Conventional and complex modal analyses of a finite element model of human head and neck

This study employs both the traditional and the complex modal analyses of a detailed finite element model of human head–neck system to determine modal responses in terms of resonant frequencies and mode shapes. It compares both modal responses without ignoring mode shapes, and these results are reasonably in agreement with the literature. Increasing displacement contour loops within the brain in higher frequency modes probably exhibits the shearing and twisting modes of the brain. Additional and rarely reported modal responses such as ‘mastication’ mode of the mandible and flipping mode of nasal lateral cartilages are identified. This suggests a need for detailed modelling to identify all the additional frequencies of each individual part. Moreover, it is found that a damping factor of above 0.2 has amplifying effect in reducing higher frequency modes, while a diminishing effect in lowering peak biomechanical responses, indicating the importance of identifying the appropriate optimised damping factor.     

Dynamic Causal Modeling and subspace identification methods

The main contribution of the paper is in formulating the problem of detection of brain regions structure within the framework of dynamic system theory. The motivation is to see if the mature domain of experimental identification of dynamic systems can provide a methodology alternative to Dynamic Causal Modeling (DCM) which is currently used as an exclusive tool to estimate the structure of interconnections among a given set of brain regions using the measured data from functional magnetic resonance imaging (fMRI). The key tool proposed for modeling the structure of brain interconnections in this paper is subspace identification methods which produce linear state-space model, thus neglecting the bilinear term from DCM. The procedure is illustrated using a simple two-region model with maximally simplified linearized hemodynamics. We assume that the underlying system can be modeled by a set of linear differential equations, and identify the parameters (in terms of state space matrices), without any a priori constraints. We then transform the hidden states so that the implicit state matrix has a form or structure that is consistent with the generation of (region-specific) hemodynamic signals by coupled neuronal states.     

A test for constant natural frequencies in electrocortical activity under lateral hypothalamic control

An initial test for a theory of lateral hypothalamic regulation of electrocortical activity is undertaken. The theory supposes lateral hypothalamic input directly or indirectly damps telencephalic resonances involving linear wave phenomena, enabling this pathway to act as parametric control of information processing in cortical neural networks. Relative changes in left and right electrocortical power spectra are used to test for the presence of resonant modes with constant natural frequencies in conditions of asymmetrical damping, following unilateral lesion of the lateral hypothalamus. Natural frequency values for the modes clustered about center frequencies in the EEG band are obtained. This method has the advantage of minimising the effects of time-variation and the recorded signal's distortion from the electrocortical local spatial average, but limits consideration to five dominant modes of resonance. The uncertainty of true model order, and errors in curve-fitting impose limitations on the test.     

A linear theory for global electrocortical activity and its control by the lateral hypothalamus

A linear model for electrocortical waves and their control by the lateral hypothalamus is proposed. It is argued that such a linear model is not in contradition to non-linearity of neural elements on the microscopic scale. Telencephalic structures are treated as a mass of linked oscillators generating activity with a number of resonant modes. The lateral hypothalamus is regarded as controlling damping of activity in the telencephalic mass, and therefore exerting a specific parametric control over all signal processing in the cortical networks. An initial test is proposed to assess the constancy of telencephalic natural frequencies, with variation in lateral hypothalamic damping.     

Modeling protein conformational changes by iterative fitting of distance constraints using reoriented normal modes

Recently we have developed a normal-modes-based algorithm that predicts the direction of protein conformational changes given the initial state crystal structure together with a small number of pairwise distance constraints for the end state. Here we significantly extend this method to accurately model both the direction and amplitude of protein conformational changes. The new protocol implements a multisteps search in the conformational space that is driven by iteratively minimizing the error of fitting the given distance constraints and simultaneously enforcing the restraint of low elastic energy. At each step, an incremental structural displacement is computed as a linear combination of the lowest 10 normal modes derived from an elastic network model, whose eigenvectors are reorientated to correct for the distortions caused by the structural displacements in the previous steps. We test this method on a list of 16 pairs of protein structures for which relatively large conformational changes are observed (root mean square deviation >3 angstroms), using up to 10 pairwise distance constraints selected by a fluctuation analysis of the initial state structures. This method has achieved a near-optimal performance in almost all cases, and in many cases the final structural models lie within root mean square deviation of 1 approximately 2 angstroms from the native end state structures.     

Metabolic pathways reconstruction by frequency and amplitude response to forced glycolytic oscillations in yeast

The hypothesis that frequency and amplitude response can be used in a complicated metabolic pathway kinetics model for optimal parameter estimation, as speculated by its successful prior usage for a mechanical oscillator and a heterogeneous chemical system, is tested here. Given the complexity of the glycolysis model of yeast chosen, this question is limited to three kinetics parameters of the 87 in the in vitro model developed in the literature. The direct application of the approach, used with the uninformed selection of operating conditions for the oscillation of external glucose concentration, led to miring the data assimilation process in local minima. Application of linear systems theory, however, identified two natural resonant frequencies that, when excited by external forced oscillations of the same frequency, result in the expression of many harmonics in the Fourier spectra, that is, information-rich experiments. A single such information-rich experiment at one of the resonant frequencies was sufficient to break away from the local minima to find the optimum kinetics parameter estimates. The resonant frequencies themselves represent oscillation modes in glycolysis akin to those previously observed. Furthermore, operation of the bioreactor with large amplitude oscillations of glucose feed (25%) leads to enhanced ethanol average yield by 1.6% at the resonant frequency.     

Timing in the absence of clocks: encoding time in neural network states

Decisions based on the timing of sensory events are fundamental to sensory processing. However, the mechanisms by which the brain measures time over ranges of milliseconds to seconds remain unclear. The dominant model of temporal processing proposes that an oscillator emits events that are integrated to provide a linear metric of time. We examine an alternate model in which cortical networks are inherently able to tell time as a result of time-dependent changes in network state. Using computer simulations we show that within this framework, there is no linear metric of time, and that a given interval is encoded in the context of preceding events. Human psychophysical studies were used to examine the predictions of the model. Our results provide theoretical and experimental evidence that, for short intervals, there is no linear metric of time, and that time may be encoded in the high-dimensional state of local neural networks.     

Peculiarities of Formation and Reversibility of Neurogenic Stress-Related Emotional Disorders in Rats

In experiments on rats, we modeled neurogenic stress-induced emotional disorders (stress was evoked by repetitive nociceptive stimulation) and studied their peculiarities within the stressory and post-stressory periods. In these animals, drastic changes in the brain electrical activity and emotional behavior gradually developed; such changes were manifested over a long time period after cessation of the stressory influences. Our experiments demonstrated that tight and stable interrelations among brain limbic structures and negative hypothalamic emotional centers are formed under conditions of prolonged action of emotional stress. This results in the development of a protracted state of negative emotional excitation. The hippocampus is considered one of the key limbic structures responsible for the development of stable pathological stress-related reactions of the brain. Within the post-stressory period, we observed dramatic worsening of the general functional state of the animals, which developed in a parallel manner with intensification of the activity of the negative emotiogenic brain system. It is probable that the existence of periods of unstable equilibrium between oppositely directed emotional reactions in the dynamics of stress and after cessation of stressory influences is a common rule. Such periods reflect peculiarities of rearrangements in the adaptive brain mechanisms under conditions of a stable change in the mode of brain functioning in one particular situation or another.     

Musical ratios in sounds from the human cochlea

The physiological roots of music perception are a matter of long-lasting debate. Recently light on this problem has been shed by the study of otoacoustic emissions (OAEs), which are weak sounds generated by the inner ear following acoustic stimulation and, sometimes, even spontaneously. In the present study, a high-resolution time-frequency method called matching pursuit was applied to the OAEs recorded from the ears of 45 normal volunteers so that the component frequencies, amplitudes, latencies, and time-spans could be accurately determined. The method allowed us to find that, for each ear, the OAEs consisted of characteristic frequency patterns that we call resonant modes. Here we demonstrate that, on average, the frequency ratios of the resonant modes from all the cochleas studied possessed small integer ratios. The ratios are the same as those found by Pythagoras as being most musically pleasant and which form the basis of the Just tuning system. The statistical significance of the results was verified against a random distribution of ratios. As an explanatory model, there are attractive features in a recent theory that represents the cochlea as a surface acoustic wave resonator; in this situation the spacing between the rows of hearing receptors can create resonant cavities of defined lengths. By adjusting the geometry and the lengths of the resonant cavities, it is possible to generate the preferred frequency ratios we have found here. We conclude that musical perception might be related to specific geometrical and physiological properties of the cochlea.     

Two fish species competition model with nonlinear interactions and equilibrium catches

Two species competition model is built up by assuming the hypothetical second order interactions in order to consider effects of exploitation on two competing fish species with non-linear interactions. Most important characteristic of this model, compared withLotka-Volterra type linear competition model, is that this model can possess multiple stable equilibrium points. Therefore there is a possibility that two species keeping the equilibrium state at one stable equilibrium point will be attracted to the other stable equilibrium point after a heavy perturbation. In this model reversible change of the fishing pressure does not always results in that of the equilibrium catch. In this sence MSY concept for single species can not be extended to this model. If there are multiple stable equilibrium points, the change of the dominant fish species, catastrophic and irreversible change of each equilibrium catch may be observed when the perturbation by the exploitation is added. This phenomenon immediately reminds us of the change of the dominant fish species between Japanese common mackerel and Pacific saury in the northwest Pacific Ocean. In case of the management of two competing fish species with nonlinear interactions, the consideration on the balance between the fishing pressure for each species may be as important as the decision on the catch limit for each species. MSY level for each species based on the single-species theory could be quite erroneous.     

Red Queens and ESS: the coevolution of evolutionary rates

Summary The Red Queen principle states that a set of interacting species reaches an evolutionary equilibrium at which all their rates of coevolution exactly balance each other. The lag-load model, which is one way of searching for Red Queens, has, by itself, previously predicted that they do not exist. But this model has assumed that infinite maladaptedness is possible. The lag-load model is improved by assuming that once the lag load of all but one species is determined, so is that of the final species. This assumption eliminates the possibility of infinite maladaptedness. Its result is to allow the lag-load model to yield Red Queen coevolution. It does this whether or not speciation and extinction rates are included. Thus the lag-load model is harmonized with the earlier Red Queen model derived from studies of predation.Because of the intercorrelation of phenotypic traits, the predatory model concluded that the eventual stable rate of coevolution must be zero (except for intermittent bursts after some correlation or compromise is successfully broken). Another model that predicts stable coevolutionary rates of zero is that of evolutionarily stable strategies (ESS).Red Queen assumes that the more extreme a phenotypic trait is, the better it is, and that there are no constraints on the growth of such a phenotypic trait value. Such traits are the key to the Red Queen prediction of progressive coevolution. ESS models make no such assumptions. Eliminating unbounded traits from the model of predator-victim evolution changed its prediction from progressive coevolution to stasis. Before this paper, no model had dealt simultaneously with both unbounded and constrained traits.To handle both sorts of phenotypic traits at the same time in the same model, we abandoned lag load as a measure of evolutionary rate (lag loads do not uniquely determine phenotype). Instead, we used the traditional assumption that rate is proportional to the slope of the adaptive landscape. A model, relying on continuous evolutionary game theory, was developed and simulated under various conditions in two or three species sets, with up to five independent traits coevolving simultaneously. The results were: (1) there was always a set of equilibrium densities eventually achieved by coevolution; if the population interaction represented by this stable coevolutionary state is also stable, then the system should persist whether it evolves further or not; (2) whenever traits were present which were unbounded and best at their most extreme values, then a Red Queen emerged; (3) whenever traits were present which were correlated with each other or constrained below infinity, then an ESS emerged; (4) if both types were present, both results occurred: Red Queen in the unbounded traits and ESS in the constrained ones.Because unbounded traits may not exist, the Red Queen may have no domain. But the domain of ESS is real. ESS should lead to the evolutionary pattern called punctuated equilibrium. The changes in design rules which punctuate stasis should lead to an ever-expanding independence of traits from each other, i.e. to more and more refined differentiation. A single set of design rules which governs a set of species is called a fitness-generating function. Such functions may help to define the concepts of adaptive zone and ecological guild.     

Resonance Raman carbonyl frequencies and ultraviolet absorption maxima as indicators of the active site environment in native and unfolded chromophoric acyl-alpha-chymotrypsin

The imidazole of chromophoric p-(dimethylamino)benzoic acid, DABIm, reacts with the serine protease alpha-chymotrypsin in the pH range of 4-7 to form a stable acyl intermediate that gives very good resonance-enhanced Raman spectra. The resonance Raman and absorption spectra of the acyl enzyme intermediate have been compared with the spectra of simple model compounds such as the corresponding chromophoric methyl ester, aldehyde, and imidazole. The resonant Raman and ultraviolet absorption spectra of these simple chromophoric model compounds change considerably with the solvent. However, each of the model compounds exhibits a linear correlation between the maximum wavelength of absorption and the frequency of the carbonyl vibration. The observed values of the acyl intermediate do not fall on the line for the methyl ester but rather on the line for the aldehyde. This shows that the chromophoric serine ester of the acyl enzyme behaves differently than an ordinary ester, which cannot be explained as a solvent effect. Thermal unfolding of the acyl enzyme brings the spectroscopic parameters close to those of the model ester. We conclude that it is the specific conformation of the native enzyme and not solvent effects that change the spectroscopic properties of the acyl chromophore. It is reasonable that these changes arise from the same forces that cause the catalytic events. The carbonyl frequencies of a series of para-substituted benzoyl methyl esters show a remarkably linear correlation with the rate of deacylation of the corresponding acyl enzymes.     

Reticular activation and the dynamics of neuronal networks

It is postulated that during arousal the cortical system is driven by a spatially and temporally noisy signal arising from non-specific reticulo-cortical pathways. An elementary unit of cortical neuroanatomy is assumed, which permits non-linear dynamics to be represented by stochastic linear equations. Under these assumptions the resonant modes of the system of cortical dendrites approach thermodynamic equilibrium. Specific sensory signals perturb the dendritic system about equilibrium, generate low frequency, linear, non-dispersive waves corresponding to the EEG, which in turn regulate action potential sequences, and instantiate internal inputs to the dendritic field. A large and distributed memory capacity in axo-synaptic couplings, resistance to interference between functionally separate logical operations, and a very large next-state function set emerge as properties of the network. The model is able to explain the close association of the EEG with cognition, the channel of low capacity corresponding to the field of immediate attention, the low overall correlation of action potentials with EEG, and specificity of action potentials in some neurons during particular cognitive activity. Predictions made from hypothesis include features of thermal equilibrium in EEG (determinable by autoregression) and expectation that the cortical evoked response can be accounted for as the response to a sensory impulse of specific time characteristics.     

Normal-modes-based prediction of protein conformational changes guided by distance constraints

Based on the elastic network model, we develop a novel method that predicts the conformational change of a protein complex given its initial-state crystal structure together with a small set of pairwise distance constraints for the end state. The predicted conformational change, which is a linear combination of multiple low-frequency normal modes that are solved from the elastic network model, is computed as a response displacement induced by a perturbation to the system Hamiltonian that incorporates the given distance constraints. For a list of test cases, we find that the computed response displacement overlaps significantly with the measured conformational changes, when only a handful of pairwise constraints are used (相似文献   

Slow oscillations in blood pressure via a nonlinear feedback model

Blood pressure is well established to contain a potential oscillation between 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the baroreflex loop. A linear feedback model, comprising delay and lag terms for the vasculature, and a linear proportional derivative controller have been proposed to account for the 0.4-Hz oscillation in blood pressure in rats. However, although this model can produce oscillations at the required frequency, some strict relationships between the controller and vasculature parameters must be true for the oscillations to be stable. We developed a nonlinear model, containing an amplitude-limiting nonlinearity that allows for similar oscillations under a very mild set of assumptions. Models constructed from arterial pressure and sympathetic nerve activity recordings obtained from conscious rabbits under resting conditions suggest that the nonlinearity in the feedback loop is not contained within the vasculature, but rather is confined to the central nervous system. The advantage of the model is that it provides for sustained stable oscillations under a wide variety of situations even where gain at various points along the feedback loop may be altered, a situation that is not possible with a linear feedback model. Our model shows how variations in some of the nonlinearity characteristics can account for growth or decay in the oscillations and situations where the oscillations can disappear altogether. Such variations are shown to accord well with observed experimental data. Additionally, using a nonlinear feedback model, it is straightforward to show that the variation in frequency of the oscillations in blood pressure in rats (0.4 Hz), rabbits (0.3 Hz), and humans (0.1 Hz) is primarily due to scaling effects of conduction times between species.     

Resonant frequencies of arms and legs identify different walking patterns

The present study is aimed at investigating changes in the coordination of arm and leg movements in young healthy subjects. It was hypothesized that with changes in walking velocity there is a change in frequency and phase coupling between the arms and the legs. In addition, it was hypothesized that the preferred frequencies of the different coordination patterns can be predicted on the basis of the resonant frequencies of arms and legs with a simple pendulum model. The kinematics of arms and legs during treadmill walking in seven healthy subjects were recorded with accelerometers in the sagittal plane at a wide range of different velocities (i.e., 0.3-1. 3m/s). Power spectral analyses revealed a statistically significant change in the frequency relation between arms and legs, i.e., within the velocity range 0.3-0.7m/s arm movement frequencies were dominantly synchronized with the step frequency, whereas from 0.8m/s onwards arm frequencies were locked onto stride frequency. Significant effects of walking speed on mean relative phase between leg and arm movements were found. All limb pairs showed a significantly more stable coordination pattern from 0.8 to 1.0m/s onwards. Results from the pendulum modelling demonstrated that for most subjects at low-velocity preferred movement frequencies of the arms are predicted by the resonant frequencies of individual arms (about 0.98Hz), whereas at higher velocities these are predicted on the basis of the resonant frequencies of the individual legs (about 0.85Hz). The results support the above-mentioned hypotheses, and suggest that different patterns of coordination, as shown by changes in frequency coupling and phase relations, can exist within the human walking mode.     

II. An electrochemical model of the brain: Collective behaviour,irreversibility and information

Here the theory developed in a previous paper is applied to a many-neuron model representing the brain. It is shown that this model may exhibit quiet states in which it functions as a system of coupled harmonic oscillators. The problems arising in the specification of the synaptic and environmental coupling parameters, and a set of compatible initial conditions are resolved, and by an analysis of the normal modes it is shown that in quiet states even a small model consisting of twelve neurons will reflect in magnitude and distribution the basic waves observed in electroencephalograms. The model also possesses a closely spaced spectrum of high frequencies characteristic of active states, which are excited by environmental interactions. When the potential in any neuron exceeds the characteristic threshold value, a firing sequence similar to that found in the isolated neuron is initiated. Such sequences are shown to be modified by and react on neighbouring neurons, and some of the simpler cooperative effects are investigated. In the final section, an information theoretic analysis is made of the model. It is shown how to establish a quantitative measure of the information available to the brain, how to relate such information to the stimuli which the brain experiences in the course of its development, and how such information influences the firing patterns which manifest themselves in the external behaviour of the animal. A tentative relation between quantal effects and decision-making processes is discussed.     

Stability of Whole Brain and Regional Network Topology within and between Resting and Cognitive States

Background

Graph-theory based analyses of resting state functional Magnetic Resonance Imaging (fMRI) data have been used to map the network organization of the brain. While numerous analyses of resting state brain organization exist, many questions remain unexplored. The present study examines the stability of findings based on this approach over repeated resting state and working memory state sessions within the same individuals. This allows assessment of stability of network topology within the same state for both rest and working memory, and between rest and working memory as well.

Methodology/Principal Findings

fMRI scans were performed on five participants while at rest and while performing the 2-back working memory task five times each, with task state alternating while they were in the scanner. Voxel-based whole brain network analyses were performed on the resulting data along with analyses of functional connectivity in regions associated with resting state and working memory. Network topology was fairly stable across repeated sessions of the same task, but varied significantly between rest and working memory. In the whole brain analysis, local efficiency, Eloc, differed significantly between rest and working memory. Analyses of network statistics for the precuneus and dorsolateral prefrontal cortex revealed significant differences in degree as a function of task state for both regions and in local efficiency for the precuneus. Conversely, no significant differences were observed across repeated sessions of the same state.

Conclusions/Significance

These findings suggest that network topology is fairly stable within individuals across time for the same state, but also fluid between states. Whole brain voxel-based network analyses may prove to be a valuable tool for exploring how functional connectivity changes in response to task demands.     

Spacetime representation of global electrocortical activity

A model for global electrocortical activity is developed by considering telencephalonic structures as mass of linked oscillators generating activity with a number of resonant modes. Equations for the signals are written in the comoving frame and then transformed into the laboratory frame. The state transition matrix is obtained in the presence of electric and magnetic fields.     

Error field amplification near the stability boundary of the modes interacting with a conducting wall

The effect is considered of the amplification of an external resonant error field near the stability boundary of the so-called resistive wall modes observed in the DIII-D tokamak. The analysis is performed in a standard cylindrical approximation. The model is based on Maxwell’s equations and Ohm’s law; therefore, the results of the analysis are valid for any large-scale modes interacting with a conducting wall. In contrast to earlier approaches, the model considers the resonant field amplification as a dynamic effect. It is shown that, when the effect is the strongest, the stationary solutions proposed earlier are inapplicable. The problem of plasma response to a probing pulse of the resonant field of a given amplitude and duration is analyzed. The relationships obtained explain the basic features of the observed phenomena in the DIII-D tokamak and allow direct experimental verification.