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[The doctrine of brain localization and its development in the 20th century].

The discovery of the cerebral motor cortex in the last third of the 19th century has decisively influenced the doctrine of cerebral localization. It has dominated brain research from there on. Its considerable practical importance for focalized local diagnosis was recognized from the clinical point of view. As a consequence, interdisciplinary institutions for brain research developed in Europe and in the USA for the study of functional localization in the brain by means of cyto- and myeloarchitecture, electrical brain stimulation and lesion experiments in close connection with clinico-neurologic centers. From this research resulted the cerebral cortical maps with more or less numerous areas linked to either sensory, motor or 'higher' psychic functions. An intensive, emotional critique developed against the brain-localization theory from its onset. This article demonstrates that the arguments of the anti-localizationists gave rise in part to new knowledge about some principles of cerebral function. Some of these are the concept of 'diaschisis' (distant effects of acute lesions and functional recovery, von Monakow, 1902), the concept of 'motor equivalence' (Lashley, 1930) and of neuronal plasticity of the cerebral cortex (Cajal, 1911). Furthermore, modern imaging techniques (position emission tomography, functional nuclear spin resonance) show that complex functions in particular, such as the natural, targeted arm and grasp synergy, are not 'localized' within a small area of the cortex but do activate multiple neuronal networks interconnected dynamically and in alternating composition in the process of movement initiation and execution.

Brain↗

Why does the single neuron activity change from trial to trial during sensory-motor task?

Single neuron activities from cortical areas of a monkey were recorded while performing a sensory-motor task (a choice reaction time task). Quantitative trial-by-trial analysis revealed that the timing of peak activity exhibited large variation from trial to trial, compared to the variation in the behavioral reaction time of the task. Therefore, we developed a multi-unit dynamic neural network model to investigate the effects of structure of neural connections on the variation of the timing of peak activity. Computer simulation of the model showed that, even though the units are connected in a cascade fashion, a wide variation exists in the timing of peak activity of neurons because of parallel organization of neural network within each unit.

Animals↗

Video rate confocal laser scanning reflection microscopy in the investigation of normal and neoplastic living cell dynamics.

The introduction of video rate confocal laser scanning microscopes (VRCLSM) used in reflection mode with high magnification, high aperture objective lenses and with further magnification by a zoom facility allowed the first detailed observations of the activity of living cytoplasm and offered a new tool for investigation of the structural transition from the living state to the specimen fixed for electron microscopy (EM). We used a Noran Odyssey VRCLSM in reflection (backscattered) mode. A greater degree of oversampling and more comfortable viewing of the liver or taped video image was achieved at zoom factor 5, giving a display monitor field width of 10 microns. A series of mesenchyme derived cell lines--from normal cells to sarcoma cells of different malignancy--was used to compare behaviour of the observed intracellular structures and results of fixation. We contrasted the dynamic behaviour of fine features in the cytoplasm of normal and neoplastic living cells and changes induced by various treatments. The tubulomembraneous 3D structure of cytoplasm in living cells is dynamic with motion observable at the new limits of resolution provided by VRCLSM. All organelles appear integrated into one functional compartment supporting the continuous 3D trafficking of small particles (vesicles). This integrated dynamic spatial network (IDSN) was found to be largest in neoplastic cells.

Animals↗

Unstable attractors induce perpetual synchronization and desynchronization.

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.

Models, Theoretical↗

Dynamical features simulated by recurrent neural networks.

The evolution of two-dimensional neural network models with rank one connecting matrices and saturated linear transfer functions is dynamically equivalent to that of piecewise linear maps on an interval. It is shown that their iterative behavior ranges from being highly predictable, where almost every orbit accumulates to an attracting fixed point, to the existence of chaotic regions with cycles of arbitrarily large period.

Journal Article↗

Identification of pre-sliding friction dynamics.

The hysteretic nonlinear dependence of pre-sliding friction force on displacement is modeled using different physics-based and black-box approaches including various Maxwell-slip models, NARX models, neural networks, nonparametric (local) models and dynamical networks. The efficiency and accuracy of these identification methods is compared for an experimental time series where the observed friction force is predicted from the measured displacement. All models, although varying in their degree of accuracy, show good prediction capability of pre-sliding friction. Finally, we show that even better results can be achieved by using an ensemble of the best models for prediction.

Journal Article↗

Dynamical coding of sensory information with competitive networks.

Based on experiments with the locust olfactory system, we demonstrate that model sensory neural networks with lateral inhibition can generate stimulus specific identity-temporal patterns in the form of stimulus-dependent switching among small and dynamically changing neural ensembles (each ensemble being a group of synchronized projection neurons). Networks produce this switching mode of dynamical activity when lateral inhibitory connections are strongly non-symmetric. Such coding uses 'winner-less competitive' (WLC) dynamics. In contrast to the well known winner-take-all competitive (WTA) networks and Hopfield nets, winner-less competition represents sensory information dynamically. Such dynamics are reproducible, robust against intrinsic noise and sensitive to changes in the sensory input. We demonstrate the validity of sensory coding with WLC networks using two different formulations of the dynamics, namely the average and spiking dynamics of projection neurons (PN).

Animals↗

Growth cone dynamics and activity-dependent processes in neuronal network development.

Many structural and functional properties of neuronal networks find their origin in the dynamic behavior of growth cones during development. The variation in dendritic morphologies can be traced back to random branching of growth cones. Segment length characteristics arise under random branching and steady growth cone propagation. Delayed outgrowth, as a result of competition between growth cones after splitting, is hypothesized to explain different lengths of paired terminal segments in Purkinje cells. The implications of activity-dependent neurite outgrowth were studied using an outgrowth function based on the theory of Kater et al. (1988, 1990). This theory embodies a homeostatic principle, according to which a neuron adapts its neuritic field so as to maintain a certain level bioelectric activity. It is shown that such homeostasis has many implications for neuromorphogenesis and network formation, as it may underlie phenomena such as overshoot during development, size differences among cells, differentiation between excitatory and inhibitory cells and compensatory sprouting. Finally, function-dependent regulation of development involves physiological as well as morphological variables. For instance, activity dependent regulation of ionic conductances such as to stabilize functional activity can result in a differentiation of certain neurons into, respectively, bursting and regular firing sub-types (Abbot et al., 1993; LeMasson et al., 1993). Similarly, the GABAergic phenotype comes fully to expression in hindbrain (cerebellar) and forebrain (neocortical) networks only if the level of ongoing excitatory activity during development is sufficiently high, whereas chronically intensified activity leads to a compensatory hypertrophy of inhibitory mechanisms (for review, see Corner 1994). Many of these results could only have been obtained by the use of mathematical models which allow rigorous analysis of the consequences of basic assumptions in the dynamics of neurite outgrowth. All in all, the findings further emphasize the role of spontaneous bioelectric activity during early development in neuronal network formation, the importance of which was first established in cultures of developing neural tissue.

Animals↗

A neural network representation of electromyography and joint dynamics in human gait.

Optimization theory and other mathematical algorithms have traditionally been used to model the relationship between muscle activity and lower-limb dynamics during human gait. We introduce here an alternative approach, based on artificial neural networks with the back-propagation algorithm, to map two different transformations: (1) EMG-->joint angles; and (2) EMG-->joint moments. Normal data for 16 muscles and three joint moments and angles (hip, knee, and ankle) were adapted from the literature [Winter (1987), The Biomechanics and Motor Control of Human Gait]. Both networks were successfully trained to map the input vector onto the output vector. The models were tested by feeding in an input vector where all 16 muscles were slightly different (20%) from the training data, and the predicted output vectors suggested that the models were valid. The trained networks were then used to perform two separate simulations: 30% reduction in soleus activity; and removal of rectus femoris. Net 2, in which electromyography was mapped onto joint moments, provided the most reasonable results, suggesting that neural networks can provide a successful platform for both biomechanical modeling and simulation. We believe that this paper has demonstrated the potential of artificial neural networks, and that further efforts should be directed towards the development of larger training sets based on normal and pathological data.

Algorithms↗

Exploring spike transfer through the thalamus using hybrid artificial-biological neuronal networks.

We use dynamic clamp to construct "hybrid" thalamic circuits by connecting a biological neuron in situ to silicon- or software-generated "neurons" through artificial synapses. The purpose is to explore cellular sensory gating mechanisms that regulate the transfer efficiency of signals during different sleep-wake states. Hybrid technology is applied in vitro to different paradigms such as: (1) simulating interactions between biological thalamocortical neurons, artificial reticular thalamic inhibitory interneurons and a simulated sensory input, (2) grafting an artificial sensory input to a wholly biological thalamic network that generates spontaneous sleep-like oscillations, (3) injecting in thalamocortical neurons a background synaptic bombardment mimicking the activity of corticothalamic inputs. We show that the graded control of the strength of intrathalamic inhibition, combined with the membrane polarization and the fluctuating synaptic noise in thalamocortical neurons, is able to govern functional shifts between different input/output transmission states of the thalamic gate.

Action Potentials↗

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks.

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Computer Simulation↗

Influence of noise on the function of a "physiological" neural network.

A model neural network with stochastic elements in its millisecond dynamics is investigated. The network consists of neuronal units which are modelled in close analogy to physiological neurons. Dynamical variables of the network are the cellular potentials, axonic currents and synaptic efficacies. The dynamics of the synapses obeys a modified Hebbian rule and, as proposed by v. d. Malsburg (1981, 1985), develop on a time scale of a tenth of a second. In a previous publication (Buhmann and Schulten 1986) we have confirmed that the resulting noiseless auto-associative network is capable of the well-known computational tasks of formal associative networks (Cooper 1973; Kohonen et al. 1984, 1981; Hopfield 1982). In the present paper we demonstrate that random fluctuations of the membrane potential improve the performance of the network. In comparison to a deterministic network a noisy neural network can learn at lower input frequencies and with lower average neural firing rates. The electrical activity of a noisy network is very reminiscent of that observed by physiological recordings. We demonstrate furthermore that associative storage reduces the effective dimension of the phase space in which the electrical activity of the network develops.

Animals↗

Interrelations between dynamical properties and structural characteristics of signal transduction networks.

We present a theoretical approach for understanding the interrelations between dynamics and structure of signal transduction pathways. We consider large sets of networks with a specific number of kinases and phosphatases. Our methods are based on nonlinear differential equations and pathway dynamics is characterised in terms of signal amplification and signal duration. We show that networks with a high number of kinases, high connectivities and low phosphatase activities tend to be unstable and run, therefore, the risk to display autoactivation. Analysis of signal transduction pathways retrieved from databases reveals that several structural characteristics required for pathway stability are fulfilled for networks of very large size.

Animals↗

Dynamic light scattering study of fine semiflexible fibrin networks.

Fine fibrin networks have been investigated using the dynamic light scattering (DLS) technique. At the shortest delay times, t, the dynamic structure factor s(q,t) is found to depend on time according to an exponential function and, at intermediate delay times (up to 1 ms), to a stretched exponential. At longer times (t > 1 ms), a progressively increasing deviation from the stretched exponential behaviour has been observed. These results are in agreement with the theoretical predictions of a recently forwarded model for semiflexible polymers in semidilute solutions [K. Kroy and E. Frey, Physical Review E 55 (1996) p. 3092.], despite the fact that fibrin networks are made up of crosslinked branched polymers. The model, moreover, allows the calculation from the initial decay rate gamma q(0) of the average diameter of the fibrin fibres, a. The value of a = 30 +/- 2 nm, at fibrinogen concentration c(f) = 1676 nM and ionic strength 0.5, fits well into the data reported in electron microscopy studies. A concentration dependence of the average diameter of the fibrin fibres has been observed which saturates at the highest concentrations. The diameter of fibrin fibres is an important component in determining the physical properties of the fibrin networks, since the radial growth of fibrin fibres is limited by twisting during protofibrils aggregation. Our results indicate the importance of taking into account intrinsic semiflexibility in studying the physical properties of 'real' polymers and emphasize the high sensitivity of the DLS technique to investigate biological polymers also at the lowest concentrations where the systems are very fragile.

Buffers↗

Classification of low back pain from dynamic motion characteristics using an artificial neural network.

STUDY DESIGN: Data were collected from 183 subjects who were randomly assigned to the training and test groups. During testing of the classification system, knowledge of the low back pain condition or motion characteristics of the patients in the test group was not made available to the system. OBJECTIVES: To determine specific characteristics of trunk motion associated with different categories of spinal disorders and to determine whether a neural network analysis system can be effective in distinguishing patterns. SUMMARY OF BACKGROUND DATA: Numerous studies have established the difficulty of evaluating lower back pain. Imaging techniques are expensive and ineffective in many cases. A technique for evaluation of lower back pain was developed on the basis of analysis of such dynamic motion features as shape, velocity, and symmetry of movements, using a neural network classification system. METHODS: Dynamic motion data were collected from 183 subjects using a triaxial goniometer. Features of the movement were extracted and provided as input to a two-stage neural network classifier governed by a radial basis function architecture. After training, the output of the classifier was compared with Québec Task Force pain classifications obtained for the patients. Linear and nonlinear classification techniques were compared. RESULTS: The system could determine low back pain classification from motion characteristics. The neural network classifier produced the best results with up to 85% accuracy on novel "validation" data. CONCLUSIONS: A neural network based on kinematic data is an excellent predictive model for classification of lower back pain. Such a system could markedly improve the management of lower back pain in the individual patient.

Adult↗

Dynamical analysis of continuous higher-order hopfield networks for combinatorial optimization.

In this letter, the ability of higher-order Hopfield networks to solve combinatorial optimization problems is assessed by means of a rigorous analysis of their properties. The stability of the continuous network is almost completely clarified: (1) hyperbolic interior equilibria, which are unfeasible, are unstable; (2) the state cannot escape from the unitary hypercube; and (3) a Lyapunov function exists. Numerical methods used to implement the continuous equation on a computer should be designed with the aim of preserving these favorable properties. The case of nonhyperbolic fixed points, which occur when the Hessian of the target function is the null matrix, requires further study. We prove that these nonhyperbolic interior fixed points are unstable in networks with three neurons and order two. The conjecture that interior equilibria are unstable in the general case is left open.

Animals↗

The dynamics of substance use and sex networks in HIV transmission.

This article (1) reviews the research to identify mechanisms that may underlie HIV heterosexual transmission in developed and developing countries, (2) examines linkages between sex and substance use HIV transmission risks, and (3) describes sex network measurement issues relevant to developing HIV preventive interventions. The research contributions of developed countries to understanding sexually transmitted HIV have long recognized the influence of substance use and sex networks. Research in developing countries has contributed significantly to the environmental and biological understanding of HIV sexual transmission dynamics. Although much of the research in developing countries has recruited participants from venues where alcohol or other substance use is pervasive (e.g., truck stops), few studies have explicitly examined the relationship between HIV sex risk and substance use in these contexts. Finally, sex network characteristics and structural features, which have been found to play identifiable roles in the spread of HIV, are measurable at the individual level and can contribute substantively to the development and the evaluation of HIV-preventive interventions implemented at the network or community level.

Developed Countries↗