Applications of nonlinear dynamics to clinical cardiology

Clinical applications of heart rate variability in the triage and assessment of traumatically injured patients

Heart rate variability (HRV) is a method of physiologic assessment which uses fluctuations in the RR intervals to evaluate modulation of the heart rate by the autonomic nervous system (ANS). Decreased variability has been studied as a marker of increased pathology and a predictor of morbidity and mortality in multiple medical disciplines. HRV is potentially useful in trauma as a tool for prehospital triage, initial patient assessment, and continuous monitoring of critically injured patients. However, several technical limitations and a lack of standardized values have inhibited its clinical implementation in trauma. The purpose of this paper is to describe the three analytical methods (time domain, frequency domain, and entropy) and specific clinical populations that have been evaluated in trauma patients and to identify key issues regarding HRV that must be explored if it is to be widely adopted for the assessment of trauma patients.

Heart rate variability - a historical perspective

Heart rate variability (HRV), the beat-to-beat variation in either heart rate or the duration of the R-R interval - the heart period, has become a popular clinical and investigational tool. The temporal fluctuations in heart rate exhibit a marked synchrony with respiration (increasing during inspiration and decreasing during expiration - the so called respiratory sinus arrhythmia, RSA) and are widely believed to reflect changes in cardiac autonomic regulation. Although the exact contributions of the parasympathetic and the sympathetic divisions of the autonomic nervous system to this variability are controversial and remain the subject of active investigation and debate, a number of time and frequency domain techniques have been developed to provide insight into cardiac autonomic regulation in both health and disease. It is the purpose of this essay to provide an historical overview of the evolution in the concept of HRV. Briefly, pulse rate was first measured by ancient Greek physicians and scientists. However, it was not until the invention of the "Physician's Pulse Watch" (a watch with a second hand that could be stopped) in 1707 that changes in pulse rate could be accurately assessed. The Rev. Stephen Hales (1733) was the first to note that pulse varied with respiration and in 1847 Carl Ludwig was the first to record RSA. With the measurement of the ECG (1895) and advent of digital signal processing techniques in the 1960s, investigation of HRV and its relationship to health and disease has exploded. This essay will conclude with a brief description of time domain, frequency domain, and non-linear dynamic analysis techniques (and their limitations) that are commonly used to measure HRV.

New measures of heart-rate complexity: effect of chest trauma and hemorrhage

BACKGROUND

Traditional vital signs such as heart rate, blood pressure, and oxygen saturation are not ideal for timely and accurate assessment of physiologic status after trauma (TR) and hemorrhagic shock (HS). Analysis of the complex beat-to-beat variability present in the heart-rate time series has been proposed as a "new vital sign" in this setting. We determined the effect of chest TR and HS on heart-rate complexity (HRC) in a porcine model.

METHODS

Anesthetized swine in group II (n = 20) underwent blunt right chest TR with a modified captive-bolt stunner; then, 10 minutes later, hemorrhage of 12 mL/kg over 10 minutes, followed by resuscitation with lactated Ringer's solution, and reinfusion of blood. Group I (n = 15) served as time controls. Two hundred beat sections of EKG waveforms were analyzed at 7 time points: at baseline, after TR, immediately after hemorrhage (HS), and 1 hour, 2 hours, 4 hours, and 5 hours after HS. Several computationally different measures of HRC were calculated, including sample entropy, similarity of distribution, and point correlation dimension.

RESULTS

HRC was decreased after TR, HS, and at 1 hour, manifested by decreased sample entropy and point correlation dimension and increased similarity of distribution. These HRC measures were all restored by resuscitation.

CONCLUSIONS

Several independent measures demonstrated decreased HRC after combined TR/HS and restored HRC with resuscitation. Complexity analysis may be useful for diagnosis of TR/HS and for monitoring resuscitation.

Lessons from Jurassic Park: patients as complex adaptive systems

RATIONALE

With realization that non-linearity is generally the rule rather than the exception in nature, viewing patients and families as complex adaptive systems may lead to a better understanding of health and illness. Doctors who successfully practise the 'art' of medicine may recognize non-linear principles at work without having the jargon needed to label them.

METHODS

Complex adaptive systems are systems composed of multiple components that display complexity and adaptation to input. These systems consist of self-organized components, which display complex dynamics, ranging from simple periodicity to chaotic and random patterns showing trends over time.

RESULTS

Understanding the non-linear dynamics of phenomena both internal and external to our patients can (1) improve our definition of 'health'; (2) improve our understanding of patients, disease and the systems in which they converge; (3) be applied to future monitoring systems; and (4) be used to possibly engineer change.

CONCLUSION

Such a non-linear view of the world is quite congruent with the generalist perspective.

Characterizing heart rate variability by scale-dependent Lyapunov exponent

Previous studies on heart rate variability (HRV) using chaos theory, fractal scaling analysis, and many other methods, while fruitful in many aspects, have produced much confusion in the literature. Especially the issue of whether normal HRV is chaotic or stochastic remains highly controversial. Here, we employ a new multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), to characterize HRV. SDLE has been shown to readily characterize major models of complex time series including deterministic chaos, noisy chaos, stochastic oscillations, random 1/f processes, random Levy processes, and complex time series with multiple scaling behaviors. Here we use SDLE to characterize the relative importance of nonlinear, chaotic, and stochastic dynamics in HRV of healthy, congestive heart failure, and atrial fibrillation subjects. We show that while HRV data of all these three types are mostly stochastic, the stochasticity is different among the three groups.

Gait variability is altered in patients with peripheral arterial disease

OBJECTIVE

Claudication is the most common presentation of peripheral arterial disease (PAD), producing significant ambulatory compromise. Claudicating patients, most of whom are elderly, have reduced mobility and poor health outcomes, including an increased risk of falls. The gait of elderly fallers is characterized by increased variability. Increase in the variability of the locomotor system makes the gait more noisy and unstable. The purpose of this study is to investigate gait variability in patients with PAD.

METHODS

Nineteen symptomatic PAD patients (age, 63.6 +/- 9.8 years; body mass, 82.1 +/- 18.5 kg; height, 1.71 +/- 0.06 m) walked on a treadmill in the absence of pain or claudication symptoms while joint flexion and extension kinematics were captured. Results were compared with results obtained from 17 matched healthy controls (age, 65.2 +/- 12.5 years; body mass, 82.0 +/- 25.9.5 kg; height, 1.73 +/- 0.08 m). Relative joint angles were calculated for the ankle, knee, and hip flexion/extension, and the stride-to-stride variability of joint flexion and extension was calculated from at least 30 consecutive footfalls. Variability was expressed using the largest Lyapunov exponent, standard deviation, and coefficient of variation. Independent t tests were used to compare gait variability between groups.

RESULTS

Symptomatic PAD patients had significantly higher largest Lyapunov exponent values and coefficient of variation values for all joints, and higher standard deviation values at the ankle and the hip (P < .05).

CONCLUSION

Symptomatic PAD patients have increased gait variability at the ankle, knee, and hip joints at baseline ambulation in the absence of claudication pain. Our findings indicate significant baseline deterioration in the locomotor system of symptomatic PAD patients. This deterioration results in increased noise and instability of gait and is a potential contributing factor to the falls and mobility problems experienced by symptomatic PAD patients.

Circadian rhythmic fractal scaling of heart rate variability in health and coronary artery disease

BACKGROUND

In clinical cardiology, heart rate variability is a putative index of autonomic cardiovascular function. Signs of reduced vagal activity are not only associated with an enhanced risk of sudden cardiac death, but such impaired heart rate variability became a new predictor of sudden cardiac death and other mortality in patients with a variety of diseased states.

HYPOTHESIS

It is postulated (1) that the time structure (chronome) of heart rate variability in clinical health includes a circadian rhythm and deterministic chaos, the latter gauged by the correlation dimensions of RR intervals; and (2) that this chronome is altered in patients with coronary artery disease (CAD).

METHODS

From 24-h Holter records of 11 healthy controls and 10 patients with CAD, 500-s sections around 02:00, 06:00, 10:00, 14:00, 18:00 and 22:00 hours were analyzed for smoothed RR intervals sampled at 4 Hz. Correlation integrals were estimated for embedding dimensions from 1 to 20 with a 1.0-s time lag, using an algorithm modified from Grassberger and Procaccia. The Wilcoxon signed-rank test compares circadian end points assessed by cosinor between the CAD patients and age-matched controls.

RESULTS

A circadian rhythm characterizes the correlation dimension of healthy subjects peaking during the night (p < 0.005). Patients with CAD have a lowered correlation dimension (p < 0.05) and an altered circadian variation which requires the consideration of an approximately 12-h (circasemidian) component.

CONCLUSION

The results demonstrate the sensitivity of circadian rhythms for the detection of disease. A partial 24- to 12-h (circadian-to-circasemidian) frequency multiplication (or partial variance transposition) in CAD of the correlation dimension, apart from being a potential clue to the etiology of the disease, adds a new feature to a chronocardiology combining, with the fractal scaling, an assessment of circadian and circasemidian components as measures of predictable variability to be tested for use in diagnosis, prognosis, and as putative guides to treatment timing.

Multimodal signal processing for the analysis of cardiovascular variability

Cardiovascular (CV) variability as a primary vital sign carrying information about CV regulation systems is reviewed by pointing out the role of the main rhythms and the various control and functional systems involved. The high complexity of the addressed phenomena fosters a multimodal approach that relies on data analysis models and deals with the ongoing interactions of many signals at a time. The importance of closed-loop identification and causal analysis is remarked upon and basic properties, application conditions and methods are recalled. The need of further integration of CV signals relevant to peripheral and systemic haemodynamics, respiratory mechanics, neural afferent and efferent pathways is also stressed.

Methods derived from nonlinear dynamics for analysing heart rate variability

Methods from nonlinear dynamics (NLD) have shown new insights into heart rate (HR) variability changes under various physiological and pathological conditions, providing additional prognostic information and complementing traditional time- and frequency-domain analyses. In this review, some of the most prominent indices of nonlinear and fractal dynamics are summarized and their algorithmic implementations and applications in clinical trials are discussed. Several of those indices have been proven to be of diagnostic relevance or have contributed to risk stratification. In particular, techniques based on mono- and multifractal analyses and symbolic dynamics have been successfully applied to clinical studies. Further advances in HR variability analysis are expected through multidimensional and multivariate assessments. Today, the question is no longer about whether or not methods from NLD should be applied; however, it is relevant to ask which of the methods should be selected and under which basic and standardized conditions should they be applied.

Heart-rate complexity for prediction of prehospital lifesaving interventions in trauma patients

BACKGROUND

Traditional vital signs often fail to identify critically injured patients soon enough to permit timely intervention. To improve our ability to forecast the need for prehospital lifesaving interventions (LSIs), we applied heart-rate complexity (HRC) analysis to the electrocardiogram (ECG) of patients en route to trauma centers.

METHODS

Analysis of ECG and clinical data from 374 patients en route by helicopter to three urban Level I trauma centers was conducted. Waveforms from 182 patients were excluded (because of ectopy, noise, or inadequate length). Of the remaining 192 patients, 54 received 66 LSIs in the field (LSI group): intubation (n = 52), cardiopulmonary resuscitation (n = 5), cricothyroidotomy (n = 2), and pneumothorax decompression (n = 7); 138 patients did not (non-LSI group). In the field, heart rate, blood pressure, and the Glasgow Coma Scale score (GCS(TOTAL)) and its motor component (GCS(MOTOR)) were recorded. ECG was recorded during flight. Ectopy-free, 800-beat sections of ECG were identified off-line and analyzed by HRC methods including Sample Entropy (SampEn) and Detrended Fluctuations Analysis (DFA).

RESULTS

There was no difference between LSI and non-LSI patients in heart rate or blood pressure. SampEn was lower in LSI than in non-LSI (0.88 +/- 0.03 vs. 1.11 +/- 0.03), as was DFA (1.09 +/- 0.05 vs. 1.33 +/- 0.03) and GCS(MOTOR) (3.4 +/- 0.4 vs. 5.7 +/- 0.1) (all p < 0.0001). By logistic regression, SampEn, DFA, and GCS(MOTOR) were independently associated with LSIs (area under the receiver operating characteristic curve, 0.897).

CONCLUSIONS

Decreased HRC is associated with LSIs in prehospital trauma patients. HRC may be useful as a new vital sign for identification of the severely injured.

Complexity of chronic asthma and chronic obstructive pulmonary disease: implications for risk assessment, and disease progression and control

Although assessment of asthma control is important to guide treatment, it is difficult since the temporal pattern and risk of exacerbations are often unpredictable. In this Review, we summarise the classic methods to assess control with unidimensional and multidimensional approaches. Next, we show how ideas from the science of complexity can explain the seemingly unpredictable nature of bronchial asthma and emphysema, with implications for chronic obstructive pulmonary disease. We show that fluctuation analysis, a method used in statistical physics, can be used to gain insight into asthma as a dynamic disease of the respiratory system, viewed as a set of interacting subsystems (eg, inflammatory, immunological, and mechanical). The basis of the fluctuation analysis methods is the quantification of the long-term temporal history of lung function parameters. We summarise how this analysis can be used to assess the risk of future asthma episodes, with implications for asthma severity and control both in children and adults.

Assessment of cardiovascular regulation after burns by nonlinear analysis of the electrocardiogram

Critical illness and hypovolemia are associated with loss of complexity of the R-to-R interval (RRI) of the electrocardiogram, whereas recovery is characterized by restoration thereof. Our goal was to investigate the dynamics of RRI complexity in burn patients. We hypothesized that the postburn period is associated with a state of low RRI complexity, and that successful resuscitation restores it. Electrocardiogram was acquired from 13 patients (age 55 +/- 5 years, total body surface area burned 36 +/- 6%, 11 +/- 5% full thickness) at 8, 12, 24, and 36 hours during postburn resuscitation. RRI complexity was quantified by approximate entropy (ApEn) and sample entropy (SampEn) that measure RRI signal irregularity, as well as by symbol distribution entropy and bit-per-word entropy that assess symbol sequences within the RRI signal. Data (in arbitrary units) are means +/- SEM. All patients survived resuscitation. Changes in heart rate and blood pressure were not significant. ApEn at 8 hours was abnormally low at 0.89 +/- 0.06. ApEn progressively increased after burn to 1.22 +/- 0.04 at 36 hours. SampEn showed similar significant changes. Symbol distribution entropy and bit-per-word entropy increased with resuscitation from 3.63 +/- 0.22 and 0.61 +/- 0.04 respectively at 8 hours postburn to 4.25 +/- 0.11 and 0.71 +/- 0.02 at 24 hours postburn. RRI complexity was abnormally low during the early postburn period, possibly reflecting physiologic deterioration. Resuscitation was associated with a progressive improvement in complexity as measured by ApEn and SampEn and complementary changes in other measures. Assessment of complexity may provide new insight into the cardiovascular response to burns.

Prehospital loss of R-to-R interval complexity is associated with mortality in trauma patients

BACKGROUND

To improve our ability to identify physiologic deterioration caused by critical injury, we applied nonlinear analysis to the R-to-R interval (RRI) of the electrocardiogram of prehospital trauma patients.

METHODS

Ectopy-free, 800-beat sections of electrocardiogram from 31 patients were identified. Twenty patients survived (S) and 11 died (NonS) after hospital admission. Demographic data, heart rate, blood pressure, field Glasgow Coma Scale (GCS) score, and survival times were recorded. RRI complexity was assessed via nonlinear statistics, which quantify entropy or fractal properties.

RESULTS

Age and field heart rate and blood pressure were not different between groups. Mean survival time (NonS) was 129 hours +/- 62 hours. NonS had a lower GCS score (8.6 +/- 1.7 vs. 13.2 +/- 0.8, p < 0.05). RRI approximate entropy (ApEn; 0.87 +/- 0.06 vs. 1.09 +/- 0.07, p < 0.01), sample entropy (SampEn; 0.80 +/- 0.08 vs. 1.10 +/- 0.05, p < 0.01) and fractal dimension by dispersion analysis (1.08 +/- 0.02 vs. 1.13 +/- 0.01, p < 0.05) were lower in NonS. Distribution of symbol 2 (Dis_2), a symbol-dynamics measure of RRI distribution, was higher in NonS (292.6 +/- 34.4 vs. 222 +/- 21.3, p < 0.10). For RRI data, logistic regression analysis revealed ApEn and Dis_2 as independent predictors of mortality (area under the receiver-operating characteristic curve = 0.96). When GCSMOTOR was considered, it replaced Dis_2 whereas ApEn was retained (area under curve = 0.92). When Injury Severity Score was considered, it replaced GCSMOTOR; ApEn was retained.

CONCLUSIONS

Prehospital loss of RRI complexity, as evidenced by decreased entropy, was associated with mortality in trauma patients independent of GCS score or Injury Severity Score.

Heart rate variability as a measure of autonomic regulation of cardiac activity for assessing stress and welfare in farm animals -- a review

Measurement of heart rate variability (HRV) is a non-invasive technique that can be used to investigate the functioning of the autonomic nervous system, especially the balance between sympathetic and vagal activity. It has been proven to be very useful in humans for both research and clinical studies concerned with cardiovascular diseases, diabetic autonomic dysfunction, hypertension and psychiatric and psychological disorders. Over the past decade, HRV has been used increasingly in animal research to analyse changes in sympathovagal balance related to diseases, psychological and environmental stressors or individual characteristics such as temperament and coping strategies. This paper discusses current and past HRV research in farm animals. First, it describes how cardiac activity is regulated and the relationships between HRV, sympathovagal balance and stress and animal welfare. Then it proceeds to outline the types of equipment and methodological approaches that have been adapted and developed to measure inter-beats intervals (IBI) and estimate HRV in farm animals. Finally, it discusses experiments and conclusions derived from the measurement of HRV in pigs, cattle, horses, sheep, goats and poultry. Emphasis has been placed on deriving recommendations for future research investigating HRV, including approaches for measuring and analysing IBI data. Data from earlier research demonstrate that HRV is a promising approach for evaluating stress and emotional states in animals. It has the potential to contribute much to our understanding and assessment of the underlying neurophysiological processes of stress responses and different welfare states in farm animals.

Loss of complexity characterizes the heart rate response to experimental hemorrhagic shock in swine

OBJECTIVE

To improve our ability to identify physiologic deterioration caused by critical illness, we applied nonlinear and frequency-domain analytical methods to R-to-R interval (RRI) and systolic arterial pressure (SAP) time series during hemorrhagic shock.

DESIGN

Prospective, randomized, controlled trial.

SETTING

Animal laboratory of a government research institute.

SUBJECTS

Twenty swine (weight 36.4+/-0.11 kg).

INTERVENTIONS

Fixed-volume hemorrhage followed by resuscitation; off-line analysis of RRI and SAP data.

MEASUREMENTS AND MAIN RESULTS

Anesthetized swine (shock group, n=12) underwent withdrawal of 30 mL/kg blood in 10 mL/kg decrements. A control group (n=8) received maintenance fluids only. Electrocardiogram and arterial pressure waveforms were acquired at 500 Hz. Eight hundred-beat data sets were analyzed at six time points: at baseline, after each blood withdrawal, after lactated Ringer's resuscitation, and after infusion of shed blood. Nonlinear methods were used to estimate the complexity (approximate entropy, sample entropy, Lempel-Ziv entropy, normalized entropy of symbol dynamics), RRI bits per word, and fractal dimension by curve lengths and by dispersion analysis of the RRI and SAP time series. Fast Fourier transformation was used to measure the high-frequency and low-frequency powers of RRI and SAP. Baroreflex sensitivity was assessed in the time domain with the sequence method. Hemorrhagic shock caused decreases in RRI complexity as quantified by approximate entropy, sample entropy, and symbol dynamics; these changes were reversed by resuscitation. Similar but statistically insignificant changes in fractal dimension by curve lengths were seen. RRI high-frequency power decreased with hemorrhagic shock-indicating withdrawal of vagal cardiac input-and was restored by resuscitation. Similar changes in baroreflex sensitivity were seen. Hemorrhagic shock did not affect SAP complexity.

CONCLUSIONS

Hemorrhagic shock caused a reversible decrease in RRI complexity; these changes may be mediated by changes in vagal cardiac control. Assessment of RRI complexity may permit identification of casualties with hemorrhagic shock.

Recurrence plots and Shannon entropy for a dynamical analysis of asynchronisms in noninvasive mechanical ventilation

Recurrence plots were introduced to quantify the recurrence properties of chaotic dynamics. Hereafter, the recurrence quantification analysis was introduced to transform graphical interpretations into statistical analysis. In this spirit, a new definition for the Shannon entropy was recently introduced in order to have a measure correlated with the largest Lyapunov exponent. Recurrence plots and this Shannon entropy are thus used for the analysis of the dynamics underlying patient assisted with a mechanical noninvasive ventilation. The quality of the assistance strongly depends on the quality of the interactions between the patient and his ventilator which are crucial for tolerance and acceptability. Recurrence plots provide a global view of these interactions and the Shannon entropy is shown to be a measure of the rate of asynchronisms as well as the breathing rhythm.

Asynchrony and cyclic variability in pressure support noninvasive ventilation

Noninvasive mechanical ventilation is an effective procedure to manage patients with acute or chronic respiratory failure. Most ventilators act as flow generators that assist spontaneous respiratory cycles by delivering inspiratory and expiratory pressures. This allows the patient to improve alveolar ventilation and subsequent pulmonary gas exchanges. The interaction between the patient and his ventilator are therefore crucial for tolerance and acceptability and part of this interaction is the facility to trigger the ventilator at the beginning of the inspiration. This is directly related to patients' discomfort which is not quantified today. Phase portraits reconstructed from the airflow and first-return maps built on the total breath duration were used to investigate the quality of the patient-ventilator interaction. Phase synchronization can be identified from phase portrait and the breath-to-breath variability is well characterized by return maps. This paper is a first step in the direction of automatically estimating the comfort from measurements and not from a necessarily subjective answer given by the patient. These tools could be helpful for the physicians to set the ventilator parameters.

Heart rate variability: a review

Heart rate variability (HRV) is a reliable reflection of the many physiological factors modulating the normal rhythm of the heart. In fact, they provide a powerful means of observing the interplay between the sympathetic and parasympathetic nervous systems. It shows that the structure generating the signal is not only simply linear, but also involves nonlinear contributions. Heart rate (HR) is a nonstationary signal; its variation may contain indicators of current disease, or warnings about impending cardiac diseases. The indicators may be present at all times or may occur at random-during certain intervals of the day. It is strenuous and time consuming to study and pinpoint abnormalities in voluminous data collected over several hours. Hence, HR variation analysis (instantaneous HR against time axis) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system. Computer based analytical tools for in-depth study of data over daylong intervals can be very useful in diagnostics. Therefore, the HRV signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. In this paper, we have discussed the various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV.

Heart rate variability: a review

Heart rate variability (HRV) is a reliable reflection of the many physiological factors modulating the normal rhythm of the heart. In fact, they provide a powerful means of observing the interplay between the sympathetic and parasympathetic nervous systems. It shows that the structure generating the signal is not only simply linear, but also involves nonlinear contributions. Heart rate (HR) is a nonstationary signal; its variation may contain indicators of current disease, or warnings about impending cardiac diseases. The indicators may be present at all times or may occur at random-during certain intervals of the day. It is strenuous and time consuming to study and pinpoint abnormalities in voluminous data collected over several hours. Hence, HR variation analysis (instantaneous HR against time axis) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system. Computer based analytical tools for in-depth study of data over daylong intervals can be very useful in diagnostics. Therefore, the HRV signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. In this paper, we have discussed the various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV.

Heart rate variability: a review

Heart rate variability (HRV) is a reliable reflection of the many physiological factors modulating the normal rhythm of the heart. In fact, they provide a powerful means of observing the interplay between the sympathetic and parasympathetic nervous systems. It shows that the structure generating the signal is not only simply linear, but also involves nonlinear contributions. Heart rate (HR) is a nonstationary signal; its variation may contain indicators of current disease, or warnings about impending cardiac diseases. The indicators may be present at all times or may occur at random-during certain intervals of the day. It is strenuous and time consuming to study and pinpoint abnormalities in voluminous data collected over several hours. Hence, HR variation analysis (instantaneous HR against time axis) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system. Computer based analytical tools for in-depth study of data over daylong intervals can be very useful in diagnostics. Therefore, the HRV signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. In this paper, we have discussed the various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV.

Nonlinear Heart Rate Variability Analysis May Predict Atrial Fibrillation After Coronary Artery Bypass Grafting

BACKGROUND

Heart rate variability might predict arrhythmias after coronary artery bypass grafting.

METHODS

Off-line processing of 10-min electrocardiogram recordings of consecutive patients provided R-R intervals for time domain, frequency domain, Poincaré, and point correlation analyses and subsequent association with postoperative atrial fibrillation by stepwise multivariate logistic regression.

RESULTS

Of 88 patients who met entry criteria, 13 developed atrial fibrillation. Peak point correlation dimension (odds ratio 3.985/unit, P = 0.0096) and age (odds ratio 1.144/yr, P = 0.0019) were independently associated with atrial fibrillation (c-statistic = 0.839).

CONCLUSIONS

Further study should confirm the ability of peak point correlation dimension to predict atrial fibrillation after coronary artery surgery with cardiopulmonary bypass.

Differences in heart rate dynamics before the spontaneous onset of long and short episodes of paroxysmal atrial fibrillation

BACKGROUND

Altered heart rate (HR) dynamics precede the spontaneous onset of atrial fibrillation (AF), but the factors related to the perpetuation and duration of paroxysmal AF episodes are not well established. This study was designed to test the hypothesis that HR dynamics preceding the onset of (AF) may influence the duration of AF.

METHODS

Traditional time and frequency domain HR variability indices, along with a short-term fractal scaling exponent (alpha(1)) and approximate entropy (ApEn), were analyzed in 20-minute intervals before 92 episodes of spontaneous paroxysmal AF in 22 patients without structural heart disease. AF episodes were divided into two groups according to the duration of the arrhythmia episodes.

RESULTS

The high-frequency (HF) spectral component in normalized units (nu) of heart rate variability was higher and low-frequency (LF) component lower before long (> 200 s, n = 41) compared to short (< 200 s, n = 51) AF episodes (HF nu; 40.1 +/- 14.8 vs 31.5 +/- 16.4, P < 0.0001 and LF nu; 59.9 +/- 14.8 vs 68.5 +/- 16.4, P < 0.0001). Short-term scaling exponent values also were lower before long compared to short AF episodes (e.g., alpha(1); 1.12 +/- 0.21 vs 1.24 +/- 0.23, P < 0.0001). Women had a larger number of long AF episodes than men, but the duration of AF was not related to any other clinical or demographic features or antiarrhythmic medication.

CONCLUSION

Increased HF oscillations and decreased short-term correlation properties of R-R intervals, reflecting altered sympathovagal balance before the onset of AF, predispose to perpetuation of spontaneous arrhythmia episodes in patients with vulnerability to paroxysmal AF and without structural heart disease.

The paradigm of complexity in clinical neurocognitive science

Neurocognitive science represents the modern approach to integrating the subdisciplines aimed at a scientific study of the brain-mind system. This relatively new discipline recognizes, implicitly or explicitly, that this is a complex system whose states and processes are determined by multiple bio-psycho-social variables and order parameters. In a generic perspective, all neurocognitive science is complex, as it is multidisciplinary, but in some studies, complexity has become a more defined scientific paradigm using its own specific empirical and theoretical tools. Some neuroscientists consider complexity science as a specific and formalized paradigm. Between their contributions, the author will try to highlight some current promising paths and new frontiers for neuroscience. In this perspective, he will mostly focus on those contributions directly related to clinical perspectives. This is the reason why some seminal contributions more focused on physiological functioning might not be mentioned.

Gait variability: methods, modeling and meaning

The study of gait variability, the stride-to-stride fluctuations in walking, offers a complementary way of quantifying locomotion and its changes with aging and disease as well as a means of monitoring the effects of therapeutic interventions and rehabilitation. Previous work has suggested that measures of gait variability may be more closely related to falls, a serious consequence of many gait disorders, than are measures based on the mean values of other walking parameters. The Current JNER series presents nine reports on the results of recent investigations into gait variability. One novel method for collecting unconstrained, ambulatory data is reviewed, and a primer on analysis methods is presented along with a heuristic approach to summarizing variability measures. In addition, the first studies of gait variability in animal models of neurodegenerative disease are described, as is a mathematical model of human walking that characterizes certain complex (multifractal) features of the motor control's pattern generator. Another investigation demonstrates that, whereas both healthy older controls and patients with a higher-level gait disorder walk more slowly in reduced lighting, only the latter's stride variability increases. Studies of the effects of dual tasks suggest that the regulation of the stride-to-stride fluctuations in stride width and stride time may be influenced by attention loading and may require cognitive input. Finally, a report of gait variability in over 500 subjects, probably the largest study of this kind, suggests how step width variability may relate to fall risk. Together, these studies provide new insights into the factors that regulate the stride-to-stride fluctuations in walking and pave the way for expanded research into the control of gait and the practical application of measures of gait variability in the clinical setting.

Forecasting epilepsy from the heart rate signal

Information contained in the R-R interval series, specific to the pre-ictal period, was sought by applying an unsupervised fuzzy clustering algorithm to the N-dimensional phase space of N consecutive interval durations or the absolute value of duration differences. Data sources were individual, complex partial seizures of temporal-lobe epileptics and generalised seizures of rats rendered epileptic with hyperbaric oxygen. Forecasting success was 86% and 82% (zero false positives in resistant rats), respectively, at times ranging from 10 min to 30 s prior to seizure onset Although certain forecasting clusters predominated in the patient group and different ones predominated in the animal group, forecasting on the whole was seizure-specific. The high prediction sensitivity of this method, which matches that of EEG-based methods, seems promising. It is believed that an on-line version of the algorithm, trained on each patient's peri-ictal ECG, could serve as a basis for a simple seizure alarm system.

Heart rate turbulence after atrial premature beats before spontaneous onset of atrial fibrillation

OBJECTIVES

This study was designed to assess the temporal changes in vagal responses to atrial premature beats before spontaneous onset of atrial fibrillation (AF).

BACKGROUND

Enhanced vagal activity plays a major role in the onset and perpetuation of experimental AF, but the role of vagal activation in the onset of clinical AF episodes is not so well established.

METHODS

We calculated heart rate turbulence after atrial premature impulses occurring 0 to 60 min before the onset of AF ("prior to AF") and compared it with the hourly means of the other hours of the 24-h electrocardiogram recordings ("non-AF hours") in 39 patients with structural heart disease and 29 patients with lone AF. Traditional heart rate variability measurements and approximate entropy (ApEn) were also analyzed.

RESULTS

Turbulence onset (TO) was significantly less negative during the 1 h preceding AF than during the non-AF hours (0.71 +/- 1.76 vs. -0.35 +/- 1.46, p < 0.00001). Less negative TO before AF was observed among both the patients with structural heart disease (1.16 +/- 1.73 vs. 0.07 +/- 1.23; p < 0.0001) and those with lone AF (0.17 +/- 1.67 vs. -0.85 +/- 1.56; p < 0.0001). No significant difference was seen in the turbulence slope between the two periods, and none of the traditional frequency and time domain measurements differentiated between the periods; ApEn was significantly lower before AF than during the non-AF hours (p < 0.01).

CONCLUSIONS

Altered heart rate dynamics, suggesting transient enhancement of vagal outflow after premature atrial excitation, are temporally related to spontaneous onset of clinical AF.

Using heart rate variability to stratify risk of obstetric patients undergoing spinal anesthesia

In this study, we evaluated whether point correlation dimension (PD2), a measure of heart rate variability, can predict hypotension accompanying spinal anesthesia for cesarean delivery. After the administration of spinal anesthesia with bupivacaine, hypotension was defined as systolic blood pressure </=75% of baseline within 20 min of intrathecal injection. Using the median prespinal PD2 (3.90) to form 2 groups, LO and HI, all 11 hypotensive patients were in the LO group, and all 11 patients without hypotension were in the HI group. Baseline heart rate in the LO group was 95 bpm (10.2 sd), versus 81 bpm (9.6 sd) in the HI group. PD2 shows promise as a predictor of hypotension in pregnant women receiving spinal anesthesia.

Experimental analysis of heart rate variability of long-recording electrocardiograms in normal subjects and patients with coronary artery disease and normal left ventricular function

The heart rate signal contains valuable information about cardiac health, which cannot be extracted without the use of appropriate computerized methods. This paper presents an analysis of various electrocardiograms, the aim of which is to categorize them into two distinct groups. Group A represents young male subjects with no prior occurrence of coronary disease events and Group B represents middle-aged male subjects who have symptomatic coronary artery disease without myocardial infarction and whose 12-lead ECGs do not contain any abnormalities, thus wrongly indicating a normal subject. Electrocardiographic recordings are approximately 2h in length and acquired under conditions that favor the stationarity of collected data. Linear and nonlinear characteristics are studied by applying several techniques including Fourier analysis, Correlation Dimension Estimation, Approximate Entropy, and the Discrete Wavelet Transform. The small variations of the diagnostic information given by each one of the methods as well as the slightly different conclusions among similar studies indicate the necessity of further investigation, combined use, and complementary application of different approaches.

Women's health and complexity science

Conceptual frameworks in science have shifted from reductionism and its focus on ever-smaller parts to complexity, an outgrowth of chaos theory that views those parts in relation to one another, to the larger entity they form and to the environment in which that entity exists. Examples of this conceptual shift are occurring in many areas of science, but nowhere is it more germane than in the medical sciences that serve women. After a historical focus on reproduction and the development of obstetrics-gynecology, medicine has now gained a broader view of the woman using sex- and gender-based science, and a new field called "women's health" is evolving. Complexity science does not invalidate or eliminate the need for reductionist science, it simply makes a wider array of phenomena understandable. Its method allows going beyond the metaphor of the body as a machine and challenges the user to re-examine how health and illness are understood. This article explores how these changes in science must inform the development of an academic discipline in women's health. The conceptual framework of complexity science also advances the discussions about women's health from reproduction to a totally new and exciting exploration of the interactions between reproduction and all other organ functioning that occurs in women in the contexts of their lives.

Early detection of acute allograft rejection by linear and nonlinear analysis of heart rate variability

OBJECTIVE

The first months after orthotopic heart transplantation are associated with the highest risk of acute allograft rejection. This study explores the utility and reliability of linear and novel nonlinear metrics of heart rate variability as predictors of graft rejection. The underlying hypothesis is that the transplanted heart, in response to inflammatory mediators, alters the dynamic properties of its rhythm-generating system.

METHODS

In a cross-sectional study of 45 patients who had undergone heart transplantation, spanning a period of 4 months after the operation, heart rate variability was examined by time- and frequency-domain analysis. The nonlinear features of heart rate variability were studied by computing a pointwise correlation dimension of R-R interval time series. The results of heart rate variability analysis were compared with those of endomyocardial surveillance biopsy studies using the International Society for Heart and Lung Transplantation scoring system.

RESULTS

Duration of heart transplantation itself exhibited a significant (P<.05) association with the onset of rejection. Specific predictors of acute rejection based on heart rate variability were identified, including shortening of the R-R interval (from 700 +/- 68 to 648 +/- 72 ms), an increase in the ratio of low-frequency (0.04-0.15 Hz) to high-frequency (0.15-0.40 Hz) spectral power (from 0.3 +/- 0.2 to 0.6 +/- 0.4), and a decrease in pointwise correlation dimension values (from 1.7 +/- 0.7 to 0.9 +/- 0.3 units). Multivariable logistic regression analysis (R (2) = 0.4) revealed that the only significant independent risk predictors were pointwise correlation dimension (odds ratio, 2.2 per 0.1 unit) and duration of heart transplantation (odds ratio, 1.7 per week).

CONCLUSION

Nonlinear measures of heart rate variability provide noninvasive means for identifying patients undergoing cardiac transplantation with acute rejection, thereby enabling the assessment of the time-dependent adaptive response of the donor heart to its host.

Threshold modeling of autonomic control of heart rate variability

Even in the absence of external perturbation to the human cardiovascular system, measures of cardiac function, such as heart rate, vary with time in normal physiology. The primary source of the variation is constant regulation by a complex control system which modulates cardiac function through the autonomic nervous system. Here, we present methods of characterizing the statistical properties of the underlying processes that result in variations in ECG R-wave event times within the framework of an integrate-and-fire model. We first present techniques for characterizing the noise processes that result in heart rate variability even in the absence of autonomic input. A relationship is derived that relates the spectrum of R-R intervals to the spectrum of the underlying noise process. We then develop a technique for the characterization of the dynamic nature of autonomically related variability resulting from exogenous inputs, such as respiratory-related modulation. A method is presented for the estimation of the transfer function that relates the respiratory-related input to the variations in R-wave event times. The result is a very direct analysis of autonomic control of heart rate variability through noninvasive measures, which provides a method for assessing autonomic function in normal and pathological states.

Is fractal geometry useful in medicine and biomedical sciences?

Fractal geometry has become very useful in the understanding of many phenomena in various fields such as astrophysics, economy or agriculture and recently in medicine. After a brief intuitive introduction to the basis of fractal geometry, the clue is made about the correlation between Df and the complexity or the irregularity of a structure. However, fractal analysis must be applied with certain caution in natural objects such as bio-medical ones. The cardio-vascular system remains one of the most important fields of application of these kinds of approach. Spectral analysis of the R-R interval, morphology of the distal coronary arteries constitute two examples. Other very interesting applications are founded in bacteriology, medical imaging or ophthalmology. In our institution, we apply fractal analysis in order to quantitate angiogenesis and other vascular processes.

Autonomic nervous system disorders in stroke

Disturbances of the autonomic nervous system are common in patients with various cerebrovascular diseases. They are attributed to damage of the central autonomic network, particularly in the frontoparietal cortical areas and in the brain stem, or to a disruption of the autonomic pathways descending from the hypothalamus via the mesencephalon, pons, and medulla to the spinal cord. The most common clinical problems include abnormalities in heart rate and blood pressure regulation, reflecting cardiovascular autonomic dysfunction, and asymmetric sweating with cold hemiplegic limbs, reflecting changes in the sudomotor and vasomotor regulatory systems. Bladder and bowel dysfunction and impotence are also frequent complaints after stroke, but the present knowledge concerning their prevalence and clinical significance is still limited. Cardiovascular autonomic dysfunction, which is mainly related to increased sympathetic activity, is most evident in the acute phase of stroke, whereas other autonomic disorders, such as abnormal sweating, are long-standing or even irreversible. In addition to the well-established sympathetic hyperfunction, abnormalities of the parasympathetic nervous system may also contribute to the autonomic imbalance after stroke. Reliable recognition of autonomic dysfunction using quantitative analysis methods is important, because these disturbances are not only subjectively disabling and uncomfortable, but they may also be prognostically unfavorable. Moreover, quantitative measurements also form the ground for successive treatment of various stroke-related autonomic disorders.

Human fetuses have nonlinear cardiac dynamics

Approximate entropy (ApEn) is a statistic that quantifies regularity in time series data, and this parameter has several features that make it attractive for analyzing physiological systems. In this study, ApEn was used to detect nonlinearities in the heart rate (HR) patterns of 12 low-risk human fetuses between 38 and 40 wk of gestation. The fetal cardiac electrical signal was sampled at a rate of 1,024 Hz by using Ag-AgCl electrodes positioned across the mother's abdomen, and fetal R waves were extracted by using adaptive signal processing techniques. To test for nonlinearity, ApEn for the original HR time series was compared with ApEn for three dynamic models: temporally uncorrelated noise, linearly correlated noise, and linearly correlated noise with nonlinear distortion. Each model had the same mean and SD in HR as the original time series, and one model also preserved the Fourier power spectrum. We estimated that noise accounted for 17.2-44.5% of the total between-fetus variance in ApEn. Nevertheless, ApEn for the original time series data still differed significantly from ApEn for the three dynamic models for both group comparisons and individual fetuses. We concluded that the HR time series, in low-risk human fetuses, could not be modeled as temporally uncorrelated noise, linearly correlated noise, or static filtering of linearly correlated noise.

A characterization of HRV's nonlinear hidden dynamics by means of Markov models

A study of the 24-h heart rate variability's (HRV) hidden dynamic is performed hour by hour, in order to investigate the evolution of the nonlinear structure of the underlying nervous system. A hierarchy of null hypotheses of nonlinear Markov models with increasing order n is tested against the hidden dynamic of the HRV time series. The minimum accepted Markov order supplies information about the nonlinearity of the HRV's hidden dynamic and consequently of the underlying nervous system. The Markov model with minimum order is detected for each hour of the RR time series extracted from seven 24-h electrocardiogram records of patients in different pathophysiological conditions, some including ventricular tachycardia episodes. Heart rate, pNN30, and LF/HF index plots are reported to serve as a reference for the description of the patient's cardiovascular frame during each examined hour. The minimum Markov order shows to be a promising index for quantifying the average nonlinearity of the autonomic nervous system's activity.

Biological variation of glucose and insulin includes a deterministic chaotic component

Serial data of glucose and insulin values of individual patients vary over short periods of time; this phenomenon has been called biological variation. The classic homeostatic control model assumes that the physiological mechanisms maintaining the concentrations of glucose and insulin are linear. The only deviations over a short period of time one should observe are in relation to a glucose load or major hormonal disturbance. Otherwise, the values of these analytes should be constant and any variations seen are due to random disturbances. We investigated previously published serial data (three for glucose and one for insulin) with nonlinear analytical methods, such as embedding space, correlation dimension, Lyapunov exponents, singular value decomposition and phase portraits, as well as linear methods, such as power spectra and autocorrelation functions. The power spectra failed to show dominant frequencies, but the autocorrelation functions showed significant correlation, consistent with a deterministic process. The correlation dimension was finite, around 4.0, the first Lyapunov exponent was positive, indicative of a deterministic chaotic process. Furthermore, the phase portraits showed directional flow. Therefore, the short-term biological variation observed for analytes arises from nonlinear, deterministic chaotic behavior instead of random variation.

Chaos and spectral analyses of heart rate variability during head-up tilting in essential hypertension

To investigate nonlinear and linear components of heart rate variability (HRV) in essential hypertension (EHT), we analyzed HRV by chaos and spectral analyses in patients with EHT (n = 18) and normotensives (n = 10) during head-up tilting. We used the correlation dimension (CD) and Lyapunov exponents as the parameters of chaos. The CD, an index of complexity, was lower at rest in EHT group than in normotensives, and did not change in EHT group in response to head-up tilting, but decreased in normotensives. Head-up tilting did not change the Lyapunov exponents, an index of sensitive dependence on initial condition, a hallmark of chaos, in both groups. In the spectral analysis, the normalized high-frequency component (%HF) was decreased in EHT group at rest, and head-up tilting increased the low- to high-frequency ratio (L/H) and reduced the %HF in both groups. The CD and Lyapunov exponents at rest were correlated with the %HF and L/H. These results suggest that chaos analysis can assess the different aspect of HRV from spectral analysis and that nonlinear components of HRV may be associated with hypertension through an impaired dynamic regulation of HRV.

Correlation dimension estimation: can this nonlinear description contribute to the characterization of blood pressure control in rats?

The application of correlation dimension estimation to the study of cardiovascular control, via the blood pressure (BP) time series was investigated. We chose to calculate the Grassberger-Procaccia (GP) correlation dimension. In order to obtain a reliable estimate of the correlation dimension, we studied impact of various parameters such as the appropriate sampling rate, the time delays, the embedding dimension, the minimal trace length required, and the number of points needed as reference points. We developed a recipe for the reliable treatment of the continuous BP signal in rats, our animal model, and discussed the possible pitfalls which demand special attention. Next, we applied the surrogate data method to a BP time series, looking for the existence of nonlinear components, in order to test whether the nonlinear modeling is necessary for accurately describing the system. We found that, indeed, the correlation dimension does reveal information which cannot be unveiled by the commonly used power spectral technique, thus, making the nonlinear modeling an important approach, providing additional insight into the cardiovascular control system.

Heart rate dynamics before spontaneous onset of ventricular fibrillation in patients with healed myocardial infarcts

The traditional methods of analyzing heart rate (HR) variability have failed to predict imminent ventricular fibrillation (VF). We sought to determine whether new methods of analyzing RR interval variability based on nonlinear dynamics and fractal analysis may help to detect subtle abnormalities in RR interval behavior before the onset of life-threatening arrhythmias. RR interval dynamics were analyzed from 24-hour Holter recordings of 15 patients who experienced VF during electrocardiographic recording. Thirty patients without spontaneous or inducible arrhythmia events served as a control group in this retrospective case control study. Conventional time- and frequency-domain measurements, the short-term fractal scaling exponent (alpha) obtained by detrended fluctuation analysis, and the slope (beta) of the power-law regression line (log power - log frequency, 10(-4)-10(-2) Hz) of RR interval dynamics were determined. The short-term correlation exponent alpha of RR intervals (0.64 +/- 0.19 vs 1.05 +/- 0.12; p <0.001) and the power-law slope beta (-1.63 +/- 0.28 vs -1.31 +/- 0.20, p <0.001) were lower in the patients before the onset of VF than in the control patients, but the SD and the low-frequency spectral components of RR intervals did not differ between the groups. The short-term scaling exponent performed better than any other measurement of HR variability in differentiating between the patients with VF and controls. Altered fractal correlation properties of HR behavior precede the spontaneous onset of VF. Dynamic analysis methods of analyzing RR intervals may help to identify abnormalities in HR behavior before VF.

Long-term heart rate fluctuations in postoperative and brain-dead patients

Long-term heart rate fluctuations in postoperative and brain-dead patients were investigated. Heart rates were monitored continuously, and the data were stored, edited, and interpolated to allow for data lost during calibration and disconnection of the sensors for various treatments. Heart rate power spectra were calculated using the fast Fourier transform method. The power spectra of the patients who recovered showed that the heart rate fluctuated and produced a 1/f relationship, termed 1/f fluctuations, whereas those of patients who died in the intensive care unit (ICU) consisted of white-noise-like signals. The power spectra in brain-dead patients showed a 1/f relationship under steady-state conditions, while the power density and variation of the frequency distribution were lower than those in a normal subject. Therefore, 1/f fluctuations appear to be universal and occur independent of the central nervous system.

Evolution in functional complexity of heart rate dynamics: a measure of cardiac allograft adaptability

The capacity of self-organized systems to adapt is embodied in the functional organization of intrinsic control mechanisms. Evolution in functional complexity of heart rate variability (HRV) was used as measure of the capacity of the transplanted heart to express newly emergent regulatory order. In a cross-sectional study of 100 patients after (0-10 yr) heart transplantation (HTX), heart rate dynamics were assessed using pointwise correlation dimension (PD2) analysis. A new observation is that, commencing with the acute event of allograft transplantation, the dynamics of rhythm formation proceed through complex phase transitions. At implantation, the donor heart manifested metronome-like chronotropic behavior (PD2 approximately 1.0). At 11-100 days, dimensional complexity of HRV reached a peak (PD2 approximately 2.0) associated with resurgence in the high-frequency component (0.15-0.5 Hz) of the power spectral density. Subsequent dimensional loss to PD2 approximately 1.0 at 20-30 mo after HTX was followed by a progressive near-linear gain in system complexity, reaching PD2 approximately 3.0 7-10 yr after HTX. The "dynamic reorganization" in the allograft rhythm-generating system, seen in the first 100 days, is a manifestation of the adaptive capacity of intrinsic control mechanisms. The loss of HRV 2 yr after HTX implies a withdrawal of intrinsic autonomic control and/or development of an entrained dynamic pattern characteristic of extrinsic sympathetic input. The subsequent long-term progressive rise in dimensional complexity of HRV can be attributed to the restoration of a functional order patterning parasympathetic control. The recognition that the decentralized heart can restitute the multidimensional state space of HR generator dynamics independent of external autonomic signaling may provide a new perspective on principles that constitute homeodynamic regulation.

Effects of maternal alcohol intake on fractal properties in human fetal breathing dynamics

Fractal methods have been found to be useful in characterizing biomedical signals. The use of fractal estimation requires the estimation of parameter H, which is directly related to the fractal dimension D. Here, we propose a new approach which is a combination of the wavelet transform and fractal estimators to characterize the human fetal breathing signals before and after the intake of two glasses of wine by a mother. This study was performed on 26 fetuses. The variances of the wavelet coefficients were estimated at each scale. The slope of the representation on a logarithmic plot from the scales 5 to 1 was found to be increased after alcohol intake. Our results suggested that fetal breathing rates have a rough structure before the alcohol intake and a smooth structure after alcohol intake.

Heart rate dynamics in low risk human fetuses

Evaluation of nonlinear heart rate (HR) dynamics has received considerable attention in the pediatric literature because such analyses not only provide insight into underlying control mechanisms, but may also help to differentiate between normal and abnormal infants. The purpose of this study was to determine, in eight low risk human fetuses, if nonlinear HR dynamics could be identified by analyzing the dispersion of interbeat intervals at slow (Ds) and fast (Df) HRs. The fetal cardiac electrical signal was captured transabdominally at a resolution of +/- 1 ms. To test the null hypothesis, that the time series is the result of a linear stochastic process, Ds and Df for the original time series were compared with the values calculated for three linear models. The linear models were constructed to preserve the major statistical properties of the original time series, including the mean, SD, and the Fourier power spectrum. For each fetus, there was no evidence of nonlinear cardiac dynamics based on analyses of Ds and Df. In contrast, the distribution of adjacent R-R intervals and the pattern of change across three successive interbeat intervals both revealed significant nonlinearities in HR control in each fetus. If the difference between normal and abnormal infants is the result of aberrant control of nonlinear processes, then our findings indicate that parameters which describe the nonlinearity may be more useful then Ds and Df in assigning a risk status.

Probing the order within neonatal heart rate variability

The mechanism by which heart rate variability (HRV) changes during neonatal illness is not known. One possibility is that reduced HRV is merely a diminished or scaled-down version of normal. Another possibility is that there is a fundamental change in the mechanism underlying HRV, resulting in a change in the ordering of RR intervals. We investigated the nature and extents of order in RR interval time series from 25 Neonatal Intensive Care Unit patients with a spectrum of clinical illness severity and HRV. We measured predictability (deviation of predicted intervals from observed), and regularity (measured as approximate entropy) of RR interval time series showing different degrees of HRV. In RR interval time series where the effects of scaling were removed, we found 1) records showing normal HRV had more order than those showing low HRV; 2) the nature of the order was more like that of a periodic process with frequencies over a large range (time series whose log-log power spectrum had a 1/f distribution) than that of chaotic one (logistic map); and 3) the nature of order did not change greatly as HRV fell. We conclude that neonatal RR interval time series are ordered by periodic processes with frequencies over a large range, and that the extent of order is less during illness when HRV is low.

Heart rate dynamics during accentuated sympathovagal interaction

Concomitant sympathetic and vagal activation can occur in various physiological conditions, but there is limited information on heart rate (HR) behavior during the accentuated sympathovagal antagonism. Beat-to-beat HR and blood pressure were recorded during intravenous infusion of incremental doses of norepinephrine in 18 healthy male volunteers (mean age 23 +/- 5 yr). HR and blood pressure spectra and two-dimensional Poincaré plots were generated from the baseline recordings and from the recordings at different doses of norepinephrine. The mean blood pressure increased (from 90 +/- 7 to 120 +/- 9 mmHg, P < 0.001), HR decreased (from 60 +/- 9 to 48 +/- 7 beats/min, P < 0.001), and the high-frequency spectral component of HR variability increased (P < 0.001) during the norepinephrine infusion as evidence of accentuated sympathovagal interaction. Abrupt aperiodic changes in sinus intervals that were not related to respiratory cycles or changes in blood pressure occurred in 14 of 18 subjects during the norepinephrine infusions. These fluctuations in sinus intervals resulted in a complex or parabola-shaped structure of the Poincaré plots of successive R-R intervals and a widening of the high-frequency spectral peak. In four subjects, the abrupt fluctuations in sinus intervals were followed by a sudden onset of fixed R-R interval dynamics with a loss of respiratory modulation of HR, resulting in a torpedo-shaped structure of the Poincaré plots. These data show that HR behavior becomes remarkably unstable during accentuated sympathovagal interaction, resembling stochastic dynamics or deterministic chaotic behavior. These features of HR dynamics can be better identified by dynamic analysis of beat-to-beat behavior of R-R intervals than by traditional analysis techniques of HR variability.