Dynamical disease: Challenges for nonlinear dynamics and medicine

Coherent light scattering from cellular dynamics in living tissues

This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.

Stability and bifurcation analysis of Alzheimer's disease model with diffusion and three delays

A reaction-diffusion Alzheimer's disease model with three delays, which describes the interaction of β-amyloid deposition, pathologic tau, and neurodegeneration biomarkers, is investigated. The existence of delays promotes the model to display rich dynamics. Specifically, the conditions for stability of equilibrium and periodic oscillation behaviors generated by Hopf bifurcations can be deduced when delay σ (σ=σ1+σ2) or σ3 is selected as a bifurcation parameter. In addition, when delay σ and σ3 are selected as bifurcation parameters, the stability switching curves and the stable region are obtained by using an algebraic method, and the conditions for the existence of Hopf bifurcations can also be derived. The effects of time delays, diffusion, and treatment on biomarkers are discussed via numerical simulations. Furthermore, sensitivity analysis at multiple time points is drawn, indicating that different targeted therapies should be taken at different stages of development, which has certain guiding significance for the treatment of Alzheimer's disease.

Interoperable and explainable machine learning models to predict morbidity and mortality in acute neurological injury in the pediatric intensive care unit: secondary analysis of the TOPICC study

Background

Acute neurological injury is a leading cause of permanent disability and death in the pediatric intensive care unit (PICU). No predictive model has been validated for critically ill children with acute neurological injury.

Objectives

We hypothesized that PICU patients with concern for acute neurological injury are at higher risk for morbidity and mortality, and advanced analytics would derive robust, explainable subgroup models.

Methods

We performed a secondary subgroup analysis of the Trichotomous Outcomes in Pediatric Critical Care (TOPICC) study (2011-2013), predicting mortality and morbidity from admission physiology (lab values and vital signs in 6 h surrounding admission). We analyzed patients with suspected acute neurological injury using standard machine learning algorithms. Feature importance was analyzed using SHapley Additive exPlanations (SHAP). We created a Fast Healthcare Interoperability Resources (FHIR) application to demonstrate potential for interoperability using pragmatic data.

Results

1,860 patients had suspected acute neurological injury at PICU admission, with higher morbidity (8.2 vs. 3.4%) and mortality (6.2 vs. 1.9%) than those without similar concern. The ensemble regressor (containing Random Forest, Gradient Boosting, and Support Vector Machine learners) produced the best model, with Area Under the Receiver Operating Characteristic Curve (AUROC) of 0.91 [95% CI (0.88, 0.94)] and Average Precision (AP) of 0.59 [0.51, 0.69] for mortality, and decreased performance predicting simultaneous mortality and morbidity (0.83 [0.80, 0.86] and 0.59 [0.51, 0.64]); at a set specificity of 0.995, positive predictive value (PPV) was 0.79 for mortality, and 0.88 for mortality and morbidity. By comparison, for mortality, the TOPICC logistic regression had AUROC of 0.90 [0.84, 0.93], but substantially inferior AP of 0.49 [0.35, 0.56] and PPV of 0.60 at specificity 0.995. Feature importance analysis showed that pupillary non-reactivity, Glasgow Coma Scale, and temperature were the most contributory vital signs, and acidosis and coagulopathy the most important laboratory values. The FHIR application provided a simulated demonstration of real-time health record query and model deployment.

Conclusions

PICU patients with suspected acute neurological injury have higher mortality and morbidity. Our machine learning approach independently identified previously-known causes of secondary brain injury. Advanced modeling achieves improved positive predictive value in this important population compared to published models, providing a stepping stone in the path to deploying explainable models as interoperable bedside decision-support tools.

The time scales of irreversibility in spontaneous brain activity are altered in obsessive compulsive disorder

We study how obsessive-compulsive disorder (OCD) affects the complexity and time-reversal symmetry-breaking (irreversibility) of the brain resting-state activity as measured by magnetoencephalography (MEG). Comparing MEG recordings from OCD patients and age/sex matched control subjects, we find that irreversibility is more concentrated at faster time scales and more uniformly distributed across different channels of the same hemisphere in OCD patients than in control subjects. Furthermore, the interhemispheric asymmetry between homologous areas of OCD patients and controls is also markedly different. Some of these differences were reduced by 1-year of Kundalini Yoga meditation treatment. Taken together, these results suggest that OCD alters the dynamic attractor of the brain's resting state and hint at a possible novel neurophysiological characterization of this psychiatric disorder and how this therapy can possibly modulate brain function.

Phenomics in sport: Can emerging methodology drive advanced insights?

Methodologies in applied sport science have predominantly driven a reductionist grounding to component-specific mechanisms to drive athlete training and care. While linear mechanistic approaches provide useful insights, they have impeded progress in the development of more complex network physiology models that consider the temporal and spatial interactions of multiple factors within and across systems and subsystems. For this, a more sophisticated approach is needed and the development of such a methodological framework can be considered a Sport Grand Challenge. Specifically, a transdisciplinary phenomics-based scientific and modeling framework has merit. Phenomics is a relatively new area in human precision medicine, but it is also a developed area of research in the plant and evolutionary biology sciences. The convergence of innovative precision medicine, portable non-destructive measurement technologies, and advancements in modeling complex human behavior are central for the integration of phenomics into sport science. The approach enables application of concepts such as phenotypic fitness, plasticity, dose-response dynamics, critical windows, and multi-dimensional network models of behavior. In addition, profiles are grounded in indices of change, and models consider the athlete's performance or recovery trajectory as a function of their dynamic environment. This new framework is introduced across several example sport science domains for potential integration. Specific factors of emphasis are provided as potential candidate fitness variables and example profiles provide a generalizable modeling approach for precision training and care. Finally, considerations for the future are discussed, including scaling from individual athletes to teams and additional factors necessary for the successful implementation of phenomics.

Catastrophe Theory Applied to Neuropsychological Data: Nonlinear Effects of Depression on Financial Capacity in Amnestic Mild Cognitive Impairment and Dementia

Financial incapacity is one of the cognitive deficits observed in amnestic mild cognitive impairment and dementia, while the combined interference of depression remains unexplored. The objective of this research is to investigate and propose a nonlinear model that explains empirical data better than ordinary linear ones and elucidates the role of depression. Four hundred eighteen (418) participants with a diagnosis of amnestic MCI with varying levels of depression were examined with the Geriatric Depression Scale (GDS-15), the Functional Rating Scale for Symptoms of Dementia (FRSSD), and the Legal Capacity for Property Law Transactions Assessment Scale (LCPLTAS). Cusp catastrophe analysis was applied to the data, which suggested that the nonlinear model was superior to the linear and logistic alternatives, demonstrating depression contributes to a bifurcation effect. Depressive symptomatology induces nonlinear effects, that is, beyond a threshold value sudden decline in financial capacity is observed. Implications for theory and practice are discussed.

Modeling pulsativity in the hypothalamic-pituitary-adrenal hormonal axis

A new mathematical model for biological rhythms in the hypothalamic–pituitary–adrenal (HPA) axis is proposed. This model takes the form of a system of impulsive time-delay differential equations which include pulsatile release of adrenocorticotropin (ACTH) by the pituitary gland and a time delay for the release of glucocorticoid hormones by the adrenal gland. Numerical simulations demonstrate that the model’s response to periodic and circadian inputs from the hypothalamus are consistent with those generated by recent models which do not include a pulsatile pituitary. In contrast the oscillatory phenomena generated by the impulsive delay equation mode occur even if the time delay is zero. The observation that the time delay merely introduces a small phase shift suggesting that the effects of the adrenal gland are “downstream” to the origin of pulsativity. In addition, the model accounts for the occurrence of ultradian oscillations in an isolated pituitary gland. These observations suggest that principles of pulse modulated control, familiar to control engineers, may have an increasing role to play in understanding the HPA axis.

Introduction to Focus Issue: Dynamical disease: A translational approach

The concept of Dynamical Diseases provides a framework to understand physiological control systems in pathological states due to their operating in an abnormal range of control parameters: this allows for the possibility of a return to normal condition by a redress of the values of the governing parameters. The analogy with bifurcations in dynamical systems opens the possibility of mathematically modeling clinical conditions and investigating possible parameter changes that lead to avoidance of their pathological states. Since its introduction, this concept has been applied to a number of physiological systems, most notably cardiac, hematological, and neurological. A quarter century after the inaugural meeting on dynamical diseases held in Mont Tremblant, Québec [Bélair et al., Dynamical Diseases: Mathematical Analysis of Human Illness (American Institute of Physics, Woodbury, NY, 1995)], this Focus Issue offers an opportunity to reflect on the evolution of the field in traditional areas as well as contemporary data-based methods.

Postural instability via a loss of intermittent control in elderly and patients with Parkinson's disease: A model-based and data-driven approach

Postural instability is one of the major symptoms of Parkinson's disease. Here, we assimilated a model of intermittent delay feedback control during quiet standing into postural sway data from healthy young and elderly individuals as well as patients with Parkinson's disease to elucidate the possible mechanisms of instability. Specifically, we estimated the joint probability distribution of a set of parameters in the model using the Bayesian parameter inference such that the model with the inferred parameters can best-fit sway data for each individual. It was expected that the parameter values for three populations would distribute differently in the parameter space depending on their balance capability. Because the intermittent control model is parameterized by a parameter associated with the degree of intermittency in the control, it can represent not only the intermittent model but also the traditional continuous control model with no intermittency. We showed that the inferred parameter values for the three groups of individuals are classified into two major groups in the parameter space: one represents the intermittent control mostly for healthy people and patients with mild postural symptoms and the other the continuous control mostly for some elderly and patients with severe postural symptoms. The results of this study may be interpreted by postulating that increased postural instability in most Parkinson's patients and some elderly persons might be characterized as a dynamical disease.

An integrate-and-fire model for pulsatility in the neuroendocrine system

A model for pulsatility in neuroendocrine regulation is proposed which combines Goodwin-type feedback control with impulsive input from neurons located in the hypothalamus. The impulsive neural input is modeled using an integrate-and-fire mechanism; namely, inputs are generated only when the membrane potential crosses a threshold, after which it is reset to baseline. The resultant model takes the form of a functional-differential equation with continuous and impulsive components. Despite the impulsive nature of the inputs, realistic hormone profiles are generated, including ultradian and circadian rhythms, pulsatile secretory patterns, and even chaotic dynamics.

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.

Electrocortical dynamics differentiate athletes exhibiting low- and high- ACL injury risk biomechanics

Anterior cruciate ligament (ACL) injuries are physically and emotionally debilitating for athletes,while motor and biomechanical deficits that contribute to ACL injury have been identified, limited knowledge about the relationship between the central nervous system (CNS) and biomechanical patterns of motion has impeded approaches to optimize ACL injury risk reduction strategies. In the current study it was hypothesized that high-risk athletes would exhibit altered temporal dynamics in their resting state electrocortical activity when compared to low-risk athletes. Thirty-eight female athletes performed a drop vertical jump (DVJ) to assess their biomechanical risk factors related to an ACL injury. The athletes' electrocortical activity was also recorded during resting state in the same visit as the DVJ assessment. Athletes were divided into low- and high-risk groups based on their performance of the DVJ. Recurrence quantification analysis was used to quantify the temporal dynamics of two frequency bands previously shown to relate to sensorimotor and attentional control. Results revealed that high-risk participants showed more deterministic electrocortical behavior than the low-risk group in the frontal theta and central/parietal alpha-2 frequency bands. The more deterministic resting state electrocortical dynamics for the high-risk group may reflect maladaptive neural behavior-excessively stable deterministic patterning that makes transitioning among functional task-specific networks more difficult-related to attentional control and sensorimotor processing neural regions.

Uncovering complex central autonomic networks at rest: a functional magnetic resonance imaging study on complex cardiovascular oscillations

This study aims to uncover brain areas that are functionally linked to complex cardiovascular oscillations in resting-state conditions. Multi-session functional magnetic resonance imaging (fMRI) and cardiovascular data were gathered from 34 healthy volunteers recruited within the human connectome project (the '100-unrelated subjects' release). Group-wise multi-level fMRI analyses in conjunction with complex instantaneous heartbeat correlates (entropy and Lyapunov exponent) revealed the existence of a specialized brain network, i.e. a complex central autonomic network (CCAN), reflecting what we refer to as complex autonomic control of the heart. Our results reveal CCAN areas comprised the paracingulate and cingulate gyri, temporal gyrus, frontal orbital cortex, planum temporale, temporal fusiform, superior and middle frontal gyri, lateral occipital cortex, angular gyrus, precuneous cortex, frontal pole, intracalcarine and supracalcarine cortices, parahippocampal gyrus and left hippocampus. The CCAN visible at rest does not include the insular cortex, thalamus, putamen, amygdala and right caudate, which are classical CAN regions peculiar to sympatho-vagal control. Our results also suggest that the CCAN is mainly involved in complex vagal control mechanisms, with possible links with emotional processing networks.

Early warning signals for critical transitions in cardiopulmonary health, related to air pollution in an urban Chinese population

Respiratory, and cardio-cerebrovascular health-related diseases significantly threaten human health and together with air pollution form a complex pathophysiological system. Other complex biological systems show that increased variance and autocorrelations in time series may act as valid early warning signals for critical transitions. On population level, we determined the likelihood that increased variance and autocorrelation of hospital visit on cardiopulmonary disease preceded critical transitions in population health by human-pollution interactions. We investigated long-term hospital visits from a hospital in Nanjing City, China during 2006-2016 for the most important cardiopulmonary diseases likely to be influenced by air pollution: cerebrovascular accident disease (CVAD), coronary artery disease (CAD), chronic obstructive pulmonary disease (COPD), lung cancer disease (LCD), and the grouped categories of respiratory system disease (RESD) and cardio-cerebrovascular system disease (CCD). The time series of standard deviations (SDs) and autocorrelation at-lag-1 (AR-1) were studied as potential Early-Warning Indicators (EWIs) of transitions in population health. Elevated SDs provided an early warning for critical transitions in visit for LCD and overall CCD and CVAD, for the period of 2012-2013, after which a real transition of increased visit occurred for these disease categories. Statistical testing showed that these SDs were significantly increased (p < 0.1). The long-term air pollution together with intermittent pollution episodes may have triggered critical transitions in population health for cardiopulmonary disease. It is recommended to consider significant increases in variability in time series of relevant system parameters, such as visit, as early warning signs for future transitions in populations' health states.

Quantifying resilience of humans and other animals

All life requires the capacity to recover from challenges that are as inevitable as they are unpredictable. Understanding this resilience is essential for managing the health of humans and their livestock. It has long been difficult to quantify resilience directly, forcing practitioners to rely on indirect static indicators of health. However, measurements from wearable electronics and other sources now allow us to analyze the dynamics of physiology and behavior with unsurpassed resolution. The resulting flood of data coincides with the emergence of novel analytical tools for estimating resilience from the pattern of microrecoveries observed in natural time series. Such dynamic indicators of resilience may be used to monitor the risk of systemic failure across systems ranging from organs to entire organisms. These tools invite a fundamental rethinking of our approach to the adaptive management of health and resilience.

Is dynamic desaturation better than a static index to quantify the mortality risk in heart failure patients with Cheyne-Stokes respiration?

Cheyne-Stokes respiration (CSR) is a periodic, highly dynamic, respiratory pattern and a known comorbidity in congestive heart failure (CHF) patients. It is generally seen as an indicator for a negative prognosis, even if no distinction in degree is known or understood. This paper aims to improve on existing attempts by creating a quantification of the behavior of the dynamic desaturation process of oxygen in the blood. We performed this work on a cohort of 11 subjects with CHF, reduced left ventricular ejection fraction, and CSR. The dynamic desaturation process was evaluated according to changes to peripheral capillary oxygenation S p O 2 resulting from highly nonlinear relationships in the ventilatory system perturbed by periodic breathing. Hypoxaemic burden expressed as a static index T 90 was compared to a novel relative desaturation index R D I , developed in this paper. While T 90 represents a single value calculated using a static cut-off value of 90 % S p O 2 , the R D I is more sensitive to dynamic influences as it uses the specific maximum change in saturation for each CSR episode. The threshold of T 90 = 22 min per night as suggested by Oldenburg et al. could not be confirmed to predict survival, but all central apneas resulting in a relative desaturation of S p O 2 above a cut-off value of 8 % were a 100 % positive predictor of mortality. The R D I proved sufficiently stable in intraindividual measurements across CSR epochs. Across the cohort, it showed a bimodal distribution for the deceased group, indicative of a possible aetiological difference. Hence, it is our conclusion that a dynamic approach to analyse desaturation of oxygen during Cheyne-Stokes respiration is to be strongly favoured over a static approach to analysis.

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.

Resting-state brain correlates of cardiovascular complexity

While estimates of complex heartbeat dynamics have provided effective prognostic and diagnostic markers for a wide range of pathologies, brain correlates of complex cardiac measures in general and of complex sympatho-vagal dynamics in particular are still unknown. In this study we combine resting state functional Magnetic Resonance Imaging (fMRI) and physiological signal acquisition from 34 healthy subjects selected from the Human Connectome Project (HCP) repository with inhomogeneous point-process approximate and sample heartbeat entropy measures (ipApEn and ipSampEn) to investigate brain areas involved in complex cardiovascular control. Our results show that activity in the Temporal Gyrus, Frontal Orbital Cortex, Temporal Fusiform and Opercular cortices, Planum Temporale, and Paracingulate cortex are negatively correlated with ipApEn dynamics. Activity in the same cortical areas as well as in the Temporal Fusiform cortex are negatively correlated with ipSampEn dynamics. No significant positive correlations were found. These pioneering results suggest that cardiovascular complexity at rest is linked to a few specific cortical brain structures, including crucial areas connected with parasympathetic outflow. This corroborates the hypothesis of a multidimensional central network which controls nonlinear cardiac dynamics under a predominantly vagally-driven tone.

How Interpersonal Coordination Affects Individual Behavior (and Vice Versa): Experimental analysis and adaptive HKB model of social memory

How one behaves after interacting with a friend may not be the same as before the interaction. The present study investigated which spontaneous coordination patterns formed between two persons and whether a remnant of the interaction remained ("social memory"). Pairs of people sat face-to-face and continuously flexed index fingers while vision between partners was manipulated to allow or prevent information exchange. Trials consisted of three successive twenty-second intervals: without vision, with vision, and again without vision. Steady, transient, or absent phase coupling was observed during vision. In support of social memory, participants tended to remain near each other's movement frequency after the interaction ended. Furthermore, the greater the stability of interpersonal coordination, the more similar partners' post-interactional frequencies became. Proposing that social memory resulted from prior frequency adaptation, a model based on Haken-Kelso-Bunz oscillators reproduced the experimental findings, even for patterns observed on individual trials. Parametric manipulations revealed multiple routes to social memory through the interplay of adaptation and other model parameters. The experimental results, model, and interpretation motivate potential future research and therapeutic applications.

Analysis of generic coupling between EEG activity and PETCO2 in free breathing and breath-hold tasks using Maximal Information Coefficient (MIC)

Brain activations related to the control of breathing are not completely known. The respiratory system is a non-linear system. However, the relationship between neural and respiratory dynamics is usually estimated through linear correlation measures, completely neglecting possible underlying nonlinear interactions. This study evaluate the linear and nonlinear coupling between electroencephalographic (EEG) signal and variations in carbon dioxide (CO₂) signal related to different breathing task. During a free breathing and a voluntary breath hold tasks, the coupling between EEG power in nine different brain regions in delta (1–3 Hz) and alpha (8–13 Hz) bands and end-tidal CO₂ (P_ET CO₂) was evaluated. Specifically, the generic associations (i.e. linear and nonlinear correlations) and a “pure” nonlinear correlations were evaluated using the maximum information coefficient (MIC) and MIC-ρ² between the two signals, respectively (where ρ² represents the Pearson’s correlation coefficient). Our results show that in delta band, MIC indexes discriminate the two tasks in several regions, while in alpha band the same behaviour is observed for MIC-ρ², suggesting a generic coupling between delta EEG power and P_ETCO₂ and a pure nonlinear interaction between alpha EEG power and P_ETCO₂. Moreover, higher indexes values were found for breath hold task respect to free breathing.

Validation of instantaneous bispectral high-frequency power of heartbeat dynamics as a marker of cardiac vagal activity

Nonlinear analysis has been advocated as a very powerful methodological framework to study physiological signals, particularly when applied to heartbeat dynamics. To this extent, estimation of high-frequency (0.15-0.40 Hz) power from bispectra of cardiovascular variability series has been engaged as a marker of nonlinear vagal activity. Nevertheless, a proper validation of this specific measure has not been yet performed. In this study, we estimate instantaneous, nonlinear bispectral indices during postural changes under sympathetic and parasympathetic nervous system blockade. The analysis was performed on data from 14 healthy subjects undergoing a control supine-to-upright routine where they were selectively administered either atropine or propanolol. Instantaneous bispectra were obtained through Laguerre-transformed, linear and nonlinear kernels of a Wiener-Volterra model applied to heartbeat dynamics, embedded into a recently proposed inhomogeneous point-process framework. Results demonstrate that the integration of bispectra accounting for nonlinear cardiovascular control dynamics within the high-frequency band provides potentially reliable markers of vagal activity.

Two distinct bifurcation routes for delayed optoelectronic oscillators

We investigate the coexistence of low- and high-frequency oscillations in a delayed optoelectronic oscillator. We identify two nearby Hopf bifurcation points exhibiting low and high frequencies and demonstrate analytically how they lead to stable solutions. We then show numerically that these two branches of solutions undergo higher order instabilities as the feedback rate is increased but remain separated in the bifurcation diagram. The two bifurcation routes can be followed independently by either progressively increasing or decreasing the bifurcation parameter.

Regime shifts driven by dynamic correlations in gene expression noise

Gene expression is a noisy process that leads to regime shifts between alternative steady states among individual living cells, inducing phenotypic variability. The effects of white noise on the regime shift in bistable systems have been well characterized, however little is known about such effects of colored noise (noise with nonzero correlation time). Here, we show that noise correlation time, by considering a genetic circuit of autoactivation, can have a significant effect on the regime shift between distinct phenotypic states in gene expression. We demonstrate this theoretically, using stochastic potential, stationary probability density function, and first-passage time based on the Fokker-Planck description, where the Ornstein-Uhlenbeck process is used to model colored noise. We find that an increase in noise correlation time in the degradation rate can induce a regime shift from a low to a high protein concentration state and enhance the bistable regime, while an increase in noise correlation time in the basal rate retains the bimodal distribution. We then show how cross-correlated colored noises in basal and degradation rates can induce regime shifts from a low to a high protein concentration state, but reduce the bistable regime. We also validate these results through direct numerical simulations of the stochastic differential equation. In gene expression understanding the causes of regime shift to a harmful phenotype could improve early therapeutic intervention in complex human diseases.

Instantaneous Transfer Entropy for the Study of Cardiovascular and Cardiorespiratory Nonstationary Dynamics

OBJECTIVE

Measures of transfer entropy (TE) quantify the direction and strength of coupling between two complex systems. Standard approaches assume stationarity of the observations, and therefore are unable to track time-varying changes in nonlinear information transfer with high temporal resolution. In this study, we aim to define and validate novel instantaneous measures of TE to provide an improved assessment of complex nonstationary cardiorespiratory interactions.

METHODS

We here propose a novel instantaneous point-process TE (ipTE) and validate its assessment as applied to cardiovascular and cardiorespiratory dynamics. In particular, heartbeat and respiratory dynamics are characterized through discrete time series, and modeled with probability density functions predicting the time of the next physiological event as a function of the past history. Likewise, nonstationary interactions between heartbeat and blood pressure dynamics are characterized as well. Furthermore, we propose a new measure of information transfer, the instantaneous point-process information transfer (ipInfTr), which is directly derived from point-process-based definitions of the Kolmogorov-Smirnov distance.

RESULTS AND CONCLUSION

Analysis on synthetic data, as well as on experimental data gathered from healthy subjects undergoing postural changes confirms that ipTE, as well as ipInfTr measures are able to dynamically track changes in physiological systems coupling.

SIGNIFICANCE

This novel approach opens new avenues in the study of hidden, transient, nonstationary physiological states involving multivariate autonomic dynamics in cardiovascular health and disease. The proposed method can also be tailored for the study of complex multisystem physiology (e.g., brain-heart or, more in general, brain-body interactions).

The Use of Neurocomputational Models as Alternatives to Animal Models in the Development of Electrical Brain Stimulation Treatments

Recent publications call for more animal models to be used and more experiments to be performed, in order to better understand the mechanisms of neurodegenerative disorders, to improve human health, and to develop new brain stimulation treatments. In response to these calls, some limitations of the current animal models are examined by using Deep Brain Stimulation (DBS) in Parkinson's disease as an illustrative example. Without focusing on the arguments for or against animal experimentation, or on the history of DBS, the present paper argues that given recent technological and theoretical advances, the time has come to consider bioinspired computational modelling as a valid alternative to animal models, in order to design the next generation of human brain stimulation treatments. However, before computational neuroscience is fully integrated in the translational process and used as a substitute for animal models, several obstacles need to be overcome. These obstacles are examined in the context of institutional, financial, technological and behavioural lock-in. Recommendations include encouraging agreement to change long-term habitual practices, explaining what alternative models can achieve, considering economic stakes, simplifying administrative and regulatory constraints, and carefully examining possible conflicts of interest.

Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control

The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson's Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity.

Exploratory analysis of nonlinear coupling between EEG global field power and end-tidal carbon dioxide in free breathing and breath-hold tasks

Brain activations underlying control of breathing are not completely known. Furthermore, the coupling between neural and respiratory dynamics is usually estimated through linear correlation measures, thus totally disregarding possible underlying nonlinear interactions. To overcome these limitations, in this preliminary study we propose a nonlinear coupling analysis of simultaneous recordings of electroencephalographic (EEG) and respiratory signals at rest and after variation of carbon dioxide (CO2) level. Specifically, a CO2 increase was induced by a voluntary breath hold task. EEG global field power (GFP) in different frequency bands and end-tidal CO2 (PETCO2) were estimated in both conditions. The maximum information coefficient (MIC) and MIC-ρ2 (where ρ represents the Pearson's correlation coefficient) between the two signals were calculated to identify generic associations (i.e. linear and nonlinear correlations) and nonlinear correlations, respectively. With respect to a free breathing state, our results suggest that a breath hold state is characterized by an increased coupling between respiration activity and specific EEG oscillations, mainly involving linear and nonlinear interactions in the delta band (1-4 Hz), and prevalent nonlinear interactions in the alpha band (8-13 Hz).

Inhomogeneous Point-Processes to Instantaneously Assess Affective Haptic Perception through Heartbeat Dynamics Information

This study proposes the application of a comprehensive signal processing framework, based on inhomogeneous point-process models of heartbeat dynamics, to instantaneously assess affective haptic perception using electrocardiogram-derived information exclusively. The framework relies on inverse-Gaussian point-processes with Laguerre expansion of the nonlinear Wiener-Volterra kernels, accounting for the long-term information given by the past heartbeat events. Up to cubic-order nonlinearities allow for an instantaneous estimation of the dynamic spectrum and bispectrum of the considered cardiovascular dynamics, as well as for instantaneous measures of complexity, through Lyapunov exponents and entropy. Short-term caress-like stimuli were administered for 4.3–25 seconds on the forearms of 32 healthy volunteers (16 females) through a wearable haptic device, by selectively superimposing two levels of force, 2 N and 6 N, and two levels of velocity, 9.4 mm/s and 65 mm/s. Results demonstrated that our instantaneous linear and nonlinear features were able to finely characterize the affective haptic perception, with a recognition accuracy of 69.79% along the force dimension, and 81.25% along the velocity dimension.

Detecting the Hidden Properties of Immunological Data and Predicting the Mortality Risks of Infectious Syndromes

BACKGROUND

To extract more information, the properties of infectious disease data, including hidden relationships, could be considered. Here, blood leukocyte data were explored to elucidate whether hidden information, if uncovered, could forecast mortality.

METHODS

Three sets of individuals (n = 132) were investigated, from whom blood leukocyte profiles and microbial tests were conducted (i) cross-sectional analyses performed at admission (before bacteriological tests were completed) from two groups of hospital patients, randomly selected at different time periods, who met septic criteria [confirmed infection and at least three systemic inflammatory response syndrome (SIRS) criteria] but lacked chronic conditions (study I, n = 36; and study II, n = 69); (ii) a similar group, tested over 3 days (n = 7); and (iii) non-infected, SIRS-negative individuals, tested once (n = 20). The data were analyzed by (i) a method that creates complex data combinations, which, based on graphic patterns, partitions the data into subsets and (ii) an approach that does not partition the data. Admission data from SIRS+/infection+ patients were related to 30-day, in-hospital mortality.

RESULTS

The non-partitioning approach was not informative: in both study I and study II, the leukocyte data intervals of non-survivors and survivors overlapped. In contrast, the combinatorial method distinguished two subsets that, later, showed twofold (or larger) differences in mortality. While the two subsets did not differ in gender, age, microbial species, or antimicrobial resistance, they revealed different immune profiles. Non-infected, SIRS-negative individuals did not express the high-mortality profile. Longitudinal data from septic patients displayed the pattern associated with the highest mortality within the first 24 h post-admission. Suggesting inflammation coexisted with immunosuppression, one high-mortality sub-subset displayed high neutrophil/lymphocyte ratio values and low lymphocyte percents. A second high-mortality subset showed monocyte-mediated deficiencies. Numerous within- and between-subset comparisons revealed statistically significantly different immune profiles.

CONCLUSION

While the analysis of non-partitioned data can result in information loss, complex (combinatorial) data structures can uncover hidden patterns, which guide data partitioning into subsets that differ in mortality rates and immune profiles. Such information can facilitate diagnostics, monitoring of disease dynamics, and evaluation of subset-specific, patient-specific therapies.

Anticipating regime shifts in gene expression: The case of an autoactivating positive feedback loop

Considerable evidence suggests that anticipating sudden shifts from one state to another in bistable dynamical systems is a challenging task; examples include ecosystems, financial markets, and complex diseases. In this paper, we investigate the effects of additive, multiplicative, and cross-correlated stochastic perturbations on determining the regime shifts in a bistable gene regulatory system, which gives rise to two distinct states of low and high concentrations of protein. We obtain the stationary probability density and mean first-passage time of the system. We show that increasing the additive (multiplicative) noise intensity induces a regime shift from a low (high) to a high (low) protein concentration state. However, an increase in the cross-correlation intensity always induces regime shifts from a high to a low protein concentration state. For both bifurcation-induced (often called the tipping point) and noise-induced (called stochastic switching) regime shifts, we further explore the robustness of recently developed critical-down-based early warning signal (EWS) indicators (e.g., rising variance and lag-1 autocorrelation) on our simulated time-series data. We identify that using EWS indicators, prediction of an impending bifurcation-induced regime shift is relatively easier than that of a noise-induced regime shift in the considered system. Moreover, the success of EWS indicators also strongly depends upon the nature of the noise.

Dynamic transitions in a model of the hypothalamic-pituitary-adrenal axis

Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations.