Bart Verheyden
email: bart.verheyden@med.kuleuven.be

Janneke Gisolf

Frank Beckers

John M Karemaker

Karel H Wesseling

André E Aubert

Wouter Wieling

Impact of age on the vasovagal response provoked by sublingual nitroglycerine in routine tilt testing

Keywords: vasovagal syncope, age, nitroglycerine, head-up tilt

Nitroglycerine (NTG) is used in routine tilt testing to elicit a vasovagal response. We hypothesized that with increasing age NTG triggers a more gradual blood pressure decline due to a diminished baroreflex buffering capacity. The purpose was to examine the effect of NTG on baroreflex control of blood pressure in patients with distinct agerelated vasovagal collapse patterns.

The study groups consisted of 29 patients (16-71 yrs, 17 females) with clinically suspected VVS and a positive tilt test. Mean finger arterial pressure (MAP) was monitored continuously (Finapres). Left ventricular stroke volume (SV), cardiac output (CO) and systemic vascular resistance (SVR) were computed from the pressure pulsations (Modelflow). Spontaneous baroreflex control of heart rate (BRS) was estimated in the time domain.

In the first 3 minutes after NTG, blood pressure was well maintained in all patients. This implies an adequate arterial resistance response to compensate for steeper reductions in SV and CO with increasing age. Heart rate (HR) increased and the BRS decreased after NTG. The rate of MAP-fall leading to presyncope was inversely related to age (r = 0.51, p = 0.005). Accordingly, patients with a MAP-fall > 1.44 mmHg/s (median) were generally younger compared to patients with a slower MAP-fall (30 ± 10 yrs vs. 51 ± 17 yrs; p = 0.001). The main determinant of the rate blood pressure drop on approach of presyncope was the rate of fall in HR (r = 0.75, p < 0.001).

It is concluded that, in the older patients, sublingual NTG provokes a more gradual blood pressure decline compared to the younger. This gradual decline cannot be ascribed to failure of the baroreflex buffering capacity with increasing age. Age-related differences in the laboratory presentation of a vasovagal episode depend on the magnitude of the underlying bradycardic response.

INTRODUCTION

Vasovagal syncope (VVS) is a common clinical problem that afflicts patients of all ages [START_REF] Colman | Epidemiology of reflex syncope[END_REF]. Although the sequence of hemodynamic events associated with VVS should be investigated during spontaneous episodes, this request makes adequate hemodynamic study practically impossible, for obvious reasons. Therefore, head-up tilting has become a widespread diagnostic test to document a tendency toward VVS [START_REF] Kenny | Head-up tilt: a useful test for investigating unexplained syncope[END_REF]. In order to increase the diagnostic yield of head-up tilting, sublingual nitroglycerine (NTG) is commonly administered [START_REF] Raviele | Value of head-up tilt testing potentiated with sublingual nitroglycerin to assess the origin of unexplained syncope[END_REF][START_REF] Bartoletti | The Italian Protocol': a simplified head-up tilt testing potentiated with oral nitroglycerin to assess patients with unexplained syncope[END_REF][START_REF] Aerts | Nitrate stimulated tilt table testing: a review of the literature[END_REF], because as potent venodilators [START_REF] Mason | The effects of nitroglycerin and amyl nitrite on arteriolar and venous tone in the human forearm[END_REF], nitrates might facilitate VVS by enhancing venous pooling in the upright posture [START_REF] Gisolf | Sublingual nitroglycerin used in routine tilt testing provokes a cardiac output-mediated vasovagal response[END_REF]. The yield of positive tilt testing has been reported to increase substantially more after NTG provocation in older compared to younger patients [START_REF] Kurbaan | Usefulness of tilt testinduced patterns of heart rate and blood pressure using a two-stage protocol with glyceryl trinitrate provocation in patients with syncope of unknown origin[END_REF][START_REF] Natale | Use of sublingual nitroglycerin during head-up tilt-table testing in patients >60 years of age[END_REF][START_REF] Kurbaan | Age and hemodynamic responses to tilt testing in those with syncope of unknown origin[END_REF]. A marked reduction in the capacity of the arterial baroreflex to buffer blood pressure responses to vasoactive drugs with physiological aging has been reported [START_REF] Jones | Baroreflex buffering is reduced with age in healthy men[END_REF]. With this information as a background, we hypothesized that presyncope induced by NTG in older patients is brought on by baroreflex failure to maintain arterial blood pressure, which, rather than presenting as a sudden vasovagal reflex, is accompanied by a more gradual blood pressure decline compared to younger patients.

The purpose of this study was to test the hypothetical baroreflex involvement by investigating the hemodynamic mechanisms underlying the direct effect of NTG, in routine tilt tests. For this we studied patients with suspected VVS, applying pulse wave analysis to the continuously measured Finapres blood pressure signal.

METHODS

Study population

This is a retrospective study. The study group consists of patients with suspected VVS who had shown a positive response to head-up tilt testing with NTG provocation at the Syncope Unit of the Academic Medical Center. A positive response was defined as a progressive fall in blood pressure and impending vasovagal syncope. The patient's medical history included at least one syncopal episode of unknown origin in the last year, in the presence of (prolonged) orthostatic stress, pain, or an unusually strong emotional trigger. Excluded were patients with a history of cardiovascular disease, carotid sinus syndrome, or any disease that might affect the autonomic nervous system, as well as patients using medication that might affect the circulation or circulatory control. In addition, we excluded patients who had experienced a vasovagal episode before administration of NTG (n = 4). A total of 29 otherwise healthy patients with a positive tilt test response (12 men and 17 women) and history of VVS were included in this study.

The mean age was 41 ± 18 years (range 16 -71, median 39 years).

Tilt-test protocol and measurements

Tests were performed between 9:00 AM and 1:00 PM in a temperature-controlled room (23°C). A manually operated tilt table with a footboard was used. The tilt test started with 5 min of supine rest, followed by 20 min head-up tilt (60°). If no vasovagal reaction developed, NTG was administered sublingually (0.4 mg) for an additional 15-min tilt duration. An impending vasovagal response was aborted by means of tilt-back, or by counter-maneuvers such as legs crossing to prevent loss of consciousness [START_REF] Krediet | Management of vasovagal syncope: controlling or aborting faints by leg crossing and muscle tensing[END_REF]. The term tilt-back is further used to indicate the moment an impending vasovagal syncope was aborted. Blood pressure was measured continuously and non-invasively using the Finapres Model 5 (TNO Biomedical Instrumentation, Amsterdam, the Netherlands). The hand was held at right atrium level and kept in place using an arm sling. The study was carried out in accordance with the Declaration of Helsinki (2000) and has been approved by the Medical Ethics Committee of the Academic Medical Center, University of Amsterdam, the Netherlands.

Hemodynamic analysis

The arterial pressure signal was analog to digital converted at 100 Hz and stored on a hard-disk. Beat-to-beat systolic and diastolic pressures were derived from the arterial pressure waveform. Mean arterial pressure (MAP) was the true integral of the arterial pressure wave over one beat divided by the corresponding beat interval. Heart rate (HR) was computed as the inverse of the inter-beat interval (IBI), and expressed as beats per minute. Beat-to-beat changes in stroke volume (SV) were estimated by modeling flow from the finger arterial pressure waveform (Modelflow, TNO Biomedical Instrumentation) [START_REF] Wesseling | Computation of aortic flow from pressure in humans using a nonlinear, three-element model[END_REF][START_REF] Jellema | Continuous cardiac output in septic shock by simulating a model of the aortic input impedance: a comparison with bolus injection thermodilution[END_REF][START_REF] Harms | Continuous stroke volume monitoring by modelling flow from non-invasive measurement of arterial pressure in humans under orthostatic stress[END_REF]. The patient's gender, age, height and weight were inserted in the model to determine Modelflow parameters using previously established equations [START_REF] Langewouters | The static elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model[END_REF]. Cardiac output (CO) was computed by the product of SV and HR. Systemic vascular resistance (SVR) was obtained through a self-adapting process in which an initial value is assumed for the first beat. The ratio of MAP to CO for this first beat defines a new resistance value which is used in the model for the next beat. Within 5 beats from the start, the model resistance stabilizes to actual SVR and further allows close tracking of changes in real SVR [START_REF] Jansen | A comparison of cardiac output derived from the arterial pressure wave against thermodilution in cardiac surgery patients[END_REF]. Due to this self-adapting process to estimate SVR, the tracking precision of the model is unaffected by administration of vasoactive drugs like NTG [START_REF] Jansen | A comparison of cardiac output derived from the arterial pressure wave against thermodilution in cardiac surgery patients[END_REF]. Stroke volume, CO and SVR were set at 100% (baseline) in the upright posture, 3 min before NTG, and variations were expressed as percentages (%) of this baseline. Beat-to-beat hemodynamic values were averaged per 30-s periods; slopes were calculated over the initial 3-min time frame starting at NTG administration to assess hemodynamic trends after NTG in all patients.

Rate of arterial pressure fall in the presyncopal episode

The rate of arterial pressure fall (mmHg/s) in the presyncopal episode was computed in each individual patient by calculating the first derivative of a 6 th order Givens polynomial approximation of MAP in the hypotensive 30-s episode prior to tilt-back (Figure 1). The same procedure was adopted to calculate the rate of IBI-increase (bradycardic response) during the presyncopal episode (ms/s).

Baroreflex sensitivity (BRS)

Time domain analysis of spontaneous BRS was performed using the cross-correlation method [START_REF] Westerhof | Time-domain cross-correlation baroreflex sensitivity: performance on the EUROBAVAR data set[END_REF]. The SAP and IBI time series were resampled at 1 Hz. In a 10-s window, the correlation and regression slope between SAP and IBI were computed. Delays of 0-to 5s increments in IBI were computed, and the delay with the highest positive coefficient of correlation was selected. The slope between SAP and IBI was recorded as a BRS estimate if the correlation was significant at p = 0.01.

Statistical analysis

Statistical analysis was performed with SPSS version 11.5 for windows (Scientific Packages for Social Sciences, Inc., Chicago, IL, USA). Variables were tested for normality using the Kolmogorov-Smirnov test and expressed as the mean value ± SD, unless stated otherwise. The BRS was transformed by calculating its natural logarithm to achieve a normal distribution. Pearson's correlation coefficient (r) was computed to evaluate the relationship between age and the rate of arterial pressure fall at presyncope. Differences between patients with distinct blood pressure patterns at presyncope were analyzed using the Student t-test or by analysis of variance with statistical correction for age as a continuous covariable.

RESULTS

Study population

In all 29 patients, prodromal symptoms and signs such as pallor, diaphoresis, lightheadedness and/or impending loss of consciousness were present within 4 to 11 minutes after NTG provocation. All patients recovered by counter-maneuvers or on return to the supine position. Figures 1A and1B show blood pressure tracings during 3min periods (180 s) prior to tilt-back in two representative patients, aged 31 (upper panel) and 69 years (lower panel). In both patients there is a reduction in blood pressure during the vasovagal episode. However, the rate of blood pressure fall was much more rapid in the younger compared to the older patient (3.5 versus 0.7 mmHg/s). When tested in all patients, the rate of blood pressure fall in the presyncopal episode was shown to be inversely related to age (r = 0.51, p = 0.005) (Figure 2). The median rate of arterial pressure fall was 1.44 mmHg/s. Patients with a steeper blood pressure fall (> 1.44 mmHg/s) were regarded as Type A responders. Patients with a more gradual blood pressure decline (≤ 1.44 mmHg/s) were regarded as Type B responders. The time from NTG administration to tilt-back was not different in patients with a Type A (426 ± 165 s) or Type B (379 ± 129 s) blood pressure response (p = NS). This implies that blood pressure started to fall earlier after NTG administration in those patients with a Type B blood pressure response (257 ± 127 vs. 361 ± 166 s, p = 0.047).

Distribution of age and gender

Figure 3 shows the age-distribution in patients with a Type A or Type B vasovagal response. Patients with a Type A response were younger compared to Type B responders (30 ± 10 vs. 51 ± 17 years; p < 0.001). All patients with a Type A response (n = 14) were below 50 years old. Of those patients with a Type B response (n = 15), 67 % (n = 10) were older than 50 years. Accordingly, the analysis of possible age-effects on the baroreflex response to NTG is further presented in terms of Type A or Type B blood pressure patterns in the presyncopal episode. The distribution of gender was not different between patients with a Type A (5 men and 9 women) or Type B (7 men and 8 women) vasovagal response.

Circulatory response to NTG

Cardiovascular trends in patients who experienced a Type A or Type B vasovagal response are shown in Figure 4. Before NTG, all patients were asymptomatic, and the average HR was 86 beats/min (range 61 to 134 beats/min; no difference between Type A and Type B). Mean blood pressure tended to be higher in Type B patients; however, this difference was not significant (91 ± 7 vs. 85 ± 11 mmHg, p = 0.11). The cardiac BRS was reduced with age (r = -0.51, p = 0.003). Accordingly, Type B patients had a lower BRS compared to Type A (5 ± 2 vs. 8 ± 3 ms/mmHg, p = 0.001). Stroke volume, CO and SVR were stable before NTG in both groups of patients (Figure 4). Hemodynamic trends after NTG were analyzed by calculation of the slope during the first 3 minutes after NTG provocation (Figure 4). Type B patients had a steeper drop in SV compared with Type A (-11.8 ± 2.1 vs. -7.6 ± 1.5, p = 0.023). Because the concomitant rise in HR was similar in both groups, Type B patients had a larger drop in CO (-6.3 ± 1.4 vs. -2.0 ± 1.4, p = 0.046). This was adequately compensated by a greater rise in SVR compared to Type A (6.2 ± 2.7 vs. 1.0 ± 1.7, p = 0.045). In both groups, MAP was well maintained during the first 3 min after NTG in all patients (Figure 4). There was a similar reduction in BRS after the hemodynamic changes induced by NTG. After introduction of age as a covariate, no significant differences were observed in the hemodynamic slopes following NTG provocation.

Vasovagal episode

There was marked hypotension, both in patients with a Type A and a Type B vasovagal response (Figure 4). During the last 15 s before tilt-back, MAP averaged respectively 49 mmHg (range 25 to 87 mmHg) and 55 mmHg (range 45 to 68 mmHg) (p = NS). Heart rate dropped below 60 beats/min in 9 Type A patients (64%) compared to only 4 Type B patients (27%). Consequently, during the last 15 s before tilt-back, HR was lower on average in patients with a Type A vasovagal response (62 ± 21 vs. 82 ± 17 beats/min, p = 0.041) (Figure 5). The slope of the bradycardic response in the last 30 seconds before tiltback was related to the rate of fall in blood pressure within the same time period (r = -0.75, p < 0.001) (Figure 6). In all patients, the last 30 seconds before tilt-back were characterized by a marked reduction in CO, which was not compensated for by a further increase in SVR (Figure 4, shaded area). The drop in CO was mediated by significant

DISCUSSION

This study describes the impact of age on hemodynamic patterns induced by sublingual NTG during routine tilt testing in patients with suspected VVS.

1. Analysis of blood pressure patterns during the presyncopal episode shows agerelated differences. We observed a gradient in the rate of arterial pressure fall from the younger to the older patients, with the younger patients being more likely to have a more rapid blood pressure fall compared to the older (Figure 2).

The main determinant of the rate blood pressure drop on approach of presyncope appears to be the rate of fall in heart rate (Figure 6).

2. The first 3 min after NTG, arterial blood pressure was well maintained, both in patients with a rapid (Type A) and more gradual (Type B) blood pressure fall prior to tilt-back (Figure 4). Cardiac output decreased more in Type B patients.

This implies an (initially) adequate arterial vasoconstrictor response in the older patients to NTG-induced venous pooling.

The present findings support our hypothesis that, in the older patients, sublingual NTG provokes a more gradual blood pressure decline compared to the younger patients.

However, this gradual fall in arterial pressure cannot be attributed to the hypothesized failure of the arterial baroreflex buffering capacity with increasing age. Age-related differences in the rate of fall in arterial pressure appear to depend on the bradycardic response in the presyncopal episode.

The initial circulatory response to NTG (first 3 minutes)

The circulatory response to NTG was characterized by a rapid drop in SV, and despite a rise in HR, CO was diminished. Furthermore, BRS was decreased in the early period after NTG, which, together with the rise in HR and SVR suggests sympathetic activation.

Interestingly, sublingual NTG provoked a steeper drop in SV in the first three minutes after application in the older patients with a Type B vasovagal response (Figure 4). This steeper drop in SV in Type B patients may be surprising because, in the older patients, reduced venous compliance is reported to account for a diminished peripheral fluid shift, which attenuates the reduction in SV during the hypovolemic stress of lower-body negative pressure [START_REF] Tsutsui | Cardiovascular responses to lower body negative pressure in the elderly: role of reduced leg compliance[END_REF]. Two factors may be involved. First, pooling in the splanchnic area of the upright human body seems more important than previously reported in studies using simulated orthostasis by applying lower-body negative pressure [START_REF] Taneja | Differential effects of lower body negative pressure and upright tilt on splanchnic blood volume[END_REF]. Thus, increased splanchnic pooling may be hypothesized in patients with a Type B vasovagal response. On the other hand, in the older subjects, increased myocardial stiffness and impaired diastolic relaxation make the heart more dependent on cardiac preload to adequately fill the left ventricle [START_REF] Lipsitz | Reduced supine cardiac volumes and diastolic filling rates in elderly patients with chronic medical conditions. Implications for postural blood pressure homeostasis[END_REF]. This age effect becomes particularly important if heart rate is increased and thus diastolic filling time is shortened [22;23]. Therefore, age-related impairments in diastolic left ventricular filling may account for the greater SV reduction induced by sublingual NTG in our patients with a Type B blood pressure pattern in the presyncopal episode (Figure 4).

Unlike the reduction in SV, the concomitant rise in HR after NTG provocation was similar in Type A and Type B patients (Figure 4). Thus, in patients with a Type B vasovagal response, a steeper drop in SV after NTG is not accompanied by a larger baroreflex-mediated rise in HR. This can be ascribed to a diminished HR regulation with increasing age [START_REF] Laitinen | Age dependency of cardiovascular autonomic responses to head-up tilt in healthy subjects[END_REF], which is further supported in this study by a lower spontaneous cardiac baroreflex sensitivity (BRS) in the patients with a Type B vasovagal respopnse.

The steeper fall in CO compared to Type A patients is adequately compensated by a greater rise in SVR, supporting the concept that orthostatic blood pressure control essentially relies on sympathetic vasomotor responses [START_REF] Laitinen | Age dependency of cardiovascular autonomic responses to head-up tilt in healthy subjects[END_REF][START_REF] Imholz | Orthostatic circulatory control in the elderly evaluated by non-invasive continuous blood pressure measurement[END_REF][START_REF] Wieling | Disparities in circulatory adjustment to standing between young and elderly subjects explained by pulse contour analysis[END_REF].

The precise sequence of events leading to the hypotensive, presyncopal episode is still matter of debate. Certain data suggest that orthostatic hypotension results from inadequate compensatory responses of the venous system [START_REF] Manyari | Abnormal reflex venous function in patients with neuromediated syncope[END_REF][START_REF] Stewart | Relation of postural vasovagal syncope to splanchnic hypervolemia in adolescents[END_REF][START_REF] Fuca | The venous system is the main determinant of hypotension in patients with vasovagal syncope[END_REF]; other data point more to an underlying arterial vascular resistance deficit [START_REF] Sneddon | Impaired immediate vasoconstrictor responses in patients with recurrent neurally mediated syncope[END_REF][START_REF] Thomson | Abnormal forearm vascular responses during dynamic leg exercise in patients with vasovagal syncope[END_REF][START_REF] De | Incidence and hemodynamic characteristics of near-fainting in healthy 6-to 16-year old subjects[END_REF]. In agreement with Gisolf et al. [START_REF] Gisolf | Sublingual nitroglycerin used in routine tilt testing provokes a cardiac output-mediated vasovagal response[END_REF], the present data signify that the NTG-triggered vasovagal response is COmediated and is not preceded by a decrease in SVR (Figure 4). The reduction in CO relies on the bradycardic response within the last 30 seconds prior to tilt-back; the rate of fall in HR is clearly associated with the rate of arterial pressure fall in the presyncopal episode (Figure 6). Within the last 15 seconds before tilt-back, average HR was lower in patients with a Type A versus Type B vasovagal response (Figure 5). Therefore, the main determinant of age-related differences in the laboratory presentation of a NTG-triggered vasovagal response appears to be the rate of fall in HR.

The final vasovagal response

The more gradual development of a vasovagal response with increasing age was formerly labeled as a dysautonomic response [START_REF] Brignole | New classification of haemodynamics of vasovagal syncope: beyond the VASIS classification. Analysis of the pre-syncopal phase of the tilt test without and with nitroglycerin challenge. Vasovagal Syncope International Study[END_REF], suggesting that vasomotor failure might be involved. In the new Vasovagal Syncope International Study (VASIS) classification of tilt-induced VVS [START_REF] Brignole | Guidelines on management (diagnosis and treatment) of syncope[END_REF], patients with a decrease in HR of less than 10% are labeled as 'vasodepressor' responders, further pointing to sympathetic vasomotor failure with a decrease in SVR as the underlying mechanism. In this study, we found that SVR did not decrease in the presyncopal episode, but remained above baseline (100%) in all Type B patients. This, together with the adequate steady-state arterial vasoconstrictor response to NTG-induced venous pooling, shows that the previous assumption of sympathetic vasomotor failure in the older patients is rather unlikely. Instead, the NTG-triggered vasovagal response appears to be CO-mediated and is not preceded by a decrease in SVR [START_REF] Gisolf | Sublingual nitroglycerin used in routine tilt testing provokes a cardiac output-mediated vasovagal response[END_REF].

Previous studies associated tilt-table testing in younger patients with an increased incidence of severe vagal-cardiac inhibition [10;35;36]. A much stronger vagal-cardiac neural outflow in younger subjects may be involved here [37;38]. The decrease in vagal cardiac outflow with aging is reflected in the present study by a lower cardiac BRS in patients with a Type B vasovagal response (Figure 4). Although the occurrence of a bradycardic response during tilt testing seems predominant in younger patients, the use of an implantable loop recorder (ILR) has learned that, during spontaneous vasovagal events, asystolic syncope is a very frequent observation in older adult and elderly patients [39;40]. At present, these contradictory findings are hard to explain. The fact that HR usually starts to fall after the onset of hypotension may be involved [START_REF] Sra | Comparison of cardiac pacing with drug therapy in the treatment of neurocardiogenic (vasovagal) syncope with bradycardia or asystole[END_REF]. Only in those patients with fully developed vasovagal faints does a marked heart rate decrement occur, without exception [42]. Thus, the timing to abort oncoming syncope, by tilt-back, may affect the extent of reflex bradycardia. The more rapid vasovagal symptoms develop, the more likely this will be associated with severe bradycardia in routine tilt testing.

Alternatively, the spontaneous asystolic events observed during ILR could result from other than vasovagal mechanisms, e.g. early stage of sick sinus syndrome and/or Adam-Stokes syndrome in the older patients.

Study limitations

Results were obtained in subjects with no cardiovascular or neurological disease and no medication. The older patients therefore represent a very healthy part of the total of older patients referred for unexplained syncope (selection bias). Included were only those patients who did not have a vasovagal episode before NTG, thus excluding the most outspoken cases. Whether the present findings also account for spontaneous vasovagal events should be addressed in future studies.

Conclusion

It is concluded that, in the older patients, sublingual NTG generally provokes a more gradual blood pressure decline compared to the younger. This gradual decline cannot be attributed to failure of the baroreflex buffering capacity with increasing age. Age-related differences in the rate of development of vasovagal symptoms depend on the bradycardic response in the hypotensive, presyncopal episode.

10 Clinical

 10 Science Immediate Publication. Published on 15 May 2007 as manuscript CS20070042 © 2007 The Authors Journal compilation © 2007 Biochemical Society

12 Clinical

 12 Science Immediate Publication. Published on 15 May 2007 as manuscript CS20070042 © 2007 The Authors Journal compilation © 2007 Biochemical Society

13 Clinical

 13 Science Immediate Publication. Published on 15 May 2007 as manuscript CS20070042 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Figure legends : Figure 1 :

 :1 Figure legends:Figure 1: Blood pressure tracings during 3-min periods (180 s) preceding tilt-back in two patients, aged 31 (A) and 69 (B) years old. The rate of arterial pressure fall in the hypotensive presyncopal episode is computed by calculating the first derivative of a 6 th order Givens polynomial approximation during 30-s periods prior to tilt-back or countermaneuver. The blood pressure fall was more rapid in the younger (A) compared to the older (B) patient (3.5 versus 0.7 mmHg/s).

Figure 2 :

 2 Figure 2: Relationship between age and the rate of arterial pressure fall in the presyncopal episode (r = 0.51, p = 0.005). The median rate of arterial pressure fall was 1.44 mmHg/s. Patients with a steeper blood pressure fall (> 1.44 mmHg/s) were regarded as Type A responders. Patients with a more gradual blood pressure attenuation (≤ 1.44 mmHg/s) were regarded as Type B responders.

Figure 3 :

 3 Figure 3: Distribution of age in patients with a rapid (Type A) and more gradual (TypeB) arterial blood pressure fall in the presyncopal episode. Note that all patients with a Type A blood pressure response were younger than 50 yrs.

Figure 4 :

 4 Figure 4: Hemodynamic response to NTG during 60° tilt table testing. Data are presented as 30-s averages and SEM and cover 3-min time periods before and after NTG administration. In addition, data from the last 4 min before tilt-back are presented. Note the discontinuity in the X-axis. Shaded areas correspond to the final minute before tiltback. Closed circles = Type A, open circles = Type B. MAP = mean arterial pressure, HR = heart rate, BRS = baroreflex sensitivity, SV = stroke volume, CO = cardiac output, SVR = systemic vascular resistance.

Figure 5 :

 5 Figure 5: Distribution of mean heart rate (HR) during the last 15 seconds before tilt-back in patients with a Type A and Type B vasovagal blood pressure response.

Figure 6 :

 6 Figure 6: Relationship between the rate of blood pressure fall and the bradycardic response (rate of IBI-enlargement) during the last 30 seconds prior to tilt-back or countermaneuver (r = -0.75, p < 0.001).

Figure 1A Figure 1B Clinical

 1A1B Figure 1A

  Figure 2

  Figure 3

Figure 4 26

 4 Figure 4

  Figure 5

  Figure 6

Clinical Science Immediate Publication. Published on 15 May 2007 as manuscript CS20070042 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Clinical Science Immediate Publication. Published on 15 May 2007 as manuscript CS20070042 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Clinical Science Immediate Publication. Published on 15 May 2007 as manuscript CS20070042 © 2007 The Authors Journal compilation © 2007 Biochemical Society

ACKNOWLEDGEMENTS

We thank Harry Meijer for his assistance in data collection. 14

This work was funded by the PRODEX Program managed by the European Space

Agency in collaboration with the Belgian Federal Science Policy Office. There are no conflicts of interest.


Gian Domenico Pinna
email: gdpinna@fsm.it

Roberto Maestri

Antoni Torunski

Ludmila Danilowicz-Szymanowicz

Malgorzata Szwoch

Maria Teresa

La Rovere

Grzegorz Raczak

HEART RATE VARIABILITY MEASURES: A FRESH LOOK AT RELIABILITY

Keywords: heart rate variability, reproducibility, repeatability, reliability, paced breathing

Despite its extensive use in physiological and clinical research, the analysis of heart rate variability (HRV) is still poorly supported by sound reliability studies. The main aim of this study was to make an in-depth assessment of absolute and relative reliability of standard indexes of HRV from short-term laboratory recordings.

In 39 healthy subjects (mean age (min-max): 38 (26-56) years, 18 men and 21 women) we recorded 5 + 5 min of supine ECG during spontaneous and paced (15 breaths/min) breathing. The test was repeated on the next day in the same conditions. From RR intervals we computed standard indexes of HRV: SDNN, RMSSD, LF and HF power (absolute and normalized units) and LF/HF. Absolute reliability was assessed by the 95% limits of random variation (RV); relative reliability was assessed by the intraclass correlation coefficient (ICC). The sample size needed to detect a mean difference ≥30% of the between-subject SD was also estimated.

Although there was no significant mean change between the two tests, we found that in individual subjects the second measurement can be as high/low as 1.9/0.5 times (SDNN, best case) and 3.5/0.3 times (LF/HF, worst case) the first measurement, due to pure random variation. For most parameters the ICC was > 0.8 (range: 0.65-0.88). The estimated sample size ranged from 24 to 98 subjects.

Reliability indexes tended to improve during paced breathing.

We conclude that short-term HRV parameters are subject to large day-to-day random variations.

Random error, however, represents a limited portion of between-subject variability; therefore observed differences between individuals reflect mostly differences in the subjects' error-free value rather than random error. Overall, paced breathing improves reliability.

INTRODUCTION

After almost 25 years since the publication of the pioneering paper from Akselrod and co-workers [START_REF] Akselrod | Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control[END_REF], heart rate variability (HRV) is still a matter of great interest in clinical and physiological research.

According to Pubmed database, from 2000 to 2006 the number of yearly publications related to HRV has steadily increased from 391 to 584, and this trend is going to be confirmed in 2007. Although such a broad use of this methodology would implicitly assume that the reliability of HRV measurements has been thoroughly evaluated previously, an unprejudiced look at available reliability studies clearly shows that this evaluation has often been inadequate [START_REF] Sandercock | The reliability of short-term measurements of heart rate variability[END_REF]. This is particularly true for HRV indexes derived from short-term laboratory experiments, which are those most commonly used in non-invasive investigations of autonomic cardiovascular control. Major methodological limitations of published reliability studies include: 1) inadequate protocol (e.g.: replicate measurements were taken too far from each other), 2) insufficient sample size, 3) too short or too long recordings according to current guidelines [START_REF]Task force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heart rate variability. Standards of measurement, physiological interpretation and clinical use[END_REF], 4) limited selection of studied HRV parameters, 5) inadequate assessment of reliability due to the use of inappropriate reliability indexes or to misapplication/incomplete inclusion of appropriate indexes, and 6) lack of indications on the practical implications of computed reliability indexes (e.g., for the assessment of individual responses or for sample size estimation). A detailed review of these issues can be found in recently published papers [START_REF] Sandercock | The reliability of short-term measurements of heart rate variability[END_REF][START_REF] Schroeder | Repeatability of heart rate variability measures[END_REF][START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF].

In this study we accurately and comprehensively assessed the reliability of short-term HRV measurements in healthy individuals, in order to overcome major methodological limitations of previous investigations. Both absolute and relative reliability have been considered and implications for sample size calculation and assessment of individual changes are presented. As laboratory recordings are mostly carried out during spontaneous and/or paced breathing, both experimental conditions have been considered.

METHODS

Subjects

We studied 39 healthy volunteers (mean age (min-max): 38 (26-56) years, 18 men and 21 women.

None of them was on medication or suffered from chronic or acute disease. The study was approved by the local Ethical Committee and all subjects gave their written informed consent before participation. All tests were performed between 8.00 a.m. and 1.00 p.m., with the subjects in the supine position in a quiet and dimmed room at a comfortable temperature. All subjects fasted for more than 2 hours and refrained from smoking, alcohol or coffee for the 24 hours preceding the study.

Study protocol

After instrumentation, subjects carried out a session of familiarization with the paced breathing protocol [START_REF] Pinna | Effect of paced breathing on ventilatory and cardiovascular variability parameters during short-term investigations of autonomic function[END_REF]. They followed a recorded voice instruction to breathe in and out at a frequency of 0.25 Hz. After 15 minutes for signal stabilization, subjects breathed spontaneously for 8 min, and then breathed at the paced breathing frequency for another 8 min. During these two sessions ECG was recorded. An identical session was repeated on the next day at the same hour.

Signal analysis and measurements

Beat-by-beat RR interval values (resolution 1 ms) were obtained from the ECG signals using a software package developed in-house [START_REF] Maestri | POLYAN: a computer program for polyparametric analysis of cardiorespiratory variability signals[END_REF]. The RR interval time series were then re-sampled at 2 Hz by cubic spline interpolation. The analysis was carried out on the central 5-min window of each recording.

This analysis window has become the standard one in short-term HRV [START_REF]Task force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heart rate variability. Standards of measurement, physiological interpretation and clinical use[END_REF].

After detrending via least-square second-order polynomial fitting, the power spectral density of RR time series was estimated by the Blackman-Tukey method using a Parzen window with a spectral bandwidth of 0.015 Hz [START_REF] Pinna | Application of time series spectral analysis theory: analysis of cardiovascular variability signals[END_REF]. The power in the low frequency (LF, 0.04-0.15 Hz) and high frequency (HF, 0.15-0.45 Hz) bands were obtained by numerical integration. These spectral indexes will be referred to as LF_BT and HF_BT. Spectral analysis was also performed using the autoregressive method (Burg algorithm) with spectral decomposition (Johnsen and Andersen algorithm).

Autoregressive model order was set at 26, but was interactively increased when negative components appeared in the spectral decomposition table [START_REF] Pinna | Application of time series spectral analysis theory: analysis of cardiovascular variability signals[END_REF]. Spectral powers of the LF and HF bands (LF_AR, HF_AR) were computed summing the respective spectral components. Components showing < 10% of the overall power in the band were ignored as they probably represented pure noise contributions. The LF power in normalized units (LFnu) was computed as LF_AR/(LF_AR+HF_AR). The HF power in normalized units (=1-LFnu) was not analyzed, to avoid redundancy.

We also computed time-domain HRV parameters suitable for short-term analysis: the standard deviation of normal-to-normal beats (SDNN) and the root mean square of successive differences (RMSSD) [START_REF]Task force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heart rate variability. Standards of measurement, physiological interpretation and clinical use[END_REF]. Although mean RR interval is not, strictly speaking, an HRV parameter, it was included in the analysis as a major index of cardiac autonomic control.

Statistical analysis

The reader is referred to the appendix for a short introduction to the statistical basis for the assessment of reliability. The key point is that observed measurements are assumed to be the sum of i) a fixed quantity, which represents the true or error-free value of the characteristic being measured in each subject, and ii) a random quantity, commonly referred to as random error of measurement, which accounts for within-subject variability. According to these concepts, we first examined the distribution of measurements obtained in the two tests, as well as of their difference, to detect and discard possible outliers. An observed value was deemed to be an outlier if it was greater/less than the upper/lower quartile plus/minus 1.5 times the interquartile range [START_REF] Wilcox | Fundamentals of Modern Statistical Methods[END_REF]. This method required a preliminary logtransformation of skewed variables (assessed by the Shapiro-Wilk test for normality).

Following the recommendations of Bland and Altman [START_REF] Bland | Measuring agreement in method comparison studies[END_REF], we plotted the difference between the two measurements ( 1 2 X X -) against their average. This graphical method allows to look for any systematic change between the tests and also to check whether the random error is related to the size of the characteristic being measured (this is referred to as heteroscedasticity). This qualitative investigation was followed by a formal verification of the assumptions underlying the assessment of reliability (see appendix). Specifically, we tested the hypothesis of normality and zero mean of the difference between the two tests (two-sided paired t-test at the 0.05 significance level); we also verified the homoscedasticity assumption by regressing the absolute differences between the two measurements against their average [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Bland | Measuring agreement in method comparison studies[END_REF].

Since many variables showed non-normality and heteroscedasticity, this problem was solved by logtransformation (natural logarithm, ln) [START_REF] Bland | Measuring agreement in method comparison studies[END_REF].

One-way random effects ANOVA was carried out on all variables to estimate the standard error of measurement (SEM), the major index of absolute reliability. This was obtained as the square root of the within-subject mean square (WMS) from the ANOVA table [START_REF] Fleiss | The design and analysis of clinical experiments[END_REF][START_REF] Dunn | Design and analysis of reliability studies[END_REF]. From the SEM value we derived the 95% limits of random variation, i.e. the range of values within which 95% of the differences between two measurements ( 1 2 X X -) are expected to lie due to pure random variation. For log-transformed variables, these limits were back-transformed (antilogarithm), giving the range of values within which 95% of the ratios between the two measurements ( ) are expected to lie due to pure random variation [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Bland | Measuring agreement in method comparison studies[END_REF].

From mean square values of the ANOVA table we also computed the intraclass correlation coefficient (ICC) as [START_REF] Fleiss | The design and analysis of clinical experiments[END_REF][START_REF] Dunn | Design and analysis of reliability studies[END_REF] : where BMS is the between-subject mean square. Ninety-five percent confidence intervals for ICC were calculated [START_REF] Shrout | Intraclass correlations: uses in assessing rater reliability[END_REF].

As the magnitude of the random error affects the sample size of an experiment [START_REF] Desu | Sample size methodology[END_REF], we estimated the sample size needed to detect a relevant change in the mean of HRV parameters after a treatment (test-retest experiment). Conventionally, we considered as "relevant" a change of ≥ 30% of betweensubject standard deviation. We also assumed a two-sided test with a significance level of 5% and a power of 80%.

All analyses were carried out using the SAS/STAT statistical package, release 8.02 (SAS Institute Inc., Cary, NC, USA).

RESULTS

Spontaneous breathing

All variables except mean RR interval and LFnu showed a marked right-skewed distribution (Shapiro-Wilk test: p< 0.01). One subject showed an outlier in RMSSD, HF_BT and HF_AR, while another one showed an outlier only in RMSSD. These measurements and those derived from them (i.e., LFnu and LF/HF) were ignored in the subsequent analysis. Descriptive statistics of measured parameters in the two tests are reported in table 1.

Bland-Altman plots of the difference between the two measurements against their average displayed a symmetrical distribution of points around the zero line in all parameters, indicating absence of a systematic change. The width of the scatter around the same line, however, showed a clear increasing trend in SDNN, RMSSD, LF_BT, LF_AR, HF_BT, HF_AR and LF/HF, indicating heteroscedasticity.

Two representative examples of respectively an homoscedastic variable (mean RR) and an heteroscedastic variable (LF_BT power) are displayed in figure 1 3a. If we consider LFnu, the limits of random variation indicate that, in order to be 95% confident that a real change has occurred in an individual, the observed difference between two measurements has to be > 0.29 or < -0.29. For the same parameter, the ICC indicates that 65% of the variability of LFnu measurements across the studied population is due to variability in the true value of the subjects, while the remaining 35% is due to random error. The last column of table 3a shows that 98 subjects are needed in a test-retest experiment to detect a change in mean LFnu of ≥ 0.04 (30% of between-subject standard deviation), with a significance level of 5% and a power of 80%.

Reliability indexes for heteroscedastic HRV parameters are reported in table 4a. Since the statistical analysis of these variables was carried out after log-transformation, the SEM and the change in the mean for the estimation of the sample size, are expressed in log units. The limits of random variation indicate that in order to be 95% confident that a real change has occurred in a given parameter, the ratio between two measurements ( 1 2 X X

) has to lie outside the indicated interval. The asymmetry of this interval is simply the result of the antilogarithmic transformation. It can be seen that for all spectral parameters the second measurement can be as large/small as about 3.5/0.3 times the first measurement due to pure random variation. To relate these inferential figures to the data of the study, figure 2 shows the plots of the ratio 1 2 X X against the mean of the two measurements. Note the close agreement between theoretical 95% limits of variation and raw data.

ICC values reported in table 4a

show that the proportion of total measurement variability of heteroscedastic HRV parameters explained by the variability of the subjects' error-free value ranged from 70% (LF_HF) to 86% (HF_BT and HF_AR); therefore random error accounted for 30% to 14% of total measurement variability.

Paced breathing

Descriptive statistics of HRV parameters derived from paced breathing recordings are reported in table 2. There was only one outlier in RMSSD. As for spontaneous breathing, SDNN, RMSSD, LF_BT, LF_AR, HF_BT, HF_AR and LF/HF exhibited an heteroscedasticity behavior and were successfully log-transformed. The difference between transformed measurements was largely non significant.

Reliability indexes for homoscedastic and heteroscedastic variables are reported in

DISCUSSION

Despite its extensive use in physiological and clinical research, the analysis of HRV is still poorly supported by sound reliability studies, and further investigations in this field has recently been advocated [START_REF] Sandercock | The reliability of short-term measurements of heart rate variability[END_REF]. In this study we carried out an in-depth assessment of absolute and relative reliability of standard indexes of HRV from short-term laboratory recordings in healthy subjects during spontaneous and paced breathing. The experimental protocol and the analysis of collected data were performed according to state-of-the art methodology and best-practice criteria. We found that HRV parameters were characterized by large random variations within individuals, thus showing low absolute reliability. Random error, however, in most parameters represented a limited portion of total measurement variability across individuals, thus indicating good relative reliability. Overall, paced breathing improved the reliability of spectral parameters, particularly those derived from ratios of raw quantities (LFnu and LF/HF).

Reliability of HRV parameters: absolute reliability

Our study reveals the presence of a large random error (SEM) in all HRV parameters, particularly in those computed in the frequency domain. Indeed increases as great as about 3.5 times and decreases of as much as about 30% may occur from one measurement to the next due to pure random variation.

Limits of random variation are lower for time-domain indexes, being about 1.9-2.4 times and 50-60%

for SDNN and RMSSD respectively. These results question the use of HRV indexes in assessing treatment effects in individual subjects. Of note, in all HRV parameters but LFnu random error increases as the magnitude of the parameter increases, which is the hallmark of heteroscedasticity.

Random error of HRV parameters is in part due to sampling variability of the estimated parameters, as they are nothing but statistics computed on a finite number of RR intervals. Therefore, they are subjected to random changes from one sample to another [START_REF] Pinna | Effects of record length selection on the accuracy of spectral estimates of heart rate variability: a simulation study[END_REF]. Part of intra-subject variability is also due to an intrinsic lability of HRV parameters -probably because they are under the influence of such factors as mood, alertness and mental activity which are very difficult to control for in any study.

Changes associated with frequency and depth of respiration also play an important role [START_REF] Pinna | Effect of paced breathing on ventilatory and cardiovascular variability parameters during short-term investigations of autonomic function[END_REF].

In the two previous reliability studies that provide estimates of the SEM (or equivalently of the within-subject standard deviation), slightly greater values of this index were found [START_REF] Pitzalis | Short-and long-term reproducibility of time and frequency domain heart rate variability measurements in normal subjects[END_REF][START_REF] Lord | Low-frequency heart rate variability: reproducibility in cardiac transplant recipients and normal subjects[END_REF]. This might be due to differences in the experimental protocol.

Reliability of HRV parameters: relative reliability

The ICC of HRV parameters ranged between 0.65 and 0.88. Although the definition of a categorical rating of relative reliability based on ICC is still controversial, these values can reasonably be considered as indicating substantial to good reliability [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Fleiss | The design and analysis of clinical experiments[END_REF][START_REF] Donner | Sample size requirements for reliability studies[END_REF]. For most measurements the ICC was > 0.80, indicating that they reflect mostly the true value of HRV parameters relative to random error.

From the mathematical definition of ICC (se the appendix), it clearly appears that such high values of relative reliability are the consequence of a large between-subject variability, a fact well-known to investigators involved in HRV analysis. The lowest values of ICC were found in the LFnu and LF/HF parameters during spontaneous breathing (0.65 and 0.70 respectively). This result probably derives from a relatively greater random error, as LFnu and LF/HF "carry" the error of both the LF and HF power. A further insight into the practical meaning of observed ICCs can be gained by remembering that in the context of our test-retest reliability study the ICC equals the correlation coefficient between paired measurements [START_REF] Dunn | Design and analysis of reliability studies[END_REF].

The estimated ICCs for time-domain HRV parameters are very close to those reported by Sinnreich et al [START_REF] Sinnreich | Five minute recordings of heart rate variability for population studies: repeatability and age-sex characteristics[END_REF] and similar to those found by Schroeder et al. [START_REF] Schroeder | Repeatability of heart rate variability measures[END_REF]. Lower ICCs were obtained in the same parameters by Pitzalis et al. [START_REF] Pitzalis | Short-and long-term reproducibility of time and frequency domain heart rate variability measurements in normal subjects[END_REF] and Gerritsen at al. [START_REF] Gerritsen | Measures of cardiovascular autonomic nervous function: agreement, reproducibility, and reference values in middle age and elderly subjects[END_REF]; their estimates, however, were based on raw (i.e., not transformed) data. The ICCs of spectral parameters were similar to or higher than those found by others [START_REF] Schroeder | Repeatability of heart rate variability measures[END_REF][START_REF] Pitzalis | Short-and long-term reproducibility of time and frequency domain heart rate variability measurements in normal subjects[END_REF][START_REF] Sinnreich | Five minute recordings of heart rate variability for population studies: repeatability and age-sex characteristics[END_REF]. A comparatively reduced LFnu during spontaneous breathing was also observed by Sandercock et al [START_REF] Sandercock | Reliability of three commercially available heart rate variability instruments using short-term (5-min) recordings[END_REF].

Implications of reliability in sample size estimation

A major implication of measurement reliability is the size of the sample needed to test a scientific hypothesis with a preset significance level and power. We explored this point by simulating a simple test-retest study to investigate the effect of a treatment on the mean value of HRV parameters. Since reference values as to what change in HRV parameters would be clinically relevant are lacking, we conventionally adopted the criterion of 30% of between-subject standard deviation. The rationale is that the more the subjects have dispersed values, the larger the shift in mean value should be to be clinically relevant. We found that the sample size can largely vary from parameter to parameter and that it is inversely proportional to the ICC. The latter result also applies to the estimation of the sample size in group comparison studies [START_REF] Fleiss | The design and analysis of clinical experiments[END_REF].

Spontaneous versus paced breathing

Paced breathing substantially improved the reliability of LFnu and LF/HF, with a consequent dramatic reduction (> 50%) of the estimated sample size. This result is in agreement with the findings of Pitzalis and coworkers [START_REF] Pitzalis | Short-and long-term reproducibility of time and frequency domain heart rate variability measurements in normal subjects[END_REF]. Moreover, voluntary control of breathing moderately improved the reliability of the LF power, while leaving substantially unchanged that of the HF power and RMSSD, and slightly decreasing the reliability of SDNN. We argue that the improvements observed during paced breathing might be due to a better stabilization of LF oscillations brought about by the virtual abolition of respiratory-related frequency components within the LF band [START_REF] Pinna | Effect of paced breathing on ventilatory and cardiovascular variability parameters during short-term investigations of autonomic function[END_REF].

Classical versus autoregressive spectral estimation

Our study suggests that the reliability of HRV parameters is not affected by the method used for spectral estimation (classical Blackman-Tukey or autoregressive method). A similar result was found by other investigators [START_REF] Pitzalis | Short-and long-term reproducibility of time and frequency domain heart rate variability measurements in normal subjects[END_REF]. It should be stressed, however, that spectral estimates depend to a certain extent on the design criteria adopted in the analysis. For instance, autoregressive measurements depend on the criterion used for model order selection [START_REF] Pinna | Application of time series spectral analysis theory: analysis of cardiovascular variability signals[END_REF]. Therefore, the use of algorithms markedly different from those adopted in this study might yield different reliability figures.

CONCLUSION

In healthy subjects, short-term HRV parameters are subjected to large day-to-day random variations which would make difficult the detection of treatment effects in individual subjects. For most indexes, however, random variation represents a limited portion of the between-subject variability; therefore observed differences between individuals reflect mostly differences in the subjects' true value rather than random error. The sample size for an experiment markedly depends on the reliability of the HRV index considered; this implies that the design of experiments based on the measurement of a set of HRV parameters should be tuned to the indexes with lowest reliability. Paced breathing appears to provide more reliable HRV measurements, particularly those related to the spectral content of the LF band.

Appendix

Statistical basis for the assessment of reliability

A measurement is said to be to reliable when the values obtained under identical conditions on the same individuals at different times agree closely each other. Therefore, reliability is synonymous with intrasubject reproducibility, repeatability or consistency. Reliability has classically been investigated

assuming the following statistical model [START_REF] Fleiss | The design and analysis of clinical experiments[END_REF][START_REF] Dunn | Design and analysis of reliability studies[END_REF]:

ε τ + = X (1)
In this model, the measurement X made on a given subject is assumed to be the sum of a fixed quantity τ , the "true value" or "error-free value" of the characteristic being measured in that subject, and a random quantity ε , commonly referred to as random error of measurement, which accounts for intra-subject variability.

There are some basic assumptions underlying model (1): the random error ε is normality distributed, has zero mean, is uncorrelated within and between subjects, and has a fixed standard deviation independent of τ , the latter property being commonly referred to as homoscedasticity [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF].

Moreover, for a population of subjects, τ is assumed to be normally distributed. Before analyzing reliability, all these assumptions should be carefully verified or confidently assumed on the basis of a properly conducted experiment. Failure to satisfy homoscedasticity and normality assumptions is commonly dealt with by variable transformation [START_REF] Bland | Measuring agreement in method comparison studies[END_REF].

If we take two replicate measurements on the same individual under identical conditions, from equation ( 1) we have that the difference ∆X between them will be:

( ) ( ) δ ε ε ε τ ε τ = - = + - + = - = ∆ 2 2 1 2 1 2 X X X ( 2
)
where the suffixes 2 and 1 indicate the measurements at the two occasions. Equation ( 2) clearly shows that the repeatability of the measurement depends on the random quantity δ : the lower δ , the closer the two measurements will be with each other. The magnitude of δ , as expressed by its standard deviation, is

ε σ ⋅ 2
, where ε σ , the so-called standard error of measurement (SEM), is the standard deviation of ε . Therefore, the repeatability of a measurement ultimately depends on the magnitude of the SEM. Accordingly, the SEM is considered the key statistical indicator of absolute reliability [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Fleiss | The design and analysis of clinical experiments[END_REF][START_REF] Dunn | Design and analysis of reliability studies[END_REF].

The SEM has the following two major uses. First, if we take two measurements on the same is called repeatability coefficient [START_REF] Bland | Measuring agreement in method comparison studies[END_REF]. Second, the SEM is a crucial parameter in determining the sample size for an experiment [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Desu | Sample size methodology[END_REF]. This is because the higher the random error of a measurement, the greater the "noise" that will tend to obscure a possible treatment effect.

Another classical way of assessing reliability is through the intraclass correlation coefficient (ICC), which is also commonly referred to as reliability coefficient. It expresses the proportion of the variability of observed measurements that is explained by the variability of the subjects' error-free value. The ICC is then defined as [START_REF] Fleiss | The design and analysis of clinical experiments[END_REF][START_REF] Dunn | Design and analysis of reliability studies[END_REF]:

2 2 2 2 2 2 2 1 1 τ ε ε τ τ τ σ σ σ σ σ σ σ + = + = = X ICC ( 3
)
where 2

x σ total variance of observed measurements among the subjects of the considered population, 2 τ σ is the part of total variance due to differences in the patients' true value and 2 ε σ is the part due to random error (i.e., the square of the SEM).

The ICC ranges from 0 to 1: the lower the random error relative to subject-to-subject variability, the closer the ICC will be to 1; conversely, the greater the random error relative to subject-to-subject variability, the closer the ICC will be to 0. Therefore, the higher the ICC, the more a measurements will reflect the true value and the more probably we will be able to detect differences between individuals.

For these reasons the ICC is considered the key statistical indicator of relative reliability [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF]. When reliability is assessed taking two replicate measurements per subject, the ICC turns out to be mathematically equivalent to the correlation coefficient between paired measurements [START_REF] Dunn | Design and analysis of reliability studies[END_REF].

Various categories of reliability based on ICC have been proposed so far [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Fleiss | The design and analysis of clinical experiments[END_REF][START_REF] Donner | Sample size requirements for reliability studies[END_REF]. Although these criteria do not fully agree with each other, an ICC >0.8 is usually regarded as indicating good to excellent reliability, while an ICC between 0.6 and 0.8 may be taken to represent substantial reliability.

From equation ( 3) it clearly appears that the ICC, besides being dependent on the random variability of the measurement, depends on the variability (i.e.: heterogeneity) of the population being studied.

Therefore results obtained in one population can not be extrapolated to a new an possibly more/less homogeneous population [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Dunn | Design and analysis of reliability studies[END_REF].

Assessment of reliability

To assess reliability, the measurement of interest is taken on a sample of individuals during two or more replicated experiments under as close to uniform conditions as possible. To fulfill the statistical assumptions for analysis, replicated experiments should be performed neither to far apart in time, to ensure constancy of the characteristic being measured, nor too close, to avoid potential carry-over or learning effects. Collected data should be carefully checked to detect outliers and to verify the required statistical assumptions (see above) [START_REF] Dunn | Design and analysis of reliability studies[END_REF]. Graphical methods such as Bland-Altman plots as well as formal hypothesis testing are used at this purpose [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Bland | Measuring agreement in method comparison studies[END_REF][START_REF] Dunn | Design and analysis of reliability studies[END_REF]. Whenever the data do not satisfy distributional assumptions and/or the homoscedasticity requirement, variable transformation is applied [START_REF] Atkinson | Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine[END_REF][START_REF] Bland | Measuring agreement in method comparison studies[END_REF]. Indexes of absolute and relative reliability (e.g., SEM, ICC) and related parameters (e.g., 95% limits of random variation, sample size) are finally estimated. Data are expressed as mean (SD). Skewed variables are also reported after log transformation. SDNN=standard deviation of normal-to-normal beats; RMSSD=root mean square of successive differences; LF_BT, LF_AR= power in the low frequency band (0.04-0.15 Hz) according to the Blackman-Tukey (BT) or autoregressive (AR) method; HF_BT, HF_AR= power in the high frequency band (0.15-0.45 Hz) according to the Blackman-Tukey (BT) or autoregressive (AR) method; LF/HF= ratio between low frequency and high frequency power (AR method); Ln= natural logarithm. One subject showed an outlier in RMSSD, HF_BT and HF_AR, while another one showed an outlier only in RMSSD. These measurements and those derived form them (i.e., LF_nu and LF/HF) were ignored. *) p value for the test of no difference between the two measurements (one-sample t-test). For skewed variables the test was carried out after log-transformation. LFnu= low frequency power in normalized units. SEM= standard error of measurement; is the standard deviation of the random component of the measurement. The limits of random variation give the range of values within which 95% of the differences between the two measurements are expected to lie due to pure random variability. Therefore, when the observed difference lies outside this interval we can be 95% confident that a real change has occurred. ICC= intraclass correlation coefficient; is the proportion of measurement variability that is due to variability in the subjects' "true value", the remaining fraction being due to random variability. CI= confidence interval. The last column gives the estimate of the sample size needed to detect in a test-retest experiment a change in the mean of the parameter ≥30% of the between-subject standard deviation. In the computation of the sample size we assumed a two-tail test with a significance level of 5% and a power of 80%. standard deviation of the random component of the measurement (see appendix) and was computed on log-transformed data. The limits of random variation give the range of values within which 95% of the ratios between the two measurements are expected to lie due to pure random variability. Therefore, when the observed ratio lies outside this interval, we can be 95% confident that a real change has occurred. ICC= intraclass correlation coefficient; is the proportion of measurement variability that is due to variability in the subjects' true value, the remaining fraction being due to random variability. CI= confidence intervals. The last column gives the estimate of the sample size needed to detect in a test-retest experiment a change in the mean of the parameter ≥30% of the between-subject standard deviation. In the computation of the sample size we assumed a two-tail test with a significance level of 5% and a power of 80%.

Clinical

  Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

  a and b respectively. Visual findings were confirmed by regression analysis. Heteroscedastic variables were successfully log-transformed, obtaining at the same time homoscedasticity and normality. A representative Bland-Altman plot is shown in fig. 1c. For all HRV parameters the difference between the two tests was negligible and non significant, indicating absence of systematic change. Reliability indexes for homoscedastic variables (mean RR interval and LFnu) are reported in table Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Fig. 1 .

 1 Fig. 1. Representative Bland-Altman plots of the difference between the two measurements ( 1 2 X X -) against their average: (a) mean RR, (b) LF power (LF_BT, Blackman-Tukey method). The scatter of points is symmetrical around the zero line in both parameters, indicating absence of systematic change between the two tests. The magnitude of the scatter around the same line, however, is pretty homogeneous for mean RR, indicating homoscedasticity, while it steadily increases for LF power, indicating heteroscedasticity. Figure 1 (c) shows how log-transformation (natural logarithm, ln) of the LF power was successful in producing homoscedasticity. All plotted data are from recordings during spontaneous breathing.

Fig. 2 .Figure 1 Clinical

 21 Fig.2. Plots of the ratio between the two measurements ( )1 2 X Xagainst their mean for heteroscedastic heart rate variability parameters. SDNN=standard deviation of normal-to-normal beats;RMSSD=root mean square of successive differences; LF_BT, LF_AR= power in the low frequency band (0.04-0.15 Hz) according to the Blackman-Tukey (BT) and autoregressive (AR) method; HF_BT, HF_AR= power in the high frequency band (0.15-0.45 Hz); LF/HF= ratio between low frequency and high frequency power (AR method). All plotted data are from recordings during spontaneous breathing.

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055

	ICC	=	BMS BMS	+ -	WMS WMS

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society SDNN

  . Analysis indexes of the other HRV parameters were almost unchanged.

	table 3b and 4b
	respectively. Compared to spontaneous breathing we found: i) an improvement of all reliability indexes

(SEM, limits of random variation, ICC and sample size) for LF_BT, LF_AR and LF/HF, ii) an increased ICC and reduced sample size for LFnu; iii) a slight worsening of all reliability indexes for

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society individual

  before and after a treatment and want to be 95% confident that a real change has occurred,

	the observed difference has to lie outside the interval	-	. 1	96	⋅	2	⋅	SEM	,	+	1	96 .	⋅	2	⋅	SEM	, or
	-77 . 2	⋅	SEM	,	+ 77 . 2	⋅	SEM	[5, 10]. Therefore, the extremes of this interval can be viewed as the 95%
	limits of random variation. The value	2	77 .	⋅	SEM

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical SocietyTable 1 .

 1 Descriptive results for HRV parameters during spontaneous breathing in the two tests taken one day apart from each other.

		N	Measurement 1	Measurement 2 Difference (2-1)	p*
	Mean RR (ms)	39	910 (115)	927 (128)	17 (80)	0.19
	SDNN (ms)	39	43 (17)	46 (22)	3 (12)
	Ln SDNN (ln ms)	39	3.68 (0.39)	3.71 (0.48)	0.03 (0.26)	0.44
	RMSSD (ms)	37	34 (23)	39 (24)	5 (21)
	Ln RMSSD (ln ms)	37	3.35 (0.58)	3.48 (0.64)	0.13 (0.41)	0.07
	LF_BT (ms 2 )	39	687 (583)	814 (759)	127 (604)
	Ln LF_BT (ln ms 2 )	39	6.18 (0.88)	6.26 (1.01)	0.08 (0.62)	0.43
	HF_BT (ms 2 )	38	468 (542)	522 (653)	-54 (423)
	Ln HF_BT (ln ms 2 )	38	5.60 (1.11)	5.63 (1.22)	0.03 (0.63)	0.74
	LF_AR (ms 2 )	39	684 (596)	804 (771)	120 (632)
	Ln LF_AR (ln ms 2 )	39	6.16 (0.89)	6.23 (1.03)	0.07 (0.63)	0.51
	HF_AR (ms 2 )	38	464 (540)	518 (645)	54 (418)
	Ln HF_AR (ln ms 2 )	38	5.58 (1.12)	5.62 (1.22)	0.04 (0.64)	0.71
	LFnu (%)	38	62 (18)	63 (17)	1 (15)	0.66
	LF/HF	38	2.5 (2.4)	2.5 (2.3)	0.0 (1.9)
	Ln LF/HF (ln)	38	0.56 (0.86)	0.59 (0.82)	0.03 (0.69)	0.76

Table 2 .

 2 Descriptive results for HRV parameters during paced breathing in the two tests taken one day apart from each other.

		N	Measurement 1	Measurement 2 Difference (2-1)	p*
	Mean RR (ms)	39	933 (130)	928 (124)	-4 (89)	0.76
	SDNN (ms)	39	45 (23)	46 (21)	1 (15)
	Ln SDNN (ln ms)	39	3.68 (0.48)	3.74 (0.45)	0.05 (0.32)	0.30
	RMSSD (ms)	38	41 (34)	42 (27)	1 (25)
	Ln RMSSD (ln ms)	38	3.49 (0.67)	3.56 (0.64)	0.07 (0.44)	0.30
	LF_BT (ms 2 )	39	602 (780)	641 (697)	39 (638)
	Ln LF_BT (ln ms 2 )	39	5.88 (1.05)	5.94 (1.07)	0.06 (0.56)	0.48
	HF_BT (ms 2 )	39	1047 (1909)	944 (1429)	-103 (1028)
	Ln HF_BT (ln ms 2 )	39	5.88 (1.05)	5.94 (1.07)	0.08 (0.70)	0.49
	LF_AR (ms 2 )	39	599 (787)	637 (707)	38 (653)
	Ln LF_AR (ln ms 2 )	39	5.86 (1.09)	5.92 (1.10)	0.06 (0.57)	0.51
	HF_AR (ms 2 )	39	1044 (1885)	977 (1593)	-67 (987)
	Ln HF_AR (ln ms 2 )	39	6.05 (1.36)	6.13 (1.29)	0.08 (0.70)	0.45
	LFnu (%)	39	46 (22)	46 (22)	0 (14)	0.27
	LF/HF	39	1.4 (1.4)	1.3 (1.2)	-0.1 (1.1)
	Ln LF/HF (ln)	39	-0.19 (1.08)	-0.22 (1.09)	-0.03 (0.62)	0.62
	Data are expressed as mean (SD). Skewed variables are also reported after log transformation.
	SDNN=standard deviation of normal-to-normal beats; RMSSD=root mean square of successive
	differences; LF_BT, LF_AR= power in the low frequency band (0.04-0.15 Hz) according to the
	Blackman-Tukey (BT) or autoregressive (AR) method; HF_BT, HF_AR= power in the high frequency
	band (0.15-0.45 Hz) according to the Blackman-Tukey (BT) or autoregressive (AR) method; LF/HF=
	ratio between low frequency and high frequency power (AR method); Ln= natural logarithm.
	*) p value for the test of no difference between the two measurements (one-sample t-test). For skewed
	variables the test was carried out after log-transformation.

Table 3 .

 3 Reliability indexes for homoscedastic heart rate variability (HRV) parameters.

			a) Spontaneous breathing
	HRV parameter	SEM	95% limits of random variation for the difference between 2 measurements ( 1 2 X X -)	ICC (95% CI)	Change in the mean to be detected and required sample size (N)
	Mean RR interval	57 ms	-159 ms, +159 ms	0.78 (0.62-0.88)	32 ms, N=52
	LFnu	0.10	-0.29, +0.29	0.65 (0.43-0.80)	0.04, N=98
			b) Paced breathing
	HRV parameter	SEM	95% limits of random variation for the difference between 2 measurements ( 1 2 X X -)	ICC (95% CI)	Change in the mean to be detected and required sample size (N)
	Mean RR interval	62 ms	-173 ms, +173 ms	0.76 (0.59-0.87)	33 ms, N=58
	LFnu	0.10	-0.26, +0.26	0.81 (0.67-0.90)	0.06, N=42

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Table 4 .

 4 Reliability of heteroscedastic heart rate variability (HRV) parameters.

			a) Spontaneous breathing
	HRV parameter	SEM	95% limits of random variation of the ratio between 2 measurements ( 1 2 X X )	ICC (95% CI)	Change in the mean to be detected and required sample size (N)
	SDNN	0.18 ln ms	0.60, 1.67	0.82 (0.68-0.90)	0.12 ln ms, N=40
	RMSSD	0.30 ln ms	0.44, 2.29	0.76 (0.59-0.87)	0.16 ln ms, N=57
	LF_BT	0.43 ln ms 2	0.30, 3.32	0.79 (0.64-0.88)	0.25 ln ms 2 , N=48
	HF_BT	0.44 ln ms 2	0.30, 3.36	0.86 (0.75-0.92)	0.32 ln ms 2 , N=30
	LF_AR	0.44 ln ms 2	0.29, 3.42	0.79 (0.64-0.88)	0.26 ln ms 2 , N=49
	HF_AR	0.45 ln ms 2	0.29, 3.44	0.86 (0.74-0.92)	0.33 ln ms 2 , N=31
	LF/HF	0.45 ln	0.28, 3.53	0.70 (0.50-0.84)	0.21 ln, N=77
			b) Paced breathing
	HRV parameter	SEM	95% limits of random variation of the ratio between 2 measurements ( 1 2 X X )	ICC (95% CI)	Change in the mean to be detected and required sample size (N)
	SDNN	0.23 ln ms	0.54, 1.87	0.77 (0.60-0.87)	0.12 ln ms, N=55
	RMSSD	0.31 ln ms	0.42, 2.37	0.77 (0.61-0.87)	0.17 ln ms, N=54
	LF_BT	0.40 ln ms 2	0.33, 3.00	0.86 (0.75-0.92)	0.30 ln ms 2 , N=29
	HF_BT	0.45 ln ms 2	0.28, 3.51	0.88 (0.78-0.94)	0.37 ln ms 2 , N=25
	LF_AR	0.40 ln ms 2	0.33, 3.04	0.86 (0.76-0.93)	0.30 ln ms 2 , N=29
	HF_AR	0.45 ln ms 2	0.29, 3.50	0.88 (0.79-0.94)	0.38 ln ms 2 , N=24
	LF/HF	0.39 ln	0.34, 2.94	0.87 (0.76-0.93)	0.30 ln, N=28

The legend of HRV parameters is given in table 1. SEM= standard error of measurement; is the

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society

© 2007 The Authors Journal compilation © 2007 Biochemical Society

Clinical Science Immediate Publication. Published on 23 Mar 2007 as manuscript CS20070055 © 2007 The Authors Journal compilation © 2007 Biochemical Society