Artificial neural network model for the generation of muscle activation patterns for human locomotion.

Skilled locomotor behaviour requires information from various levels within the central nervous system (CNS). Mathematical models have permitted researchers to simulate various mechanisms in order to understand the organization of the locomotor control system. While it is difficult to adequately characterize the numerous inputs to the locomotor control system, an alternative strategy may be to use a kinematic movement plan to represent the complex inputs to the locomotor control system based on the possibility that the CNS may plan movements at a kinematic level. We propose the use of artificial neural network (ANN) models to represent the transformation of a kinematic plan into the necessary motor patterns. Essentially, kinematic representation of the actual limb movement was used as the input to an ANN model which generated the EMG activity of 8 muscles of the lower limb and trunk. Data from a wide variety of gait conditions was necessary to develop a robust model that could accommodate various environmental conditions encountered during everyday activity. A total of 120 walking strides representing normal walking and ten conditions where the normal gait was modified in terms of cadence, stride length, stance width or required foot clearance. The final network was assessed on its ability to predict the EMG activity on individual walking trials as well as its ability to represent the general activation pattern of a particular gait condition. The predicted EMG patterns closely matched those recorded experimentally, exhibiting the appropriate magnitude and temporal phasing required for each modification. Only 2 of the 96 muscle/gait conditions had RMS errors above 0.10, only 5 muscle/gait conditions exhibited correlations below 0.80 (most were above 0.90) and only 25 muscle/gait conditions deviated outside the normal range of muscle activity for more than 25% of the gait cycle. These results indicate the ability of single network ANNs to represent the transformation between a kinematic movement plan and the necessary muscle activations for normal steady state locomotion but they were also able to generate muscle activation patterns for conditions requiring changes in walking speed, foot placement and foot clearance. The abilities of this type of network have implications towards both the fundamental understanding of the control of locomotion and practical realizations of artificial control systems for use in rehabilitation medicine.     

A model of neural network for spatiotemporal pattern recognition

A model of neural network to recognize spatiotemporal patterns is presented. The network consists of two kinds of neural cells: P-cells and B-cells. A P-cell generates an impulse responding to more than one impulse and embodies two special functions: short term storage (STS) and heterosynaptic facilitation (HSF). A B-cell generates several impulses with high frequency as soon as it receives an impulse. In recognizing process, an impulse generated by a P-cell represents a recognition of stimulus pattern, and triggers the generation of impulses of a B-cell. Inhibitory impulses with high frequency generated by a B-cell reset the activities of all P-cells in the network.Two examples of spatiotemporal pattern recognition are presented. They are achieved by giving different values to the parameters of the network. In one example, the network recognizes both directional and non-directional patterns. The selectivities to directional and non-directional patterns are realized by only adjusting excitatory synaptic weights of P-cells. In the other example, the network recognizes time series of spatial patterns, where the lengths of the series are not necessarily the same and the transitional speeds of spatial patterns are not always the same. In both examples, the HSF signal controls the total activity of the network, which contributes to exact recognition and error recovery. In the latter example, it plays a role to trigger and execute the recognizing process. Finally, we discuss the correspondence between the model and physiological findings.     

Coupled oscillators and the design of central pattern generators

Much can be deduced about the behavior of chains of oscillators under minimal assumptions about the nature of the oscillators or the coupling. This paper reviews work on such chains, and provides a framework within which implications may be drawn about the neural networks that govern undulatory locomotion in lower vertebrates.     

Models of central pattern generators for quadruped locomotion II. Secondary gaits

We continue the analysis of the network of symmetrically coupled cells modeling central pattern generators (CPG) for quadruped locomotion proposed by Golubitsky, Stewart, Buono and Collins by studying secondary gaits. Secondary gaits are modeled by output signals from the CPG where each cell emits one of two different output signals along with exact phase shifts. Examples of secondary gaits are transverse gallop, rotary gallop, and canter. We classify secondary gaits that bifurcate when the Poincaré map of a primary gait has a real eigenvalue crossing the unit circle. In particular, we show that periodic solutions modeling transverse gallop and rotary gallop bifurcate from primary gaits. Moreover, we find gaits from period-doubling bifurcations and analyze plausible footfall patterns. Numerical simulations are performed using the Morris-Lecar equations as cell dynamics.     

Models of central pattern generators for quadruped locomotion I. Primary gaits

In this paper we continue the analysis of a network of symmetrically coupled cells modeling central pattern generators for quadruped locomotion proposed by Golubitsky, Stewart, Buono, and Collins. By a cell we mean a system of ordinary differential equations and by a coupled cell system we mean a network of identical cells with coupling terms. We have three main results in this paper. First, we show that the proposed network is the simplest one modeling the common quadruped gaits of walk, trot, and pace. In doing so we prove a general theorem classifying spatio-temporal symmetries of periodic solutions to equivariant systems of differential equations. We also specialize this theorem to coupled cell systems. Second, this paper focuses on primary gaits; that is, gaits that are modeled by output signals from the central pattern generator where each cell emits the same waveform along with exact phase shifts between cells. Our previous work showed that the network is capable of producing six primary gaits. Here, we show that under mild assumptions on the cells and the coupling of the network, primary gaits can be produced from Hopf bifurcation by varying only coupling strengths of the network. Third, we discuss the stability of primary gaits and exhibit these solutions by performing numerical simulations using the dimensionless Morris-Lecar equations for the cell dynamics.     

Neuromodulation of central pattern generators in invertebrates and vertebrates

Central pattern generators are subject to extensive modulation that generates flexibility in the rhythmic outputs of these neural networks. The effects of neuromodulators interact with one another, and modulatory neurons are themselves often subject to modulation, enabling both higher order control and indirect interactions among central pattern generators. In addition, modulators often directly mediate the interactions between functionally related central pattern generators. In systems such as the vertebrate respiratory central pattern generator, multiple pacemaker types interact to produce rhythmic output. Modulators can then alter the relative contributions of the different pacemakers, leading to substantial changes in motor output and hence to different behaviors. Surprisingly, substantial changes in some aspects of the circuitry of a central pattern generator, such as a several-fold increase in synaptic strength, can sometimes have little effect on the output of the CPG, whereas other changes have profound effects.     

A neural network model for selective attention in visual pattern recognition

A neural network model of the mechanism of selective attention in visual pattern recognition is proposed and simulated on a digital computer.When a complex figure consisting of two patterns or more is presented to the model, it is segmented into individual patterns, and each pattern is recognized separately. Even if one of the patterns to which the model is paying selective attention is affected by noise or defects, the model can recall the complete pattern from which the noise has been eliminated and the defects corrected. It is not necessary for perfect recall that the stimulus pattern should be identical in shape to the training pattern. Even though the pattern is distorted in shape or changed in size, it can be correctly recognized and the missing portions restored.The model consists of a hierarchical neural network which has efferent as well as afferent connections between cells. The afferent and the efferent signals interact with each other in the network: the efferent signals, that is, the signals for selective attention, have a facilitating effect on the afferent ones, and, at the same time, the afferent signals gate efferent signal flow. When some feature in the stimulus is not extracted in the afferent paths, the threshold for detection of that feature is automatically lowered by decreasing the efficiency of inhibition, and the model tries to extract even vague traces of the undetected feature.     

Mechanisms of frequency and pattern control in the neural rhythm generators

The locomotive motion in animals is produced in some central neural units, and basically no sensory signal from peripheral receptors is necessary to induce it. The rhythm generators do not only produce rhythms but also alter their frequencies and patterns. This paper presents some methematical models of the neural rhythm generators and discusses various aspects of the frequency and pattern control in them.     

The three-loop model: a neural network for the generation of saccadic reaction times

This paper presents a computer simulation of the three-loop model for the temporal aspects of the generation of visually guided saccadic eye movements. The intention is to reproduce complex experimental reaction time distributions by a simple neural network. The operating elements are artificial but realistic neurones. Four modules are constructed, each consisting of 16 neural elements. Within each module, the elements are connected in an all-to-all manner. The modules are working parallel and serial according to the anatomically and physiologically identified visuomotor pathways including the superior colliculus, the frontal eye fields, and the parietal cortex. Two transient-sustained input lines drive the network: one represents the visual activity produced by the onset of the saccade target, the other represents a central activity controlling the preparation of saccades, e.g. the end of active fixation. The model works completely deterministically; its stochastic output is a consequence of the stochastic properties of the input only. Simulations show how multimodal distributions of saccadic reaction times are produced as a natural consequence of the model structure. The gap effect on saccadic reaction times is correctly produced by the model: depending only on the gap duration (all model parameters unchanged) express, fast-regular, and slow-regular saccades are obtained in different numbers. In agreement with the experiments, bi- or trimodal distributions are produced only for medium gap durations (around 200 ms), while for shorter or longer gaps the express mode disappears and the distributions turn bi- or even unimodal. The effect of varying the strength of the transient-sustained components and the ongoing activity driving the hierarchically highest module are considered to account for the interindividual variability of the latency distributions obtained from different subjects, effects of different instructions to the same subject, and the observation of express makers (subjects who produce exclusively express saccades). How the model can be extended to describe the spatial aspects of the saccade system will be discussed as well as the effects of training and/or rapid adaptation to experimental conditions.     

On the derivation and tuning of phase oscillator models for lamprey central pattern generators

Using phase response curves and averaging theory, we derive phase oscillator models for the lamprey central pattern generator from two biophysically-based segmental models. The first one relies on network dynamics within a segment to produce the rhythm, while the second contains bursting cells. We study intersegmental coordination and show that the former class of models shows more robust behavior over the animal's range of swimming frequencies. The network-based model can also easily produce approximately constant phase lags along the spinal cord, as observed experimentally. Precise control of phase lags in the network-based model is obtained by varying the relative strengths of its six different connection types with distance in a phase model with separate coupling functions for each connection type. The phase model also describes the effect of randomized connections, accurately predicting how quickly random network-based models approach the determinisitic model as the number of connections increases.     

Recognition of partly occluded patterns: a neural network model

 Human beings are often able to read a letter or word partly occluded by contaminating ink stains. However, if the stains are completely erased and the occluded areas of the letter are changed to white, we usually have difficulty in reading the letter. In this article I propose a hypothesis explaining why a pattern is easier to recognize when it is occluded by visible objects than by invisible opaque objects. A neural network model is constructed based on this hypothesis. The visual system extracts various visual features from the input pattern and then attempts to recognize it. If the occluding objects are not visible, the visual system will have difficulty in distinguishing which features are relevant to the original pattern and which are newly generated by the occlusion. If the occluding objects are visible, however, the visual system can easily discriminate between relevant and irrelevant features and recognize the occluded pattern correctly. The proposed model is an extended version of the neocognitron model. The activity of the feature-extracting cells whose receptive fields cover the occluding objects is suppressed in an early stage of the hierarchical network. Since the irrelevant features generated by the occlusion are thus eliminated, the model can recognize occluded patterns correctly, provided the occlusion is not so large as to prevent recognition even by human beings. Received: 21 February 2000 / Accepted in revised form: 11 September 2000     

Ventrolateral medullary respiratory network and a model of cough motor pattern generation

The primaryhypothesis of this study was that the cough motor pattern is produced,at least in part, by the medullary respiratory neuronal network inresponse to inputs from "cough" and pulmonary stretch receptorrelay neurons in the nucleus tractus solitarii. Computer simulations ofa distributed network model with proposed connections from the nucleustractus solitarii to ventrolateral medullary respiratory neuronsproduced coughlike inspiratory and expiratory motor patterns. Predictedresponses of various "types" of neurons (I-DRIVER, I-AUG, I-DEC,E-AUG, and E-DEC) derived from the simulations were tested in vivo.Parallel and sequential responses of functionally characterizedrespiratory-modulated neurons were monitored during fictive cough indecerebrate, paralyzed, ventilated cats. Coughlike patterns in phrenicand lumbar nerves were elicited by mechanical stimulation of theintrathoracic trachea. Altered discharge patterns were measured in mosttypes of respiratory neurons during fictive cough. The resultssupported many of the specific predictions of our cough generationmodel and suggested several revisions. The two main conclusions were asfollows: 1) TheBötzinger/rostral ventral respiratory group neurons implicated inthe generation of the eupneic pattern of breathing also participate inthe configuration of the cough motor pattern.2) This altered activity ofBötzinger/rostral ventral respiratory group neurons istransmitted to phrenic, intercostal, and abdominal motoneurons via thesame bulbospinal neurons that provide descending drive during eupnea.

     

Peripheral feedback mechanisms acting on the central pattern generators for locomotion in fish and cat

The feedback mechanisms taking part in the control of locomotion in cat and fish are reviewed, particularly with regard to position- and movement-related feedback. It is shown that in both fish and cat there is a powerful position-dependent negative feedback which will act only in the position range where the muscle activity normally changes, e.g., from extensor to flexor activity. In addition, there is positive feedback in the middle of the movement range which will act in certain conditions, e.g., to promote and maintain flexor activity during the flexion of the hind limb.     

上海市景观格局的人工神经网络(ANN)模型

定量分析城市景观的空间格局,深入研究景观格局的形成机制,将有助于理解城市景观的格局与过程,分析城市化的社会、经济和生态学后果以及制定更有效的景观管理策略。研究以城市景观生态学途径,应用基于GIS的景观格局分析与人工神经网络(ANN)相结合的方法定量分析上海市城市景观格局(1994年)及其变化规律,建立了能够较好地模拟上海市景观格局对居住区用地、道路密度、人口密度、城市发展历史与黄浦江等自然、社会、经济因素响应的人工神经网络。结果表明,人工神经网络方法适于研究城市化驱动因素与城市景观格局的非线性对应关系,为景观格局形成机制和景观空间结构与生态学过程相互关系的深入研究提供了一条有效、实用的研究途径。     

A model for neural representation of temporal duration

To address how temporal duration is encoded in neural systems, we put forward a simple model for recurrent neural networks. Particular assumptions are only the following two: (1) neuronal bistability and; (2) environmental effects described by a heat bath. The results of Monte Carlo simulation show that population activity triggered at an initial time continues for a prolonged duration, followed by an abrupt self-termination. This time course seems highly suitable for neural representation of temporal duration. The time scale of this prolonged duration is much longer than the time scale of neuronal firing which is of the order of ms. The former time scale implies that of interval timing in cognition and behaviour. Thus, the model provides a possible explanation for a link between these two separated time scales. The Weber law, a hallmark of humans and animals' interval timing, can also be reproduced in our model.     

The fictively breathing tadpole brainstem preparation as a model for the development of respiratory pattern generation and central chemoreception

Spontaneous high-frequency, low-amplitude and low-frequency, high-amplitude efferent bursting patterns of cranial and spinal motor nerve activity in the in vitro brainstem preparation of the bullfrog tadpole Rana catesbeiana have been characterized as fictive gill and lung ventilation, respectively (Gdovin MJ, Torgerson CS, Remmers JE). Characterization of gill and lung ventilatory activity in cranial nerves in the spontaneously breathing tadpole Rana catesbeiana, FASEB J 1996;10(3):A642; Gdovin MJ, Torgerson CS, Remmers JE. Neurorespiratory pattern of gill and lung ventilation in the decerebrate spontaneously breathing tadpole, Respir Physiol 1998;113:135 146; Pack AI, Galante RJ, Walker RE, Kubin LK, Fishman AP. Comparative approach to neural control of respiration, In: Speck DF, Dekin MS, Revelette WR, Frazier DT, editors. Respiratory Control Central and Peripheral Mechanisms. Lexington: University of Kentucky Press, 1993:52-57). In addition, the ontogenetic dependence of central respiratory chemoreceptor stimulation on fictive gill and lung ventilation has been previously described (Torgerson CS, Gdovin MJ, Remmers JE. Fictive gill and lung ventilation in the pre- and post-metamorphic tadpole brainstem, J Neurophysiol 1998, in press). To investigate the neural substrates responsible for central respiratory rhythm generation of gill and lung ventilation in the developing tadpole, we recorded efferent activities of cranial nerve (CN) V, VII, and X and spinal nerve (SN) II during changes in superfusate PCO2 before and after multiple transection of the in vitro brainstem. The brainstem was transected between CN VIII and IX and the response to changes in PCO2 was recorded. A second transection was then made between the caudal margin of CN X and rostral to SN II. Preliminary data reveal that robust gill ventilation was recorded consistently only if the segment of brainstem included CN X, whereas the loci capable of eliciting fictive lung bursting patterns appeared to differ depending on developmental stage. These data demonstrate that the neural substrate required for fictive gill and lung ventilation exists in anatomically separate regions such that the gill central pattern generator (CPG) is located in the caudal medulla at the level of CN X throughout development, whereas the location of the lung CPG is located more rostrally at the level of CN VII in the post-metamorphic larva. Both in vivo and in vitro studies revealed two distinct neural bursting patterns associated with gill and lung ventilation. Sequential activation of CN V, VII, X were observed during gill ventilation of in vivo and fictive gill ventilation in vitro, whereas these nerve activities, along with SN II displayed more synchronous bursting patterns of activation during lung ventilation and fictive lung breaths.     

An evolving neural network for the interpretation of gene expression patterns

It is of central interest in biology to understand how gene activity networks are coordinated and integrated in the cell. Within the field of genomics, microarray technologies have become a powerful technique for monitoring simultaneously the expression patterns of thousands of genes under different sets of conditions. A main task now is to propose analytical methods that can suggest which groups of genes are activated by similar conditions. We review several techniques based on self-organizing map and clustering algorithms but implemented through a network of units controlled by biologically inspired functions (see Table 1). The computer tool, named NBIA, permits a categorization that generates a set of gene groups with coordinated expression patterns.     

Central pattern generators and the control of rhythmic movements.

Central pattern generators are neuronal circuits that when activated can produce rhythmic motor patterns such as walking, breathing, flying, and swimming in the absence of sensory or descending inputs that carry specific timing information. General principles of the organization of these circuits and their control by higher brain centers have come from the study of smaller circuits found in invertebrates. Recent work on vertebrates highlights the importance of neuro-modulatory control pathways in enabling spinal cord and brain stem circuits to generate meaningful motor patterns. Because rhythmic motor patterns are easily quantified and studied, central pattern generators will provide important testing grounds for understanding the effects of numerous genetic mutations on behavior. Moreover, further understanding of the modulation of spinal cord circuitry used in rhythmic behaviors should facilitate the development of new treatments to enhance recovery after spinal cord damage.     

A neural network model for the mechanism of feature-extraction

We propose a new multilayered neural network model which has the ability of rapid self-organization. This model is a modified version of the cognitron (Fukushima, 1975). It has modifiable inhibitory feedback connections, as well as conventional modifiable excitatory feedforward connections, between the cells of adjoining layers. If a feature-extracting cell in the network is excited by a stimulus which is already familiar to the network, the cell immediately feeds back inhibitory signals to its presynaptic cells in the preceding layer, which suppresses their response. On the other hand, the feature-extracting cell does not respond to an unfamiliar feature, and the responses from its presynaptic cells are therefore not suppressed because they do not receive any feedback inhibition. Modifiable synapses in the new network are reinforced in a way similar to those in the cognitron, and synaptic connections from cells yielding a large sustained output are reinforced. Since familiar stimulus features do not elicit a sustained response from the cells of the network, only circuits which detect novel stimulus features develop. The network therefore quickly acquires favorable pattern-selectivity by the mere repetitive presentation of set of learning patterns.