Research Paper
ClinicalAutonomic Research 1998, 8:145-153
There is evidence that the processes regulating heart rate variations reflect non-linear complexity and show 'chaotic' determinism. Data analyses using non-linear methods may therefore reveal patterns not apparent with conventional statistical approaches. We have consequently investigated two non-linear methods, the Poincar~ plot (scatterplot) and cardiac sequence (quadrant) analysis, and compared these with standard time-domain summary statistics, during a normal volunteer investigation of an agonist and antagonists of the cardiac 13-adrenoceptor. Under double-blind and randomized conditions (Latin square design), 12 normal volunteers received placebo, celiprolol ([31- and [32-adrenoceptor partial agonist), propranolol (131- and [32-adrenoceptor antagonist), atenolol ([31adrenoceptor antagonist) and combinations of these agents. Single oral doses of medication (at weekly intervals) were administered at 22:30 h with sleeping heart rates recorded overnight. The long (SDNN, SDANN) and short-term (rmsSD) time-domaln summary statistics were reduced by celiprolol - effects different from the unchanged or small increases after atenolol and propranolol alone. The Poincar~ plot was constructed by plotting each RR interval against the preceding RR interval, but unlike previous descriptions of the method, an automated computer method, with a high level of reproducibility, was employed. Scatterplot length and area were reduced following celiprolol and different from the small increases after propranolol and atenolol. The geometric analysis of the scatterplots allowed width assessment (i.e. dispersion) at fixed RR intervals. Differences between the drugs were confined to the higher percentiles (i.e. 75% and 90% of scatterplut length: low heart rate). The long-term time-domain statistics (SDNN, SDANN) correlated best with scatterplot length and area whereas the short-term heart rate variability (HRV) indices (rmsSD, pNNso) correlated strongly with scatterplot width. Cardiac sequence analysis (differences between three adjacent beats; ARR vs ARRn.1) assessed the short-term patterns of cardiac acceleration and deceleration, four patterns are identified: +/+ (a lengthening sequencing), + / - or - / + (balanced sequences), and finally - / - (a shortening sequence). A running count of events by quadrant, together with the average magnitude of the differences was computed. The 13-adrenoceptor partial agonist celiprolol increased acceleration sequences. The duration of beat-to-beat difference shortened after celiprolol; this contrasted with increased duration of beat-to-beat difference after propranolol and atenolol. These results demonstrated a shift towards sympathetic dominance after the [3-adrenoceptor partial agonist celiprolol contrasting with parasympathetic dominance after the 9" adrenoceptor antagonists propranolol and atenolol. These non-linear methods appear to be valuable tools to investigate HRV in health and in cardiovascular disease and to study the implications of alterations in autonomic control during therapeutic intervention. Clin Auton Res 8:145-153 9 1998 Lippincott-Raven Publishers
Heart rate variability effects of an agonist or antagonists of the 13-adrenoceptor assessed with scatterplot and sequence analysis B. Silke and J.G. Riddell University Department of Therapeutics and Pharmacology, The Queen's University of Belfast, Belfast, UK
Correspondence and reprint requests to B. Silke, Department of Therapeutics and Pharmacology, Whitla Medical Building, Queen's University, 97 Lisburn Road, Belfast BT9 7BL, UK. Tel: (+44) 1232 335770; Fax: (+44) 1232 438346; e-mail:
[email protected]
Received 15 June 1997," accepted as revised 15 April 1998
Keywords: heart rate variability, Poincar~ plot, scatterplot, nonlinear,/3-adrenoceptor, agonist, antagonist
Introduction Heart-rate variability (HRV) is a powerful predictor of mortality following myocardial infarction [1-3]; the relationship between disturbed autonomic imbalance and
cardiovascular mortality is recognized [4,5]. Attenuation of cardiac sympathetic stimulation with fl-adrenoceptor antagonists improves survival following myocardial infarction [6,7]; despite this research on the impact of 3-adrenoceptor antagonists on HRV is limited [8,9]. 0959-9851 9 1998 Lippincott-Raven Publishers
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Silke and Riddell
HRV may be assessed by different methods, these have been critically evaluated [10]. Time-domain statistics provide summary information on both short and longterm variations in HRV, but the pattern of the fluctuations is not evident. Spectral methods provide a time-averaged estimate of cyclic variability and are most useful in the assessment of sinusoidal or near-sinusoidal variations in HR [11,12]. Because non-linear phenomena are involved in the genesis of HRV (i.e. the heart rate shows non-linear complexity or 'chaotic' behaviour [13 ]) analyses based on non-linear dynamics may allow more precise outcome prediction [14]. The Poincar~ plot is a 'scatterplot' (return map) of current cycle plotted against the previous beat (RR vs RRn-I); scatterplot length is correlated with long-term (SDNN and SDANN) time domain statistics [15] while scatterplot width appears a specific measure of parasympathetic nervous system activity [ 15,16 ]. Quadrant analysis is a related method proposed to investigate the nature of cardiac interval sequencing [11]; here the interval difference between two consecutive beats and the next pair is evaluated (ARR vs ARRn+I). The latter method removes the dominant characteristics apparent in the Poincar~ plot, namely the high correlation between one interval and the next. This study investigated these non-linear methods compared with conventional HRV time-domain statistics in a double-blind, randomized, placebo-controlled study of the impact of/3-adrenoceptor modulation. The actions of the partial agonist [17] celiprolol (/31- or/32adrenoceptor agonist depending on dose [18]) were compared with the full antagonists propranolol (/31- and /32-adrenoceptor antagonist) and atenolol (fll-adrenoceptor antagonist) alone and in combination with celiprolol. This approach permitted the dose-dependency and selectivity of the partial agonist activity of celiprolol to be evaluated.
Methods Twelve healthy male volunteers (age 23-+ 2 (SEM) years, weight 75 -+ 3 kg; height 180 -+ 2 cm) participated in the study. Subjects were randomly assigned, using a Latin square design, to receive double blind on each study day (with an interval of at least one week), single oral doses of placebo, celiprolol 200mg, celiprolol 800 rag, propranolol 160 mg, atenolol 50 mg, celiprolol 200 mg with propranolol 160 mg or atenolol 50 mg and finally celiprolol 800 mg with propranolol 160 mg or atenolol 50 mg. Medication was administered between 22:15 and 22:45h. The dose of atenolol was chosen based on evidence that the 50 mg dose is highly selective for the /31- [19] with negligible antagonism at the /32" adrenoceptor [20]. The HRV parameters were compared between the two doses of celiprolol alone, and when celiprolol was co-administered with propranolol 160 mg or atenolol 50 rag. The selectivity and dose-dependence 146
Clinical Autonomic Research 1998,Vol 8 No 3
of the partial agonist activity of agents acting at the/3aor #2-adrenoceptor can be assessed from the sleeping heart rate, due to the low level of prevailing sympathetic drive at night [21,22]. Heart rate methods The HR was recorded (modified lead II position) using an Oxford Medilog 2-24 miniature analogue tape recorder (Oxford Medical Systems, Abingdon, UK), with a phase-locked loop motor speed control to ensure speed stability. The recording speed was 2 mm s-I. The HRV was assessed from RR interval files generated from 22:00 to 08:00h, analysed in hourly epochs. Aberrant data values, as determined by a neural network classification (B~omedlcal " " Systems ColortraceTM, S-Pace Medical, St Louis, MO, USA) were excluded; further filtering accepted only consecutive beats of normal morphological characteristics (N-N) with cycle lengths within 17.5% of the preceding cycle length. Missing data points were not interpolated. Time-domain summary statistics The summary time-domain statistical measures of HRV calculated included the standard deviation of all NN intervals (SDNN), the standard deviation of the averages of the N N intervals in all 5 rain segments of the recording (SDANN), the mean of the standard deviations of all NN intervals for all 5 rain segments of the recording (SDNN index), the square root of the mean of the sum of the squares of differences between adjacent NN intervals (rms SD) and the number of pairs of adjacent NN counts differing by more than 50ms divided by the total number of all NN intervals (pNNs0). These measures have been summarized [10]; SDNN reflects all cyclic components responsible for variability in the recording, SDANN and SDNN index represent variability over cycles longer and shorter than 5rain, respectively, while rmsSD and pNNs0, derived from interval differences, are short-term HRV measures estimating high-frequency variations in heart rate. Scatterplot methods Scatterplots were constructed by plotting each RR interval against the preceding RR interval, as previously described [15]. Unlike previous descriptions of the method, where dedicated commercial scanner software produced hard copy of the scatterplots requiring manual measurements, we developed an automated computer method. Scatterplots were initially produced using the charting feature of SPSS (Release 6.1; SPSS Inc, Chicago, IL, USA) [23], with its ability to handle large data-sets, and then stored in bitmap format (Figure 1 ). A digitizing programme (TechDig V2.0a; Ron Jones, Mundelein, IL, USA), was customized, to permit automated technician analysis of the Poincar~ plot.
Non-linear analysis of heart rate variability during beta-adrenoceptor modulation
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Initially the bounds of the x- and y-axes were defined (reference points and the numeric values for the start and end of each axis entered), using a mouse and fine crosshairs. The limits of the scatterplot length were defined by clicking on the extremes of the scatterplot diagonal. The computer calculated the scatterplot length (between the two calibration points), width (at 10ms intervals) and area; these results were available through the WindowsT M clipboard to be pasted into other spreadsheet or data management programs for statistical processing. The key to the width measurements was a test to determine if a given pixel fell inside or outside the boundaries of the scatterplot. The test counted the coloured pixels in the plot in a 9 • 21 pixel window centred at the pixel of interest. If more than 20 pixels in this window were coloured, the pixel was considered to be within the scatterplot. The width measurement was made at a given RR interval by performing this test at each pixel along the line perpendicular to the RR axis at the interval of interest. The width was defined by the difference between the first pixel in the scatterplot and the next pixel not in the scatterplot. The area was calculated by performing width measurements at 10 ms intervals and subsequent rectangular integration. Width measurements were also automatically performed at 10%, 25%, 50%, 75% and 90% of the scatterplot length as previously described [24]; the average width of the scatterplot was the measure of variance [15 ] rather than calculating the variance around the perpendicular to the line of identity (i.e. scatterplot length) [16]. In the 12 volunteers of this study, each of the placebo scatterplots was analysed on five consecutive occasions and the reproducibility for the length, area and width calculated. The average coefficient of variation (range) was for
length 1.0% (0.3-1.8), area 1.3% (0.4-3.1), plO% 3.6% (0-8.9), p25% 3.3% (0-9.0), p50% 1.4% (03.3), p75% 1.3% (0.2-3.8) and p90% 2.0% (0.5-4.9).
Cardiac sequence (quadrant) analysis The non-linear cardiac sequencing or quadrant method is as previously described [11]. Consecutive A R R and ARRn+I differences are compared [i.e. three consecutive RR values; two differences RRI-RR2 (ARR) and RR2RR3: (ARRn+I)]. This method removes the dominant characteristic apparent in comparing each beat with the next - namely the high correlation between one interval and the next. Four patterns can be identified; +/+ (a lengthening sequence - cardiac deceleration), + / - or - / + (balanced sequences), and finally - / - (a shortening sequence - cardiac acceleration). Events of each type were counted within each quadrant; in addition the average duration (i.e. of the second difference ARR,+I) of the difference within each quadrant was calculated. When the ANS is balanced, one would expect the quadrant b/c patterns to predominate (+/- or -/+) in contrast to parasympathetic (quadrant a; +/+) or sympathetic dominance (quadrant d; - / - ) .
Statistical methods Statistical analysis was undertaken using repeated measures analysis of variance (ANOVA with repeat measures: SPSS-PC) partitioning the variance between treatments, time and subjects. Where significant differences were indicated, a one-way ANOVA with post-hoc Duncan's range test for multiple means comparison was performed [25]. Clinical Autonomic Research 1998,Vol 8 No 3
147
Silke and Riddell Table 1. Effects of the drugs on time-domain HRV parameters SDNN Placebo Propranolo1160 Atenolo150 Celiprolo1200 Celiprolo1800 C200/P160 C800/P160 C200/A50 C800/A50
161 (30) a 164 (44) a'c 180 (51)b 134 (30) 126 (45) 162 (41)a 136 (40) 153 (33) 119 (38)
SDANN
SDNN index
128 (27) 124 (51) 150 (52) b 106 (33) 102 (75) 132 (47) 98 (30) 115 (28) 94 (42)
89 (18) 99 (22) 96 (26) 81 (22) 80 (19) 91 (20) 88 (25) 95 (24) 80 (22)
rmsSD 67 (20) b 74 (21)b 77 (23) b 50 (18) 45 (17) 62 (17) 55 (23) 69 (22) b
44 (18)
Data are mean (standard deviation). Groups are placebo,
propranolol 160 mg (P160), atenolol 50 mg (A50), celiprolol 200 mg (C200) and 800 mg (C800) and combinations. Statistics related to comparison with parallel placebo (one-way ANOVAwith post-hoc comparison - Duncan's test). ap < 0.05 from celiprolo1200, 800 and celiprolol 800/atenolol 50. bp < 0.05 from celiprolo1800/atenolo150. ~ < 0.05 from celiprolo1800.
Results
Time-domain methods Differences between the drugs were evident for the long (SDNN, SDANN) and short-term (rmsSD) HRV summary statistics. The SDNN was reduced by celiprolol 200, 800 mg and celiprolol 800 in combination with atenolol 50 rag; the effects of these treatments were different from those of atenolol and propranolol alone. The SDANN was significantly reduced by celiprolol 200, 800 mg and celiprolol 800 in combination with atenolol 50 mg and different from the effects of atenolol alone. There were no consistent effects observed for SDNN index (see Table 1). The short-term HRV parameter rmsSD was reduced following celiprolol 200, 800 mg and celiprolol 800 in
combination with atenolol 50 mg; these treatments were different from the effects of placebo, atenolol and propranolol alone and the celiprolol 200 mg/atenolol 50 mg combination.
Effects on scatterplot parameters There were significant differences between celiprolol and atenolol or propranolol on scatterplot length and area. A reduction in scatterplot length (Figure 2) followed celiprolol 200mg, 800mg, and both combinations of celiprolol 800 mg with propranolol and atenolol; these were significantly different from the effects of placebo, propranolol 160mg, atenolol 50rag, and celiprolol 200 mg/atenolol 50 rag. There were similar effects on scatterplot area; this was reduced after celiprolol 200 mg, 800 rag, and celiprolol 800 mg with atenoloI 50 mg and different from the effects of placebo, propranolol 160 rag, atenolol 50 mg, and celiprolol 200 mg/atenolol 50rag. It is worth noting that the between group differences were more due to the actions of the partial agonist celiprolol reducing scatterplot width and length rather than propranolol 160mg and atenolol 50mg increasing these parameters. The geometric analysis of the scatterplots allowed assessment of HRV effects at fixed RR intervals. Differences between the drugs (Figure 3) were confined to the higher percentiles (i.e. 75% and 90% of scatterplot length: low HR). At the 90% of scatterplot length (Figure 4), the width was reduced following celiprolol 200 mg, 800 mg, and celiprolol 800 mg with atenolol 50rag in comparison to the effects of propranolol 160mg, atenolol 50rag, placebo and both celiprolol 200 mg combinations.
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Clinical Autonomic Research 1998,Vol 8 No 3
Non-linear analysis of heart rate variability during beta-adrenoceptor modulation beats/7 h, respectively: P < 0.05), but not between the two doses of celiprolol when co-administered with propranolol 160 mg.
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Quadrant analysis: effect of treatment on total counts Analysis of each quadrant for total counts (3-8 h postdose), considered in turn intervals of type +/+ (a), +/(b), - / + (c), or - / (d); celiprolol shifted the autonomic balance towards sympathetic dominance contrasting with the parasympathetic predominance following propranolol and atenolol. Consecutive episodes of cardiac acceleration, as reflected for example in quadrant d (Figure 5) counts (i.e. ARR and /tkRRn+l both shortened) were increased after both doses of celiprolol alone and after the celiprolol 800 mg/atenolol 50mg combination; these contrasted with decreased episodes following propranolol 160mg and atenolol 50 mg alone. A clear difference in episodes of acceleration occurred between celiprolol 200 and 800 mg when co-administered with atenolol 50mg (5135 vs 6810
Quadrant analysis: effect of treatment on average difference The previous analysis described the qualitative nature of the changes as episodes of acceleration or deceleration by quadrant; the absolute magnitude of the shortening or lengthening was also determined. The effects were consistent but clearer in some quadrants than in others; the order of effect by quadrant in descending order was b (+/-; F=3.97 (P < 0.0004), c (-/+; F=2.37 (P < 0.02), d ( - / - F=2.05 (P < 0.05) and a (+/+; F= 1.98 (P < 0.06). For quadrant b for example, the bias towards cardiac acceleration (Figure 6) was reflected in the shortened beat-to-beat difference (ARRn+I) on celiprolol 200mg, celiprolol 800mg and celiprolol 800mg/atenolol 50mg (40.3, 40.2 and 37.1ms, respectively) different from the lengthened intervals on propranolol 160mg, atenolol 50mg and celiprolol 200mg with atenolol 50mg (60.1, 58.2 and 54.3ms, respectively: P < 0.05). There were dose-response effects between celiprolol 200 and 800mg when coadministered with concurrent atenolol (C200 vs C800 rag: 50.9 vs 35.4 ms: P < 0.05) but not between these doses when co-administered with propranolol. Correlation between the methods The standard time-domain variables SDNN, SDANN and SDNN index were all strongly correlated with the scatterplot indices. The SDNN correlated particularly strongly with scatterplot length (r=0.90) and area
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(r= 0.91). Although the short (rmsSD, pNNs0) statistics correlated best with scatterplot width, most time-domain statistics were strongly correlated, generally at levels between r = 0.74 and r = 0.86, with the scatterplot indices (see Table 2).
Discussion This study investigated the actions on HRV ofagonism or antagonism at the 3-adrenoceptor in normal volunteers, using standard time-domain summary statistics and two non-linear methods the Poincar~ plot and qua&ant
(sequence) analysis. HRV in healthy individuals has characteristics suggestive of low-dimensional chaos-like determinism, including sensitive dependence on the initial conditions [13]. Techniques derived from non-linear dynamics and chaos theory may contribute to identifying patterns and mechanisms in the data that are not detectable with traditional statistics, with greater predictive accuracy [14]. In this study, both methods suggested that HRV was reduced by the partial agonist celiprolol in contrast to the full antagonists propranolol and atenolol, where HRV parameters were unaltered or even enhanced. Thus HRV was related to the presence of agonist or antagonist activity in the 3-a&enoceptor drug [17].
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Non-linear analysis of heart rate variabil#y during beta-adrenoceptor modulation Table 2. Scatterplot and time-domain summary statistics correlations Variable SDNN SDANN SDNN index rmsSD pNN5o Deceleration counts Acceleration counts
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0.91 0.82 0.86 0.87 0.80 0.75 0.75
0.76 0.63 0.76 0.87 0.86 0.72 0.71
These observations may in turn be related to modulation of the underlying balance of the autonomic nervous system and sympathetic or vagal predominance. Scatterplot analysis is a geometric method for the visualization of beat-to-beat variations in heart rate and investigating the patterns that result from non-linear processes and non-periodic fluctuations in heart rate. Scatterplots have been used to assess HRV in obstructive sleep apnoea and in congestive heart failure. In children with obstructive sleep apnoea, beat-to-beat variability was impaired particularly at low heart rates [26]; in patients with heart failure, the Poincar~ plot had independent prognostic value for all-cause and sudden death [27]. When considering the Poincar~ plot as a tool for assessing the dynamics of heart rate several aspects need to be considered. Firstly, the dispersion of points on the x-axis represents the range of interval values over the epoch (overall variability), while the extent of dispersion along the y-axis, at a given x value, represents the instantaneous beat-to-beat variation. Second, the positive diagonal scatter of points in the Poincar~ plot arises because the heart rate changes only slowly, resulting in the high correlation between one interval and that following. The normal pattern of the plot in the 'awake' state is a large overall range (i.e. increased scatterplot length) and a decreased beat-to-beat variation (i.e. reduced width), contrasting with 'quiet' sleep where there is higher beat-to-beat variability and lower overall variation [11 ]. The ARR vs ARRn+I analysis evaluates the nature of the interval sequencing, the dominant characteristic of the strong correlation between consecutive intervals is reduced allowing the time-dependent dynamics of HRV to be assessed. Perturbations of autonomic balance, would be expected to alter the likelihood of the occurrence of particular sequences of acceleration ( - / - ) or deceleration (+/+), reflecting the shift in balance towards sympathetic or parasympathetic predominance. The normal pattern of the ARR vs ARRn+I analysis in the 'awake' state is alternation of increases and decreases in interval length, contrasting with 'quiet' sleep where sequences of progressively increasing and decreasing intervals occur [11 ].
These theoretical consideration have been confirmed in research investigations; scatterplot length was correlated with long-term variability indices [15] whereas scatterplot width was correlated with short-term HRV and parasympathetic nervous activity [15,16,28]. The impact of fl-adrenoceptor antagonism is not established; in patients with chronic heart failure bisoprolol did not alter scatterplot length but increased width at the highest percentiles (lowest heart rates) [24]. However metoprolol, in survivors of myocardial infarction, increased timedomain HRV statistics (mean RR interval, rMSSD, and proportion of adjacent RR intervals differing by >50 ms [pNNs0 (%)]) at unaltered scatterplot indices. Our data extends these earlier observations. The HRV time-domain summary statistics were within the normal range for healthy individuals [10]. The long-term timedomain variable SDNN (representing total power in frequency domain) correlated best with scatterplot length and area (overall variation), while the short-term variables (rmsSD, pNNs0) strongly correlated with the scatterplot width (p90%) suggesting that this measure of variance should prove useful in assessing parasympathetic nervous activity [16]. These studies were undertaken during sleep; due to the low level of prevailing sympathetic drive at night, the agonist or antagonist activity of agents acting at the /31- or 32-adrenoceptor can be assessed from the sleeping heart rate [21,22]. Our study demonstrated that atenolol and propranolol did not increase scatterplot length or width, although this may have been due to the minimal sympathetic drive present during the night. However, the partial agonist celiproloI significantly reduced scatterplot length and width and indeed, the data dispersion appeared largely confined to high percentages (low HR) supporting previous observations with bisoprolol [24]. It is worth noting the magnitude of the difference between the average scatter plot width reported for heart failure patients (p50% 133; range 115-151) and the healthy controls (p50% 364; range 287-465); in health even following treatment with the 800 mg dose of the partial agonist of the 13-adrenoceptor celiprolol, the scatterplot width (p90% 356; range 268-499) remained well above the width reported for heart failure patients after the/3-adrenoceptor antagonist bisoprolol (p90% 139; range 121-157). The precise influence of agents acting at the 3adrenoceptor on HRV has been debated. Short-term time-domain statistics such as rMSSD and pNNs0 increased following bisoprolol [24] and metoprolol [28,29] whereas longer-term variables such as global SD were unaltered [24] or increased [30]. Few studies have considered the implications of agonism or antagonism at the t%adrenoceptor in terms of HRV; recently fl2-agonism with inhaled salbutamol shifted cardiovascular autonomic balance towards sympathetic dominance and decreased cardiovagal nervous responsiveness [31]. Our study demonstrated consistent effects on HRV followed the partial agonist celiprolol; shortand long-term time-domain statistics were reduced as Clinical Autonomic Research 1998,Vol 8 No 3
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Silke and Riddell
were scatterplot length, area and width (at low heart rates) and sequence analysis, with the increased frequency of acceleration counts, suggested a shift in autonomic control to sympathetic dominance. In terms of the pharmacology, it is of interest to consider the mechanism of the HRV regulation by celiprolol. Previous investigations of celiprolol (200800 mg) have assessed its partial agonist activity using the sleeping HR [32], finger tremor [33], or serum potassium (/32-mediated responses [19,34]; these studies concluded that the selectivity of the partial agonist activity at the/3-adrenoceptor was dose dependent (/31specific lower doses, /31//32 higher doses). Our study demonstrated that, irrespective of the method of variability assessment, both doses of celiprolol (200 and 800 mg) decreased HRV. The prevention of a fall in HRV after celiprolol in the presence of propranolol but not in the presence of atenolol, suggested that, at the 800 mg dose, some mediation of HRV through the/32adrenoceptor. In conclusion, the non-linear methods of scatterplot and quadrant analysis permitted autonomic balance to be assessed following therapeutic intervention with agents that modulated the/3-adrenoceptor in humans. Partial agonism with celiprolol altered the balance towards sympathetic dominance. /3-adrenoceptor antagonists have improved survival following myocardial infarction [6,7]; whether the observed shift in ANS balance, with a partial agonist such as celiprolol, would offset the cardioprotective benefits of /3-adrenoceptor blockade in secondary prevention is unknown. These non-linear methods appear to be valuable tools to investigate HRV in health and in cardiovascular disease and to study the implications of alterations in autonomic control during therapeutic intervention.
Acknowledgements The authors are grateful for the 'C' programming expertise of Ms Ther~se Rafferty and Ron Jones, in developing the programmes to permit these analyses
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