Deterministic chaos and fractal complexity in the dynamics of cardiovascular behavior: perspectives on a new frontier

A pilot study to assess the origin of the spectral power increases of heart rate variability associated with transient changes in the R-R interval

Spectral analysis of heart rate variability (HRV) is used to assess cardiovascular autonomic function. In the power density spectrum calculated from a time series of the R-R interval (RRI), three main components are distinguished: very-low-frequency (VLF; 0.003-0.04 Hz), low-frequency (LF; 0.04-0.15 Hz), and high-frequency (HF; 0.15-0.4 Hz) components. However, the physiological correlates of these frequency components have yet to be determined. In this study, we conducted spectral analysis of data segments of various lengths (5, 30, 100, and 200 s) of the RRI time series during active standing. Because of the trade-off relationship between time and frequency resolution, the analysis of the RRI data segment shorter than 30 s was needed to identify the temporal relationships between individual transient increases in RRI and the resulting spectral power changes. In contrast, the segment of 200 s was needed to properly evaluate the magnitude of the increase in the VLF power. The results showed that a transient increase in the RRI was tightly associated with simultaneous increases in the powers of the VLF, LF, and HF components. We further found that the simultaneous power increases in these three components were caused by the arterial baroreceptor reflex responding to rapid blood pressure rise.

Heart Rate Variability Measurement through a Smart Wearable Device: Another Breakthrough for Personal Health Monitoring?

Heart rate variability (HRV) is a measurement of the fluctuation of time between each heartbeat and reflects the function of the autonomic nervous system. HRV is an important indicator for both physical and mental status and for broad-scope diseases. In this review, we discuss how wearable devices can be used to monitor HRV, and we compare the HRV monitoring function among different devices. In addition, we have reviewed the recent progress in HRV tracking with wearable devices and its value in health monitoring and disease diagnosis. Although many challenges remain, we believe HRV tracking with wearable devices is a promising tool that can be used to improve personal health.

RT-TRAQ: An algorithm for real-time tracking of faint quasi-periodic signals in noisy time series

We present an algorithm for live tracking of quasi-periodic faint signals in non-stationary, noisy, and phase-desynchronized time series measurements that commonly arise in embedded applications, such as wearable health monitoring. The first step of Rt-Traq is to continuously select fixed-length windows based on the rise or fall of data values in the stream. Subsequently, Rt-Traq calculates an averaged representative window, and its spectrum, whose frequency peaks reveal the underlying quasi-periodic signals. As each new data sample comes in, Rt-Traq incrementally updates the spectrum, to continuously track the signals through time. We develop several alternate implementations of the proposed algorithm. We evaluate their performance in tracking maternal and fetal heart rate using non-invasive photoplethysmography (PPG) data collected by a wearable device from animal experiments as well as a number of pregnant women who participated in our study. Our empirical results demonstrate improvements compared to competing approaches. We also analyze the memory requirement and complexity trade-offs between the implementations, which impact their demand on platform resources for real-time operation.

Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal

Fractal algorithms for signal analysis are developed from geometric fractals and can be used to describe various complex signals in nature. A roughness scaling extraction algorithm with first-order flattening (RSE-f1) was shown in our previous studies to have a high accuracy, strong noise resistance, and a unique capacity to recognize the complexity of non-fractals that are common in signals. In this study, its disadvantage of a long calculation duration was addressed by using a dichotomy-binary strategy. The accelerated RSE-f1 algorithm (A-RSE-f1) retains the three above-mentioned advantages of the original algorithm according to theoretical analysis and artificial signal testing, while its calculation speed is significantly accelerated by 13 fold, which also makes it faster than the typical Higuchi algorithm. Afterwards, the vibration signals of the milling process are analyzed using the A-RSE-f1 algorithm, demonstrating the ability to distinguish different machining statuses (idle, stable, and chatter) effectively. The results of this study demonstrate that the RSE algorithm has been improved to meet the requirements of practical engineering with both a fast speed and a high performance.

Characterizing the effect of incrementally increasing dry bulb temperature on linear and nonlinear measures of heart rate variability in nonpregnant, mid-gestation, and late-gestation sows

Characterizing the sow physiological response to an increased heat load is essential for effective heat stress mitigation. The study objective was to characterize the effects of a 400-min heating episode on sow heart rate variability (HRV) at different reproductive stages. HRV is a commonly used noninvasive proxy measure of autonomic function. Twenty-seven sows were enrolled in the study according to their gestation stage at time of selection: 1) nonpregnant (NP; n = 7), 2) mid-gestation (MID; 57.3 ± 11.8 d gestation; n = 11), and 3) late-gestation (LATE; 98.8 ± 4.9 d gestation; n = 8). The HRV data utilized in the study were collected from each pig as the dry bulb temperature in the room increased incrementally from 19.84 ± 2.15 °C to 35.54 ± 0.43 °C (range: 17.1-37.5 °C) over a 400-min period. After data collection, one 5-min set of continuous heart rate data were identified per pig for each of nine temperature intervals (19-20.99, 21-22.99, 23-24.99, 25-26.99, 27-28.99, 29-30.99, 31-32.99, 33-34.99, and 35-36.99 °C). Mean inter-beat interval length (RR), standard deviation of r-r intervals (SDNN), root mean square of successive differences (RMSSD), high frequency spectral power (HF), sample entropy (SampEn), short-term detrended fluctuation analysis (DFAα1), and three measures (%REC, DET, LMEAN) derived from recurrence quantification analysis were calculated for each data set. All data were analyzed using the PROC GLIMMIX procedure in SAS 9.4. Overall, LATE sows exhibited lower RR than NP sows (P < 0.01). The standard deviation of r-r intervals and RMSSD differed between each group (P < 0.01), with LATE sows exhibiting the lowest SDNN and RMSSD and NP sows exhibiting the greatest SDNN and RMSSD. Late-gestation sows exhibited lower HF than both MID and NP sows (P < 0.0001), greater DFA values than NP sows (P = 0.05), and greater DET compared to MID sows (P = 0.001). Late-gestation also sows exhibited greater %REC and LMEAN compared to MID (P < 0.01) and NP sows (all P < 0.01). In conclusion, LATE sows exhibited indicators of greater autonomic stress throughout the heating period compared to MID and NP sows. However, temperature by treatment interactions were not detected as dry bulb increased. Future studies are needed to fully elucidate the effect of gestational stage and increasing dry bulb temperature on sow HRV.

Strange attractors in discrete slow power-law models of bone remodeling

Recently, a family of nonlinear mathematical discrete systems to describe biological interactions was considered. Such interactions are modeled by power-law functions where the exponents involve regulation processes. Considering exponent values giving rise to hyperbolic equilibria, we show that the systems exhibit irregular behavior characterized by strange attractors. The systems are numerically analyzed for different parameter values. Depending on the initial conditions, the orbits of each system either diverge to infinity or approach a periodic orbit or a strange attractor. Such dynamical behavior is identified by their Lyapunov exponents and local dimension. Finally, an application to the biochemical process of bone remodeling is presented. The existence of deterministic chaos in this process reveals a possible explanation of reproducibility failure and variation of effects in clinical experiments.

Multi-Chaotic Analysis of Inter-Beat (R-R) Intervals in Cardiac Signals for Discrimination between Normal and Pathological Classes

Cardiac signals have complex structures representing a combination of simpler structures. In this paper, we develop a new data analytic tool that can extract the complex structures of cardiac signals using the framework of multi-chaotic analysis, which is based on the p-norm for calculating the largest Lyapunov exponent (LLE). Appling the p-norm is useful for deriving the spectrum of the generalized largest Lyapunov exponents (GLLE), which is characterized by the width of the spectrum (which we denote by W). This quantity measures the degree of multi-chaos of the process and can potentially be used to discriminate between different classes of cardiac signals. We propose the joint use of the GLLE and spectrum width to investigate the multi-chaotic behavior of inter-beat (R-R) intervals of cardiac signals recorded from 54 healthy subjects (hs), 44 subjects diagnosed with congestive heart failure (chf), and 25 subjects diagnosed with atrial fibrillation (af). With the proposed approach, we build a regression model for the diagnosis of pathology. Multi-chaotic analysis showed a good performance, allowing the underlying dynamics of the system that generates the heart beat to be examined and expert systems to be built for the diagnosis of cardiac pathologies.

Single Cell Systems Analysis: Decision Geometry In Outliers

MOTIVATION

Anti-cancer therapeutics of the highest calibre currently focus on combinatorial targeting of specific oncoproteins and tumour suppressors. Clinical relapse depends upon intratumoral heterogeneity which serves as substrate variation during evolution of resistance to therapeutic regimens.

RESULTS

The present review advocates single cell systems biology as the optimal level of analysis for remediation of clinical relapse. Graph theory approaches to understanding decision-making in single cells may be abstracted one level further, to the geometry of decision-making in outlier cells, in order to define evolution-resistant cancer biomarkers. Systems biologists currently working with omics data are invited to consider phase portrait analysis as a mediator between graph theory and deep learning approaches. Perhaps counter-intuitively, the tangible clinical needs of cancer patients may depend upon the adoption of higher level mathematical abstractions of cancer biology.

SUPPLEMENTARY INFORMATION

supplementary data available at Bioinformatics online.

Fractal Characterization of Subviral Particle Motion: On the Influence of Spatio-Temporal Interpolation Methods

Due to the rapid globalization there is an increasing danger for pandemic outbreaks. The high death toll of fast spreading diseases like the Ebola infection demand the fast development of new medicines. Thus, the automation of pharmaceutical processes is an indispensable but challenging task. In cooperation with the Institute for Virology, Philipps-University, Marburg, Germany, recently, algorithms to detect and evaluate subviral particle tracks in live-cell fluorescence image sequences were developed. In steady interdisciplinary exchange between pharmacists and engineers it turned out that new measures to identify and classify subviral particle motion are required. This article focuses on the evaluation and optimization of a new method to classify subviral particle motion using fractal dimension estimation. The influence of global and local interpolation methods on fractal dimension estimation is investigated. The methods are tested on simulated data and applied to real image sequences. The results prospect a high benefit of using the presented methods for an effective classification of subviral particle behavior.

Autonomic control is a source of dynamical chaos in the cardiovascular system

The origin of complex irregular dynamics in a cardiovascular system is still being actively debated. Some hypotheses suggest the crucial role of stochastic modulation of cardiovascular parameters, while others argue for the importance of cardiac pacemakers' chaotic deterministic dynamics. In the present study, we estimate the largest Lyapunov exponent and the correlation dimension for the 4-h experimental interbeat intervals and the chaotic signals generated by the mathematical model of the cardiovascular system. We study the complexity of the mathematical model for such cases as the autonomic blockade, the exclusion of all the stochastic components, and the absence of variability of respiration. The obtained results suggest that the complexity of the heart rate variability is largely due to the chaotic dynamics in the loops of autonomic control of circulation.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

Higuchi Fractal Dimension of Heart Rate Variability During Percutaneous Auricular Vagus Nerve Stimulation in Healthy and Diabetic Subjects

Analysis of heart rate variability (HRV) can be applied to assess the autonomic nervous system (ANS) sympathetic and parasympathetic activity. Since living systems are non-linear, evaluation of ANS activity is difficult by means of linear methods. We propose to apply the Higuchi fractal dimension (HFD) method for assessment of ANS activity. HFD measures complexity of the HRV signal. We analyzed 45 RR time series of 84 min duration each from nine healthy and five diabetic subjects with clinically confirmed long-term diabetes mellitus type II and with diabetic foot ulcer lasting more than 6 weeks. Based on HRV time series complexity analysis we have shown that HFD: (1) discriminates healthy subjects from patients with diabetes mellitus type II; (2) assesses the impact of percutaneous auricular vagus nerve stimulation (pVNS) on ANS activity in normal and diabetic conditions. Thus, HFD may be used during pVNS treatment, to provide stimulation feedback for on-line regulation of therapy in a fast and robust way.

Mediation effect of novelty ecosystems on intrapreneurial behaviour process within an organisational dynamic environment among Kenyan universities

Purpose

The purpose of this paper is to examine, explain, predict and guide the processes, mechanisms and outcomes of intrapreneurial behaviour to provide evidence that novelty ecosystems mediate the relationships between generative influence, positive deviance and intrapreneurial behaviour. It also enlightens the capacity of replicating the intrapreneurial best practices.

Design/methodology/approach

The study uses an integrated approach of entrepreneurship and complexity theories. Its subjects were full-time designated university employees in the Republic of Kenya. A total number of 244 employees were selected using snowball sampling technique from ten public and private universities in the Kenya. A self-administered questionnaire was used to collect data.

Findings

The structural equation modelling path analysis and the bootstrapping results confirmed full mediation of novelty ecosystems in the relationship between generative influence and intrapreneurial behaviour. The findings, further, verified that novelty ecosystems partially mediate the relationship between positive deviance and intrapreneurial behaviour.

Research limitations/implications

Subjective appraisals were used, despite the fact that studied variables are ultimately based on what employees perceive. Future research should generate and include more objective measures.

Practical implications

Intrapreneurial behaviour can only be explained and predicted through novelty ecosystems. University leaders need to fully understand and facilitate novelty ecosystems.

Social implications

A deeper understanding of the power of generative influence, positive deviance and novelty ecosystems will not be fully realized until researchers devote as much energy and attention to facilitation as has been devoted to conflict.

Originality/value

This study extends existing intrapreneurial research into complexity approach.

Sensitivity of Chaos Measures in Detecting Stress in the Focusing Control Mechanism of the Short-Sighted Eye

When fixating on a stationary object, the power of the eye’s lens fluctuates. Studies have suggested that changes in these so-called microfluctuations in accommodation may be a factor in the onset and progression of short-sightedness. Like many physiological signals, the fluctuations in the power of the lens exhibit chaotic behaviour. A breakdown or reduction in chaos in physiological systems indicates stress to the system or pathology. The purpose of this study was to determine whether the chaos in fluctuations of the power of the lens changes with refractive error, i.e. how short-sighted a subject is, and/or accommodative demand, i.e. the effective distance of the object that is being viewed. Six emmetropes (EMMs, non-short-sighted), six early-onset myopes (EOMs, onset of short-sightedness before the age of 15), and six late-onset myopes (LOMs, onset of short-sightedness after the age of 15) took part in the study. Accommodative microfluctuations were measured at 22 Hz using an SRW-5000 autorefractor at accommodative demands of 1 D (dioptres), 2 D, and 3 D. Chaos theory analysis was used to determine the embedding lag, embedding dimension, limit of predictability, and Lyapunov exponent. Topological transitivity was also tested for. For comparison, the power spectrum and standard deviation were calculated for each time record. The EMMs had a statistically significant higher Lyapunov exponent than the LOMs (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.64\pm 0.33$$\end{document}0.64±0.33 vs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.39\pm 0.20~\hbox {D}/\hbox {s}$$\end{document}0.39±0.20D/s) and a lower embedding dimension than the LOMs (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.28\pm 0.46$$\end{document}3.28±0.46 vs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.67\pm 0.49$$\end{document}3.67±0.49). There was insufficient evidence (non-significant p value) of a difference between EOMs and EMMs or EOMs and LOMs. The majority of time records were topologically transitive. There was insufficient evidence of accommodative demand having an effect. Power spectrum analysis and assessment of the standard deviation of the fluctuations failed to discern differences based on refractive error. Chaos differences in accommodation microfluctuations indicate that the control system for LOMs is under stress in comparison to EMMs. Chaos theory analysis is a more sensitive marker of changes in accommodation microfluctuations than traditional analysis methods.

The fractal heart - embracing mathematics in the cardiology clinic

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

Bistability of a coupled Aurora B kinase-phosphatase system in cell division

Aurora B kinase, a key regulator of cell division, localizes to specific cellular locations, but the regulatory mechanisms responsible for phosphorylation of substrates located remotely from kinase enrichment sites are unclear. Here, we provide evidence that this activity at a distance depends on both sites of high kinase concentration and the bistability of a coupled kinase-phosphatase system. We reconstitute this bistable behavior and hysteresis using purified components to reveal co-existence of distinct high and low Aurora B activity states, sustained by a two-component kinase autoactivation mechanism. Furthermore, we demonstrate these non-linear regimes in live cells using a FRET-based phosphorylation sensor, and provide a mechanistic theoretical model for spatial regulation of Aurora B phosphorylation. We propose that bistability of an Aurora B-phosphatase system underlies formation of spatial phosphorylation patterns, which are generated and spread from sites of kinase autoactivation, thereby regulating cell division.

Fibromyalgia beyond reductionism. Heart rhythm fractal analysis to assess autonomic nervous system resilience

OBJECTIVES

The prevailing linear reductionist medical model seems unable to explain complex multisymptomatic illnesses such as fibromyalgia (FM) and similar maladies. Paradigms derived from the complexity theory may provide a coherent framework for these elusive illnesses. Along these lines is the proposal that FM represents a degradation of our main complex adaptive system (the autonomic nervous system, ANS), in a failed effort to adjust to a hostile environment. Healthy complex systems have fractal structures. Heart rate fractal-like variability reflects resilient ANS performance. Our aim was to measure the heart rate variability (HRV) fractal scaling index in FM patients and to correlate this index with clinical symptoms.

METHOD

We studied 30 women with FM and 30 controls. All participants filled out questionnaires assessing the severity of FM. The HRV fractal scaling index was estimated during 24 h using detrended fluctuation analysis (DFA).

RESULTS

The fractal scaling index alpha-1 was higher in FM patients than in controls (mean ± sd: 1.22 ± 0.10 vs. 1.16 ± 0.09; p = 0.031). There was a positive correlation between the fractal scaling index alpha-1 and the visual analogue scale (VAS) for depression (Spearman's ρ = 0.36, p = 0.04).

CONCLUSIONS

The heart rate fractal exponent alpha-1 is altered in FM patients, suggesting a rigid ANS performance. This tangible non-linear finding supports the notion that FM may represent a degradation of our main complex adaptive system, namely the ANS.

[To err is human? Interests of chaotic models to study adult psychiatric disorders and developmental disorders]

BACKGROUND

Many clinical and biological parameters have nonlinear chaotic fluctuations. These variations result in unexpected pseudo-random transitions. In these models, few risk factors can lead to unexpected phenomena if oscillations and self-reinforcement patterns occur. Complex rhythms could ease the ability of a physiological system to adapt and react quickly to a constantly changing environment.

OBJECTIVES

It has been proposed that several psychiatric disorders and developmental disorders are characterized by a loss of complex rhythm in favor of a more organized pattern. We examine evidence to support these assumptions in literatures.

METHODS

We performed a literature review of the main computerized databases (Medline, PubMed) and manual searches of the literature concerning non dynamic rhythms in time series analysis, in adults with psychiatric disorder and children with developmental disorder. These results were interpreted through a developmental approach that highlights the role of the learning process in the emergence of abilities.

RESULTS

Analysis of clinical scores and electroencephalographic data have found that subjects with bipolar disorder or schizophrenia, tested over a time series, have lower chaotic rhythms compared with healthy subjects. Growing children share several properties of a complex system: the interdependence of developmental axes (motor, emotional, language, social skills), multiple hierarchical levels (i.e. genetic, biological, environmental, and cultural), the two-way transactions between the child and his environment, and the sensitivity to initial conditions. This could explain the difficulty to predict the emergence of abilities or the long-term prognosis of impairment in children. This limitation is not only due to errors in the explanatory model or the lack of explanatory variable. It is also caused by instability, which is a core characteristic of a chaotic system.

CONCLUSION

The study of chaotic rhythms in time-series clinical and nonclinical data (e.g. EEG, functional neuroimaging) could improve the prediction of an acute event, such as relapse of mood disorder. Moreover, the complex rhythms in children may play a major part in synchronicity during interactions with a caregiver, held as essential for later development of self-regulation skills, such as emotional stability.

General anesthesia suppresses normal heart rate variability in humans

The human heart normally exhibits robust beat-to-beat heart rate variability (HRV). The loss of this variability is associated with pathology, including disease states such as congestive heart failure (CHF). The effect of general anesthesia on intrinsic HRV is unknown. In this prospective, observational study we enrolled 100 human subjects having elective major surgical procedures under general anesthesia. We recorded continuous heart rate data via continuous electrocardiogram before, during, and after anesthesia, and we assessed HRV of the R-R intervals. We assessed HRV using several common metrics including Detrended Fluctuation Analysis (DFA), Multifractal Analysis, and Multiscale Entropy Analysis. Each of these analyses was done in each of the four clinical phases for each study subject over the course of 24 h: Before anesthesia, during anesthesia, early recovery, and late recovery. On average, we observed a loss of variability on the aforementioned metrics that appeared to correspond to the state of general anesthesia. Following the conclusion of anesthesia, most study subjects appeared to regain their normal HRV, although this did not occur immediately. The resumption of normal HRV was especially delayed on DFA. Qualitatively, the reduction in HRV under anesthesia appears similar to the reduction in HRV observed in CHF. These observations will need to be validated in future studies, and the broader clinical implications of these observations, if any, are unknown.

Analysis of heart rate variability signal during meditation using deterministic-chaotic quantifiers

This study investigated the level of chaos and the existence of fractal patterns in the heart rate variability (HRV) signal prior to meditation and during meditation using two quantifiers adapted from non-linear dynamics and deterministic chaos theory: (1) component central tendency measures (CCTMs) and (2) Higuchi fractal dimension (HFD). CCTM quantifies degree of variability/chaos in the specified quadrant of the second-order difference plot for HRV time series, while HFD quantifies dimensional complexity of the HRV series. Both the quantifiers yielded excellent results in discriminating the different psychophysiological states. The study found (1) significantly higher first quadrant CCTM values and (2) significantly lower HFD values during meditation state compared to pre-meditation state. Both of these can be attributed to the respiratory-modulated oscillations shifting to the lower frequency region by parasympathetic tone during meditation. It is thought that these quantifiers are most promising in providing new insight into the evolution of complexity of underlying dynamics in different physiological states.

Arterial pressure fractality is highly dependent on wave reflection

Wave reflection is an important factor that influences pressure wave morphology and becomes more significant with aging, when cardiovascular risk increases. A pressure wave, measured at any location in the arterial tree, can be decomposed into its forward and backward components and depends on the corresponding amplitude and shifting time delays. Fractal dimension (FD) quantifies the time series complexity defined by its geometrical representation.

OBJECTIVE

The aim of this study was to evaluate the arterial pressure and diameter time series in order to assess the relationship between wave reflection and arterial pressure fractal dimension (FD).

METHODS

Simultaneous aortic pressure and diameter were measured in 14 conscious dogs. A pair of ultrasonic crystals, a pressure microtransducer and a pneumatic cuff occluder were positioned in the upper third of the descending aorta.

RESULTS

Total reflection induced by the occlusion maneuver decreased FD concomitant to the aortic stiffening.

CONCLUSION

Arterial pressure fractality is highly dependent on wave reflection.

'Time and time again': oscillatory and longitudinal time patterns in dialysis patients

Oscillatory and longitudinal time patterns play a major role in human physiology. In chronic hemodialysis patients, abnormalities in both time patterns have been observed, while time patterns can also influence the response of patients to the treatment. Abnormal oscillatory patterns have been observed for ultradian rhythms (cycle time <20 h), such as an impaired heart rate variability and circadian rhythms, as reflected by reduced day-night blood pressure differences. Conversely, the circadian rhythm of body temperature may influence the hemodynamic tolerance to the dialysis treatment. With regard to infradian (cycle time >28 h) rhythms, large seasonal differences in mortality, but also in blood pressure and interdialytic weight gain, have been observed in dialysis patients. The most important longitudinal pattern is the general reduction of life span in dialysis patients. One explanation of this phenomenon relates to the concept of accelerated aging in dialysis patients, for which there are various supportive arguments. From a phenomenological point of view, this concept translates into the high prevalence of frailty, even in young dialysis patients. A multidimensional approach appears necessary to adequately address this problem. In this review, the relevance of disturbed time patterns in dialysis patients is discussed. The changes may reflect an impairment or reduction in homeostatic/homeodynamic control in dialysis patients and also may have important prognostic and therapeutic implications.

A network-oriented perspective on cardiac calcium signaling

The normal contractile, electrical, and energetic function of the heart depends on the synchronization of biological oscillators and signal integrators that make up cellular signaling networks. In this review we interpret experimental data from molecular, cellular, and transgenic models of cardiac signaling behavior in the context of established concepts in cell network architecture and organization. Focusing on the cellular Ca(2+) handling machinery, we describe how the plasticity and adaptability of normal Ca(2+) signaling is dependent on dynamic network configurations that operate across a wide range of functional states. We consider how (mal)adaptive changes in signaling pathways restrict the dynamic range of the network such that it cannot respond appropriately to physiologic stimuli or perturbation. Based on these concepts, a model is proposed in which pathologic abnormalities in cardiac rhythm and contractility (e.g., arrhythmias and heart failure) arise as a consequence of progressive desynchronization and reduction in the dynamic range of the Ca(2+) signaling network. We discuss how a systems-level understanding of the network organization, cellular noise, and chaotic behavior may inform the design of new therapeutic modalities that prevent or reverse the disease-linked unraveling of the Ca(2+) signaling network.

Explanatory models are needed to integrate RCT and observational data with the patient's unique biology

In this review, we make the case for evidence-based medicine (EBM) to include models of disease underscored by evidence in order to integrate evidence, as it is currently defined, with the patient's unique biology. This would allow clinicians to use a pathophysiologic rationale, but underscoring the pathophysiological model with evidence would create an objective evidence base for extrapolating randomized controlled trial evidence. EBM encourages practitioners not to be passive receivers of information, but to question the information. By the same token, practitioners should not be passive executors of the process by which information is generated, appraised and applied, but should question the process. We use the historical examples of the evolution of EBM to show that its subordination of a pathophysiological perspective was unintentional, and of essential hypertension to illustrate the importance of disease models and the fact that evidence supporting them comes from many sources. We follow this with an illustration of the benefits a pathophysiological perspective can bring and a suggested model of how inclusion of pathophysiological models in the EBM approach would work. From a practical perspective, information cannot be integrated with the patient's unique biology without knowledge of that biology; this is why EBM is currently so silent on how to carry out its fourth stage. It is also clear that, regardless of whether a philosophical or practical definition of evidence is used, pathophysiology is evidence and should be regarded as such.

Fractal immunology and immune patterning: potential tools for immune protection and optimization

Fractals are self-similar geometric patterns that are inherently embedded throughout nature. Their discovery and application have produced significant benefits across a wide variety of biomedical applications. Recently, complex physiological systems (e.g., neurological, respiratory, cardiovascular) have been shown to exhibit fractal dimensions that are capable of distinguishing among physiologic function versus dysfunction and, in turn, health versus disease. Additionally, fractal data suggest that the immune system operates under similar patterned relationships, and this is in keeping with the recent findings that immune-based diseases are organized according to specific patterns. This review considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain holistic information on immune-environment interactions. The potential uses of both synthetic and artificial immune systems for improved protection of the biological immune system are also discussed. The addition of holistic measures of immune status to currently collected biomarkers of immunotoxicity has the potential to increase the effectiveness of health risk assessment. The objective of extending fractal physiology analyses to the immune system would be to promote immune optimization as a public health benefit, which would include improved: (1) immunotoxicity testing and effective health risk reduction and (2) measures of effective immune management for children, adults, and aged individuals.