## Abstract

Two symbolic indexes, the percentage of sequences characterized by three heart periods with no significant variations (0V%) and that with two significant unlike variations (2UV%), have been found to reflect changes in sympathetic and vagal modulations, respectively. We tested the hypothesis that symbolic indexes may track the gradual shift of the cardiac autonomic modulation during an incremental head-up tilt test. Symbolic analysis was carried out over heart period variability series (250 cardiac beats) derived from ECG recordings during a graded head-up tilt test (0, 15, 30, 45, 60, 75, and 90°) in 17 healthy subjects. The percentage of subjects showing a significant linear correlation (Spearman rank-order correlation) with tilt angles was utilized to evaluate the performance of symbolic analysis. Spectral analysis was carried out for comparison over the same series. 0V% progressively increased with tilt angles, whereas 2UV% gradually decreased. The decline of 2UV% was greater than the increase of 0V% at low tilt angles. Linear correlation with tilt angles was exhibited in a greater percentage of subjects for 0V% and 2UV% than for any spectral index. Our findings suggest that symbolic analysis performed better than spectral analysis and, thus, is a suitable methodology for assessment of the subtle changes of cardiac autonomic modulation induced by a graded head-up tilt test. Moreover, symbolic analysis indicates that the changes of cardiac sympathetic and vagal modulations observed during this protocol were reciprocal but characterized by different absolute magnitudes.

- autonomic nervous system
- power spectral density

since the study of Akselrod et al. (1), the attempt to noninvasively assess cardiac autonomic regulation from short-term heart period variability has been mainly carried out in the frequency domain by calculation of power spectral density (PSD). Indeed, the ratio of the power of oscillations in the low-frequency (LF, 0.04–0.15 Hz) band to the power of oscillations in the high-frequency (HF, >0.15 Hz) band (LF/HF) is the most utilized noninvasive index summarizing the relative importance of cardiac sympathetic modulation with respect to parasympathetic modulation (12). The inference of sympathovagal balance from short-term heart period variability has generated a strong debate in the scientific community (5, 10, 13, 18). Although part of the debate is about the ability of heart period variability to reflect neural cardiac autonomic modulation (5, 10, 13, 18), another part of the debate is strictly related to the methodological limitations related to power spectral analysis and spectral indexes. Three methodological drawbacks influence assessment of the cardiac autonomic regulation based on conventional PSD. *1*) PSD analysis does not take into account nonlinear dynamics that may be present in specific experimental conditions, such as during paced breathing (15, 16), which is one of the most utilized experimental maneuvers for standardization of heart rate variability analysis (3). *2*) PSD analysis is strictly based on the definition of the frequency bands, the inferior and superior limits of which are set by convention and practice (19). *3*) Most importantly, all PSD indexes are helpful only in conditions characterized by reciprocal changes of sympathetic and parasympathetic modulations (9), thus leaving nonreciprocal changes of cardiac neural modulation indeterminate (8, 14). Indeed, the LF and HF powers expressed in normalized units (LFnu and HFnu) and LF/HF have been proposed under the hypotheses that an increase of sympathetic modulation corresponds to an equal decrease of vagal modulation and the HF power expressed in absolute units allows solely the assessment of parasympathetic modulation.

We recently proposed a new approach based on symbolic analysis specifically designed to overcome the above-mentioned limitations (17). This approach was found suitable to assess the prevalence of sympathetic or parasympathetic modulations induced by pharmacological interventions and able to detect nonreciprocal autonomic changes before major arrhythmias (7). Indeed, in patients with an implantable cardioverter, symbolic analysis of heart period variability showed that the period preceding the onset of major arrhythmias was characterized by an increase of cardiac sympathetic modulation without the expected decrease of vagal modulation (7). However, the ability of symbolic indexes to track the gradual changes of the cardiac autonomic modulation, such as those known to occur during a graded head-up tilt test (2, 4, 6, 11), and the potential of symbolic analysis with respect to traditional PSD analysis have not been explored.

In the present study, we tested the hypothesis that the gradual shift of cardiac autonomic regulation toward sympathetic predominance and vagal decrease during graded head-up tilt may be suitably tracked by symbolic indexes obtained from short-term heart period variability. Symbolic indexes were compared with linear indexes by conventional PSD analysis.

## METHODS

#### Experimental protocol.

We studied 17 healthy nonsmoking humans [21–54 (median 28) yr of age, 7 women and 10 men]. A detailed medical history and examination excluded the evidence of any diseases. The subjects did not take any medication, nor did they consume any caffeine- or alcohol-containing beverages in the 24 h before the recording. Measurements were performed in the morning. While the subjects were on the tilt table, they were supported by two belts at the level of the thigh and the waist, respectively, with both feet touching the footrest of the tilt table. During the protocol, the subjects breathed spontaneously but were not allowed to talk. Informed consent was obtained from all subjects. The study adheres to the principles of the Declaration of Helsinki and has been approved by our institution's review board.

ECG (lead II) and respiration via thoracic belt were recorded at rest and during head-up tilt. The signals were sampled at 1,000 Hz. After 7 min at rest, the subjects were subjected to 10 min of tilt with table angles randomly chosen within the set {15,30,45,60,75,90}. Each tilt session was always preceded by a rest session and followed by 3 min of recovery. Analyses were performed after ∼2 min from the start of the tilt maneuver. All subjects were able to complete the overall protocol with no sign of presyncope.

#### Data extraction.

After the QRS complex was detected on the ECG and the apex of the R wave was located using parabolic interpolation, the heart period was automatically calculated on a beat-to-beat basis as the time between two consecutive R wave peaks [R-R interval (RR)]. All QRS determinations were carefully checked to avoid erroneous detections or missed beats. All the RR series = {RR(*i*), *i* = 1,…,*N*} were linearly detrended. The series length *N* ranged from 220 to 260 beats and was kept constant while the experimental condition was varied in the same subject. We carefully avoided nonstationary segments, since stationarity is a prerequisite for symbolic and PSD analyses. We calculated the mean RR and the variance of the RR series (σ^{2}).

#### Spectral analysis.

Spectral analysis was performed via a parametric approach exploiting the autoregressive (AR) model (12). Briefly, the AR model describes the RR series in the time domain as a linear combination of *p* past samples weighted by the coefficients *a*_{i} plus a zero mean white noise (w_{rr}). The Levinson-Durbin recursive algorithm was utilized to estimate directly from the data the coefficients of the AR model and the variance of the white noise. The number of coefficients (*p*) was chosen according to Akaike's figure of merit. According to the maximum entropy spectral estimation approach, PSD can be computed from the AR coefficients and from w_{rr}. The PSD can be factorized in a sum of terms, usually referred to as spectral components that, transformed back in the time domain, correspond to basic AR processes with one real pole or a pair of complex and conjugated poles. The sum of spectral components provides the entire AR process (20). A spectral component was considered LF if its central frequency was in the range 0.04–0.15 Hz, whereas it was considered HF if its central frequency was within ±0.05 Hz of the respiratory frequency as detected from the respiratory signal. The respiratory rate did not drop in the LF band in any subject in any experimental condition. The LF and HF powers were defined as the sum of the powers of all spectral components, the central frequencies of which were inside the LF and HF bands, respectively. They were expressed in absolute units (ms^{2}) and designated σ_{LF}^{2} and σ_{HF}^{2}, in normalized units [nu, i.e., the ratio of σ or σ to (σ+ σ) × 100] and designated LFnu and HFnu, and as percentage (i.e., the ratio of σ or σ to σ^{2} × 100) and designated LF% and HF%. LF/HF was extracted as the ratio of LFnu to HFnu (or, equivalently, the ratio of LF% to HF%) and designated LF/HF. The frequency of the LF and HF rhythms was extracted as the central frequency of the dominant spectral component inside the band and designated *f*_{LF} and *f*_{HF}.

#### Symbolic analysis.

The approach, which has been described by Porta et al. (17), is based on *1*) transformation of heart period variability series into a sequence of integers (i.e., symbols), *2*) construction of patterns (i.e., words), *3*) reduction of the number of patterns by grouping them into a small number of families, and *4*) evaluation of the rates of occurrence of these families.

A coarse graining approach based on a uniform quantization procedure was used to transform the RR series into a sequence of symbols. Briefly, the full range of the series was spread over ξ symbols with a resolution of (RR_{max} − RR_{min})/ξ, where RR_{max} and RR_{min} were the maximum and the minimum of the series. After quantization, the RR series became a sequence RR_{ξ} = {RR_{ξ}(*i*), *i* = 1,…,*N*} of integer values ranging from 0 to ξ − 1. The technique of the delayed coordinates was used to transform the RR_{ξ} series into a sequence of patterns RR_{ξ,L} = {RR_{ξ,L}(*i*), *i* = *L*,…,*N*} with RR_{ξ,L}(*i*) = [RR_{ξ}(*i*), RR_{ξ}(*i* − 1),…, RR_{ξ}(*i* − *L* + 1)]. The number of possible RR_{ξ,L}(*i*) was ξ^{L}. Since ξ^{L} grew very rapidly with *L* and ξ, both parameters had to be small: for applications over short data sequences (∼250 samples), the best compromise was ξ = 6 and *L* = 3, and the number of possible patterns was 216. To reduce the number of patterns without losing information, we followed a procedure of redundancy reduction. All the patterns were grouped without loss into four families according to the number and types of variations from one symbol to the next. The pattern families were as follows: *1*) patterns with no variation [0V: all the symbols are equal, e.g., (2,2,2) or (4,4,4); Fig. 1, *A* and *B*], *2*) patterns with one variation [1V: 2 consecutive symbols are equal and the remaining symbol is different, e.g., (4,2,2) or (4,4,3); Fig. 1, *C* and *D*], *3*) patterns with two like variations [2LV: the 3 symbols form an ascending or descending ramp, e.g., (5,4,2) or (1,3,4); Fig. 1, *E* and *F*], and *4*) patterns with two unlike variations [2UV: the 3 symbols form a peak or a valley, e.g., (4,1,2) or (3,5,3); Fig. 1, *G* and *H*]. We evaluated the rates of occurrence of these families designated 0V%, 1V%, 2LV%, and 2UV%. To compute these indexes, we simply count the number of times a pattern RR_{ξ=6, L=3}(*i*) belonging to a specific family was found in RR_{ξ=6, L=3} ÷ [*N* − (*L* − 1)] × 100.

#### Statistical analysis.

The χ^{2} test was used to check whether the rest sessions were similar. Since no significant difference was observed during the repeated rest sessions for all the parameters, we randomly selected the rest session before 15° tilt as reference for linear regression analysis. Linear regression analysis between all the parameters and tilt angles was carried out using Spearman rank-order correlation. We expressed the tilt angles also as the sine of the tilt angles that better reflects the component of the gravity acting on the subject's body, but we did not find a different result. For global linear regression analysis, all data were pooled; for individual linear regression (ILR) analysis, only one subject was considered at a time. ILR analysis was carried out only if global linear regression analysis was significant; in this case, we evaluated the percentage of subjects with a significant ILR analysis (ILR%). *P* < 0.05 was considered significant.

## RESULTS

#### Example of spectral and symbolic analyses.

The RR series derived from a subject and the corresponding results of spectral and symbolic analyses at rest and during 90° tilt are shown in Fig. 2. PSD clearly exhibits two peaks of similar importance: the first in the LF band and the second (i.e., HF) close to the frequency of the peak detected in the PSD of the respiratory signal. Distribution of the patterns indicates that 1V is the most frequent pattern. As expected, during 90° tilt, the mean RR decreases and RR variability is dominated by slow oscillations. As a result, PSD exhibits an important peak in the LF band, whereas that close to the frequency of respiration is dramatically reduced. Symbolic analysis reveals an important increase of stable patterns (i.e., 0V) and a clear reduction of the most variable patterns (i.e., 2UV and 2LV).

#### Linear analysis.

The results of linear analysis are summarized in Table 1. RR, σ_{HF}^{2}, HFnu, and HF% progressively decreased as a function of the tilt angles, whereas LFnu, LF%, and LF/HF progressively increased. There was a trend toward a decrease of σ^{2}, even though the trend was less remarkable than that of RR, σ_{HF}^{2}, HFnu, and HF%. RR, σ^{2}, LFnu, LF%, σ_{HF}^{2}, HFnu, and HF% exhibited a tendency toward saturation at 75° tilt (the trend is more evident in the case of σ^{2}). The experimental protocol did not seem to affect σ_{LF}^{2}, *f*_{LF}, and *f*_{HF}. All indexes reported in Table 1 were subjected to global linear regression analysis, and all, except σ_{LF}^{2}, *f*_{LF}, and *f*_{HF}, were linearly correlated with tilt angles (Table 2). LFnu, LF%, and LF/HF were positively correlated with tilt angles, whereas RR, σ^{2}, σ_{HF}^{2}, HFnu, and HF% were negatively correlated. Since saturation was observed at 75° tilt, global linear regression analysis was performed after exclusion of 90° tilt as well. The same significant global correlations were found after exclusion of 90° tilt. Therefore, only σ_{LF}^{2}, *f*_{LF}, and *f*_{HF} were excluded from ILR analysis. The individual trends of all the indexes selected for ILR analysis are shown in Figs. 3 and 4. RR, σ_{HF}^{2}, HFnu, and HF% progressively decreased, whereas LFnu, LF%, and LF/HF gradually increased, as a function of the tilt angles. RR, LFnu, σ_{HF}^{2}, HFnu, and HF% exhibited saturation at 75° tilt. This saturation is less evident in the case of LF% because of the larger dispersion of the values. From Fig. 3*B*, it is difficult to visually detect the decrease of σ^{2} suggested by global linear regression analysis. The presence of some out-of-scale values in σ^{2}, LF%, σ_{HF}^{2}, and LF/HF suggests that nonparametric statistics are necessary.

The results relevant to the ILR analysis are reported in Table 2 in terms of percentage of subjects characterized by a significant ILR (ILR%). ILR analysis was performed after exclusion of 90° tilt because of the tendency of the values to be saturated at 75° tilt. In all the subjects, RR was linearly correlated with tilt angles. LF% and σ^{2} exhibited a significant individual linear correlation with tilt in a very small number of subjects, whereas the number of subjects was larger in the case of LFnu, σ_{HF}^{2}, HFnu, HF%, and LF/HF, even though the correlation was significant in <60% of the subjects.

#### Symbolic analysis.

The results of symbolic analysis are shown in Table 3. 0V% progressively increased as a function of tilt angles, with saturation at 75°, whereas 2LV% and 2UV% gradually decreased. The experimental protocol had less effect on 1V% than on the other symbolic indexes. Global linear regression analysis suggested that all indexes were linearly correlated with tilt angles (Table 4). 0V% was positively correlated with tilt angles, whereas 1V%, 2LV%, and 2UV% were negatively correlated; thus all the patterns were candidates for ILR analysis. The same significant correlation was found even after exclusion of 90° tilt. Figure 5 shows the individual trends of 0V%, 1V%, 2LV%, and 2UV% for all subjects. 0V% progressively increased as a function of tilt angles with saturation at 75° tilt, whereas 2LV% and 2UV% gradually decreased. From Fig. 5, it is difficult to visually detect the decrease of 1V% suggested by global linear regression analysis. The decrease of 2UV% at low tilt angles was more important than the increase of 0V%. This result is clearer in Fig. 6. In Fig. 6*A*, the variations are constant until 75° (i.e., the relation between 0V% and tilt angles is linear); in Fig. 6*B*, the relation between 2UV% and tilt angles is exponential, with an important change at 15° and very small variations at >45°.

The results relevant to the ILR analysis are reported in Table 4 in terms of percentage of subjects characterized by a significant ILR analysis (ILR%). As in the case of linear analysis, ILR% was evaluated after exclusion of 90° tilt. Linear correlation with tilt angles was exhibited in a greater number of subjects for 0V% and 2UV% than for any spectral parameters (i.e., LFnu, LF%, σ _{HF}^{2}, HFnu, HF%, and LF/HF), whereas the number of subjects decreased dramatically in the case of 1V% and 2LV%.

## DISCUSSION

The major findings of this study are as follows: *1*) symbolic indexes were linearly correlated with tilt angles during graded head-up tilt; *2*) linear correlation with tilt angles was exhibited in a greater percentage of subjects for 0V% and 2UV% than for any spectral index; *3*) at low tilt angles, the magnitude of the decrease of 2UV% was larger than the magnitude of the increase of 0V%.

Graded head-up tilt test is an experimental maneuver that induces a shift of the sympathovagal balance toward a sympathetic activation (4, 6). As expected, this study confirmed that mean RR is associated with the progressive sympathetic activation and parasympathetic withdrawal accompanying this maneuver (2, 4, 11): indeed, according to our data, the mean RR is negatively correlated with tilt angles in all the subjects. We confirmed that LFnu can track the gradual increase in the cardiac sympathetic modulation, whereas σ_{LF}^{2} was not correlated to tilt angles (2, 11). We found also considerably worse performance of LF% than LFnu. As expected, HFnu exhibits a reciprocal trend (11) as a result of the relationship between LFnu and HFnu (i.e., the sum of LFnu and HFnu is ∼100 if the PSD exhibits the typical profile with a clear dominant peak in LF and HF bands). Correspondingly, we also recognized the ability of σ_{HF}^{2} and HF% to follow the progressive decrease of the parasympathetic modulation (4). Finally, LF/HF is useful to describe the parasympathetic withdrawal during a graded head-up tilt test (11). Spectral indexes (i.e., LFnu, HF%, HFnu, LF/HF, and σ_{HF}^{2}) exhibit similar performances in terms of percentage of subjects characterized by a significant individual linear correlation with tilt table inclination (∼60%). This result can be explained by taking into account the strong correlation of normalized indexes (i.e., LFnu, HFnu, and LF/HF) because of the above-mentioned relationship and the similar performance of the dimensionless indexes (e.g., HFnu or HF%) and σ_{HF}^{2} in the case of insignificant changes of the variance during the experimental protocol. Therefore, although usually it is advisable to use one dimensionless index (e.g., LFnu) and σ_{HF}^{2} to characterize cardiac autonomic modulation, in this experimental protocol, one index is sufficient.

In our previous study, which was based on pharmacological interventions to induce changes of the autonomic profile (7), we found that a mild reduction of arterial pressure eliciting a reflex increase of the cardiac sympathetic modulation was attended by an increase of the symbolic index 0V%. Conversely, the reflex enhancement of cardiac parasympathetic modulation following the increase of arterial pressure during phenylephrine administration, was accompanied by an increase of 2UV%. Accordingly, in the present study, the enhancement of cardiac sympathetic modulation and the decrease of vagal modulation obtained by progressive head-up tilt was associated with an increase of 0V% and a decrease of 2UV%.

An important finding of the present study is that two symbolic indexes (i.e., 0V% and 2UV%) could follow the gradual variation of the sympathetic and parasympathetic modulations induced by a graded head-up tilt test and that their performance was better than that of any spectral index. If 2LV% and 2UV% were grouped together, as in the work of Guzzetti et al. (7), the percentage of subjects exhibiting a significant linear relationship with tilt angles would be exactly the same as that relevant to 2UV%. The best performance is achieved by 0V%, which shows a linear association with tilt angles in 82% of the subjects. This result suggests that two nonlinear symbolic indexes (i.e., 0V% and 2UV%) might represent a valid alternative to linear spectral indexes for assessment of the cardiac autonomic modulation from short-term heart period variability (1, 12). It is unclear whether this remarkable performance could be ascribed to some intrinsic characteristics of symbolic analysis, such as the interpretation of nonlinear components, to the elimination of conventional definition of frequency bands, or to the peculiar pattern decomposition scheme exploited by this analysis.

The symbolic indexes used in this study have the potential to detect nonreciprocal changes in sympathetic and parasympathetic modulations or reciprocal changes with different magnitudes. Indeed, since the sum of all symbolic parameters is equal to 100% (i.e., 0V% + 1V% + 2LV% + 2UV% = 100%), 0V% and 2UV% can increase or decrease at the expense of 1V% and 2LV%. This relationship theoretically enables us to assess the concomitant increase or decrease of cardiac sympathetic and parasympathetic modulations (i.e., nonreciprocal changes), increase of cardiac sympathetic modulation accompanied by a decrease of vagal modulation, or vice versa (i.e., reciprocal changes), and also, importantly, potential differences in the magnitude of such reciprocal changes. In our experimental protocol, the magnitude of increase of 0V% as a function of the tilt angles was constant until 75°, whereas the magnitude of decrease of 2UV% was larger at low tilt angles (15°) and became very small at >45°. This result suggests that the reduction of the parasympathetic modulation was more important than the increase of sympathetic modulation at the beginning of the task and indicates that 0V% and 2UV% describe different and potentially uncorrelated aspects of the autonomic response to a graded head-up tilt test. This result cannot be appreciated using conventional spectral indexes. Indeed, LFnu and HFnu are derived according to a model of sympathovagal balance (9) hypothesizing that an increase of cardiac sympathetic modulation corresponds to an equal decrease of vagal modulation (since the sum of LFnu and HFnu powers must remain constant, ΔLFnu + ΔHFnu = 0) and σ_{HF}^{2} (1, 3, 4) gives no quantitative indication about cardiac sympathetic modulation.

Although the ability of 2UV% to evaluate cardiac parasympathetic modulation is largely expected (cardiac vagal modulation is very fast and can produce three-beat heart period patterns with highly variable values), the ability of 0V% to evaluate cardiac sympathetic modulation might be less easily understandable. Indeed, cardiac sympathetic modulation is slower, and in this case a three-beat heart period pattern may be too short to fully reflect it. On the other hand, the normalization procedure introduced by uniform quantization makes oscillations of different amplitudes comparable. After equalization of amplitudes, slower time scales reflecting cardiac sympathetic modulation are more likely to be characterized by three-beat patterns inside the same quantization bin, thus producing stable patterns and increasing 0V%. Therefore, this consideration and differences between Fig. 6*A* and Fig. 6*B* support the notion that 0V% could reflect not only vagal withdrawal but also changes in sympathetic modulation directly observed from neural recordings during gradual head-up tilt (4, 6).

In conclusion, the nonlinear normalized indexes 0V% and 2UV% derived from symbolic analysis can assess sympathetic and parasympathetic modulations, respectively, from short-term heart period variability data in healthy subjects during a gradual head-up tilt test. Since these two indexes might be partially uncorrelated, symbolic analysis of heart period variability seems to be particularly suitable to describe not only conditions characterized by concomitant increase or decrease of the autonomic modulations of both autonomic branches but also conditions characterized by reciprocal changes of different magnitudes.

## Footnotes

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

*advertisement*” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

- Copyright © 2007 by the American Physiological Society