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

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

Difference equation model of ventricular parasystole as an interaction between cardiac pacemakers based on the phase response curve

A model of extended ventricular parasystole proposed by Moe et al. (1977) was formulated as a system of nonlinear difference equations by using the phase response curve of myocardial pacemakers. A number of ECG patterns of ventricular arrhythmia such as bigeminy, trigeminy etc. were explained from the property of periodic solutions of the equation. Characteristic properties of special kinds of arrhythmia called “concealed bigeminy” and “concealed trigeminy” were derived mathematically by assuming the model, in relation to the equation of the analog neuron model. The present study was considered to be of clinical significance as a theoretical foundation for the study of genesis of cardiac arrhythmias.     

Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern.     

Nitric oxide: an inhibitory retrograde modulator in the crustacean heart

The nervous system innervates most of the organs in the body, and controls and coordinates their activities. Effective coordination depends on accurate feedback from target organs. Recent studies have identified a target-based feedback mechanism that regulates a simple neural circuit, the cardiac ganglion-a network of nine neurons whose rhythmic bursts of action potentials drive the contractions of the crustacean heart. The feedback agent, nitric oxide (NO), is produced by the target organ (the heart), and acts on the neural circuit (the ganglion), thus serving as a retrograde, trans-synaptic signaling molecule. NO decreases the ganglionic burst rate, which has both negative chronotropic and negative inotropic effects on the heartbeat. This article will review the evidence identifying NO as an inhibitory modulator in the crustacean heart, and will present new data showing that these inhibitory effects are not mediated by cGMP, the canonical downstream agent mobilized by NO in many other systems. Rather, our data suggest that in the crustacean heart cGMP may play a secondary role in the process of adaptation that occurs in during prolonged exposures to NO.     

Stabilization of inhomogeneous patterns in a diffusion-reaction system under structural and parametric uncertainties

Many phenomena such as neuron firing in the brain, the travelling waves which produce the heartbeat, arrythmia and fibrillation in the heart, catalytic reactions or cellular organization activities, among others, can be described by a unifying paradigm based on a class of nonlinear reaction-diffusion mechanisms. The FitzHugh-Nagumo (FHN) model is a simplified version of such class which is known to capture most of the qualitative dynamic features found in the spatiotemporal signals. In this paper, we take advantage of the dissipative nature of diffusion-reaction systems and results in finite dimensional nonlinear control theory to develop a class of nonlinear feedback controllers which is able to ensure stabilization of moving fronts for the FHN system, despite structural or parametric uncertainty. In the context of heart or neuron activity, this class of control laws is expected to prevent cardiac or neurological disorders connected with spatiotemporal wave disruptions. In the same way, biochemical or cellular organization related with certain functional aspects of life could also be influenced or controlled by the same feedback logic. The stability and robustness properties of the controller will be proved theoretically and illustrated on simulation experiments.     

Estimating fish community diversity from environmental features in the Tagus estuary (Portugal): Multiple Linear Regression and Artificial Neural Network approaches

Relationships between environmental variables and diversity (Shannon‐Weaver index) of the fish communities in the Tagus estuary and adjacent coastal areas were analyzed. The focus was on the linearity or nonlinearity of these abiotic/biotic characteristics, with the aim to obtain an accurate short–medium term time‐scale diversity prediction from habitat variables alone. Multiple Linear Regressions (MLR) were used for the linear approach and Artificial Neural Networks (ANNs) for the nonlinear approach. MLR results in the external validation phase indicated a lack of model accuracy (R² = 0.0710; %SEP = 47.5868; E = ?0.0217; ARV = 1.0217; N = 43). Results of the best of the Artificial Neural Networks used in this study (12‐15‐15‐1 architecture) in the external validation phase (ANN: R² = 0.9736; %SEP = 7.8499; E = 0.9722; ARV = 0.0278; N = 43) were more accurate than those obtained with MLR. This indicates a clear nonlinear relationship between variables. In the best ANN model, nitrate concentration, depth, dissolved oxygen and temperature were the most important predictors of fish diversity in the Tagus estuary. The sensibility analysis indicated that the remaining variables (silicate, nitrite, transparency, salinity, slope, phosphate, water particulate organic matter, and chlorophyll a) played lesser roles in the model.     

A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space

Two different bifurcation scenarios of firing patterns with decreasing extracellular calcium concentrations were observed in identical sciatic nerve fibers of a chronic constriction injury (CCI) model when the extracellular 4-aminopyridine concentrations were fixed at two different levels. Both processes proceeded from period-1 bursting to period-1 spiking via complex or simple processes. Multiple typical experimental examples manifested dynamics closely matching those simulated in a recently proposed 4-dimensional model to describe the nonlinear dynamics of the CCI model, which included most cases of the bifurcation scenarios. As the extracellular 4-aminopyridine concentrations is increased, the structure of the bifurcation scenario becomes more complex. The results provide a basic framework for identifying the relationships between different neural firing patterns and different bifurcation scenarios and for revealing the complex nonlinear dynamics of neural firing patterns. The potential roles of the basic bifurcation structures in identifying the information process mechanism are discussed.     

Auditory Nerve Spike Generator Modeled as a Variable Attenuator Based on a Saddle Node on Invariant Circle Bifurcation

Mammalian inner hair cells transduce the sound waves amplified by the cochlear amplifier (CA) into a graded neurotransmitter release that activates channels on auditory nerve fibers (ANF). These synaptic channels then charge its dendritic spike generator. While the outer hair cells of the CA employ positive feedback, poising on Andronov-Hopf type instabilities which make them extremely sensitive to faint sounds and make CA output strongly nonlinear, the ANF appears to be based on different principles and a different type of dynamical instability. Its spike generator “digitizes” CA output into trains of action potentials and behaves as a linear filter, rate-coding sound intensity across a wide dynamic range. Here we model the spike generator as a 3 dimensional version of a saddle node on invariant circle (SNIC) bifurcation. The generic 2d SNIC increases its spike rate as the square root of the input current above its spiking threshold. We add negative feedback in the form of a low voltage-threshold potassium conductance that slows down the generator’s rate of increase of its spike rate. A Poisson random source simulates an inner hair cell, outputting a series of noisy periodic current pulses to the model ANF whose spikes phase lock to these pulses and have a linear frequency to current relation with a wide dynamic range. Also, the spike generator compartment has a cholinergic feedback connection from the olive and experiments show that such feedback is able to alter the amount of H conductance inside the generator compartment. We show that an olive able to decrease H would be able to shift the spike generator’s dynamic range to higher sound intensities. In a quiet environment by increasing H the olive would be able to make spike trains similar to those caused by synaptic input.     

Fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age: a new mechanistic picture of cardiac control in healthy elderly

Heart beat fluctuations exhibit temporal structure with robust long-range correlations, fractal and nonlinear features, which have been found to break down with pathologic conditions, reflecting changes in the mechanism of neuroautonomic control. It has been hypothesized that these features change and even break down also with advanced age, suggesting fundamental alterations in cardiac control with aging. Here we test this hypothesis. We analyze heart beat interval recordings from the following two independent databases: 1) 19 healthy young (average age 25.7 yr) and 16 healthy elderly subjects (average age 73.8 yr) during 2 h under resting conditions from the Fantasia database; and 2) 29 healthy elderly subjects (average age 75.9 yr) during approximately 8 h of sleep from the sleep heart health study (SHHS) database, and the same subjects recorded 5 yr later. We quantify: 1) the average heart rate (); 2) the SD sigma(R-R) and sigma(DeltaR-R) of the heart beat intervals R-R and their increments DeltaR-R; 3) the long-range correlations in R-R as measured by the scaling exponent alpha(R-R) using the Detrended Fluctuation Analysis; 4) fractal linear and nonlinear properties as represented by the scaling exponents alpha(sgn) and alpha(mag) for the time series of the sign and magnitude of DeltaR-R; and 5) the nonlinear fractal dimension D(k) of R-R using the fractal dimension analysis. We find: 1) No significant difference in (P > 0.05); 2) a significant difference in sigma(R-R) and sigma(DeltaR-R) for the Fantasia groups (P < 10(-4)) but no significant change with age between the elderly SHHS groups (P > 0.5); and 3) no significant change in the fractal measures alpha(R-R) (P > 0.15), alpha(sgn) (P > 0.2), alpha(mag) (P > 0.3), and D(k) with age. Our findings do not support the hypothesis that fractal linear and nonlinear characteristics of heart beat dynamics break down with advanced age in healthy subjects. Although our results indeed show a reduced SD of heart beat fluctuations with advanced age, the inherent temporal fractal and nonlinear organization of these fluctuations remains stable. This indicates that the coupled cascade of nonlinear feedback loops, which are believed to underlie cardiac neuroautonomic regulation, remains intact with advanced age.     

Automatic Adaptation to Fast Input Changes in a Time-Invariant Neural Circuit

Neurons must faithfully encode signals that can vary over many orders of magnitude despite having only limited dynamic ranges. For a correlated signal, this dynamic range constraint can be relieved by subtracting away components of the signal that can be predicted from the past, a strategy known as predictive coding, that relies on learning the input statistics. However, the statistics of input natural signals can also vary over very short time scales e.g., following saccades across a visual scene. To maintain a reduced transmission cost to signals with rapidly varying statistics, neuronal circuits implementing predictive coding must also rapidly adapt their properties. Experimentally, in different sensory modalities, sensory neurons have shown such adaptations within 100 ms of an input change. Here, we show first that linear neurons connected in a feedback inhibitory circuit can implement predictive coding. We then show that adding a rectification nonlinearity to such a feedback inhibitory circuit allows it to automatically adapt and approximate the performance of an optimal linear predictive coding network, over a wide range of inputs, while keeping its underlying temporal and synaptic properties unchanged. We demonstrate that the resulting changes to the linearized temporal filters of this nonlinear network match the fast adaptations observed experimentally in different sensory modalities, in different vertebrate species. Therefore, the nonlinear feedback inhibitory network can provide automatic adaptation to fast varying signals, maintaining the dynamic range necessary for accurate neuronal transmission of natural inputs.     

利用果蝇心力衰竭模型筛选果蝇第2号染色体缺失系

果蝇心脏一直以来都是研究心血管发育的极好模型,许多控制心脏分化和特化的调控基因和信号途径从果蝇到哺乳动物都是保守的.由于近年心力衰竭的发病率不断升高,我们最近又建立了果蝇心力衰竭模型用于大规模筛选和鉴定心力衰竭的相关基因.在这个模型中,适龄的成体果蝇被整齐排列在导电的载玻片上,通过电极短暂刺激30s,使果蝇的心跳频率由正常的3Hz增加到6Hz,停止后检测果蝇心率恢复情况,不能恢复正常心跳频率或出现纤维性震颤的果蝇视为心力衰竭.该模型可以在短期内大规模筛选到与心力衰竭相关的基因.利用此心力衰竭模型,我们筛选了164个果蝇2号染色体缺失系,获得33个候选缺失系.这些候选缺失系的心衰率要么与野生型品系相比差异显著,要么与tinman或panier突变系相比差异显著,提示这些缺失系中可能含有与心力衰竭相关的调控基因.     

Non-linear control of continuous bioreactors

Control of bioreactors has achieved importance in the recent years. This may be due to the fact that they are difficult to control which may be attributed to its nonlinear dynamic behavior. The model parameters of the bioreactor also vary in an unpredictable manner. The complexity of the biochemical processes inhibits the accurate modeling and also the lack of suitable sensors make the process state difficult to characterize. Considerable emphasis has been placed on the control of fed-batch fermentors because of their prevalence in industries. However, when production of biomass is to be optimized, continuous operation is desirable. Several procedures are available for the nonlinear control of processes, viz., differential geometric approach, internal model control approach, reference synthesis technique, predictive control design, etc., but the major disadvantage of these approaches is the computational time required to perform the prediction optimization. In this study, a nonlinear controller based on a polynomial discrete time model (NARMAX) is evaluated for its performance on a fermentor. It can be shown that a nonlinear self-tuning controller based on NARMAX model can be extended to the control of fermentors. The response is smooth for both load and setpoint changes even when process parameters are assumed to be zero and uncertainty in parameters are present and in the presence of controller constraints. The control action can be made more or less robust by changing the design parameters appropriately. Therefore, nonlinear self-tuning controller is suitable for control of industrial processes.     

Photosensitive neurogenic heart of the isopod crustacean Ligia exotica

The heart of animals is regulated through the central nervous system in response to external sensory stimuli. We found, however, that the adult neurogenic heart of the isopod crustacean Ligia exotica has photosensitivity. The beat frequency of the isolated heart decreased in response to a light stimulus. Magnitude of the response was stimulus intensity dependent and the heartbeat frequency decreased to less than 80% of the dark value during illumination of the white light with an intensity of 6.0 mW cm-2. The spectral sensitivity curve of the heart photoresponse peaked at a wavelength around 520 nm. In response to 530 nm monochromatic light, the relationship between light intensity and response magnitude was linear and the threshold intensity was 7.26 x 1012 quanta cm-2 s-1. Bursting activity of the cardiac ganglion, which is located in the heart and acts as the cardiac pacemaker deceased in frequency in response to illumination by white light. This fact suggests that the heart photoresponse of L. exotica results from the photosensitivity of the cardiac ganglion neurons. The photoresponse of the heart therefore contributes to regulation of cardiac output in addition to other regulatory systems.     

Improving the Efficiency of Abdominal Aortic Aneurysm Wall Stress Computations

An abdominal aortic aneurysm is a pathological dilation of the abdominal aorta, which carries a high mortality rate if ruptured. The most commonly used surrogate marker of rupture risk is the maximal transverse diameter of the aneurysm. More recent studies suggest that wall stress from models of patient-specific aneurysm geometries extracted, for instance, from computed tomography images may be a more accurate predictor of rupture risk and an important factor in AAA size progression. However, quantification of wall stress is typically computationally intensive and time-consuming, mainly due to the nonlinear mechanical behavior of the abdominal aortic aneurysm walls. These difficulties have limited the potential of computational models in clinical practice. To facilitate computation of wall stresses, we propose to use a linear approach that ensures equilibrium of wall stresses in the aneurysms. This proposed linear model approach is easy to implement and eliminates the burden of nonlinear computations. To assess the accuracy of our proposed approach to compute wall stresses, results from idealized and patient-specific model simulations were compared to those obtained using conventional approaches and to those of a hypothetical, reference abdominal aortic aneurysm model. For the reference model, wall mechanical properties and the initial unloaded and unstressed configuration were assumed to be known, and the resulting wall stresses were used as reference for comparison. Our proposed linear approach accurately approximates wall stresses for varying model geometries and wall material properties. Our findings suggest that the proposed linear approach could be used as an effective, efficient, easy-to-use clinical tool to estimate patient-specific wall stresses.     

Initiation of walk and tiptoe of a planar nine-link biped

A nine-link planar biped model is studied. Its nonlinear differential equations are derived. Constraints due to the connections of the links and the contact between the model and the ground are analyzed, and forces of constraint are specified as functions of the state and inputs. With large external forces acting on the model, connection constraints are maintained by the ligaments and other soft tissue structures. It is shown that ligamentious structures contribute to the stability of the system and help maintain the integrity of the joint. By using linear feedback control, the nine-link model is stabilized around the vertical stance. The stable motion of the system in the vicinity of the vertical is studied by computer simulation of walking and tiptoe gaits.     

Recovery of the Xenopus laevis heart from ROS-induced stress utilizes conserved pathways of cardiac regeneration

Urodele amphibians and some fish are capable of regenerating up to a quarter of their heart tissue after cardiac injury. While many anuran amphibians like Xenopus laevis are not capable of such feats, they are able to repair lesser levels of cardiac damage, such as that caused by oxidative stress, to a far greater degree than mammals. Using an optogenetic stress induction model that utilizes the protein KillerRed, we have investigated the extent to which mechanisms of cardiac regeneration are conserved during the restoration of normal heart morphology post oxidative stress in X. laevis tadpoles. We focused particularly on the processes of cardiomyocyte proliferation and dedifferentiation, as well as the pathways that facilitate the regulation of these processes. The cardiac response to KillerRed-induced injury in X. laevis tadpole hearts consists of a phase dominated by indicators of cardiac stress, followed by a repair-like phase with characteristics similar to mechanisms of cardiac regeneration in urodeles and fish. In the latter phase, we found markers associated with partial dedifferentiation and cardiomyocyte proliferation in the injured tadpole heart, which, unlike in regenerating hearts, are not dependent on Notch or retinoic acid signaling. Ultimately, the X. laevis cardiac response to KillerRed-induced oxidative stress shares characteristics with both mammalian and urodele/fish repair mechanisms, but is nonetheless a unique form of recovery, occupying an intermediate place on the spectrum of cardiac regenerative ability. An understanding of how Xenopus repairs cardiac damage can help bridge the gap between mammals and urodeles and contribute to new methods of treating heart disease.