Chaos and chaos control in biology

Improved Mathematical Models of Parkinson's Disease with Hopf Bifurcation and Huntington's Disease with Chaos

Using delay differential equations to study mathematical models of Parkinson's disease and Huntington's disease is important to show how important it is for synchronization between basal ganglia loops to work together. We used the delay circuit RLC (resistor, inductor, capacitor) model to show how the direct pathway and the indirect pathway in the basal ganglia excite and inhibit the motor cortex, respectively. A term has been added to the mathematical model without time delay in the case of the hyperdirect pathway. It is proposed to add a non-linear term to adjust the synchronization. We studied Hopf bifurcation conditions for the proposed models. The desynchronization of response times between the direct pathway and the indirect pathway leads to different symptoms of Parkinson's disease. Tremor appears when the response time in the indirect pathway increases at rest. The simulation confirmed that tremor occurs and the motor cortex is in an inhibited state. The direct pathway can increase the time delay in the dopaminergic pathway, which significantly increases the activity of the motor cortex. The hyperdirect pathway regulates the activity of the motor cortex. The simulation showed bradykinesia occurs when we switch from one movement to another that is less exciting for the motor cortex. A decrease of GABA in the striatum or delayed excitation of the substantia nigra from the subthalamus may be a major cause of Parkinson's disease. An increase in the response time delay in one of the pathways results in the chaotic movement characteristic of Huntington's disease.

Food-limited plant-herbivore model: Bifurcations, persistence, and stability

This research paper delves into the two-dimensional discrete plant-herbivore model. In this model, herbivores are food-limited and affect the plants' density in their environment. Our analysis reveals that this system has equilibrium points of extinction, exclusion, and coexistence. We analyze the behavior of solutions near these points and prove that the extinction and exclusion equilibrium points are globally asymptotically stable in certain parameter regions. At the boundary equilibrium, we prove the existence of transcritical and period-doubling bifurcations with stable two-cycle. Transcritical bifurcation occurs when the plant's maximum growth rate or food-limited parameter reaches a specific boundary. This boundary serves as an invasion boundary for populations of plants or herbivores. At the interior equilibrium, we prove the occurrence of transcritical, Neimark-Sacker, and period-doubling bifurcations with an unstable two-cycle. Our research also establishes that the system is persistent in certain regions of the first quadrant. We demonstrate that the local asymptotic stability of the interior equilibrium does not guarantee the system's persistence. Bistability exists between boundary attractors (logistic dynamics) and interior equilibrium for specific parameters' regions. We conclude that changes to the food-limitation parameter can significantly alter the system's dynamic behavior. To validate our theoretical findings, we conduct numerical simulations.

A clinical practice review of therapeutic movement-based anterior cruciate ligament reconstruction return to sports bridge program: the biological, biomechanical and behavioral rationale

This clinical practice review describes the biological, biomechanical and behavioral rationale behind a return to sport bridge program used predominantly with non-elite, youth and adolescent high school and college athletes following anterior cruciate ligament (ACL) reconstruction. Post-physiotherapy, this program has produced outcomes that meet or exceed previous reports. With consideration for athletic identity and the Specific Adaptations to Imposed Demands (SAID) principle, the early program focus was on restoring non-impaired bilateral lower extremity joint mobility and bi-articular musculotendinous extensibility. Building on this foundation, movement training education, fundamental bilateral lower extremity strength and power, and motor learning was emphasized with use of external focus cues and ecological dynamics-social cognition considerations. Plyometric and agility tasks were integrated to enhance fast twitch muscle fiber recruitment, anaerobic metabolic energy system function, and fatigue resistance. The ultimate goal was to achieve the lower extremity neuromuscular control and activation responsiveness needed for bilateral dynamic knee joint stability. The rationale and conceptual basis of selected movement tasks and general philosophy of care concepts are described and discussed in detail. Based on the previously reported efficacy of this movement-based therapeutic exercise program we recommend that supplemental programs such as this become standard practice following release from post-surgical physiotherapy and before return to sports decision-making.

On the qualitative study of a discrete-time phytoplankton-zooplankton model under the effects of external toxicity in phytoplankton population

The current manuscript studies a discrete-time phytoplankton-zooplankton model with Holling type-II response. The original model is modified by considering the condition that the phytoplankton population is getting infected with an external toxic substance. To obtain the discrete counterpart from a continuous-time system, Euler's forward method is applied. Moreover, a consistent discrete-time phytoplankton-zooplankton model is obtained by using a nonstandard difference scheme. The boundedness character for every positive solution is discussed, and the local stability of obtained system about each of its fixed points is discussed. The existence of period-doubling bifurcation at a positive equilibrium point is discussed for the discrete system obtained by Euler's forward method. In addition, the comparison of the consistent discrete-time version with its inconsistent counterpart is provided. It is proved that the discrete-time system obtained by using a nonstandard scheme is dynamically consistent as there is no chance for the existence of period-doubling bifurcation in that system. In order to control the period-doubling bifurcation and Neimark-Sacker bifurcation, an improved hybrid control strategy is applied. Finally, we have provided some interesting numerical examples to explain our theoretical results.

Chaotic and stochastic dynamics of epileptiform-like activities in sclerotic hippocampus resected from patients with pharmacoresistant epilepsy

The types of epileptiform activity occurring in the sclerotic hippocampus with highest incidence are interictal-like events (II) and periodic ictal spiking (PIS). These activities are classified according to their event rates, but it is still unclear if these rate differences are consequences of underlying physiological mechanisms. Identifying new and more specific information related to these two activities may bring insights to a better understanding about the epileptogenic process and new diagnosis. We applied Poincaré map analysis and Recurrence Quantification Analysis (RQA) onto 35 in vitro electrophysiological signals recorded from slices of 12 hippocampal tissues surgically resected from patients with pharmacoresistant temporal lobe epilepsy. These analyzes showed that the II activity is related to chaotic dynamics, whereas the PIS activity is related to deterministic periodic dynamics. Additionally, it indicates that their different rates are consequence of different endogenous dynamics. Finally, by using two computational models we were able to simulate the transition between II and PIS activities. The RQA was applied to different periods of these simulations to compare the recurrences between artificial and real signals, showing that different ranges of regularity-chaoticity can be directly associated with the generation of PIS and II activities.

Temporal lobe epilepsy (TLE) is the most prevalent type of epilepsy in adults and hippocampal sclerosis is the major pathophysiological substrate of pharmaco-refractory TLE. Different patterns of epileptiform-like activity have been described in human hippocampal sclerosis, but the standard analysis applied to characterize the activities usually do not consider the nonlinear features that epileptiform patterns exhibit. Here, using Poincaré map and Recurrence Quantitative Analysis we characterized the most prevalent type of epileptiform-like activities—interictal-like events (II) and periodic ictal spiking (PIS), recorded in vitro from resected hippocampi of pharmacoresistant patients with TLE—according to their levels of stochasticity, chaoticity and determinism. The II activities showed to be more chaotic with complex rhythmicity than PIS activities. The nonlinear dynamic differences between II and PIS leads us to conjecture that they are expressions of different seizure susceptibility. We also identified that each hippocampal subfield expresses II and PIS activities in a specific and different way. Finally, from the modulation of internal parameters of two computational models, we show the conversion of one type of activity into the other, showing how specific neuron networks synchronize over time, leading to II and PIS activities and then into a generalized seizure.

Qualitative analysis of a discrete-time phytoplankton-zooplankton model with Holling type-II response and toxicity

The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankton and zooplankton interaction with nonoverlapping generations. In such type of generations a new age group swaps the older group after regular intervals of time. Keeping in observation the dynamical reliability for continuous-time mathematical models, we convert a continuous-time phytoplankton-zooplankton model into its discrete-time counterpart by applying a dynamically consistent nonstandard difference scheme. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of obtained system about all its equilibrium points and show the existence of Neimark-Sacker bifurcation about unique positive equilibrium under some mathematical conditions. To control the Neimark-Sacker bifurcation, we apply a generalized hybrid control technique. For explanation of our theoretical results and to compare the dynamics of obtained discrete-time model with its continuous counterpart, we provide some motivating numerical examples. Moreover, from numerical study we can see that the obtained system and its continuous-time counterpart are stable for the same values of parameters, and they are unstable for the same parametric values. Hence the dynamical consistency of our obtained system can be seen from numerical study. Finally, we compare the modified hybrid method with old hybrid method at the end of the paper.

Chaotic activation of developmental signalling pathways drives idiopathic pulmonary fibrosis

Idiopathic pulmonary fibrosis (IPF) is characterised by an important remodelling of lung parenchyma. Current evidence indicates that the disease is triggered by alveolar epithelium activation following chronic lung injury, resulting in alveolar epithelial type 2 cell hyperplasia and bronchiolisation of alveoli. Signals are then delivered to fibroblasts that undergo differentiation into myofibroblasts. These changes in lung architecture require the activation of developmental pathways that are important regulators of cell transformation, growth and migration. Among others, aberrant expression of profibrotic Wnt-β-catenin, transforming growth factor-β and Sonic hedgehog pathways in IPF fibroblasts has been assessed. In the present review, we will discuss the transcriptional integration of these different pathways during IPF as compared with lung early ontogeny. We will challenge the hypothesis that aberrant transcriptional integration of these pathways might be under the control of a chaotic dynamic, meaning that a small change in baseline conditions could be sufficient to trigger fibrosis rather than repair in a chronically injured lung. Finally, we will discuss some potential opportunities for treatment, either by suppressing deleterious mechanisms or by enhancing the expression of pathways involved in lung repair. Whether developmental mechanisms are involved in repair processes induced by stem cell therapy will also be discussed.

Chemical Resonance, Beats, and Frequency Locking in Forced Chemical Oscillatory Systems

Resonance, beats, and synchronization are general and fundamental phenomena in physics. Their existence and their in-depth understanding in physical systems have led to several applications and technological developments shaping our world today. Here we show the existence of chemical resonance, chemical beats, and frequency locking phenomena in periodically forced pH oscillatory systems (sulfite-hydrogen peroxide and sulfite-formaldehyde-gluconolactone pH oscillatory systems). Periodic forcing was realized by a superimposed sinusoidal modulation on the inflow rates of the reagents in the continuous-flow stirred tank reactor. The dependence of the time period of beats follows the relation known from classical physics for forced physical oscillators. Our developed numerical model describes qualitatively the resonance and beat phenomena experimentally revealed. Application of periodic forcing in autonomously oscillating systems can provide new types of oscillators with a controllable frequency and new insight into controlling irregular chemical oscillation regimes.

Time Series Analysis of the Bacillus subtilis Sporulation Network Reveals Low Dimensional Chaotic Dynamics

Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering evidence for the chaotic behavior of the system, and by suggesting candidate molecules driving chaos in the system. The results of our chaos analysis can increase our understanding of the intricacies of the regulatory network under analysis, and suggest experimental work to refine our behavior of the mechanisms underlying B. subtilis sporulation initiation control.

QT variability improves risk stratification in patients with dilated cardiomyopathy

Recently it could be demonstrated that systolic and diastolic blood pressure variability (BPV) as well as segmented Poincare plot analysis (SPPA) contribute to risk stratification in patients suffering from dilated cardiomyopathy (DCM). The aim of this study was to improve the risk stratification applying a multivariate technique including QT variability (QTV). We enrolled and significantly separated 56 low risk and 13 high risk DCM patients by nearly all applied BPV and QTV methods, but not with traditional heart rate variability analysis. The optimum set of two indices calculating the multivariate discriminate analysis (DA) included one BPV index calculated by symbolic dynamics method (DBP(Shannon)) and one index calculated from QTV (QTV(log)) achieving an area under the receiver operating characteristics curve (AUC) of 92%, sensitivity of 92.3% and specificity of 89.3%. Performing only electrocardiogram analysis, the optimum multivariate approach including indices from segmented Poincaré plot analysis and QTV still achieved a remarkable AUC of 88.3%. Increasing the number of indices for multivariate DA up to three, we achieved an AUC of 95.7%, sensitivity of 100% and specificity of 85.7% including one clinical, one BPV and one QTV index. Summarizing, we identified DCM patients with an increased risk of sudden cardiac death applying QTV analysis in a multivariate approach.

The hypothalamic-pituitary-adrenal-leptin axis and metabolic health: a systems approach to resilience, robustness and control

Glucocorticoids contribute to obesity and metabolic syndrome; however, the mechanisms are unclear, and prognostic measures are unavailable. A systems level understanding of the hypothalamic-pituitary-adrenal (HPA)-leptin axis may reveal novel insights. Eighteen obese premenopausal women provided blood samples every 10 min over 24 h, which were assayed for cortisol, adrenocorticotropin releasing hormone (ACTH) and leptin. A published personalized HPA systems model was extended to incorporate leptin, yielding three parameters: (i) cortisol inhibitory feedback signalling, (ii) ACTH-adrenal signalling, and (iii) leptin-cortisol antagonism. We investigated associations between these parameters and metabolic risk profiles: fat and lean body mass (LBM; using dual-energy X-ray absorptiometry), and insulin resistance. Decreased cortisol inhibitory feedback signalling was significantly associated with greater fat (kg; p = 0.01) and insulin resistance (p = 0.03) but not LBM. Leptin significantly antagonized cortisol dynamics in eight women, who exhibited significantly lower 24 h mean leptin levels, LBM and higher ACTH-adrenal signalling nocturnally (all p < 0.05), compared with women without antagonism. Traditional neuroendocrine measures did not predict metabolic health, whereas a dynamic systems approach revealed that lower central inhibitory cortisol feedback signalling was significantly associated with greater metabolic risk. While exploratory, leptin-cortisol antagonism may reflect a 'neuroendocrine starvation' response.

Dynamic processes in regulation and some implications for biofeedback and biobehavioral interventions

Systems theory has long been used in psychology, biology, and sociology. This paper applies newer methods of control systems modeling for assessing system stability in health and disease. Control systems can be characterized as open or closed systems with feedback loops. Feedback produces oscillatory activity, and the complexity of naturally occurring oscillatory patterns reflects the multiplicity of feedback mechanisms, such that many mechanisms operate simultaneously to control the system. Unstable systems, often associated with poor health, are characterized by absence of oscillation, random noise, or a very simple pattern of oscillation. This modeling approach can be applied to a diverse range of phenomena, including cardiovascular and brain activity, mood and thermal regulation, and social system stability. External system stressors such as disease, psychological stress, injury, or interpersonal conflict may perturb a system, yet simultaneously stimulate oscillatory processes and exercise control mechanisms. Resonance can occur in systems with negative feedback loops, causing high-amplitude oscillations at a single frequency. Resonance effects can be used to strengthen modulatory oscillations, but may obscure other information and control mechanisms, and weaken system stability. Positive as well as negative feedback loops are important for system function and stability. Examples are presented of oscillatory processes in heart rate variability, and regulation of autonomic, thermal, pancreatic and central nervous system processes, as well as in social/organizational systems such as marriages and business organizations. Resonance in negative feedback loops can help stimulate oscillations and exercise control reflexes, but also can deprive the system of important information. Empirical hypotheses derived from this approach are presented, including that moderate stress may enhance health and functioning.

Effects of ganglionated plexi ablation on ventricular electrophysiological properties in normal hearts and after acute myocardial ischemia

BACKGROUND

Ganglionated plexi (GP) ablation has been shown to play an important role in atrial fibrillation (AF) initiation and maintenance. Also, GP ablation increases chances for prevention of AF recurrence. This study investigated the effects of GP ablation on ventricular electrophysiological properties in normal dog hearts and after acute myocardial ischemia (AMI).

METHODS

Fifty anesthetized dogs were assigned into normal heart group (n=16) and AMI heart group (n=34). Ventricular dynamic restitution, effective refractory period (ERP), electrical alternans and ventricular fibrillation threshold (VFT) were measured before and after GP ablation in the normal heart group. In the AMI heart group, the incidence of ventricular arrhythmias and VFT were determined.

RESULTS

In the normal heart group, GP ablation significantly prolonged ERP, facilitated electrical alternans but did not increase ERP dispersion, the slope of restitution curves and its spatial dispersion. Also, GP ablation did not cause significant change of VFT. In the AMI heart group, the incidence of ventricular arrhythmias after GP ablation was significantly higher than that in the control group or the GP plus stellate ganglion (SG) ablation group (P<0.05). Spontaneous VF occurred in 8/12, 1/10 and 2/12 dogs in the GP ablation group, the GP plus SG ablation group and the control group, respectively (P<0.05). VFT in the GP ablation group showed a decreased trend though a significant difference was not achieved compared with the control or the GP plus SG ablation group.

CONCLUSIONS

GP ablation increases the risk of ventricular arrhythmias in the AMI heart compared to the normal heart.

Anticipated synchronization and the predict-prevent control method in the FitzHugh-Nagumo model system

We study the synchronization region of two unidirectionally coupled FitzHugh-Nagumo systems, in a master-slave configuration, under the influence of external forcing terms. In the particular region where the slave anticipates the dynamics of the master system, we observe that the synchronization is robust to the different types of forcings. We then use the predict-prevent control method to suppress unwanted pulses in the master system by using the information of the slave output. We find that this method is more efficient than the direct control method based on the master dynamics. Finally, we observe that a perfect matching between the parameters of the master and the slave is not necessary for the control to be efficient. Moreover, this parameter mismatch can, in some cases, improve the control.

FINITE DIMENSIONAL STRUCTURE OF THE GPI DISCHARGE IN PATIENTS WITH PARKINSON'S DISEASE

Stochastic systems are infinitely dimensional and deterministic systems are low dimensional, while real systems lie somewhere between these two limit cases. If the calculation of a low (finite) dimension is in fact possible, one could conclude that the system under study is not purely random. In the present work we calculate the maximal Lyapunov exponent from interspike intervals time series recorded from the internal segment of the Globus Pallidusfrom patients with Parkinson's disease. We show the convergence of the maximal Lyapunov exponent at a dimension equal to 7 or 8, which is therefore our estimation of the embedding dimension for the system. For dimensions below 7 the observed behavior is what would be expected from a stochastic system or a complex system projecting onto lower dimensional spaces. The maximal Lyapunov exponent did not show any differences between tremor and akineto-rigid forms of the disease. However, it did decay with the value of motor Unified Parkinson's Disease Rating Scale -OFF scores. Patients with a more severe disease (higher UPDRS-OFF score) showed a lower value of the maximal Lyapunov exponent. Taken together, both indexes (the maximal Lyapunov exponent and the embedding dimension) remark the importance of taking into consideration the system's non-linear properties for a better understanding of the information transmission in the basal ganglia.

Quantification of compensatory processes of postnatal hypoxia in newborn piglets applying short-term nonlinear dynamics analysis

Background

Newborn mammals suffering from moderate hypoxia during or after birth are able to compensate a transitory lack of oxygen by adapting their vital functions. Exposure to hypoxia leads to an increase in the sympathetic tone causing cardio-respiratory response, peripheral vasoconstriction and vasodilatation in privileged organs like the heart and brain. However, there is only limited information available about the time and intensity changes of the underlying complex processes controlled by the autonomic nervous system.

Methods

In this study an animal model involving seven piglets was used to examine an induced state of circulatory redistribution caused by moderate oxygen deficit. In addition to the main focus on the complex dynamics occurring during sustained normocapnic hypoxia, the development of autonomic regulation after induced reoxygenation had been analysed. For this purpose, we first introduced a new algorithm to prove stationary conditions in short-term time series. Then we investigated a multitude of indices from heart rate and blood pressure variability and from bivariate interactions, also analysing respiration signals, to quantify the complexity of vegetative oscillations influenced by hypoxia.

Results

The results demonstrated that normocapnic hypoxia causes an initial increase in cardiovascular complexity and variability, which decreases during moderate hypoxia lasting one hour (p < 0.004). After reoxygenation, cardiovascular complexity parameters returned to pre-hypoxic values (p < 0.003), however not respiratory-related complexity parameters.

Conclusions

In conclusion, indices from linear and nonlinear dynamics reflect considerable temporal changes of complexity in autonomous cardio-respiratory regulation due to normocapnic hypoxia shortly after birth. These findings might be suitable for non-invasive clinical monitoring of hypoxia-induced changes of autonomic regulation in newborn humans.

Neuromechanical tuning of nonlinear postural control dynamics

Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

Transient response analysis of the eukaryotic chemosensory system to intra-cellular fluctuations

Like prokaryotic cells, those of eukaryotes are also subjected to noise from within the cells. While the cells have a built-in mechanism to attenuate the noise, conditions may arise where this is beyond the cell's ability to regulate. Start-up perturbations and those induced by metabolic shifts are examples of such situations. Then, it becomes useful to understand how the cells respond. For a eukaryotic chemosensory system, this has been studied by applying response coefficient analysis to a recent model. With even three dependent variables - an activator, an inhibitor, and a response element - the response coefficients differ widely with time and from one variable to another. These differences are interpreted in terms of the chemosensory mechanism and its robustness. The results complement similar recent studies of Escherichia coli chemotaxis, thus supporting their credibility and versatility.

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.

Beyond the oncogene paradigm: understanding complexity in cancerogenesis

In the past decades, an enormous amount of precious information has been collected about molecular and genetic characteristics of cancer. This knowledge is mainly based on a reductionistic approach, meanwhile cancer is widely recognized to be a 'system biology disease'. The behavior of complex physiological processes cannot be understood simply by knowing how the parts work in isolation. There is not solely a matter how to integrate all available knowledge in such a way that we can still deal with complexity, but we must be aware that a deeply transformation of the currently accepted oncologic paradigm is urgently needed. We have to think in terms of biological networks: understanding of complex functions may in fact be impossible without taking into consideration influences (rules and constraints) outside of the genome. Systems Biology involves connecting experimental unsupervised multivariate data to mathematical and computational approach than can simulate biologic systems for hypothesis testing or that can account for what it is not known from high-throughput data sets. Metabolomics could establish the requested link between genotype and phenotype, providing informations that ensure an integrated understanding of pathogenic mechanisms and metabolic phenotypes and provide a screening tool for new targeted drug.

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.

The sociobiologic integrative model (SBIM): enhancing the integration of sociobehavioral, environmental, and biomolecular knowledge in urban health and disparities research

Disentangling the myriad determinants of disease, within the context of urban health or health disparities, requires a transdisciplinary approach. Transdisciplinary approaches draw on concepts from multiple scientific disciplines to develop a novel, integrated perspective from which to conduct scientific investigation. Most historic and contemporary conceptual models of health were derived either from the sociobehavioral sciences or the biomolecular sciences. Those models deriving from the sociobehavioral sciences generally lack detail on involved biological mechanisms whereas those derived from the biomolecular sciences largely do not consider socioenvironmental determinants. As such, advances in transdisciplinary characterizations of health in complex systems like the urban environment or health disparities may be impeded. This paper suggests a sociobiologic organizing model that encourages a multilevel, integrative perspective in the study of urban health and health disparities.

Adaptive targeting of chaotic response in periodically stimulated neural systems

We demonstrate a technique for the enhancement of chaos in a computational model of a periodically stimulated excitable neuron. "Anticontrol" of chaos is achieved through intermittent adaptive intervention, which is based on finite-time Lyapunov exponents measured from the time series. Our results suggest that an adaptive strategy for chaos anticontrol is viable for increasing the complexity in physiological systems that are typically both noisy and nonstationary.

Dynamic control by sinusoidal perturbation and by Gaussian noise of a system of two nonlinear oscillators: computation and experimental results

In this paper we report numerical and experimental studies of the dynamic control of the inter-anode plasma of a double electrical discharge and of a system of two coupled nonlinear oscillators modeling this plasma. We compare the transition between chaotic dynamics and periodic dynamics induced by a sinusoidal perturbation and by small-dispersion Gaussian noise. Besides considerable differences between the effect of the two types of perturbation we also find important similarities. For small amplitude, both the sinusoidal and the white noise perturbations can induce the system to change from chaotic to regular dynamics. In the case of sinusoidal perturbation, the transition time from the chaotic to regular state has a definite duration that depends on the values of the perturbation parameters. The suppression of the perturbation has no influence on the state - the system remains in the same regular state. Subsequent reinstatement of the same type of perturbation with the same amplitude does not change the periodic state of the system but, for considerably higher amplitude, the system is switched back to its chaotic state. For moderate-amplitude sinusoidal perturbation, intermittent transitions between the chaotic and regular states is observed. Most of these predictions of the model have been observed experimentally in a system of two coupled electrical discharges. Our results suggest practical methods that can be used for controlling the discharge plasma dynamics.

Complexity science and homeopathy: a synthetic overview

Homeopathy is founded on 'holistic' and 'vitalistic' paradigms, which may be interpreted--at least in part--in terms of a framework provided by the theory of dynamic systems and of complexity. The conceptual models and some experimental findings from complexity science may support the paradoxical claims of similia principle and of dilution/dynamization effects. It is argued that better appreciation of three main properties of complex systems: non-linearity, self-organization, and dynamicity, will not only add to our basic understanding of homeopathic phenomena but also illuminate new directions for experimental investigations and therapeutic settings.

The Electrical Restitution Curve Revisited:

The electrical restitution curve (ERC) traditionally describes the recovery of action potential duration (APD) as a function of the interbeat interval or, more correctly, the diastolic interval (DI). Often overlooked in modeling studies, the normal ventricular ERC is triphasic, starting with a steep initial recovery at the shortest DIs, a transient decline, and a final asymptotic rise to a plateau phase reached at long DIs. Recent studies have proposed that it would be advantageous to lower the slope of the ERC by drug intervention, as this might reduce the potential for electrical alternans and ventricular fibrillation. This review discusses the pros and cons of a flat versus steep slope of the ERC and draws attention to mechanisms thatjustify the (physiologically) steep slope, rather than a flat slope, as a better design against arrhythmias. Five potential mechanisms are discussed, which allows for a different interpretation of the effect of the slope on arrhythmogenicity. The most important appears to be the physiologic rate adaptive shortening of APD that, by reciprocal lengthening of the DI, allows the subsequent APD to move more quickly from the steep initial ERC phase onto the flat phase. A less steep initial ERC phase would protract the transition toward more fully recovered APD and, in fact, may perpetuate electrical alternans. The triphasic ERC time course in normal myocardium cannot be explained by or fitted to single exponentials or single ion channel recovery kinetics. A simple tri-ionic model is suggested that may help explain the shape of the ERC at various repolarization levels and place APD recovery into perspective with intracellular calcium recycling and recovery of contractile force.

Is there chaos in the brain? II. Experimental evidence and related models

The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The methods used in each of these studies have almost invariably combined the analysis of experimental data with simulations using formal models, often based on modified Huxley and Hodgkin equations and/or of the Hindmarsh and Rose models of bursting neurons. Due to technical limitations, the results of these simulations have prevailed over experimental ones in studies on the nonlinear properties of large cortical networks and higher brain functions. Yet, and although a convincing proof of chaos (as defined mathematically) has only been obtained at the level of axons, of single and coupled cells, convergent results can be interpreted as compatible with the notion that signals in the brain are distributed according to chaotic patterns at all levels of its various forms of hierarchy. This chronological account of the main landmarks of nonlinear neurosciences follows an earlier publication [Faure, Korn, C. R. Acad. Sci. Paris, Ser. III 324 (2001) 773-793] that was focused on the basic concepts of nonlinear dynamics and methods of investigations which allow chaotic processes to be distinguished from stochastic ones and on the rationale for envisioning their control using external perturbations. Here we present the data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system. We first provide a short mathematical description of the models of excitable cells and of the different modes of firing of bursting neurons (Section 1). The deterministic behavior reported in giant axons (principally squid), in pacemaker cells, in isolated or in paired neurons of Invertebrates acting as coupled oscillators is then described (Section 2). We also consider chaotic processes exhibited by coupled Vertebrate neurons and of several components of Central Pattern Generators (Section 3). It is then shown that as indicated by studies of synaptic noise, deterministic patterns of firing in presynaptic interneurons are reliably transmitted, to their postsynaptic targets, via probabilistic synapses (Section 4). This raises the more general issue of chaos as a possible neuronal code and of the emerging concept of stochastic resonance Considerations on cortical dynamics and of EEGs are divided in two parts. The first concerns the early attempts by several pioneer authors to demonstrate chaos in experimental material such as the olfactory system or in human recordings during various forms of epilepsies, and the belief in 'dynamical diseases' (Section 5). The second part explores the more recent period during which surrogate-testing, definition of unstable periodic orbits and period-doubling bifurcations have been used to establish more firmly the nonlinear features of retinal and cortical activities and to define predictors of epileptic seizures (Section 6). Finally studies of multidimensional systems have founded radical hypothesis on the role of neuronal attractors in information processing, perception and memory and two elaborate models of the internal states of the brain (i.e. 'winnerless competition' and 'chaotic itinerancy'). Their modifications during cognitive functions are given special attention due to their functional and adaptive capabilities (Section 7) and despite the difficulties that still exist in the practical use of topological profiles in a state space to identify the physical underlying correlates. The reality of 'neurochaos' and its relations with information theory are discussed in the conclusion (Section 8) where are also emphasized the similarities between the theory of chaos and that of dynamical systems. Both theories strongly challenge computationalism and suggest that new models are needed to describe how the external world is represented in the brain.

Heart rate variability: a noninvasive approach to measure stress in calves and cows

The aim of this study was to evaluate the usefulness of heart rate variability (HRV) and its specific parameters as a new approach to assess stress load in cattle. We recorded HRV in 52 calves in three groups and in 31 cows in two groups. In calves we divided Group 1 with no obvious stress load (n=18), Group 2 with external stress load (n=17), and Group 3 with internal stress load from sickness (n=17). In cattle we divided lactating cows (n=21) and nonlactating cows (n=10). HRV parameters were analyzed in the time domain and in the frequency domain. Moreover, we applied Recurrence Quantification Analysis (RQA) to quantify nonlinear components of HRV. In calves, linear HRV parameter decreased from Group 1 to Group 3 (P<.05). However, not a single parameter showed significant differences regarding all three groups. The value of all nonlinear measurements increased at the same time (P<.05). The only parameter that exhibited significant differences between all three groups was the longest diagonal line segment in the recurrence plot (L(MAX)) which is inversely related to the Lyapunov exponent. We did not find differences concerning the linear HRV parameters between the two groups in the cows. The nonlinear parameter Determinism showed significant higher values in lactating cows compared to nonlactating cows. The importance of particular HRV-parameters was tested by applying a discriminant analysis approach. In calves and cattle nonlinear parameters were most important to indicate the level of stress load on the animals. Based on the results we assume HRV to be a valuable physiological indicator for stress load in animals. Whereas linear parameters of HRV are supposed to be useful to separate qualitative different level of stress, nonlinear components of HRV distinguish quantitative different challenges for the animals.

Optical tomographic imaging of dynamic features of dense-scattering media

Methods used in optical tomography have thus far proven to produce images of complex target media (e.g., tissue) having, at best, relatively modest spatial resolution. This presents a challenge in differentiating artifact from true features. Further complicating such efforts is the expectation that the optical properties of tissue for any individual are largely unknown and are likely to be quite variable due to the occurrence of natural vascular rhythms whose amplitudes are sensitive to a host of autonomic stimuli that are easily induced. We recognize, however, that rather than frustrating efforts to validate the accuracy of image features, the time-varying properties of the vasculature can be exploited to aid in such efforts, owing to the known structure-dependent frequency response of the vasculature and to the fact that hemoglobin is a principal contrast feature of the vasculature at near-infrared wavelengths. To accomplish this, it is necessary to generate a time series of image data. In this report we have tested the hypothesis that through analysis of time-series data, independent contrast features can be derived that serve to validate, at least qualitatively, the accuracy of imaging data, in effect establishing a self-referencing scheme. A significant finding is the observation that analysis of such data can produce high-contrast images that reveal features that are mainly obscured in individual image frames or in time-averaged image data. Given the central role of hemoglobin in tissue function, this finding suggests that a wealth of new features associated with vascular dynamics can be identified from the analysis of time-series image data.

Restricted feedback control of one-dimensional maps

Dynamical control of biological systems is often restricted by the practical constraint of unidirectional parameter perturbations. We show that such a restriction introduces surprising complexity to the stability of one-dimensional map systems and can actually improve controllability. We present experimental cardiac control results that support these analyses. Finally, we develop new control algorithms that exploit the structure of the restricted-control stability zones to automatically adapt the control feedback parameter and thereby achieve improved robustness to noise and drifting system parameters.

Fractal analysis: an objective method for identifying atypical nuclei in dysplastic lesions of the cervix uteri

OBJECTIVES

Fractal geometry is a tool used to characterize irregularly shaped and complex figures. It can be used not only to generate biological structures (e.g., the human renal artery tree), but also to derive parameters such as the fractal dimension in order to quantify the shapes of structures. As such, it allows user-independent evaluation and does not rely on the experience level of the examiner.

METHODS

We applied a box-counting algorithm to determine the fractal dimension of atypical nuclei in dysplastic cervical epithelium. An automatic algorithm was used to determine the fractal dimension of nuclei in order to prevent errors from manual segmentation. Four groups of patients (CIN 1-3 and control) with 10 subjects each were examined. In total, the fractal dimensions of 1200 nuclei were calculated.

RESULTS

We found that the fractal dimensions of the nuclei increased as the degree of dysplasia increased. There were significant differences between control and atypical nuclei found by an analysis of variance. Atypical nuclei associated with CIN 1, CIN 2, and CIN 3 also differed significantly among these groups.

CONCLUSION

We conclude that the fractal dimension is a valuable tool for detecting irregularities in atypical nuclei of the cervix uteri and thus allows objective nuclear grading.

Chaos and the transition to ventricular fibrillation: a new approach to antiarrhythmic drug evaluation

Sudden cardiac death resulting from ventricular fibrillation can be separated into 2 components: initiation of tachycardia and degeneration of tachycardia to fibrillation. Clinical drug studies such as CAST and SWORD demonstrated that focusing exclusively on the first component is inadequate as a therapeutic modality. The hope for developing effective pharmacological therapy rests on a comprehensive understanding of the second component, the transition from tachycardia to fibrillation. We summarize evidence that the transition from tachycardia to fibrillation is a transition to spatiotemporal chaos, with similarities to the quasiperiodic transition to chaos seen in fluid turbulence. In this scenario, chaos results from the interaction of multiple causally independent oscillatory motions. Simulations in 2-dimensional cardiac tissue suggest that the destabilizing oscillatory motions during spiral-wave reentry arise from restitution properties of action potential duration and conduction velocity. The process of spiral-wave breakup in simulated cardiac tissue predicts remarkably well the sequence by which tachycardia degenerates to fibrillation in real cardiac tissue. Modifying action potential duration and conduction velocity restitution characteristics can prevent spiral-wave breakup in simulated cardiac tissue, suggesting that drugs with similar effects in real cardiac tissue may have antifibrillatory efficacy (the Restitution Hypothesis). If valid for the real heart, the Restitution Hypothesis will support a new paradigm for antiarrhythmic drug classification, incorporating an antifibrillatory profile based on effects on cardiac restitution and the traditional antitachycardia profile (classes 1 through 4).

Chaos theories and therapeutic commonalities among depression, Parkinson's disease, and cardiac arrhythmias

This report reviews and compares all therapies that have shown efficacy in depression and Parkinson's disease, although some are not in current use and others are at the experimental stage. They include pharmacological modification of neurotransmitter pathways, electroconvulsive therapy (ECT), sleep deprivation, psychosurgery, electrical stimulation through cerebral electrodes, and transcranial magnetic stimulation. Stemming from a pathophysiological model that stresses the brain as an open, complex, and nonlinear system, all therapies have been attributed a common mechanism of action. This report suggests that the therapeutic isomorphism is related to their ability to help the CNS deactivate cortical-subcortical circuits that are dysfunctionally coupled. These circuits are self-organized among neurons of their informational subsystem (rapid conduction) and modulating subsystem (slow conduction). Finally, this report extends the analysis and comparison of these therapies to some cardiac arrhythmias.

An investigation into the spatial relationship between complexity and motility within the oesophagus

Nonlinear analysis techniques have recently been used in the characterization of complex physiological signals seen in pathological disorders such as epilepsy and cardiac fibrillation. In this study a series of controlled swallows from an asymptomatic demonstration group was investigated using oesophageal manometry. The nonlinear measure of complexity, largest Lyapunov exponents and phase portraits were then used to explore the complexity of motility patterns at different points within the oesophagus. Results indicate greater complexity within the region of the striated muscle in the upper oesophagus than that observed within the region of smooth muscle in the lower oesophagus. Phase portraits showed that manometry patterns within the asymptomatic demonstration group could be quite different, highlighting the problems in clinical diagnosis. The characterization of motility disorders associated with complex manometry patterns such as diffuse oesophageal spasm (DOS) and nonspecific motility disorder (NOMD) still represents a diagnostic challenge. The use of nonlinear techniques enabling the quantitative and qualitative measurement of oesophageal complexity is considered in the classification of such disorders.

On the holistic approach in cellular and cancer biology: nonlinearity, complexity, and quasi-determinism of the dynamic cellular network

A keystone of the molecular reductionist approach to cellular biology is a specific deductive strategy relating genotype to phenotype-two distinct categories. This relationship is based on the assumption that the intermediary cellular network of actively transcribed genes and their regulatory elements is deterministic (i.e., a link between expression of a gene and a phenotypic trait can always be identified, and evolution of the network in time is predetermined). However, experimental data suggest that the relationship between genotype and phenotype is nonbijective (i.e., a gene can contribute to the emergence of more than just one phenotypic trait or a phenotypic trait can be determined by expression of several genes). This implies nonlinearity (i.e., lack of the proportional relationship between input and the outcome), complexity (i.e. emergence of the hierarchical network of multiple cross-interacting elements that is sensitive to initial conditions, possesses multiple equilibria, organizes spontaneously into different morphological patterns, and is controlled in dispersed rather than centralized manner), and quasi-determinism (i.e., coexistence of deterministic and nondeterministic events) of the network. Nonlinearity within the space of the cellular molecular events underlies the existence of a fractal structure within a number of metabolic processes, and patterns of tissue growth, which is measured experimentally as a fractal dimension. Because of its complexity, the same phenotype can be associated with a number of alternative sequences of cellular events. Moreover, the primary cause initiating phenotypic evolution of cells such as malignant transformation can be favored probabilistically, but not identified unequivocally. Thermodynamic fluctuations of energy rather than gene mutations, the material traits of the fluctuations alter both the molecular and informational structure of the network. Then, the interplay between deterministic chaos, complexity, self-organization, and natural selection drives formation of malignant phenotype. This concept offers a novel perspective for investigation of tumorigenesis without invalidating current molecular findings. The essay integrates the ideas of the sciences of complexity in a biological context.

Reproducibility of ventricular fibrillation characteristics in patients undergoing implantable cardioverter defibrillator implantation

INTRODUCTION

The purpose of this study was to evaluate the immediate reproducibility of local electrogram characteristics recorded during repeated episodes of induced ventricular fibrillation (VF) in patients undergoing implantable cardioverter defibrillator (ICD) implantation.

METHODS AND RESULTS

Power spectral analysis (using a fast Fourier transform algorithm) of electrograms recorded during 3 seconds of VF were analyzed in 24 patients undergoing ICD implantation using a Medtronic Transvene lead. Patients had 2 to 7 episodes of VF that were induced during defibrillation threshold testing. VF was induced by burst pacing (n = 20) or T wave shock (n = 4). Simultaneous electrograms during VF were recorded from a Medtronic Transvene lead with the following configurations: (1) a narrow spaced (12 mm) dedicated bipole used clinically for sensing; (2) a unipolar electrogram from the right ventricular coil; and (3) a widely spaced (18.3 mm) integrated bipole using the distal tip and the coil. Intraclass correlation coefficients (ICCs) were determined to examine the reproducibility of these VF characteristics among VF episodes in each patient. Recordings from both bipolar configurations had ICCs from 0.40 to 0.55, whereas unipolar recordings ICCs were below 0.40. Reproducibility was similar for dedicated and integrated recordings.

CONCLUSIONS

Frequency characteristics of repeated episodes of VF induced in the same subjects show fair-to-good but not excellent reproducibility. Bipolar recordings were far more reproducible than unipolar recordings, but both bipolar configurations had similar reproducibility. These findings have implications for both the pathophysiology of induced VF and the design of VF detection algorithms.

Low-dimensional dynamics in sensory biology. 1: Thermally sensitive electroreceptors of the catfish

We report the results of a search for evidence of periodic unstable orbits in the electroreceptors of the catfish. The function of these receptor organs is to sense weak external electric fields. In addition, they respond to the ambient temperature and to the ionic composition of the water. These quantities are encoded by receptors that make use of an internal oscillator operating at the level of the membrane potential. If such oscillators have three or more degrees of freedom, and at least one of which also exhibits a nonlinearity, they are potentially capable of chaotic dynamics. By detecting the existence of stable and unstable periodic orbits, we demonstrate bifurcations between noisy stable and chaotic behavior using the ambient temperature as a parameter. We suggest that the technique developed herein be regarded as an additional tool for the analysis of data in sensory biology and thus can be potentially useful in studies of functional responses to external stimuli. We speculate that the appearance of unstable orbits may be indicative of a state of heightened sensory awareness by the animal.

Controlling the dynamical behavior of a circle map model of the human heart

One-dimensional circle maps are good models for describing the nonlinear dynamical behavior of two interacting oscillators. They have been employed to characterize the interaction between a periodic external forcing stimulus and an in vitro preparation of chick embryonic cardiac cells. They have also been used to model some human cardiac arrythmias such as modulated ventricular parasystole. In this paper, we describe several techniques involving engineering feedback control theory applied to a circle map model of human heart parasystole. Through simulations of the mathematical model, we demonstrate that a desired target phase relationship between the normal sinus rhythm and an abnormal ectopic pacemaker can be achieved rapidly with low-level external stimulation applied to the system. Specifically, we elucidate the linear, self-tuning, and nonlinear feedback approaches to control. The nonlinear methods are the fastest and most accurate, yet the most complex and computationally expensive to implement of the three types. The linear approach is the easiest to implement but may not be accurate enough in real applications, and the self-tuning methods are a compromise between the other two. The latter was successful in tracking a variety of period-1, period-2, and period-3 target phase trajectories of the heart model.

Three-dimensional modelling of tumor-induced ovarian angiogenesis

It is now well established that unrestricted growth of tumors is dependent upon angiogenesis. However, previous studies on tumor growth have not yet revealed how the transition to an angiogenetic state in ovarian malignancy is reflected in the vascular architecture of the ovary. We report here our preliminary observations based upon three-dimensional imaging of normal and tumor-induced ovarian angiogenesis created with a computer-assisted three-dimensional interactive application. The findings suggest that tumor-induced angiogenesis creates a bizarre vascular architecture, with a possible link to chaotic behavior.