Decreased chaos and increased nonlinearity of heart rate time series in patients with panic disorder

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Abstract

In this study, we investigated measures of nonlinear dynamics and chaos of heart rate time series in 30 normal control subjects and 36 age-matched patients with panic disorder in supine and standing postures. We obtained minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies system's complexity, LLE predictability and NL, deviation from linear processes. There was a significant increase in complexity (p<0.00001), an increase in predictability (decreased chaos) (p<0.00001) and an increase in nonlinearity (Snet GS) (p=0.00001), especially in supine posture in patients with panic disorder. Increased NL score in supine posture may be due to a relative increase in cardiac sympathetic activity and an overall decrease in LLE may indicate an impaired cardiac autonomic flexibility in these patients due possibly to a decrease in cardiac vagal activity. These findings may further explain the reported higher incidence of cardiovascular mortality in patients with anxiety disorders.

Introduction

Panic disorder is an anxiety disorder characterized by autonomic symptoms such as palpitations, shortness of breath, chest pain, choking sensation, dizziness, tremulousness, in addition to a feeling of intense anxiety, fear of losing control and sometimes a fear of a heart attack. Several studies suggest that patients with panic disorder and other patients with anxiety disorders are at a higher risk for significant cardiovascular mortality and sudden death Coryell et al., 1986, Weissmann et al., 1990, Kawachi et al., 1994. Recent literature has shown the utility of HR variability as a noninvasive tool to study cardiac autonomic function Malik and Camm, 1990, Malliani et al., 1991, Yeragani, 1995. Spectral power in the high-frequency (HF: 0.15–0.5 Hz) band reflects respiratory sinus arrhythmia (RSA) and thus, cardiac vagal activity. Low-frequency (LF: 0.04–0.15 Hz) power is related to baroreceptor control and is dually mediated by vagal and sympathetic systems. Very low-frequency (VLF: 0.0033–0.04 Hz) power appears to be related to thermoregulatory and vascular mechanisms and renin–angiotensin systems Akselrod et al., 1981, Pomeranz et al., 1985, Lindqvist et al., 1990. Decreased HRV is an important predictor of sudden cardiac death in patients with cardiac disease as well as normal subjects Kleiger et al., 1987, Bigger et al., 1992, Molgaard et al., 1991.

Recent reports have repeatedly stressed on the importance of nonlinear techniques to study HRV in health as well as disease Goldberger and West, 1987, West and Goldberger, 1987, Kobayashi and Musha, 1982, Katz, 1988, Glenny et al., 1991, Pincus et al., 1991, Guzzetti et al., 1996, Lombardi et al., 1996, Voss et al., 1996, Ho et al., 1997, Braun et al., 1998, Storella et al., 1998, Kagiyama et al., 1999, Silipo et al., 1999. Some of these techniques may be valuable additions to the linear measures of HR variability Pincus et al., 1991, Yeragani et al., 1993b, Yeragani et al., 1997, Yeragani et al., 1998b, Yeragani et al., 2000a, Yeragani et al., 2000d, Guzzetti et al., 1996, Lombardi et al., 1996, Voss et al., 1996, Ho et al., 1997, Braun et al., 1998, Kagiyama et al., 1999, Makikallio et al., 1999.

Analysis of time series using methods of nonlinear dynamics also includes estimation of Lyapunov exponents (LE) and degree of nonlinearity (NL). The predictability is quantified by LE. Interaction of the dynamical parameters is quantified by the degree of nonlinearity. Kanters et al. (1997) suggest that though the correlation dimension of R–R intervals is due to linear correlations in the R–R intervals, a small but significant part is due to nonlinear correlations between R–R intervals and thus, these various measures are not redundant. Thus, heart rate variability cannot be a single chaotic system and consists of intertwined periods with different nonlinear dynamics. Guzzetti et al. (1996) also suggest that nonlinear dynamics are present in HR variability and that system complexity decreases in transplant patients. Casaleggio et al. (1997) also report similar nonlinear chaotic characteristics with cardiovascular signals.

Several reports have suggested that patients with multiple sclerosis have decreased HR variability and also a significant decrease in the values of LLE (Ganz et al., 1993). A decrease in HR variability is also seen in brain stem lesions and other neurological conditions suggesting an impaired cardiac autonomic function reflecting decreased vagal activity (Ganz and Faustmann, 1994, Faustmann and Ganz, 1994, Yotsukura et al., 1998, Nordenbo et al., 1989, Monge-Argiles et al., 1998, Monge-Argiles et al., 2000). In our previous study, we hypothesized that NL scores may be related to cardiac sympathetic activity as these scores increased significantly in standing posture in normal controls (Radhakrishna et al., 2000). In our ongoing studies on the pathophysiology of panic attacks, we have found that these patients show a decrease in cardiac vagal function and a relative increase in sympathetic activity Yeragani et al., 1990, Yeragani et al., 1992, Yeragani et al., 1993a, Yeragani et al., 1994, Yeragani et al., 1995, Yeragani et al., 1998a, Yeragani et al., 2000a. We have shown this using both linear as well as nonlinear techniques such as symbolic dynamics in regards to HR variability (Yeragani et al., 2000a). We are in the pursuit of new nonlinear techniques that might better discriminate between normal controls and patients with even subtle cardiovascular abnormalities.

The aim of the present study was to evaluate the utility of MED, LLE and NL scores in patients with panic disorder and normal controls. We specifically hypothesized that patients with panic disorder will have significantly lower values of LLE and higher NL scores compared to controls.

Section snippets

Subjects

Thirty normal controls (19 males, 11 females; 29.8±7.1 years (mean±S.D.)) and 36 patients with panic (16 males and 20 females; 29.9±5.3 years) disorder participated in this study. We have used means and standard deviations through out the text and tables of this paper. These studies were approved by the Institutional Review Boards at the Wayne State University School of Medicine, Detroit, MI and the Wright State University School of Medicine, Dayton, OH, USA. All subjects were healthy and

Statistical analysis

We used BMDP statistical package (Berkley, CA, USA) for all the analyses. We used two-way ANOVA for repeated measures with patients vs. controls as the grouping factor and supine vs. standing posture as the repeated measure. Significant effects were followed up by paired t-tests to compare patients and controls for supine and standing postures separately. All tests were two-tailed and a probability value of 0.05 was accepted as significant. As we have done two post-hoc t-tests after each ANOVA,

Results

Table 1 shows the results of anxiety ratings, supine and standing HR, and nonlinear measures of HR. Patients were significantly more anxious than controls. Table 2 shows the results of ANOVA for supine and standing measures between patients and controls. Patients had significantly higher HR. MED and Snet GS were also significantly higher in patients Fig. 1, Fig. 2. LLE was highly significantly lower in the patient group (Fig. 2). There was a significant decrease in MED while there were

Discussion

The main findings of this study are that patients with panic disorder have a lower degree of chaos and an increased nonlinearity of their heart rate time series, especially in supine posture. In our previous study on normal controls, we suggested that the NL scores probably reflect sympathetic function (Radhakrishna et al., 2000). These findings suggest a possible increase in relative sympathetic function in the patient group. These differences were also highly significant (p=0.00001) compared

Conclusions

The present study of HRV time series using nonlinear techniques has shown highly significant differences between normal controls and patients with panic disorder. Decreased LLE and increased NL scores should be investigated further in future studies of cardiac autonomic function in different illnesses and the effect of successful treatment on these measures. These techniques may be applicable to the study of other nonlinear time series as well.

References (82)

  • J Theiler et al.

    Testing for nonlinearity in time series: the method of surrogate data

    Physica D

    (1992)
  • A Wolf et al.

    Determining Lyapunov exponents from a time series

    Physica D

    (1985)
  • V.K Yeragani et al.

    Decreased heart rate variability in panic disorder patients: a study of power spectral analysis of heart rate

    Psychiatry Res.

    (1993)
  • V.K Yeragani et al.

    Effects of isoproterenol on heart rate variability in patients with panic disorder

    Psychiatry Res.

    (1995)
  • V.K Yeragani et al.

    Decreased heart period variability in patients with panic disorder: a study of Holter ECG records

    Psychiatry Res.

    (1998)
  • V.K Yeragani et al.

    Increased QT variability in patients with panic disorder and depression

    Psychiatry Res.

    (2000)
  • M Yotsukura et al.

    Nine-year follow-up study of heart rate variability in patients with Duchenne-type progressive muscular dystrophy

    Am. Heart J.

    (1998)
  • S Akselrod et al.

    Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control

    Science

    (1981)
  • W.L Atiga et al.

    Beat-to-beat repolarization lability identifies patients at risk for sudden cardiac death

    J. Cardiovasc. Electrophysiol.

    (1998)
  • W.L Atiga et al.

    Temporal repolarization lability in hypertensive cardiomyopathy caused by beta-chain heavy gene mutations

    Circulation

    (2000)
  • R.D Berger et al.

    An efficient algorithm for spectral analysis of heart rate variability

    IEEE. Trans. Biomed. Engg.

    (1986)
  • R.D Berger et al.

    Beat-to-beat QT interval variability. Novel evidence for repolarization lability in ischemic and nonischemic dilated cardiomyopathy

    Circulation

    (1997)
  • J.T Bigger et al.

    Frequency domain measures of heart period variability and mortality after myocardial infarction

    Circulation

    (1992)
  • C Braun et al.

    Demonstration of nonlinear components in heart rate variability of healthy persons

    Am. J. Physiol.

    (1998)
  • A Casaleggio et al.

    Study of the Lyapunov exponents in heart rate variability signals

    Methods Inf. Med.

    (1997)
  • S.S Chugh et al.

    Sudden cardiac death with apparently normal heart

    Circulation

    (2000)
  • W Coryell et al.

    Mortality among outpatients with anxiety disorders

    Am. J. Psychiatry

    (1986)
  • A Di Garbo et al.

    Nonlinearity tests using the extrema of a time series

    Int. J. Bifurcation Chaos

    (1998)
  • P.M Faustmann et al.

    Central cardioautonomic disorganization in interictal states of epilepsy detected by phase space analysis

    Int. J. Neurosci.

    (1994)
  • D.M Ficker

    Sudden unexplained death and injury in epilepsy

    Epilepsia

    (2000)
  • R.E Ganz et al.

    Central Autonomic Disorganization in the Early Stages of Experimental Meningitis in Rabbits Induced by Complement C5A-fragment: A Pathophysiological Validation of the Largest Lyapunov Exponent of Heart Rate Dynamics.

    (1994)
  • R.E Ganz et al.

    The Lyapunov exponents of heart rate dynamics as a sensitive marker of central autonomic organization: an exemplary study of early multiple sclerosis

    Int. J. Neurosci.

    (1993)
  • R.W Glenny et al.

    Application of fractal analysis to physiology

    J. Appl. Physiol.

    (1991)
  • A.L Goldberger et al.

    Fractals in physiology and medicine

    Yale J. Biol. Med.

    (1987)
  • P Grassberger et al.

    Characterization of strange attractors

    Phys. Rev. Lett.

    (1983)
  • S Guzzetti et al.

    Non-linear dynamics and chaotic indices in heart rate variability of normal subjects and heart-transplanted patients

    Cardiovasc. Res.

    (1996)
  • I Hagerman et al.

    Chaos deterministic regulation of heart rate variability in time and frequency domains: effects of autonomic blockade and exercise

    Cardiovasc. Res.

    (1996)
  • K.K Ho et al.

    Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics

    Circulation

    (1997)
  • J.K Kanters et al.

    Influence of forced respiration on nonlinear dynamics in heart rate variability

    Am. J. Physiol.

    (1997)
  • D.T Kaplan et al.

    Aging and the complexity of cardiovascular dynamics

    Biophys. J.

    (1991)
  • I Kawachi et al.

    Symptoms of anxiety and risk of coronary heart disease: the normative aging study

    Circulation

    (1994)
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