Dynamical diseases

Advances in Understanding Fractals in Affective and Anxiety Disorders

In this chapter, we review the research that has applied fractal measures to the study of the most common psychological disorders, that is, affective and anxiety disorders. Early studies focused on heart rate, but diverse measures have also been examined, from variations in subjective mood, or hand movements, to electroencephalogram or magnetoencephalogram data. In general, abnormal fractal dynamics in different physiological and behavioural outcomes have been observed in mental disorders. Despite the disparity of variables measured, fractal analysis has shown high sensitivity in discriminating patients from healthy controls. However, and because of this heterogeneity in measures, the results are not straightforward, and more studies are needed in this promising line.

Chaotic dynamics of the Hénon map and neuronal input-output: A comparison with neurophysiological data

In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson's and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input-output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher's information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity-entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.

HRV analysis: undependability of approximate entropy at locating optimum complexity in malnourished children

INTRODUCTION

Approximate Entropy is an extensively enforced metric to evaluate chaotic responses and irregularities of RR intervals sourced from an eletrocardiogram. However, to estimate their responses, it has one major problem - the accurate determination of tolerances and embedding dimensions. So, we aimed to overt this potential hazard by calculating numerous alternatives to detect their optimality in malnourished children.

MATERIALS AND METHODS

We evaluated 70 subjects split equally: malnourished children and controls. To estimate autonomic modulation, the heart rate was measured lacking any physical, sensory or pharmacologic stimuli. In the time series attained, Approximate Entropy was computed for tolerance (0.1→0.5 in intervals of 0.1) and embedding dimension (1→5 in intervals of 1) and the statistical significances between the groups by their Cohen's ds and Hedges's gs were totalled.

RESULTS

The uppermost value of statistical significance accomplished for the effect sizes for any of the combinations was -0.2897 (Cohen's ds) and -0.2865 (Hedges's gs). This was achieved with embedding dimension = 5 and tolerance = 0.3.

CONCLUSIONS

Approximate Entropy was able to identify a reduction in chaotic response via malnourished children. The best values of embedding dimension and tolerance of the Approximate Entropy to identify malnourished children were, respectively, embedding dimension = 5 and embedding tolerance = 0.3. Nevertheless, Approximate Entropy is still an unreliable mathematical marker to regulate this.

Autonomic Modulation in Duchenne Muscular Dystrophy During a Computer Task: A Prospective Transversal Controlled Trial Assessment by Non-linear Techniques

Introduction: Due to functional and autonomic difficulties faced by individuals with Duchenne Muscular Dystrophy (DMD), the use of assistive technology is critical to provide or facilitate functional abilities. The key objective was to investigate acute cardiac autonomic responses, by application of Heart Rate Variability (HRV), during computer tasks in subjects with DMD via techniques based on non-linear dynamics.

Method: HRV was attained via a Polar RS800CX. Then, was evaluated by Chaotic Global Techniques (CGT). Forty-five male subjects were included in the DMD group and age-matched with 45 in the healthy Typical Development (TD) control group. They were assessed for 20 min at rest sitting, and then 5 min whilst performing the maze task on a computer.

Results: Both TD and DMD subjects exhibited a significantly reduced HRV measured by chaotic global combinations when undertaking the computer maze paradigm tests. DMD subjects presented decreased HRV during rest and computer task than TD subjects.

Conclusion: While there is an impaired HRV in subjects with DMD, there remains an adaptation of the ANS during the computer tasks. The identification of autonomic impairment is critical, considering that the computer tasks in the DMD community may elevate their level of social inclusion, participation and independence.

Complexity Measures of Heart-Rate Variability in Amyotrophic Lateral Sclerosis with Alternative Pulmonary Capacities

OBJECTIVE

the complexity of heart-rate variability (HRV) in amyotrophic lateral sclerosis (ALS) patients with different pulmonary capacities was evaluated.

METHODS

We set these according to their pulmonary capacity, and specifically forced vital capacity (FVC). We split the groups according to FVC (FVC > 50% (n = 29) and FVC < 50% (n = 28)). In ALS, the presence of an FVC below 50% is indicative of noninvasive ventilation with two pressure levels and with the absence of other respiratory symptoms. As the number of subjects per group was different, we applied the unbalanced one-way analysis of variance (uANOVA1) test after three tests of normality, and effect size by Cohen's d to assess parameter significance.

RESULTS

with regard to chaotic global analysis, CFP4 (p < 0.001; d = 0.91), CFP5 (p = 0.0022; d = 0.85), and CFP6 (p = 0.0009; d = 0.92) were enlarged. All entropies significantly increased. Shannon (p = 0.0005; d = 0.98), Renyi (p = 0.0002; d = 1.02), Tsallis (p = 0.0004; d = 0.99), approximate (p = 0.0005; d = 0.97), and sample (p < 0.0001; d = 1.22). Detrended fluctuation analysis (DFA) (p = 0.0358) and Higuchi fractal dimension (HFD) (p = 0.15) were statistically inconsequential between the two groups.

CONCLUSIONS

HRV complexity in ALS subjects with different pulmonary capacities increased via chaotic global analysis, especially CFP5 and 3 out of 5 entropies.

Describing the evolution of myeloid-derived leucocytes in treated B-lineage paediatric acute lymphoblastic leukaemia with a data-driven granulocyte-monocyte-blast model

Acute lymphoblastic leukaemia (ALL) is associated with a compromised myeloid system. Understanding the state of granulopoiesis in a patient during treatment, places the clinician in an advantageous position. Mathematical models are aids able to present the clinician with insight into the behaviour of myeloid-derived leucocytes. The main objective of this investigation was to determine whether a proposed model of ALL during induction therapy would be a usable descriptor of the system. The model assumes the co-occurrence of the independent leukaemic and normal marrow populations. It is comprised of four delay-differential equations, capturing the fundamental characteristics of the blood and bone marrow myeloid leucocytes and B-lineage lymphoblasts. The effect of treatment was presumed to amplify cell loss within both populations. Clinical data was used to inform the construction, calibration and examination of the model. The model is promising-presenting a good foundation for the development of a clinical supportive tool. The predicted parameters and forecasts aligned with clinical expectations. The starting assumptions were also found to be sound. A comparative investigation highlighted the differing responses of similarly diagnosed patients during treatment and further testing on patient data emphasized patient specificity. Model examination recommended the explicit consideration of the suppressive effects of treatment on the normal population production. Additionally, patient-related factors that could have resulted in such different responses between patients need to be considered. The parameter estimates require refinement to incorporate the action of treatment. Furthermore, the myeloid populations require separate consideration. Despite the model providing explanation, incorporating these recommendations would enhance both model usability and predictive capacity.

Flickering of cardiac state before the onset and termination of atrial fibrillation

Complex dynamical systems can shift abruptly from a stable state to an alternative stable state at a tipping point. Before the critical transition, the system either slows down in its recovery rate or flickers between the basins of attraction of the alternative stable states. Whether the heart critically slows down or flickers before it transitions into and out of paroxysmal atrial fibrillation (PAF) is still an open question. To address this issue, we propose a novel definition of cardiac states based on beat-to-beat (RR) interval fluctuations derived from electrocardiogram data. Our results show the cardiac state flickers before PAF onset and termination. Prior to onset, flickering is due to a "tug-of-war" between the sinus node (the natural pacemaker) and atrial ectopic focus/foci (abnormal pacemakers), or the pacing by the latter interspersed among the pacing by the former. It may also be due to an abnormal autonomic modulation of the sinus node. This abnormal modulation may be the sole cause of flickering prior to termination since atrial ectopic beats are absent. Flickering of the cardiac state could potentially be used as part of an early warning or screening system for PAF and guide the development of new methods to prevent or terminate PAF. The method we have developed to define system states and use them to detect flickering can be adapted to study critical transition in other complex systems.

Vocal wow in an adapted reflex resonance model

Vocal wow and tremor are slow modulations of the voice presumed to result from integration of auditory and somatosensory feedback, respectively. This distinction has important implications for diagnosis and treatment of neurological disorders that may differentially impact these systems, but the underlying mechanisms remain poorly understood. An important contribution on this matter is the reflex resonance model [Titze et al. (2002). J. Acoust. Soc. Am. 111(5), 2272-2282], which demonstrates that a 4-7 Hz vibrato (or tremor) can indeed be elicited by adjusting feedback parameters in a simple model of laryngeal muscle activation, mediated by time-delayed somatosensory feedback. This paper expands on this model by incorporating an auditory feedback loop and shows that wow emerges as feedback parameters exceed critical values described by a Hopf bifurcation. The wow period increases with delay and is almost invariant with respect to gain for delays above 200 ms. Parametric formulas for recovering feedback parameters from the acoustic signal are presented. With both feedback loops in place, auditory and somatosensory parameters interact and alter vocal modulations. Model predictions are illustrated in two subjects, one with a diagnosis of multiple sclerosis and intermittent tremor. Findings suggest that phonatory instabilities provide considerable insight into normal and pathogenic changes to the sensorimotor control of voice.

Complexity of Cardiac Autonomic Modulation in Diabetes Mellitus: A New Technique to Perceive Autonomic Dysfunction

Backgound and aims. In this study we analyzed heart rate variability (HRV) via chaotic global techniques so as to discriminate diabetics from control subjects. Matherial and method. Chaotic global analysis of the RR-intervals from the electrocardiogram and preprocessing adjustments were undertaken. The effect of varying two parameters to adjust the Multi-Taper Method (MTM) power spectrum were evaluated. Then, cubic spline interpolations from 1Hz to 13Hz were applied whilst the spectral parameters were fixed. Precisely 1000 RR-intervals of data were recorded. Results. CFP1 and CFP3 are the only significant combinations of chaotic globals when the default standard conditions are enforced. MTM spectral adjustments and cubic spline interpolation are trivial at effecting the outcome between the two datasets. The most influencial constraint on the outcome is data length. Conclusion. Chaotic global analysis was offered as a reliable, low-cost and robust technique to detect autonomic dysfunction in subjects with diabetes mellitus.

Non-linear regulation of cardiac autonomic modulation in obese youths: interpolation of ultra-short time series

BACKGROUND

In this study, we applied ultra-short time series of interbeat intervals (RR-intervals) to evaluate heart rate variability through default chaotic global techniques with the purpose of discriminating obese youths from non-obese youth patients.

METHOD

Chaotic global analysis of the RR-intervals from the electrocardiogram and pre-processing adjustments was undertaken. The effect of cubic spline interpolations was assessed, while the spectral parameters remained fixed. Exactly, 125 RR-intervals of data were recorded.

RESULTS

CFP1, CFP3, and CFP6 were the only significant combinations of chaotic globals when the standard conditions were enforced and at the level p<0.01 (or <1%). These significances were acheived via Kruskal-Wallis and Cohen's ds effects sizes tests of significance after Anderson-Darling and Lilliefors statistical tests indicated non-normal distributions in the majority of cases. Adjustments of the cubic spline interpolation from 1 to 13 Hz were revealed to be inconsequential when measured by Kruskal-Wallis and Cohen's ds, regarding the outcome between the two datasets.

CONCLUSION

Chaotic global analysis was offered as a robust technique to distinguish autonomic dysfunction in obese youths. It can discriminate the two different groups using ultra-short data lengths, and no cubic spline interpolations need be applied.

Non-Linear Dynamical Analysis of Resting Tremor for Demand-Driven Deep Brain Stimulation

Parkinson's Disease (PD) is currently the second most common neurodegenerative disease. One of the most characteristic symptoms of PD is resting tremor. Local Field Potentials (LFPs) have been widely studied to investigate deviations from the typical patterns of healthy brain activity. However, the inherent dynamics of the Sub-Thalamic Nucleus (STN) LFPs and their spatiotemporal dynamics have not been well characterized. In this work, we study the non-linear dynamical behaviour of STN-LFPs of Parkinsonian patients using ε -recurrence networks. RNs are a non-linear analysis tool that encodes the geometric information of the underlying system, which can be characterised (for example, using graph theoretical measures) to extract information on the geometric properties of the attractor. Results show that the activity of the STN becomes more non-linear during the tremor episodes and that ε -recurrence network analysis is a suitable method to distinguish the transitions between movement conditions, anticipating the onset of the tremor, with the potential for application in a demand-driven deep brain stimulation system.

Integrative and theoretical research on the architecture of a biological system and its disorder

An organism stems from assemblies of a variety of cells and proteins. This complex system serves as a unit, and it exhibits highly sophisticated functions in response to exogenous stimuli that change over time. The complete sequencing of the entire human genome has allowed researchers to address the enigmas of life and disease at the gene- or molecular-based level. The consequence of such studies is the rapid accumulation of a multitude of data at multiple levels, ranging from molecules to the whole body, that has necessitated the development of entirely new concepts, tools, and methodologies to analyze and integrate these data. This necessity has given birth to systems biology, an advanced theoretical and practical research framework that has totally changed the directions of not only basic life science but also medicine. During the symposium of the 95th Annual Meeting of The Physiological Society of Japan 2018, five researchers reported on their respective studies on systems biology. The topics included reactions of drugs, ion-transport architecture in an epithelial system, multi-omics in renal disease, cardiac electrophysiological systems, and a software platform for computer simulation. In this review article these authors have summarized recent achievements in the field and discuss next-generation studies on health and disease.

Heart Rate Variability Analysis: Higuchi and Katz’s Fractal Dimensions in Subjects with Type 1 Diabetes Mellitus

Background and aims: Statistical markers are valuable when assessing physiological status over periods of time and in certain disease states. We assess if type 1 diabetes mellitus promote modification in the autonomic nervous system using the main two types of algorithms to estimate a Fractal Dimension: Higuchi and Katz.

Material and methods: 46 adults were divided into two equal groups. The autonomic evaluation consisted of recording heart rate variability (HRV) for 30 minutes in supine position in absence of any other stimuli. Fractal dimensions ought then able to determine which series of interbeat intervals are derived from diabetics’ or not. We then equated results to observe which assessment gave the greatest significance by One-way analysis of variance (ANOVA1), Kruskal-Wallis technique and Cohen’s d effect sizes.

Results: Katz’s fractal dimension is the most robust algorithm when assisted by a cubic spline interpolation (6 Hz) to increase the number of samples in the dataset. This was categorical after two tests for normality; then, ANOVA1, Kruskal-Wallis and Cohen’s d effect sizes (p≈0.01 and Cohen’s d=0.814143 –medium effect size).

Conclusion: Diabetes significantly reduced the chaotic response as measured by Katz’s fractal dimension. Katz’s fractal dimension is a viable statistical marker for subjects with type 1 diabetes mellitus.

From mind to molecules and back to mind-Metatheoretical limits and options for systems neuropsychiatry

Psychiatric illnesses like dementia are increasingly relevant for public health affairs. Neurobiology promises progress in diagnosis and treatment of these illnesses and exhibits a rapid increase of knowledge by new neurotechnologies. In order to find generic patterns in huge neurobiological data sets and by exploring formal brain models, non-linear science offers many examples of fruitful insights into the complex dynamics of neuronal information processing. However, it should be minded that neurobiology neither can bridge the explanatory gap between brain and mind nor can substitute psychological and psychiatric categories and knowledge. For instance, volition is impaired in many mental disorders. In experimental setups, a "preactional" brain potential was discovered that occurs 0.5 s before a consciously evoked motor action. Neglecting the specific experimental conditions, this finding was over-interpreted as the empirical falsification of the philosophical (!) concept of "free volition/will." In contrast, the psychology of volition works with models that are composed of several stage-related hierarchically nested mental process cycles that were never tested in obviously "theory-free" neurobiology. As currently neurobiology shows a network turn (or systemic turn), this is one good reason to enhance systemic approaches in theoretical psychology, independently from neurobiology that still lacks "theory." Cybernetic control loop models and system models should be integrated and elaborated and in turn could give new impulses to neuropsychology and neuropsychiatry that conceptually can more easily connect to a network-oriented neurobiology. In this program, the conceptual background of nonlinear science is essential to bridge gaps between neurobiology and psychiatry, defining a real "theoretical" field of neuropsychiatry.

Using visual stimuli to enhance gait control

Gait control challenges commonly coincide with vestibular dysfunction and there is a long history in using balance and gait activities to enhance functional mobility in this population. While much has been learned using traditional rehabilitation exercises, there is a new line of research emerging that is using visual stimuli in a very specific way to enhance gait control. For example, avatars can be created in an individualized manner to incorporate specific gait characteristics. The avatar could then be used as a visual stimulus to which the patient can synchronize their own gait cycle. This line of research builds upon the rich history of sensorimotor control research in which augmented sensory information (visual, haptic, or auditory) is used to probe, and even enhance, human motor control. This review paper focuses on gait control challenges in patients with vestibular dysfunction, provides a brief historical perspective on how various visual displays have been used to probe sensorimotor and gait control, and offers some recommendations for future research.

Risk Assessment of Diabetes Mellitus by Chaotic Globals to Heart Rate Variability via Six Power Spectra

Background: The priniciple objective here is to analyze cardiovascular dynamics in diabetic subjects by actions related to heart rate variability (HRV). The correlation of chaotic globals is vital to evaluate the probability of dynamical diseases.

Methods: Forty-six adults were split equally. The autonomic evaluation consisted of recording HRV for 30 minutes in supine position without any additional stimuli. “Chaotic globals” are then able to statistically determine which series of interbeat intervals are diabetic and which are not. Two of these chaotic globals, spectral Entropy and spectral Detrended fluctuation analysis were derived from six alternative power spectra: Welch, Multi-Taper Method, Covariance, Burg, Yule-Walker and the Periodogram. We then compared results to observe which power spectra provided the greatest significance by three statistical tests: One-way analysis of variance (ANOVA1); Kruskal-Wallis technique and the multivariate technique, principal component analysis (PCA).

Results: The Chaotic Forward Parameter One (CFP1) applying all three parameters is proven the most robust algorithm with Welch and MTM spectra enforced. This was proven following two tests for normality where ANOVA1 (p=0.09) and Kruskal-Wallis (p=0.03). Multivariate analysis revealed that two principal components represented 99.8% of total variance, a steep scree plot, with CFP1 the most influential parameter.

Conclusion: Diabetes reduced the chaotic response.

Dynamical disease: Challenges for nonlinear dynamics and medicine

Dynamical disease refers to illnesses that are associated with striking changes in the dynamics of some bodily function. There is a large literature in mathematics and physics which proposes mathematical models for the physiological systems and carries out analyses of the properties of these models using nonlinear dynamics concepts involving analyses of the stability and bifurcations of attractors. This paper discusses how these concepts can be applied to medicine.

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

Organization and identification of solutions in the time-delayed Mackey-Glass model

Multistability in the long term dynamics of the Mackey-Glass (MG) delayed model is analyzed by using an electronic circuit capable of controlling the initial conditions. The system's phase-space is explored by varying the parameter values of two families of initial functions. The evolution equation of the electronic circuit is derived and it is shown that, in the continuous limit, it exactly corresponds to the MG model. In practice, when using a finite set of capacitors, an excellent agreement between the experimental observations and the numerical simulations is manifested. As the delay is increased, different periodic or aperiodic solutions appear. We observe abundant periodic solutions that have the same period but a different alternation of peaks of dissimilar amplitudes and propose a novel symbolic method to classify these solutions.

Structural defects lead to dynamic entrapment in cardiac electrophysiology

Biological networks are typically comprised of many parts whose interactions are governed by nonlinear dynamics. This potentially imbues them with the ability to support multiple attractors, and therefore to exhibit correspondingly distinct patterns of behavior. In particular, multiple attractors have been demonstrated for the electrical activity of the diseased heart in situations where cardioversion is able to convert a reentrant arrhythmia to a stable normal rhythm. Healthy hearts, however, are typically resilient to abnormal rhythms. This raises the question as to how a healthy cardiac cell network must be altered so that it can support multiple distinct behaviors. Here we demonstrate how anatomic defects can give rise to multi-stability in the heart as a function of the electrophysiological properties of the cardiac tissue and the timing of activation of ectopic foci. This leads to a form of hysteretic behavior, which we call dynamic entrapment, whereby the heart can become trapped in aberrant attractor as a result of a transient change in tissue properties. We show that this can lead to a highly inconsistent relationship between clinical symptoms and underlying pathophysiology, which raises the possibility that dynamic entrapment may underlie other forms of chronic idiopathic illness.

Understanding migraine using dynamic network biomarkers

Background

Mathematical modeling approaches are becoming ever more established in clinical neuroscience. They provide insight that is key to understanding complex interactions of network phenomena, in general, and interactions within the migraine-generator network, in particular.

Purpose

In this study, two recent modeling studies on migraine are set in the context of premonitory symptoms that are easy to confuse for trigger factors. This causality confusion is explained, if migraine attacks are initiated by a transition caused by a tipping point.

Conclusion

We need to characterize the involved neuronal and autonomic subnetworks and their connections during all parts of the migraine cycle if we are ever to understand migraine. We predict that mathematical models have the potential to dismantle large and correlated fluctuations in such subnetworks as a dynamic network biomarker of migraine.

Dynamic mechanisms of neocortical focal seizure onset

Recent experimental and clinical studies have provided diverse insight into the mechanisms of human focal seizure initiation and propagation. Often these findings exist at different scales of observation, and are not reconciled into a common understanding. Here we develop a new, multiscale mathematical model of cortical electric activity with realistic mesoscopic connectivity. Relating the model dynamics to experimental and clinical findings leads us to propose three classes of dynamical mechanisms for the onset of focal seizures in a unified framework. These three classes are: (i) globally induced focal seizures; (ii) globally supported focal seizures; (iii) locally induced focal seizures. Using model simulations we illustrate these onset mechanisms and show how the three classes can be distinguished. Specifically, we find that although all focal seizures typically appear to arise from localised tissue, the mechanisms of onset could be due to either localised processes or processes on a larger spatial scale. We conclude that although focal seizures might have different patient-specific aetiologies and electrographic signatures, our model suggests that dynamically they can still be classified in a clinically useful way. Additionally, this novel classification according to the dynamical mechanisms is able to resolve some of the previously conflicting experimental and clinical findings.

According to the WHO fact sheet, epilepsy is a neurological disorder affecting about 50 million people worldwide. Even today 30% of epilepsy patients do not respond well to drug therapies. Neocortical focal epilepsy is a particular type of epilepsy in which drug treatments fail and surgical success rate is low. Hence, research is essential to improve the treatment of this type of epilepsy. Recent advances in brain recording methods have led to new observations regarding the nature of neocortical focal epilepsy. However, some of the observations appear to be contradictory. Here, we develop a computational modelling framework that can explain the different observations as different aspects of possible mechanisms that can all lead to seizure onset. Specifically, we classify three main conditions under which focal seizure onset can happen. This classification is clinically important, as our model predicts different treatment strategies for each class. We conclude that focal seizures are diverse, not only in their electrographic appearance and aetiology, but also in their onset mechanism. Combined multiscale recordings as well as stimulation studies are required to elucidate the onset mechanism in each patient. Our work provides the first classification of possible onset mechanism.

HRV Analysis: A Clinical and Diagnostic Tool in Chronic Obstructive Pulmonary Disease

This study's aim is to analyze heart rate dynamics in subjects with chronic obstructive pulmonary disease (COPD) by measures of heart rate variability (HRV). HRV is a simple and noninvasive measure of autonomic impulses. 38 adults were divided into two equal groups based on respiratory function: COPD and normal. HRV was monitored in the supine position for 30 minutes. After tests of normality, Kruskal-Wallis was used for the statistical analysis, with the level of significance set at P < 0.05. Principal component analysis identified two components representing 99.5% of total variance. Furthermore, it is suggested that the chaos forward parameter (CFP) which applies all three “chaotic globals” is the most influential, although others are statistically more significant. The COPD subjects exhibited a decrease in the CFP. COPD can be termed a dynamical condition, decreasing the chaotic response. The perceived benefits of such analysis include quantitative assessment and suitable pharmacological intervention in the respiratory condition, especially of other related dynamical diseases such as cardiac failure.

Migraine generator network and spreading depression dynamics as neuromodulation targets in episodic migraine

Migraine is a common disabling headache disorder characterized by recurrent episodes sometimes preceded or accompanied by focal neurological symptoms called aura. The relation between two subtypes, migraine without aura (MWoA) and migraine with aura (MWA), is explored with the aim to identify targets for neuromodulation techniques. To this end, a dynamically regulated control system is schematically reduced to a network of the trigeminal nerve, which innervates the cranial circulation, an associated descending modulatory network of brainstem nuclei, and parasympathetic vasomotor efferents. This extends the idea of a migraine generator region in the brainstem to a larger network and is still simple and explicit enough to open up possibilities for mathematical modeling in the future. In this study, it is suggested that the migraine generator network (MGN) is driven and may therefore respond differently to different spatio-temporal noxious input in the migraine subtypes MWA and MWoA. The noxious input is caused by a cortical perturbation of homeostasis, known as spreading depression (SD). The MGN might even trigger SD in the first place by a failure in vasomotor control. As a consequence, migraine is considered as an inherently dynamical disease to which a linear course from upstream to downstream events would not do justice. Minimally invasive and noninvasive neuromodulation techniques are briefly reviewed and their rational is discussed in the context of the proposed mechanism.

Quantifying memory in complex physiological time-series

In a time-series, memory is a statistical feature that lasts for a period of time and distinguishes the time-series from a random, or memory-less, process. In the present study, the concept of “memory length” was used to define the time period, or scale over which rare events within a physiological time-series do not appear randomly. The method is based on inverse statistical analysis and provides empiric evidence that rare fluctuations in cardio-respiratory time-series are ‘forgotten’ quickly in healthy subjects while the memory for such events is significantly prolonged in pathological conditions such as asthma (respiratory time-series) and liver cirrhosis (heart-beat time-series). The memory length was significantly higher in patients with uncontrolled asthma compared to healthy volunteers. Likewise, it was significantly higher in patients with decompensated cirrhosis compared to those with compensated cirrhosis and healthy volunteers. We also observed that the cardio-respiratory system has simple low order dynamics and short memory around its average, and high order dynamics around rare fluctuations.

Cyborg psychiatry to ensure agency and autonomy in mental disorders. A proposal for neuromodulation therapeutics

Neuromodulation therapeutics—as repeated Transcranial Magnetic Stimulation (rTMS) and neurofeedback—are valuable tools for psychiatry. Nevertheless, they currently face some limitations: rTMS has confounding effects on neural activation patterns, and neurofeedback fails to change neural dynamics in some cases. Here we propose how coupling rTMS and neurofeedback can tackle both issues by adapting neural activations during rTMS and actively guiding individuals during neurofeedback. An algorithmic challenge then consists in designing the proper recording, processing, feedback, and control of unwanted effects. But this new neuromodulation technique also poses an ethical challenge: ensuring treatment occurs within a biopsychosocial model of medicine, while considering both the interaction between the patients and the psychiatrist, and the maintenance of individuals' autonomy. Our solution is the concept of Cyborg psychiatry, which embodies the technique and includes a self-engaged interaction between patients and the neuromodulation device.

Towards dynamical network biomarkers in neuromodulation of episodic migraine

Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine.

Complexity and schizophrenia

Complexity estimators have been broadly utilized in schizophrenia investigation. Early studies reported increased complexity in schizophrenia patients, associated with a higher variability or "irregularity" of their brain signals. However, further investigations showed reduced complexities, thus introducing a clear divergence. Nowadays, both increased and reduced complexity values are reported. The explanation of such divergence is a critical issue to understand the role of complexity measures in schizophrenia research. Considering previous arguments a complementary hypothesis is advanced: if the increased irregularity of schizophrenia patients' neurophysiological activity is assumed, a "natural" tendency to increased complexity in EEG and MEG scans should be expected, probably reflecting an abnormal neuronal firing pattern in some critical regions such as the frontal lobes. This "natural" tendency to increased complexity might be modulated by the interaction of three main factors: medication effects, symptomatology, and age effects. Therefore, young, medication-naïve, and highly symptomatic (positive symptoms) patients are expected to exhibit increased complexities. More importantly, the investigation of these interacting factors by means of complexity estimators might help to elucidate some of the neuropathological processes involved in schizophrenia.

Scroll wave filaments self-wrap around unexcitable heterogeneities

Scroll waves are three-dimensional excitation vortices rotating around one-dimensional phase singularities called filaments. In experiments with a chemical reaction-diffusion system and in numerical simulations, we study the pinning of closed filament loops to inert cylindrical heterogeneities. We show that the filament wraps itself around the heterogeneity and thus avoids contraction and annihilation. This entwining steadily increases the total length of the pinned filament and reshapes the entire rotation backbone of the vortex. Self-pinning is fastest for thin cylinders with radii not much larger than the core of the unpinned rotor. The process ends when the filament is attached to the entire length of the cylinder. The possible importance of self-pinning in cardiac systems is discussed.

Phase space approach for modeling of epileptic dynamics

Epileptic electroencephalography recordings can be described in terms of four prototypic wave forms: fast sinusoidal oscillations, large slow waves, fast spiking, and spike waves. On the macroscopic level, these wave forms have been modeled by different mechanistic models which share canonical features. Here we derive a minimal model of excitatory and inhibitory processes with features common to all previous models. We can infer that at least three interacting processes are required to support the prototypic epileptic dynamics. Based on a separation of time scales we analyze the model in terms of interacting manifolds in phase space. This allows qualitative reverse engineering of all epileptic wave forms and transitions between them. We propose this method as a complement to traditional approaches to modeling epileptiform rhythms.

Brain oscillatory complexity across the life span

OBJECTIVE

Considering the increasing use of complexity estimates in neuropsychiatric populations, a normative study is critical to define the 'normal' behaviour of brain oscillatory complexity across the life span.

METHOD

This study examines changes in resting-state magnetoencephalogram (MEG) complexity - quantified with the Lempel-Ziv complexity (LZC) algorithm - due to age and gender in a large sample of 222 (100 males/122 females) healthy participants with ages ranging from 7 to 84 years.

RESULTS

A significant quadratic (curvilinear) relationship (p<0.05) between age and complexity was found, with LZC maxima being reached by the sixth decade of life. Once that peak was crossed, complexity values slowly decreased until late senescence. Females exhibited higher LZC values than males, with significant differences in the anterior, central and posterior regions (p<0.05).

CONCLUSIONS

These results suggest that the evolution of brain oscillatory complexity across the life span might be considered a new illustration of a 'normal' physiological rhythm.

SIGNIFICANCE

Previous and forthcoming clinical studies using complexity estimates might be interpreted from a more complete and dynamical perspective. Pathologies not only cause an 'abnormal' increase or decrease of complexity values but they actually 'break' the 'normal' pattern of oscillatory complexity evolution as a function of age.

Complexity analysis of spontaneous brain activity: effects of depression and antidepressant treatment

Magnetoencephalography (MEG) allows the real-time recording of neural activity and oscillatory activity in distributed neural networks. We applied a non-linear complexity analysis to resting-state neural activity as measured using whole-head MEG. Recordings were obtained from 20 unmedicated patients with major depressive disorder and 19 matched healthy controls. Subsequently, after 6 months of pharmacological treatment with the antidepressant mirtazapine 30 mg/day, patients received a second MEG scan. A measure of the complexity of neural signals, the Lempel-Ziv Complexity (LZC), was derived from the MEG time series. We found that depressed patients showed higher pre-treatment complexity values compared with controls, and that complexity values decreased after 6 months of effective pharmacological treatment, although this effect was statistically significant only in younger patients. The main treatment effect was to recover the tendency observed in controls of a positive correlation between age and complexity values. Importantly, the reduction of complexity with treatment correlated with the degree of clinical symptom remission. We suggest that LZC, a formal measure of neural activity complexity, is sensitive to the dynamic physiological changes observed in depression and may potentially offer an objective marker of depression and its remission after treatment.

Coexistence of exponentially many chaotic spin-glass attractors

A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N < 1, where P stands for the number of stored patterns, the chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.

PUPILLARY HIPPUS: AN UNRECOGNIZED EXAMPLE OF BIOLOGIC CHAOS

We analyzed the pupil size vs time from six subjects using pupilography and nonlinear techniques. The correlation dimensions ranged from 4.08 to 5.7. The Hurst exponents ranged from 0.132 to 0.546. All data sets contained at least one positive Lyapunov exponent. The use of surrogate yielded statistically significant differences for the correlation dimension. Phase space analysis yields a definite flow, and in subject two, period-doubling is evident. The accumulated evidence supports the notion that dynamics of pupil size are governed by deterministic chaos rather than a stochastic or linear process. This implies that one might discern between well and disease states using pupillography and that the dynamics can be mechanistically modeled.

Modeling the effector - regulatory T cell cross-regulation reveals the intrinsic character of relapses in Multiple Sclerosis

Background

The relapsing-remitting dynamics is a hallmark of autoimmune diseases such as Multiple Sclerosis (MS). Although current understanding of both cellular and molecular mechanisms involved in the pathogenesis of autoimmune diseases is significant, how their activity generates this prototypical dynamics is not understood yet. In order to gain insight about the mechanisms that drive these relapsing-remitting dynamics, we developed a computational model using such biological knowledge. We hypothesized that the relapsing dynamics in autoimmunity can arise through the failure in the mechanisms controlling cross-regulation between regulatory and effector T cells with the interplay of stochastic events (e.g. failure in central tolerance, activation by pathogens) that are able to trigger the immune system.

Results

The model represents five concepts: central tolerance (T-cell generation by the thymus), T-cell activation, T-cell memory, cross-regulation (negative feedback) between regulatory and effector T-cells and tissue damage. We enriched the model with reversible and irreversible tissue damage, which aims to provide a comprehensible link between autoimmune activity and clinical relapses and active lesions in the magnetic resonances studies in patients with Multiple Sclerosis. Our analysis shows that the weakness in this negative feedback between effector and regulatory T-cells, allows the immune system to generate the characteristic relapsing-remitting dynamics of autoimmune diseases, without the need of additional environmental triggers. The simulations show that the timing at which relapses appear is highly unpredictable. We also introduced targeted perturbations into the model that mimicked immunotherapies that modulate effector and regulatory populations. The effects of such therapies happened to be highly dependent on the timing and/or dose, and on the underlying dynamic of the immune system.

Conclusion

The relapsing dynamic in MS derives from the emergent properties of the immune system operating in a pathological state, a fact that has implications for predicting disease course and developing new therapies for MS.

The rise of hemodialysis machines: new technologies in minimizing cardiovascular complications

Hemodialysis (HD) is a life-saving treatment for more than 1,700,000 patients with chronic kidney disease (CKD) stage V. Every year the HD population becomes increasingly older (average age: 75 years) and more ill due to the associated comorbidities such as cardiovascular disease (heart failure, coronary heart disease and peripheral vascular disease), diabetes, hypertension and peripheral vascular disease. Most of the complications associated with HD involve the cardiovascular system. HD machines have been greatly improved over the last 30 years. We have moved from HD machines simply allowing extracorporeal circulation to high technological medical devices capable of very precisely controlling ultrafiltration, dialysis dose, the patient's core temperature, circulating plasma volume, plasma sodium and producing unlimited volumes of ultrapure dialysate. In this article, we will focus on some of the fundamental achievements in HD machine technology, with particular reference to monitoring tools and bioengineering approaches for biosignal analysis. We propose that along these lines of further development, HD machines in the future will enable a better online identification of patients at higher cardiovascular risk, thus allowing clinicians to select more appropriate treatment modalities and parameters.

Effects of Velocity and Limb Loading on the Coordination Between Limb Movements During Walking

The authors investigated the effects of velocity (increasing from 0.5 to 5.0 km/hr in steps of 0.5 km/hr) and limb loading on the coordination between arm and leg movements during treadmill walking in 7 participants. Both the consistency of the individual limb movements and the stability of their coordination increased with increasing velocity; the frequency coordination between arm and leg movements was 2:1 at the lower velocities and 1:1 at the higher velocities. The mass manipulation affected the individual limb movements but not their coordination, indicating that a stable walking pattern was preserved. The results differed qualitatively from those obtained in studies on bimanual interlimb coordination, implying that the dynamical principles identified therein are not readily applicable to locomotion.

Epilepsy as a dynamic disease: a tutorial of the past with an eye to the future

How can clinical epileptologists and computational neuroscientists learn to function together within the confines of interdisciplinary teams to develop new and more effective treatment strategies for epilepsy? Here we introduce epileptologists to the way modelers think about epilepsy as a dynamic disease. Not only is there terminology to be learned, but also it is necessary to identify those areas where clinical input might be expected to have the greatest impact. It is concluded that both groups have major roles to play in educating, evaluating, and shaping the direction of the efforts of each other.

An investigation of EEG dynamics in an animal model of temporal lobe epilepsy using the maximum Lyapunov exponent

Analysis of intracranial electroencephalographic (iEEG) recordings in patients with temporal lobe epilepsy (TLE) has revealed characteristic dynamical features that distinguish the interictal, ictal, and postictal states and inter-state transitions. Experimental investigations into the mechanisms underlying these observations require the use of an animal model. A rat TLE model was used to test for differences in iEEG dynamics between well-defined states and to test specific hypotheses: 1) the short-term maximum Lyapunov exponent (STL(max)), a measure of signal order, is lowest and closest in value among cortical sites during the ictal state, and highest and most divergent during the postictal state; 2) STL(max) values estimated from the stimulated hippocampus are the lowest among all cortical sites; and 3) the transition from the interictal to ictal state is associated with a convergence in STL(max) values among cortical sites. iEEGs were recorded from bilateral frontal cortices and hippocampi. STL(max) and T-index (a measure of convergence/divergence of STL(max) between recorded brain areas) were compared among the four different periods. Statistical tests (ANOVA and multiple comparisons) revealed that ictal STL(max) was lower (p<0.05) than other periods, STL(max) values corresponding to the stimulated hippocampus were lower than those estimated from other cortical regions, and T-index values were highest during the postictal period and lowest during the ictal period. Also, the T-index values corresponding to the preictal period were lower than those during the interictal period (p<0.05). These results indicate that a rat TLE model demonstrates several important dynamical signal characteristics similar to those found in human TLE and support future use of the model to study epileptic state transitions.

ABSENCE SEIZURES AS RESETTING MECHANISMS OF BRAIN DYNAMICS

To understand the increase in age-related incidence and frequency of absence seizures in the rat brain, we investigated the effect of these seizures on brain dynamics. This paper puts forward the hypothesis that age-related differences in the expression of absence seizures are associated with the ability of the seizures to reset brain dynamics.

Controlling the onset of Hopf bifurcation in the Hodgkin-Huxley model

It is a challenging problem to establish safe and simple therapeutic methods for various complicated diseases of the nervous system, particularly dynamical diseases such as epilepsy, Alzheimer's disease, and Parkinson's disease. From the viewpoint of nonlinear dynamical systems, a dynamical disease can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameter. Therefore, the theory of bifurcation control may have potential applications in the diagnosis and therapy of dynamical diseases. In this study, we employ a washout filter-aided dynamic feedback controller to control the onset of Hopf bifurcation in the Hodgkin-Huxley (HH) model. Specifically, by the control scheme, we can move the Hopf bifurcation to a desired point irrespective of whether the corresponding steady state is stable or unstable. In other words, we are able to advance or delay the Hopf bifurcation, so as to prevent it from occurring in a certain range of the externally applied current. Moreover, we can control the criticality of the bifurcation and regulate the oscillation amplitude of the bifurcated limit cycle. In the controller, there are only two terms: the linear term and the nonlinear cubic term. We show that while the former determines the location of the Hopf bifurcation, the latter regulates the criticality of the Hopf bifurcation. According to the conditions of the occurrence of Hopf bifurcation and the bifurcation stability coefficient, we can analytically deduce the linear term and the nonlinear cubic term, respectively. In addition, we also show that mixed-mode oscillations (MMOs), featuring slow action potential generation, which are frequently observed in both experiments and models of chemical and biological systems, appear in the controlled HH model. It is well known that slow firing rates in single neuron models could be achieved only by type-I neurons. However, the controlled HH model is still classified as a type-II neuron, as is the original HH model. We explain that the occurrence of MMOs can be related to the presence of the canard explosion where a small oscillation grows through a sequence of canard cycles to a relaxation oscillation as the control parameter moves through an interval of exponentially small width.

Dinâmica não-linear e psiquiatria: a natureza dinâmica das doenças mentais

A psiquiatria moderna adotou a postura reducionista de associar psicopatologia à fisiologia sináptica. Isto produziu avanços importantes na farmacoterapia dos transtornos mentais. Entretanto, a introdução de princípios da dinâmica não-linear promoveu uma mudança do enfoque sináptico para o enfoque das vias específicas patologicamente autônomas envolvidas nos fenômenos psicopatológicos. Esta tendência teve início nos anos 1990 e trouxe um conceito mais sistêmico de fisiopatologia e tratamento em psiquiatria.

Multistability in spiking neuron models of delayed recurrent inhibitory loops

We consider the effect of the effective timing of a delayed feedback on the excitatory neuron in a recurrent inhibitory loop, when biological realities of firing and absolute refractory period are incorporated into a phenomenological spiking linear or quadratic integrate-and-fire neuron model. We show that such models are capable of generating a large number of asymptotically stable periodic solutions with predictable patterns of oscillations. We observe that the number of fixed points of the so-called phase resetting map coincides with the number of distinct periods of all stable periodic solutions rather than the number of stable patterns. We demonstrate how configurational information corresponding to these distinct periods can be explored to calculate and predict the number of stable patterns.