Comparison of the energetic properties and the dynamical stability in a mathematical model of the stretch reflex

The previous studies on finite-time thermodynamic engines have shown that some of the parameters affecting their thermodynamic performance also affect their stability. Moreover, such parameters have to be tuned to reach an optimal trade-off between these two generic properties. In the present work we carry out a similar analysis on a mathematical model of the stretch reflex regulatory pathway, which is a simplified version of a previously published model. We show that the model has a unique stable fixed point in the absence of time delays. However, when the system inherent time delays are considered, they can destabilize the fixed point and engender a stable limit cycle. We further explore the parameter space to analyse the sensitivity of the system stability to variations in the parameter values. Particular attention is paid to the parameter here denoted as α, which has been shown to determine the muscle thermodynamic properties during steady-state contractions: larger values of α mean more powerful and less efficient muscles. Our results indicate that the stretch reflex pathway is less stable in the more powerful and less efficient muscles. We finally compare these observations with those obtained on thermal engines.     

Effect of Rolling Massage on Particle Moving Behaviour in Blood Vessels

The rolling massage manipulation is a classic Chinese massage, which is expected to eliminate many diseases. Here the effect of the rolling massage on the particle moving property in the blood vessels under the rolling massage manipulation is studied by the lattice Boltzmann simulation. The simulation results show that the particle moving behaviour depends on the rolling velocity, the distance between particle position and rolling position. The average values, including particle translational velocity and angular velocity, increase as the rolling velocity increases almost linearly. The result is helpful to understand the mechanism of the massage and develop the rolling techniques.     

Frequency Selectivity Behaviour in the Auditory Midbrain： Implications of Model Study

By numerical simulations on frequency dependence of the spiking threshold, i.e. on the critical amplitude of periodic stimulus, for a neuron to fire, we find that bushy cells in the cochlear nuclear exhibit frequency selec- tivity behaviour. However, the selective frequency band of a bushy cell is far away from that of the preferred spectral range in human and mammal auditory perception. The mechanism underlying this neural activity is also discussed. Further studies show that the ion channel densities have little impact on the selective frequency band of bushy cells. These findings suggest that the neuronal behaviour of frequency selectivity in bushy cells at both the single cell and population levels may be not functionally relevant to frequency discrimination. Our results may reveal a neural hint to the reconsideration on the busily cell functional role in auditory information processing of sound frequency.     

Bifurcation in neuronal networks with hub structure

We investigate bifurcations in neuronal networks with a hub structure. It is known that hubs play a leading role in characterizing the network dynamical behavior. However, the dynamics of hubs or star-coupled systems is not well understood. Here, we study rather subnetworks with a star-like configuration. This coupled system is an important motif in complex networks. Thus, our study is a basic step for understanding structure formation in large networks. We use the Morris-Lecar neuron with class I and class II excitabilities as a node. Homogeneous (coupling the same class neurons) and heterogeneous (coupling different class neurons) cases are considered for both excitatory and inhibitory coupling. For the homogeneous system class II neurons are suitable for achieving both complete and cluster synchronization in excitatory and inhibitory coupling, respectively. For the heterogeneous system with inhibitory coupling, the class I hub neuron has a wider parameter region of synchronous firings than the class II hub. Moreover, the class I hub neuron with the excitatory synapse gives rise to bifurcations of synchronized states and multi-stability (coexistence of a few different states) is observed.     

Lattice Boltzmann Simulations of Particle-Particle Interaction in Steady Poiseuille Flow

The moving behaviour of two- and three-particles in a pressure-driven flow is studied by the lattice Boltzmann simulation in two dimensions. The time-dependent values, including particles＇ radial positions, translational velocities, angular velocities, and the x-directional distance between the particles are analysed extensively. The effect of flow Reynolds number on particle motion is also investigated numerically. The simulation results show that the leading particle equilibrium position is closer to the channel centre while the trailing particle equilibrium position is closer to the channel wall. If Reynolds number Re is less than 85.30, the larger flow Reynolds number results in the smaller x-directional equilibrium distance, otherwise the x-directional distance increases almost linearly with the increase of time and the particles separate finally. The simulation results are helpful to understand the particle-particle interaction in suspensions with swarms of particles.     

New Evidence of Active Tuning in Cochlea

The wonderful performance of hearing systems is mainly attributed to the tuning tiltering of basilar membrane （BM）. Although theory of the cochlear mechanism has been greatly developed since the 1970s and the amplification or sensitivity of the cochlea has been concluded due to the out hair cells, the mechanics underlying the sharp-tuning or frequency selectivity of cochlea remains a puzzle. We use the cochlear translation function derived from the data of an experiment of the BM in vivo to calculate basilar responses to tone bursts, and find that there are resonant peaks with the characteristic frequency at the corresponding place in the initial and terminal part of the responses. However, when the translation function is shallower, there will be no resonant peaks in the responses. The result indicates that the sharp tuning is due to existence of the active resonant tuning mechanism.     

Suprathreshold Stochastic Resonance in a Single Comparator

Stochastic resonance usually appears when stimulus is too weak to overcome barriers in a nonlinear system. Unusually, we demonstrate that in a simple competitor as a prototype model, stochastic resonance can still occur when the stimulus is predominantly suprathreshold. This result provides new knowledge for understanding of mechanism underlying information process in biological systems and aIso finds appfications in signal processing.     

A Tsallis’ statistics based neural network model for novel word learning

We invoke the Tsallis entropy formalism, a nonextensive entropy measure, to include some degree of non-locality in a neural network that is used for simulation of novel word learning in adults. A generalization of the gradient descent dynamics, realized via nonextensive cost functions, is used as a learning rule in a simple perceptron. The model is first investigated for general properties, and then tested against the empirical data, gathered from simple memorization experiments involving two populations of linguistically different subjects. Numerical solutions of the model equations corresponded to the measured performance states of human learners. In particular, we found that the memorization tasks were executed with rather small but population-specific amounts of nonextensivity, quantified by the entropic index q. Our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems.     

Directional Motion of Droplets in a Conical Tube or on a Conical Fibre

Manipulating the directional movement of liquid droplets is of significance for design and fabrication of some microfluidic devices, An energy-based method is adopted to analyse the directional movement of a droplet deposited in a conical tube or on a conical fibre. We perform an experiment to investigate the directional motion of a droplet in an open conical tube. Our theoretical analysis and experimental observations both demonstrate that surface tension can drive the droplet to move in the conical tube. The critical condition of the liquid moving in the conical tube is presented. We also analyse a droplet on a conical hydrophilic fibre, which can move from the thinner to the thicker end.     

Effects of disease characteristics and population distribution on dynamics of epidemic spreading among residential sites

We investigate the spreading processes of epidemic diseases among many residential sites for different disease characteristics and different population distributions by constructing and solving a set of integrodifferential equations for the evolutions of position-dependent infected and infective rates, taking into account the infection processes both within a single site and among different sites. In a spreading process the states of an individual include susceptible (S), incubative (I), active (A) and recovered (R) states. Although the transition from S to I mainly depends on the active rate, the susceptible rate and the connectivity among individuals, the transitions from I to A and from A to R are determined by intrinsic characteristics of disease development in individuals. We adopt incubation and infection periods to describe the intrinsic features of the disease. By numerically solving the equations we find that the asymptotic behavior of the spreading crucially depends on the infection period and the population under affection of an active individual. Other factors, such as the structure of network and the popular distribution, play less important roles. The study may provide useful information for analyzing the key parameters affecting the dynamics and the asymptotic behavior.     

Generalized relative entropy in functional magnetic resonance imaging

The generalized Kullback-Leibler distance D_q (q is the Tsallis parameter) is shown to be an useful measure for analysis of functional magnetic resonance imaging (fMRI) data series. This generalized form of entropy is used to evaluate the “distance” between the probability functions p₁ and p₂ of the signal levels related to periods of stimulus and non-stimulus in event-related fMRI experiments. The probability densities of the mean distance (averaged over the N epochs of the entire experiment) are obtained through numerical simulations for different values of signal-to-noise ratio (SNR) and found to be fitted very well by Gamma distributions (χ²<0.0008) for small values of N (N<30). These distributions allow us to determine the sensitivity and specificity of the method by construction of the receiver operating characteristic (ROC) curves. The performance of the method is also investigated in terms of the parameters q and L (number of signal levels) and our results indicate that the optimum choice is q=0.8 and L=3. The entropic index q is found to exert control on both sensitivity and specificity of the method. As q (q>0) is raised, sensitivity increases but specificity decreases. Finally, the method is applied in the analysis of a real event-related fMRI motor stimulus experiment and the resulting maps show activation in primary and secondary motor brain areas.     

Minimal attractors in digraph system models of neuronal networks

We study a class of discrete dynamical systems models of neuronal networks. In these models, each neuron is represented by a finite number of states and there are rules for how a neuron transitions from one state to another. In particular, the rules determine when a neuron fires and how this affects the state of other neurons. In an earlier paper [D. Terman, S. Ahn, X. Wang, W. Just, Reducing neuronal networks to discrete dynamics, Physica D 237 (2008) 324-338], we demonstrate that a general class of excitatory-inhibitory networks can, in fact, be rigorously reduced to the discrete model. In the present paper, we analyze how the connectivity of the network influences the dynamics of the discrete model. For randomly connected networks, we find two major phase transitions. If the connection probability is above the second but below the first phase transition, then starting in a generic initial state, most but not all cells will fire at all times along the trajectory as soon as they reach the end of their refractory period. Above the first phase transition, this will be true for all cells in a typical initial state; thus most states will belong to a minimal attractor of oscillatory behavior (in a sense that is defined precisely in the paper). The exact positions of the phase transitions depend on intrinsic properties of the cells including the lengths of the cells’ refractory periods and the thresholds for firing. Existence of these phase transitions is both rigorously proved for sufficiently large networks and corroborated by numerical experiments on networks of moderate size.     

The effects of neuron heterogeneity and connection mechanism in cortical networks

The mammalian cortices show an specific architecture close to the optimum, represented by the high clustering, short processing steps and short wiring length. What are the key factors that influence the layout of neural connectivity networks? Here a model to investigate the conditions leading to the small-world cortical networks with minimal global wiring is presented. The essential factors in this model are the introductions of the unequal number distribution of heterogeneous neurons and two connection mechanisms, the preferential attachment to neurons with large spatial coverage (PANLSC) and distance preference. Outcomes show that the specific architecture close to the optimum can only result from the PANLSC when the number distribution of neurons with diverse spatial coverage is highly unequal. This suggests the PANLSC may be an important connection mechanism in cortical systems.     

Modelling Human Cortical Network in Real Brain Space

Highly specific structural organization is of great significance in the topology of cortical networks. We introduce a human cortical network model, taking the specific cortical structure into account, in which nodes are brain sites placed in the actual positions of cerebral cortex and the establishment of edges depends on the spatial path length rather than the linear distance. The resulting network exhibits the essential features of cortical connectivity, properties of small-world networks and multiple clusters structure. Additionally, assortative mixing is also found in this model. All of these findings may be attributed to the specific cortical architecture.     

Two mechanisms of spiral-pair-source creation in excitable media

Two new modes of generating spiral pairs in an excitable medium have been found. They depend on a geometrical structure (GS) inside the medium. This may be formed e.g. as a result of scars or fibrosis in the heart tissue, or artificially built in a chemical reaction substrate. Both sources involve a GS composed of a circular “convergent lens” bounded by two opaque “walls”. One mode can be induced by a single wave and behaves as a “flip-flop” type of a limit cycle. The other mode is generated by a train of plane waves impinging on the GS, and is created at the focus of the converging wave-fragments.     

Entropy of electromyography time series

A nonlinear analysis based on Renyi entropy is applied to electromyography (EMG) time series from back muscles. The time dependence of the entropy of the EMG signal exhibits a crossover from a subdiffusive regime at short times to a plateau at longer times. We argue that this behavior characterizes complex biological systems. The plateau value of the entropy can be used to differentiate between healthy and low back pain individuals.     

Intermittent Chaotic Neural Firing Characterized by Non-Smooth Features

A chaotic firing pattern, characterized by non-smooth features and generated through the routine of intermittency from period 3, is observed in biological experiments on a neural firing pacemaker and reproduced in simulations by using a theoretical neuronal model with multiple time scales. This chaotic activity exhibits a scale law very similar to those of both the type-Ⅰ intermitteney generated in smooth systems and the type-Ⅴ intermittency in non-smooth systems.     

Two Different Bifurcation Scenarios in Neural Firing Rhythms Discovered in Biological Experiments by Adjusting Two Parameters

Two different bifurcation scenarios, one is novel and the other is relatively simpler, in the transition procedures of neural firing patterns are studied in biological experiments on a neural pacemaker by adjusting two parameters. The experimental observations are simulated with a relevant theoretical model neuron. The deterministic non-periodic firing pattern lying within the novel bifurcation scenario is suggested to be a new case of chaos, which has not been observed in previous neurodynamical experiments.     

Nematic liquid crystals formed by living amoeboid cells

Interacting cells have the ability to form liquid crystal phases: (i) A cluster of a polar nematic liquid crystal is formed by cells which emit molecules for attracting other cells and (ii) an apolar nematic liquid crystal is formed by elongated cells which have an anisotropic steric repulsion. The angle distribution function is predicted by using the characteristics of an automatic controller where the extracellular guiding field is approximated by two-dimensional mean-field. The nematic liquid crystal state is quite well described by the model. Received 7 September 1998 and Received in final form 4 March 1999     

Genetically engineered cardiac pacemaker: Stem cells transfected with HCN2 gene and myocytes—A model

One of the successfully tested methods to design genetically engineered cardiac pacemaker cells consists in transfecting a human mesenchymal stem cell (hMSC) with a HCN2 gene and connecting it to a myocyte. We develop and study a mathematical model, describing a myocyte connected to a hMSC transfected with a HCN2 gene. The cardiac action potential is described both with the simple Beeler-Reuter model, as well as with the elaborate dynamic Luo-Rudy model. The HCN2 channel is described by fitting electrophysiological records, in the spirit of Hodgkin-Huxley. The model shows that oscillations can occur in a pair myocyte-stem cell, that was not observed in the experiments yet. The model predicted that: (1) HCN pacemaker channels can induce oscillations only if the number of expressed IK1 channels is low enough. At too high an expression level of IK1 channels, oscillations cannot be induced, no matter how many pacemaker channels are expressed. (2) At low expression levels of IK1 channels, a large domain of values in the parameter space (n, N) exists, where oscillations should be observed. We denote N the number of expressed pacemaker channels in the stem cell, and n the number of gap junction channels coupling the stem cell and the myocyte. (3) The expression levels of IK1 channels observed in ventricular myocytes, both in the Beeler-Reuter and in the dynamic Luo-Rudy models are too high to allow to observe oscillations. With expression levels below ∼1/4 of the original value, oscillations can be observed. The main consequence of this work is that in order to obtain oscillations in an experiment with a myocyte-stem cell pair, increasing the values of n, N is unlikely to be helpful, unless the expression level of IK1 has been reduced enough. The model also allows us to explore levels of gene expression not yet achieved in experiments, and could be useful to plan new experiments, aimed at improving the robustness of the oscillations.