycle/min). The combination of these three sine waves generates a complex wave signal that can be compared to the signal obtained when the heart rate is expressed on a temporal graph (tachogram). Moreover, the calculation of the area covered by each frequency band (which is proportional to the square of the amplitude of the original signal and hence, in this case, is expressed in ms2) enables one to separate the amount of variance (power) ascribed to each frequency. This allows for a more detailed study of the individual participation of each of the divisions of the ANS (sympathetic and parasympathetic) in different physiological and pathological situations, as well as its relationship with the main systems that interfere with HRV (respiratory, vasomotor, thermoregulatory, renin-angiotensin and central nervous systems). In fact, this is the main difference between spectral analysis and time domain analysis, since the latter generally fails to distinguish the dominant rhythms or oscillations that give the heart rate its

Spectral components are usually measured in absolute values of power (ms2). However, the values of LF and HF can also be expressed in normalized units (nu), which represent the value of each of these components in relation to the total power (TP) minus the VLF component. These values are calculated by means of the following formulas: HF (nu) = HF/(TP – VLF) x 100 and LF (nu) = LF/(TP – VLF) x 100. This minimizes the effects of changes in the VLF range on the other two components with faster frequencies (LF and HF). Another frequently used measure is the LF/HF ratio, which can provide useful information about the balance between the sympathetic and parasympathetic systems. It should also be noted that, because absolute values in ms2 are highly variable and distributed

asymmetrically, they usually require logarithmic transformation (Task Force, 1996).

1996).

variability (Task Force, 1996).

Figure 2 illustrates the analysis of the RRI (ms) of a volunteer at rest in the supine position, using the power spectrum of the autoregressive model for a better view of the spectral components. Three spectral frequency bands were obtained: 1) VLF, corresponding to frequencies varying from 0 to 0.04 Hz; LF, corresponding to the interval of 0.04 Hz to 0.15 Hz; and AF, corresponding to the interval of 0.15 Hz to 0.40Hz. The LF and HF components are expressed in normalized units (UN) which correspond to the percentage of the total power spectrum subtracted from the VLF component. These components were also expressed as the ratio between the absolute areas of low and high frequency (LF/HF ratio), which is indicative of the vagosympathetic equilibrium. Figure 2 illustrates the temporal series of the RRI corresponding to the 256 values of analysis selected previously.

Fig. 2. Temporal series of 256 values of R-R intervals (ms) of a volunteer in the supine position

Because the HR presents fluctuations that are, in large part, periodic, a continuous electrocardiographic record over short or long periods (24 h) and a subsequent graphical representation of the normal R-R intervals over time (tachogram) produce a complex undulatory phenomenon that can be decomposed into simpler waves through mathematical algorithms, such as the FFT or the autoregressive model. This process, called spectral analysis, enables the electrocardiographic signal from the temporal series (tachogram) to be decomposed into its different frequency components, i.e., into so-called frequency bands. It should be noted that frequency refers to the number of times a given phenomenon (e.g., a 172 Fourier Transform Applications

Figure 2 illustrates the analysis of the RRI (ms) of a volunteer at rest in the supine position, using the power spectrum of the autoregressive model for a better view of the spectral components. Three spectral frequency bands were obtained: 1) VLF, corresponding to frequencies varying from 0 to 0.04 Hz; LF, corresponding to the interval of 0.04 Hz to 0.15 Hz; and AF, corresponding to the interval of 0.15 Hz to 0.40Hz. The LF and HF components are expressed in normalized units (UN) which correspond to the percentage of the total power spectrum subtracted from the VLF component. These components were also expressed as the ratio between the absolute areas of low and high frequency (LF/HF ratio), which is indicative of the vagosympathetic equilibrium. Figure 2 illustrates the temporal series of the RRI corresponding to the 256 values of analysis

50 100 150 200 250

50 100 150 200 250

Number of points

Because the HR presents fluctuations that are, in large part, periodic, a continuous electrocardiographic record over short or long periods (24 h) and a subsequent graphical representation of the normal R-R intervals over time (tachogram) produce a complex undulatory phenomenon that can be decomposed into simpler waves through mathematical algorithms, such as the FFT or the autoregressive model. This process, called spectral analysis, enables the electrocardiographic signal from the temporal series (tachogram) to be decomposed into its different frequency components, i.e., into so-called frequency bands. It should be noted that frequency refers to the number of times a given phenomenon (e.g., a

Fig. 2. Temporal series of 256 values of R-R intervals (ms) of a volunteer in the supine

1080

1060

1040

1020

1000

980

960

940

920

900

880

selected previously.

1080

1060

1040

1020

1000

R-R Intervals (ms)

980

960

940

920

900

880

position

sound wave, electric current or any form of cyclic wave) occurs over time. Normally, the frequency unit employed is Hertz (Hz), which is equivalent to one cycle per second. Figure 3 shows the application of an autoregressive model to view the power spectrum of the analysis of heart rate variability corresponding to these values of a volunteer of this study.

In long records (24 h), the total power is decomposed into four distinct bands: 1) high frequency band (HF), oscillating at a frequency of 0.15 a 0.40 Hz, i.e., 9-24 cycles/min, corresponding to the heart rate variations related to the respiratory cycle (respiratory sinus arrhythmia), which are typically modulated by parasympathetic activity; 2) low frequency or LF band (0.04 to 0.15 Hz or 2.4 to 9 cycles/min), modulated by both sympathetic and parasympathetic activities, with a predominance of sympathetic in some specific situations, and which reflects the oscillations of the baroreceptors system; 3) very low frequency or VLF band (0.003 to 0.04 Hz or 0.2 to 2.4 cycles/min), depending on the thermoregulatory mechanisms and the renin-angiotensin system, which is also regulated by sympathetic and parasympathetic activities; and 4) ultra low frequency or ULF band (< 0.003 Hz or < 0.2 cycles/min), which corresponds to most of the total variance, but whose physiological significance is not yet well defined. This band is influenced by the parasympathetic and sympathetic systems and is obviously absent from short duration records. It appears to be related with the neuroendocrine system, circadian rhythm, and other systems (Task Force, 1996).

A high frequency component equivalent to 0.25 Hz (15 cycles/min = 15 cycles/60 s = 0.25 cycles/s = 0.25 Hz), a low frequency component equivalent to 0.1 Hz (6 cycles/min) and a very low frequency component of 0.016 Hz (1 cycle/min). The combination of these three sine waves generates a complex wave signal that can be compared to the signal obtained when the heart rate is expressed on a temporal graph (tachogram). Moreover, the calculation of the area covered by each frequency band (which is proportional to the square of the amplitude of the original signal and hence, in this case, is expressed in ms2) enables one to separate the amount of variance (power) ascribed to each frequency. This allows for a more detailed study of the individual participation of each of the divisions of the ANS (sympathetic and parasympathetic) in different physiological and pathological situations, as well as its relationship with the main systems that interfere with HRV (respiratory, vasomotor, thermoregulatory, renin-angiotensin and central nervous systems). In fact, this is the main difference between spectral analysis and time domain analysis, since the latter generally fails to distinguish the dominant rhythms or oscillations that give the heart rate its variability (Task Force, 1996).

Spectral components are usually measured in absolute values of power (ms2). However, the values of LF and HF can also be expressed in normalized units (nu), which represent the value of each of these components in relation to the total power (TP) minus the VLF component. These values are calculated by means of the following formulas: HF (nu) = HF/(TP – VLF) x 100 and LF (nu) = LF/(TP – VLF) x 100. This minimizes the effects of changes in the VLF range on the other two components with faster frequencies (LF and HF). Another frequently used measure is the LF/HF ratio, which can provide useful information about the balance between the sympathetic and parasympathetic systems. It should also be noted that, because absolute values in ms2 are highly variable and distributed asymmetrically, they usually require logarithmic transformation (Task Force, 1996).

Spectral Analysis of Heart Rate Variability in Women 175

Carter et al. (2009) observed no effects of OC use on the sympathetic modulation of the heart during orthostatic stress, nor differences in that regard between the phase of intake of active pills and that of intake of inactive pills. Women with greater physical activity, both users and non-users of OCs, showed a predominance of parasympathetic modulation and presented a greater complexity of pattern distribution and less regularity and predictability of sequential patterns than sedentary groups. Wenner et al. (2006) evaluated amenorrheic and eumenorrheic athletes who were users and non-users of OCs, and observed no influence on cardiac autonomic function. However, other studies suggest that there is a relationship between OC use and autonomic HR modulation, which the authors attribute to changes in vagal peripheral modulation caused by high levels of circulating estrogen

Santos et al. (2008) analyzed the autonomic modulation of HR based on frequency domain (LF, HF and LF/HF) indices and found that the use of contraceptives did not affect the results, since they detected no difference among the groups under study. This finding may be attributed to the pharmacological properties of low estrogen/progesterone dosages, as well as to the maintenance of the integrity of the autonomic modulation of HR, since the values found here fall within the range of normality. The results of this study suggest that low estrogen/progesterone dosages do not impair autonomic modulation in the age group

The aging process causes changes in the autonomic modulation of the cardiovascular system, and particularly in HR. The literature reports that parasympathetic activity in the sinus node decreases with age, leading to a reduction in HRV and a greater risk for cardiovascular events (Lipsitz et al., 1990). Structural and functional changes in the blood vessels, in the cardiac conduction system and in the sensitivity of baroreceptors, as well as increased myocardial stiffness, leading to greater force of contraction and reduced ventricular filling, contribute to reduce the functional capacity of the cardiovascular and hemodynamic system (Walsh, 1987). In addition, with increasing age, submaximal physical activity and decline in functional capacity lead to increased physiological stress (Perini et al.,

The incidence of cardiovascular diseases among premenopausal women is low when compared to that of men in the same age group, but increases significantly after this period (Gensini et al., 1996). In several countries, cardiovascular diseases are the major cause of morbidity and mortality among postmenopausal women, representing an important public health problem (Mosca et al., 1997). The increase in the incidence of cardiovascular events among middle-aged women has been associated with the hypoestrogenism typical of this

With regard to autonomic heart function, some studies have demonstrated the harmful effects of hypoestrogenism on HRV. Mercuro et al. (2000) found a reduction in HRV indices, analyzed in the time and frequency domains, after bilateral oophorectomy, i.e., through the interruption of estrogen production, as occurs in menopause. Liu et al. (2003) demonstrated higher values of HRV, analyzed in the time domain, in premenopausal

(Minson, 2000; Leicht et al., 2003).

**5. Heart rate variability and hormonal therapy** 

period of women's lives (Greendale et al., 1999).

under study.

2002).

Fig. 3. Power spectrum of the analysis of HRV obtained by applying an autoregressive model to a dataset of 256 values of R-R intervals in the supine position from one of the volunteers of this study, showing the VLF (light gray), LF (medium gray) and HF (dark gray) bands
