Application of chaos theory to a model biological system: evidence of self-organization in the intrinsic cardiac nervous system

Studying gene expression system regulation at the program level

Understanding how gene expression systems influence biological outcomes is an important goal for diverse areas of research. Gene expression profiling allows for the simultaneous measurement of expression levels for thousands of genes and the opportunity to use this information to increase biological understanding. Yet, the best way to relate this immense amount of information to biological outcomes is far from clear. Here, a novel approach to gene expression systems research is presented that focuses on understanding gene expression systems at the level of gene expression program regulation. It is suggested that such an approach has important advantages over current techniques and may provide novel insights into how gene expression systems are regulated to shape biological outcomes such as the development of disease or response to treatment.

Mathematical modeling the neuroregulation of blood pressure using a cognitive top-down approach

Background:

The body′s physiological stability is maintained by the influence of the autonomic nervous system upon the dynamic interaction of multiple systems. These physiological systems, their nature and structure, and the factors which influence their function have been poorly defined. A greater understanding of such physiological systems leads to an understanding of the synchronised function of organs in each neural network i.e. there is a fundamental relationship involving sensory input and/or sense perception, neural function and neural networks, and cellular and molecular biology. Such an approach compares with the bottom-up systems biology approach in which there may be an almost infinite degree of biochemical complexity to be taken into account.

Aims:

The purpose of this article is to discuss a novel cognitive, top-down, mathematical model of the physiological systems, in particular its application to the neuroregulation of blood pressure.

Results:

This article highlights the influence of sensori-visual input upon the function of the autonomic nervous system and the coherent function of the various organ networks i.e. the relationship which exists between visual perception and pathology.

Conclusions:

The application of Grakov′s model may lead to a greater understanding of the fundamental role played by light e.g. regulating acidity, levels of Magnesium, activation of enzymes, and the various factors which contribute to the regulation of blood pressure. It indicates that the body′s regulation of blood pressure does not reside in any one neural or visceral component but instead is a measure of the brain′s best efforts to maintain its physiological stability.

A new potential marker for abnormal cardiac physiology in depression

The purpose of the study was to determine if a nonlinear estimate of dimensional complexity, Pointwise correlation dimension (Pd2), could be used to identify abnormal cardiac physiology associated with depression in primary care outpatients. The subjects were 22 medical controls and 30 general medical outpatients with depression who wore a cardiac monitor for 24 h. There was a significant difference between depressed and control subjects for Pd2 based on the entire cardiac time-series, with depressed subjects exhibiting higher Pd2 values. A cutoff score reflecting high dimensional complexity was selected, and an odds ratio was calculated demonstrating that patients with Pd2 values above the cut-off were 8.8 times more likely to fall in the depressed group than the control group. Additional research is needed to determine if Pd2 is useful for identifying physiological markers of depression.

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.

Nonlinear dynamics of heart rate variability during experimental hemorrhage in ketamine-anesthetized rats

Indexes of heart rate variability (HRV) based on linear stochastic models are independent risk factors for arrhythmic death (AD). An index based on a nonlinear deterministic model, a reduction in the point correlation dimension (PD2i), has been shown in both animal and human studies to have a higher sensitivity and specificity for predicting AD. Dimensional reduction subsequent to transient ischemia was examined previously in a simple model system, the intrinsic nervous system of the isolated rabbit heart. The present study presents a new model system in which the higher cerebral centers are blocked chemically (ketamine inhibition of N-methyl-D-aspartate receptors) and the system is perturbed over a longer 15-min interval by continuous hemorrhage. The hypothesis tested was that dimensional reduction would again be evoked, but in association with a more complex relationship between the system variables. The hypothesis was supported, and we interpret the greater response complexity to result from the larger autonomic superstructure attached to the heart. The complexities observed in the nonlinear heartbeat dynamics constitute a new genre of autonomic response, one clearly distinct from a hardwired reflex or a cerebrally determined defensive reaction.

Event-related dimensional reductions in the primary auditory cortex of the conscious cat are revealed by new techniques for enhancing the non-linear dimensional algorithms

The analytic algorithms derived from non-linear deterministic models may be more sensitive to differences in physiological data than those based on linear stochastic models. Among the non-linear algorithms the time-dependent dimensional ones appear to be the most sensitive discriminators. In the present study dimensional responses were examined in both electronically and mathematically generated data and in high-resolution physiological data. The latter were event-related potentials (ERPs) recorded from the primary auditory cortex of cats during classical conditioning. Two techniques were found to lengthen and stabilize the linear scaling region in the correlation integral of the dimensional algorithms: (1) linking trials to increase data length; and (2) gain reduction to lower integer-values of noise, combined with algorithmic setting of slopes < 0.5 to zero. Of the three dimensional algorithms examined, only the time-dependent Point Correlation Dimension (PD2i) showed low error rates when tracking the dimensional shifts in non-stationary generated data. This algorithm also uniquely distinguished between the conditioned and unconditioned physiological responses. The ERPs had corresponding PD2i's that were significantly different from each other as well as from their own randomized-phase surrogates. The brief dimensional reduction that follows a conditioned stimulus is interpreted to be related to 'cooperativity' among the underlying cortical neurons that contribute to its electrogenesis.

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.

Heart rate variability in the human transplanted heart: nonlinear dynamics and QT vs RR-QT alterations during exercise suggest a return of neurocardiac regulation in long-term recovery

RATIONALE

Functional reinnervation of the transplanted human heart by the autonomic nervous system has not been demonstrated. A lack of autonomic control of the transplanted allograft is reflected by an increased resting heart rate, a sluggish heart rate response to dynamical exercise and a reduced heart rate variability. Recent evidence suggests that a measure of deterministic chaos in the heartbeat interval series (point correlation dimension, PD2i) is superior to the conventional power spectrum or other stochastic measures in detecting changes in the mechanism underlying heartbeat generation.

METHODS

The PD2i is based on the presumption that the variability is determined and patterned, whereas the stochastic measures all assume that the variability is around a stationary mean and is noise. The PD2i reconstructs the degrees of freedom (number of independent variables) in the system that generates the time series examined, and does this irrespective of whether the system is stochastic or deterministic and is stationary in time.

RESULTS

PD2i was determined for heartbeat intervals (RR, ECG digitized at 1200 Hz; supine posture) of 23 heart transplant recipients (HTR: 9 adults, 14 children; 0.04-7.7 years after transplantation) and 21 healthy control subjects (CTL; 13 adults, 8 children). The PD2i (+/-SD) averaged 5.4 +/- 0.7 for the CTL adults and 5.4 +/- 0.6 for the CTL children. Mean PD2i was reduced after transplantation to 1.1 +/- 0.1 in 6 HTRs recorded within 1 year after surgery; in one HTR recorded 2 weeks after surgery the mean PD2i was 3.7. Between 1 to 2 years PD2i was found increased in 2 of 3 subjects and between 2 to 8 years it was increased in 13 of 13, but not to control levels. In normal hearts the QT subinterval of each heartbeat cycle is associated with inotropy and the RR-QT remainder with chronotropy (i.e., the dyastolic interval during which RR is primarily regulated). To examine more closely the residual and returning heartbeat dynamics of the HTR subjects, these subinterval series were examined during mild exercise (40 to 90 Watts) and its recovery. In recent HTRs, resting QT and RR-QT were moderately reduced and modulated by exercise and recovery, but with an approximate 100 beat latency. In long-term (7-8 years) HTR subjects there was a rapid and larger response to exercise/recovery, but compared to normal the range was smaller and the complexity of the subinterval trajectories in time was simpler.

CONCLUSIONS

Recurrence of low-dimensional deterministic dynamics after transplantation suggests recovery of neurocardiac control attributable to 1) reorganization of the viable intrinsic cardiac nervous system, 2) reinnervation by the extrinsic autonomic nervous system, or 3) both.