Periodic modes of group dominance in fully coupled neural networks

Nonlinear systems of differential equations with delay, which are mathematical models of fully connected networks of impulse neurons, are considered. Purpose of this work is to study the dynamic properties of one special class of solutions to these systems. Large parameter methods are used to study the existence and stability in сonsidered models of special periodic motions – the so-called group dominance or k-dominance modes, where k ∈ N. Results. It is shown that each such regime is a relaxation cycle, exactly k components of which perform synchronous impulse oscillations, and all other components are asymptotically small. The maximum number of stable coexisting group dominance cycles in the system with an appropriate choice of parameters is 2m − 1, where m is the number of network elements. Conclusion. Considered model with maximum possible number of couplings allows us to describe the most complex and diverse behavior that may be observed in biological neural associations. A feature of the k-dominance modes we have considered is that some of the network neurons are in a non-working (refractory) state. Each periodic k-dominance mode can be associated with a binary vector (α1, α2, . . . , αm), where αj = 1 if the j-th neuron is active and αj = 0 otherwise. Taking this into account, we come to the conclusion that these modes can be used to build devices with associative memory based on artificial neural networks.

Inhibitory and Stimulatory Micropeptides Preferentially Bind to Different Conformations of the Cardiac Calcium Pump

The ATP-dependent ion pump SERCA sequesters Ca2+ in the endoplasmic reticulum to establish a reservoir for cell signaling. Because of its central importance in physiology, this transporter is tightly controlled by physical interactions with tissue-specific regulatory micropeptides that tune SERCA function to match changing physiological conditions. In the heart, phospholamban (PLB) inhibits SERCA, while dwarf open reading frame (DWORF) stimulates SERCA. These competing interactions determine cardiac performance by modulating the amplitude of Ca2+ signals that drive the contraction/relaxation cycle. The distinct functions of these peptides may relate to their reciprocal preferences for SERCA binding. While SERCA binds PLB more avidly at low cytoplasmic Ca2+, it binds DWORF better at high Ca2+. In the present study, we determined that this opposing Ca2+ sensitivity is due to preferential binding of DWORF and PLB to different intermediate conformations that the pump samples during the Ca2+ transport cycle. The results suggest a mechanistic basis for inhibitory and stimulatory micropeptide function. In addition, fluorescence resonance energy transfer (FRET) measurements revealed dynamic shifts in SERCA-micropeptide binding equilibria during cellular Ca2+ elevations. The data suggest Ca2+-dependent dynamic exchange of inhibitory and stimulatory micropeptides from SERCA during the cardiac cycle. Together, these mechanisms provide beat-to-beat modulation of cardiac Ca2+ handling and contribute to the heart's adaptation to the increased physiological demands of exercise.

Effects of Lead and/or Cadmium on the Contractile Function of the Rat Myocardium Following Subchronic Exposure and Its Attenuation with a Complex of Bioprotectors

Background: As by-products of copper smelting, lead and cadmium pollute both workplace air at metallurgical plants and adjacent territories. Their increased levels in the human body pose a higher risk of cardiovascular diseases. The objective of our study was evaluate changes in the rat myocardium contractile function following moderate subchronic exposure to soluble lead and/or cadmium salts and its attenuation by means of a complex of bioprotectors. Materials and methods: The subchronic exposure of rats was modelled by intraperitoneal injections of 3-H2O lead acetate and/or 2.5-H2O cadmium chloride in single doses, 6.01 mg of Pb and 0.377 mg of Cd per kg of body weight, respectively, 3 times a week during 6 weeks. The myosin heavy chains isoform ratio was estimated by gel electrophoresis. Biomechanical measurements were performed on isolated multicellular preparations of the myocardium (trabeculae and papillary muscles) from the right ventricle. Results: The subchronic lead exposure slowed down the contraction and relaxation cycle and increased myosin expression towards slowly cycling V3 isomyosins. Cadmium intoxication, on the contrary, shortened the contraction and relaxation cycle and shifted the ratio of isomyosin forms towards rapidly cycling V1. Following the combined exposure to lead and cadmium, some contractile characteristics changed in the direction typical of the effect of lead while others – in that of cadmium. We observed that the metal combination either neutralized or enhanced the isolated damaging effect of each heavy metal. The use of a complex of bioprotectors normalized the myocardial contractility impaired by the exposure to lead and cadmium either partially or completely. Discussion: Despite the changes in myocardial contractility following the subchronic lead and cadmium exposure, the mechanisms of heterometric regulation were maintained. The adverse cardiotoxic effect of the combination of these industrial contaminants may be weakened by administering a complex of bioprotectors.

Higher Order Approximation to the Guidewire Model used in Simulators of Cardiac Catheterization and Multiple Segment Relaxations

Cardiac catheterism is important since it offers many advantages in comparison to open surgery, e.g. fewer injuries, lower risk of infections, and shorter recovery times. Simulators play a fundamental role in training packages and virtual learning environments are less stressful. Moreover, they can also be used in certification boards and in performance assessments. A realistic and interactive simulator must be fast. In this work, the physical model of the guidewire used in catheter simulations has been improved. In particular, we determined a simple analytic expression to calculate the direction of a guidewire segment, which minimizes the total energy. The surface energy resulting from the guidewire-artery interaction and the bending energy of the guidewire is approximated up to the second order, which gives rise to interactions between segments. Furthermore, the multiple segment relaxations is introduced, enhancing the convergence especially at the beginning of the relaxation cycle. The formulas are written in matrix form of dimension [Formula: see text], where [Formula: see text] represents the number of segments varied in the update step. The method results in a more stable static solution.

Calculating Frictional Losses in Belleville Springs by Geometrical Interpolation

The use of Belleville springs has been proven to be beneficial in tackling the problems related to elastic interaction, creep, differential thermal expansion or in the isolation of seismic vibrations in bolted joints. Because of its high and easily variable spring rates, the use of these springs can also be observed in passive vibration assisted rotary drilling (VARD) tools. Because of relative movement of spring with respect to supporting surfaces and the mating spring surfaces, frictional losses in the spring take place during each compression and relaxation cycle leading to a slightly different load-deflection curve from what has been defined in the literature. The geometry of the spring combined with different stacking configurations complicate the study of frictional losses in these kinds of springs. This work presents a new method to calculate the displacement of different points of Belleville springs during its loading and unloading using geometrical interpolation method. The results of spring displacement are then used to develop a model to calculate frictional load as a function of spring deflection, which is used to analyse load-deflection curves of springs with different dimensional and frictional parameters. The developed methodology is used to plot and understand characteristics curves of four different kind of Belleville springs; High Load, Standard, Force Limiting and Force Adjusting Belleville springs by plotting the graphs for different free-height to thickness and diameter ratios. In the later section of the paper, the proposed methodology has been used to visualize the load-deflection characteristics of Belleville springs used in the p-VARD tool of the Large Drilling Simulator, one of the state-of-the-art drilling simulators at Memorial University of Newfoundland. Results show that understanding of the characteristic curves of different spring configuration helps to plan to drill with desired WOB using a p-VARD tool.

New Approach to Gene Network Modeling

The article is devoted to the mathematical modeling of artificial genetic networks. A phenomenological model of the simplest genetic network called repressilator is considered. This network contains three elements unidirectionally coupled into a ring. More specifically, the first of them inhibits the synthesis of the second, the second inhibits the synthesis of the third, and the third, which closes the cycle, inhibits the synthesis of the first one. The interaction of the protein concentrations and of mRNA (message RNA) concentration is surprisingly similar to the interaction of six ecological populations — three predators and three preys. This allows us to propose a new phenomenological model, which is represented by a system of unidirectionally coupled ordinary differential equations. We study the existence and stability problem of a relaxation periodic solution that is invariant with respect to cyclic permutations of coordinates. To find the asymptotics of this solution, a special relay system is constructed. It is proved in the paper that the periodic solution of the relay system gives the asymptotic approximation of the orbitally asymptotically stable relaxation cycle of the problem under consideration.

Oscillation and Extinction Scenarios in the New Continuous Model of the Eruptive Phase of Alien Species Invasion

The paper considers the issue of modeling the development of those special population processes that include the passage of the eruptive phase of dynamics. Such brief hurricane regimes of change are often associated with the consequences of invasions of undesirable species. Processes in the introduction of a species can often develop through the delayed phase of a rapid increase in its abundance. The completion of the phase depends on many factors. Outbreaks of many species exert such a strong pressure on the environment that achieving a non-zero balance equilibrium is problematic. Such phenomena are interpreted by us as an extreme transition process to an uncertain state of the biotic environment before the beginning of the process. Depending on the counteraction, which is clearly seen in the examples of the dynamics of insect pests, simulated scenarios of similar phenomena can develop in various ways, including destruction of the habitat. The new model based on the equation with a deviating argument describes the variant of developing the repeated flash of catastrophic character. The scenario is implemented when non-harmonic cycle N*(rτ, t) occurs, which can not be orbitally stable under the given conditions, but becomes transitive. The cycle ends with the trivial-zero value. The scenario of the most abrupt form of the eruptive phase that we simulate ends in a computational experiment by the death of the invasive population, but without forming an unbounded trajectory from the oscillations, as was the case with the destruction of the relaxation cycle of the extreme amplitude in the population flash equation in our previous work.

Hypothermia elongates the contraction-relaxation cycle in explanted human failing heart decreasing the time for ventricular filling during diastole

Targeted temperature management is part of the standardized treatment for patients in cardiac arrest. Hypothermia decreases cerebral oxygen consumption and induces bradycardia; thus, increasing the heart rate may be considered to maintain cardiac output. We hypothesized that increasing heart rate during hypothermia would impair diastolic function. Human left ventricular trabeculae obtained from explanted hearts of patients with terminal heart failure were stimulated at 0.5 Hz, and contraction-relaxation cycles were recorded. Maximal developed force (Fmax), maximal rate of development of force [(dF/d t)max], time to peak force (TPF), time to 80% relaxation (TR80), and relaxation time (RT = TR80 − TPF) were measured at 37, 33, 31, and 29°C. At these temperatures, stimulation frequency was increased from 0.5 to 1.0 and to 1.5 Hz. At 1.5 Hz, concentration-response curves for the β-adrenergic receptor (β-AR) agonist isoproterenol were performed. Fmax, TPF, and RT increased when temperature was lowered, whereas (dF/d t)max decreased. At all temperatures, increasing stimulation frequency increased Fmax and (dF/d t)max, whereas TPF and RT decreased. At 31 and 29°C, resting tension increased at 1.5 Hz, which was ameliorated by β-AR stimulation. At all temperatures, maximal β-AR stimulation increased Fmax, (dF/d t)max, and maximal systolic force, whereas resting tension decreased progressively with lowering temperature. β-AR stimulation reduced TPF and RT to the same extent at all temperatures, despite the more elongated contraction-relaxation cycle at lower temperatures. Diastolic dysfunction during hypothermia results from an elongation of the contraction-relaxation cycle, which decreases the time for ventricular filling. Hypothermic bradycardia protects the heart from diastolic dysfunction and increasing the heart rate during hypothermia should be avoided. NEW & NOTEWORTHY Decreasing temperature increases the duration of the contraction-relaxation cycle in the human ventricular myocardium, significantly reducing the time for ventricular filling during diastole. During hypothermia, increasing heart rate further reduces the time for ventricular filling and in some situations increases resting tension further impairing diastolic function. Modest β-adrenergic receptor stimulation can ameliorate these potentially detrimental changes during diastole while improving contractile force generation during targeted temperature management.

EFFECTS OF SUBCHRONIC LEAD INTOXICATION ON THE MYOCARDIUM CONTRACTILITY OF RATS

While it is known that chronic lead intoxication in humans induces arterial hypertension and thus can lead to some secondary disturbances of heart function, possible effects of this intoxication on myocardium contractility has never been proved. In our experiments outbred male rats were repeatedly injected IP with sub-lethal doses of lead acetate 3 times a week during 5 weeks. They developed an explicit even if moderate lead intoxication characterized by typical hematological and some other features. Next day after the last injection the heart of each animal was excised, and trabecules and papillary muscles from right ventricle were used for modeling in vitro isometric regimes of contraction-relaxation cycle. Several well-established parameters of this model proved to be changed as compared with preparations taken from hearts of healthy control rats. Against the background of in vivocalcium treatment both systemic and cardiotoxic effects of lead were somewhat attenuated. For the first time we showed that at subchronic intoxication with lead the myocardial preparations in a wide range of lengths react with decrease in their time and speed parameters of isometric contraction while keeping its amplitude, and with decrease in the passive stiffness of the trabecules. Features of the reaction of different structures of the heart and the shifting of isomyosin ratio to the slow isoform were demonstrated. Mechanistic and toxicological inferences from the results obtained are discussed.