Mechanisms for lateral turns in lamprey in response to descending unilateral commands: a modeling study

 Straight locomotion in the lamprey is, at the segmental level, characterized by alternating bursts of motor activity with equal duration and spike frequency on the left and the right sides of the body. Lateral turns are characterized by three main changes in this pattern: (1) in the turn cycle, the spike frequency, burst duration, and burst proportion (burst duration/cycle duration) increase on the turning side; (2) the cycle duration increases in both the turn cycle and the succeeding cycle; and (3) in the cycle succeeding the turn cycle, the burst duration increases on the non-turning side (rebound). We investigated mechanisms for the generation of turns in single-segment models of the lamprey locomotor spinal network. Activation of crossing inhibitory neurons proved a sufficient mechanism to explain all three changes in the locomotor rhythm during a fictive turn. Increased activation of these cells inhibits the activity of the opposite side during the prolonged burst of the turn cycle, and slows down the locomotor rhythm. Secondly, this activation of the crossing inhibitory neurons is accompanied by an increased calcium influx into the cells. This gives a suppressed activity on the turning side and a contralateral rebound after the turn, through activation of calcium-dependent potassium channels. Received: 28 June 2000 / Accepted for publication: 10 May 2001     

Simple models for excitable and oscillatory neural networks

 Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators providing input to a kinematic musculature model of lamprey.. Received: 25 November 1996 / Revised version: 9 December 1997     

Postural control system

The postural control system has two main functions: first, to build up posture against gravity and ensure that balance is maintained; and second, to fix the orientation and position of the segments that serve as a reference frame for perception and action with respect to the external world. This dual function of postural control is based on four components: reference values, such as orientation of body segments and position of the center of gravity (an internal representation of the body or postural body scheme); multisensory inputs regulating orientation and stabilization of body segments; and flexible postural reactions or anticipations for balance recovery after disturbance, or postural stabilization during voluntary movement. The recent data related to the organization of this system will be discussed in normal subjects (during ontogenesis), the elderly and in patients with relevant deficits.     

Control model of human stance using fuzzy logic

 A control model of human stance is proposed based on knowledge from behavioral experiments and physiological systems. The proposed model is based on the control of global variables specific to body orientation and alignment, rather than on the control of the body’s center of mass within the base of support. Furthermore, the proposed control model is not based on purely inverted pendulum body mechanics where only motion at one joint is controlled, as for instance the ankle. In the proposed model, the degrees of freedom are controlled by using reciprocal and synergistic muscle actions at multiple joints. The control model is based on three sets of different global variables which act in parallel: (1) limb length and its derivative, (2) limb orientation and its derivative, and (3) trunk attitude and its derivative. An important feature of the control model is the use of fuzzy logic, which enables us to model experimental findings and physiological knowledge in a meaningful and explicit way using fuzzy if-then rules. In the control model, 36 fuzzy if-then rules are implemented and applied using a four-linked segment model consisting of a trunk, thigh, shank and foot. Uni- and biarticular limb muscles and trunk muscles are represented as torque actuators at each individual joint. In the model, three sets of global variables act in parallel and make corrective and coordinated responses to internal, self-induced perturbations. The data show that the use of global variables and fuzzy logic successfully enables us to model human standing with sway about a point of equilibrium. Small changes in, for example, total body sway are comparable to those seen during natural sway in human stance. The selected controllers—limb length, limb orientation and trunk attitude—seem to be appropriate for human stance control. Received: 30 October 1996/Accepted in revised form: 7 April 1997     

Leg orientation as a clinical sign for pusher syndrome

Background  

Effective control of (upright) body posture requires a proper representation of body orientation. Stroke patients with pusher syndrome were shown to suffer from severely disturbed perception of own body orientation. They experience their body as oriented 'upright' when actually tilted by nearly 20° to the ipsilesional side. Thus, it can be expected that postural control mechanisms are impaired accordingly in these patients. Our aim was to investigate pusher patients' spontaneous postural responses of the non-paretic leg and of the head during passive body tilt.     

A multisensory integration model of human stance control

A model is presented to study and quantify the contribution of all available sensory information to human standing based on optimal estimation theory. In the model, delayed sensory information is integrated in such a way that a best estimate of body orientation is obtained. The model approach agrees with the present theory of the goal of human balance control. The model is not based on purely inverted pendulum body dynamics, but rather on a three-link segment model of a standing human on a movable support base. In addition, the model is non-linear and explicitly addresses the problem of multisensory integration and neural time delays. A predictive element is included in the controller to compensate for time delays, necessary to maintain erect body orientation. Model results of sensory perturbations on total body sway closely resemble experimental results. Despite internal and external perturbations, the controller is able to stabilise the model of an inherently unstable standing human with neural time delays of 100 ms. It is concluded, that the model is capable of studying and quantifying multisensory integration in human stance control. We aim to apply the model in (1) the design and development of prostheses and orthoses and (2) the diagnosis of neurological balance disorders. Received: 25 August 1997 / Accepted in revised form: 8 December 1998     

Comparative neurobiology of postural control

In recent years, studies of nervous mechanisms for the control of body posture have been performed on animal models of different complexity - cat, rabbit, lamprey and the mollusc Clione. These studies have greatly expanded our knowledge of how the control system operates, how the system can change the stabilized body orientation and how the postural functions are distributed within different parts of the CNS. For simpler animal models, the postural network has been analyzed in considerable detail and main cell types and their interactions have been identified.     

Biomechanical analysis of movement strategies in human forward trunk bending. II. Experimental study

 The large mass of the human upper trunk, its elevated position during erect stance, and the small area limited by the size of the feet, stress the importance of equilibrium control during trunk movements. The objective of the present study was to perform a biomechanical analysis of fast forward trunk movements in order to understand the coordination between movement and posture. The analysis is based on a comparison between experimentally observed bending and hypothetical “optimal bending” performed on an infinitely narrow support, as presented in a companion paper. The experimental data were obtained from 16 subjects who performed fast forward bending while standing on a wide platform or on a narrow beam. The analysis is performed by decomposition of the movement into three dynamically independent components, each representing a movement along one of the three eigenvectors of the motion equation. The eigenmovements are termed “hip”, “ankle”, and “knee” eigenmovements, according to the dominant joint. The experimentally observed movement is characterized mainly by the hip and ankle eigenmovements, whereas the knee eigenmovement is negligible. Similarly to the “optimal bending” the ankle eigenmovement starts earlier and lasts longer than the hip eigenmovement. An early forward acceleration of the center of gravity in the ankle eigenmovement is caused by anticipatory changes in the ankle joint torque. This clarifies the role of the early tibialis anterior burst and/or soleus inhibition usually observed in electromyographic recordings during forward bending. The results suggest that the hip and the ankle eigenmovements can be treated as independently controlled motion units aimed at functionally different behavioral goals: the bending per se and postural adjustment. It is proposed that the central nervous system has to control these motion units sequentially in order to perform the movement and maintain equilibrium. It is also suggested that the hip and ankle eigenmovements can be regarded as a biomechanical background for the hip and ankle strategies introduced by Horak and Nashner (1986) on the basis of electromyographic recordings and kinematic patterns in response to postural perturbations. Received: 1 July 1999 / Accepted in revised form: 23 October 2000     

A linear canal-otolith interaction model to describe the human vestibulo-ocular reflex

A control systems model of the vestibulo-ocular reflex (VOR) originally derived for yaw rotation about an eccentric axis (Crane et al. 1997) was applied to data collected during ambulation and dynamic posturography. The model incorporates a linear summation of an otolith response due to head translation scaled by target distance, adding to a semi-circular canal response that depends only on angular head rotation. The results of the model were compared with human experimental data by supplying head angular velocity as determined by magnetic search coil recording as the input for the canal branch of the model and supplying linear acceleration as determined by flux gate magnetometer measurements of otolith position. The model was fit to data by determining otolith weighting that enabled the model to best fit the data. We fit to the model experimental data from normal subjects who were: standing quietly, walking, running, or making active sinusoidal head movements. We also fit data obtained during dynamic posturography tasks of: standing on a platform sliding in a horizontal plane at 0.2 Hz, standing directly on a platform tilting at 0.1 Hz, and standing on the tilting platform buffered by a 5-cm thick foam rubber cushion. Each task was done with the subject attending a target approximately 500, 100, or 50 cm distant, both in light and darkness. The model accurately predicted the observed VOR response during each test. Greater otolith weighting was required for near targets for nearly all activities, consistent with weights for the otolith component found in previous studies employing imposed rotations. The only exceptions were for vertical axis motion during standing, sliding, and tilting when the platform was buffered with foam rubber. In the horizontal axis, the model always fit near target data better with a higher otolith component. Otolith weights were similar with the target visible and in darkness. The model predicts eye movement during both passive whole-body rotation and free head movement in space implying that the VOR is controlled by a similar mechanism during both situations. Factors such as vision, proprioception, and efference copy that are available during head free motion but not during whole-body rotation are probably not important to gaze stabilization during ambulation and postural stabilizing movement. The linearity of the canal-otolith interaction was tested by re-analysis of the whole body rotation data on which the model is based (Crane et al. 1997). Normalized otolith-mediated gain enhancement was determined for each axis of rotation. This analysis uncovered minor non-linearities in the canal-otolith interaction at frequencies above 1.6 Hz and when the axis of rotation was posterior to the head. Received: 11 March 1998 / Received in revised form: 1 March 1999     

Effect of imbalance in activities between ON- and OFF-center LGN cells on orientation map formation

 It has been reported that the OFF responses of cells in the visual pathway are stronger, on average, than the ON responses early in the life of cats and ferrets. In this study, we theoretically investigate the effects of this imbalance in activity on the orientation map formation. We carry out computer simulations based on our previously proposed self-organization model, in which the correlated activities between ON- and OFF-center cells in the lateral geniculate nucleus regulate the formation of orientation maps in the visual cortex. When imbalance between the activities of these ON- and OFF-center cells is assumed, we obtain orientation maps with spatial periodicity, as observed in the experiments. On the other hand, when balanced activities are assumed, orientation maps do not show periodicity. This suggests that the imbalance in activities between ON- and OFF-center cells contributes to the elaboration of orientation maps during the critical period. Received: 8 July 1999 / Accepted in revised form: 18 February 2000     

Postural responses to vibrostimulation of the neck muscle proprioceptors in man

Postural responses to vibrostimulation (50–100 Hz, 0.5 mm, 4–8 sec) of muscles of the back surface of the neck were studied in healthy subjects. In the sitting position, vibrostimulation evoked local displacements (backward head deflection), but global postural responses (forward inclination of the whole body) developed in the standing position. The amplitude of the evoked body inclination was dependent upon the site of the vibrostimuli application along the vertebral column. Asymmetrical application of vibrostimuli to the muscles of the right or left neck side was accompanied by development of a lateral component in the postural response. Changes in the spatial orientation of the head led to the changes in postural response direction: head turning to the right resulted in right-side body deviation during vibration, and vice versa. Illusions of head bend caused by habituation to its static turning were accompanied by precisely the same changes in the direction of body deviation. It is assumed that neck-evoked motor events are mediated via central mechanisms that are involved in perception of the head and body position in space.Translated from Neirofiziologiya, Vol. 25, No. 2, pp. 101–108, March–April, 1993.     

Simultaneous Postural Adjustments (SPA) scrutinized using the Lissajous method

The goal of this research was to study the postural adjustments that occur during the course of a voluntary movement (Simultaneous Postural Adjustments: SPA). A pointing task performed at maximal velocity was considered and upper limb kinematics and body kinetics were recorded. A 2-DOF model was elaborated that distinguishes between the body segments that are mobilized in order to perform the pointing movement. These segments are the right upper limb (termed the “focal” component) and the rest of the body (termed the “postural” component). This model allowed for the calculation of both sub-systems? kinetics and a comparison of the resultant reaction (RoSh) with the corresponding action (AoSh) at the shoulder level. The analysis was based on the ellipsoidal shape of their relationship. The ellipse computation (“Lissajous ellipse”) allowed the time lag to be estimated. The results showed that the kinetics of the postural component preceded that of the focal ones and that the time lag during the SPA was not statistically different from the APA duration (dAPA). In addition, the kinetics of the postural component were found to be opposed to the perturbation induced by the pointing movement, but only during part of the SPA time interval. It was concluded that the postural component plays a dual role during the movement, which consists of postural stabilization and propulsive action, with one prevailing over the other depending on the time-instant of movement evolution. This new evidence in healthy subjects is helpful to further specify differences associated with motor impairments.     

Biomechanical analysis of movement strategies in human forward trunk bending. I. Modeling

 Two behavioral goals are achieved simultaneously during forward trunk bending in humans: the bending movement per se and equilibrium maintenance. The objective of the present study was to understand how the two goals are achieved by using a biomechanical model of this task. Since keeping the center of pressure inside the support area is a crucial condition for equilibrium maintenance during the movement, we decided to model an extreme case, called “optimal bending”, in which the movement is performed without any center of pressure displacement at all, as if standing on an extremely narrow support. The “optimal bending” is used as a reference in the analysis of experimental data in a companion paper. The study is based on a three-joint (ankle, knee, and hip) model of the human body and is performed in terms of “eigenmovements”, i.e., the movements along eigenvectors of the motion equation. They are termed “ankle”, “hip”, and “knee” eigenmovements according to the dominant joint that provides the largest contribution to the corresponding eigenmovement. The advantage of the eigenmovement approach is the presentation of the coupled system of dynamic equations in the form of three independent motion equations. Each of these equations is equivalent to the motion equation for an inverted pendulum. Optimal bending is constructed as a superposition of two (hip and ankle) eigenmovements. The hip eigenmovement contributes the most to the movement kinematics, whereas the contributions of both eigenmovements into the movement dynamics are comparable. The ankle eigenmovement moves the center of gravity forward and compensates for the backward center of gravity shift that is provoked by trunk bending as a result of dynamic interactions between body segments. An important characteristic of the optimal bending is the timing of the onset of each eigenmovement: the ankle eigenmovement onset precedes that of the hip eigenmovement. Without an earlier onset of the ankle eigenmovement, forward bending on the extremely narrow support results in falling backward. This modeling approach suggests that during trunk bending, two motion units – the hip and ankle eigenmovements – are responsible for the movement and for equilibrium maintenance, respectively. Received: 1 July 1999 / Accepted in revised form: 23 October 2000     

Habitat selection by larvae of a fluvial lamprey, <Emphasis Type="Italic">Lethenteron reissneri</Emphasis>, in a small stream and an experimental aquarium

Habitat selection by fluvial lamprey larvae, Lethenteron reissneri (Petromyzontidae), was studied in a natural stream and an experimental aquarium to clarify microhabitat requirements for future conservation of natural populations. A gross collection survey of lamprey larvae in the Monbetsu River, southeastern Hokkaido, Japan, revealed a remarkable bias toward distribution in sandy-mud beds. An analysis using Jacobs' electivity index showed that the larvae selectively utilized spaces having regard to shallow water, weak current, deep sandy-mud, and fine substrate particles. A comparison of microhabitat use between small- (≤5 cm) and large-sized larvae (>5 cm) indicated that the latter utilized the space with greater ranges in both water depth and substrate particle size than the former. Both the field survey and laboratory experiments on larval selectivity of physical habitat variables clearly demonstrated that substrate particle size was the most important variable for small-sized larvae whereas both water depth and substrate depth were more important for large larvae. These findings should be applicable in directing attempts at fluvial habitat restoration for conservation of this endangered lamprey species. Received: November 1, 2000 / Revised: September 12, 2001 / Accepted: October 18, 2001     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes (11, 12), thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger (11) is extended here to assess the consequences of recently discovered receptor phenomena: “down-regulation” of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference inrelative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference inabsolute receptor occupancy). However, in the context of receptor “signal noise,” the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond (10). From this cell orientation model we can estimate the effective timeaveraging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

Reconstruction of equilibrium trajectories during whole-body movements

The framework of the equilibrium-point hypothesis was used to reconstruct equilibrium trajectories (ETs) of the ankle, hip and body center of mass during quick voluntary hip flexions (`Japanese courtesy bow') by standing subjects. Different spring loads applied to the subject's back were used to introduce smooth perturbations that are necessary to reconstruct ETs based on a series of trials at the same task. Time patterns of muscle torques were calculated using inverse dynamics techniques. A second-order linear model was employed to calculate the instantaneous position of the spring-like joint or center of mass characteristic at different times during the movement. ETs of the joints and of the center of mass had significantly different shapes from the actual trajectories. Integral measures of electromyographic bursts of activity in postural muscles demonstrated a relation to muscle length corresponding to the equilibrium-point hypothesis. Received: 3 March 1997 / Accepted in revised form: 2 November 1998     

An adaptive model of sensory integration in a dynamic environment applied to human stance control

An adaptive estimator model of human spatial orientation is presented. The adaptive model dynamically weights sensory error signals. More specific, the model weights the difference between expected and actual sensory signals as a function of environmental conditions. The model does not require any changes in model parameters. Differences with existing models of spatial orientation are that: (1) environmental conditions are not specified but estimated, (2) the sensor noise characteristics are the only parameters supplied by the model designer, (3) history-dependent effects and mental resources can be modelled, and (4) vestibular thresholds are not included in the model; instead vestibular-related threshold effects are predicted by the model. The model was applied to human stance control and evaluated with results of a visually induced sway experiment. From these experiments it is known that the amplitude of visually induced sway reaches a saturation level as the stimulus level increases. This saturation level is higher when the support base is sway referenced. For subjects experiencing vestibular loss, these saturation effects do not occur. Unknown sensory noise characteristics were found by matching model predictions with these experimental results. Using only five model parameters, far more than five data points were successfully predicted. Model predictions showed that both the saturation levels are vestibular related since removal of the vestibular organs in the model removed the saturation effects, as was also shown in the experiments. It seems that the nature of these vestibular-related threshold effects is not physical, since in the model no threshold is included. The model results suggest that vestibular-related thresholds are the result of the processing of noisy sensory and motor output signals. Model analysis suggests that, especially for slow and small movements, the environment postural orientation can not be estimated optimally, which causes sensory illusions. The model also confirms the experimental finding that postural orientation is history dependent and can be shaped by instruction or mental knowledge. In addition the model predicts that: (1) vestibular-loss patients cannot handle sensory conflicting situations and will fall down, (2) during sinusoidal support-base translations vestibular function is needed to prevent falling, (3) loss of somatosensory information from the feet results in larger postural sway for sinusoidal support-base translations, and (4) loss of vestibular function results in falling for large support-base rotations with the eyes closed. These predictions are in agreement with experimental results. Received: 12 November 1999 / Accepted in revised form: 30 June 2000     

Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory

We study the dynamics and stability of legged locomotion in the horizontal plane. Motivated by experimental studies of insects, we develop two- and three-degree-of freedom rigid body models with pairs of ‘virtual’ elastic legs in intermittent contact with the ground. We focus on conservative compliant-legged models, but we also consider prescribed forces, prescribed leg displacements, and combined strategies. The resulting mechanical systems exhibit periodic gaits whose stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. Most strikingly, we show that mechanics alone can confer asymptotic stability in heading and body orientation. In a companion paper, we apply our results to rapidly running cockroaches. Received: 6 September 1999 / Accepted in revised form: 8 May 2000     

Multisensory fusion and the stochastic structure of postural sway

 We analyze the stochastic structure of postural sway and demonstrate that this structure imposes important constraints on models of postural control. Linear stochastic models of various orders were fit to the center-of-mass trajectories of subjects during quiet stance in four sensory conditions: (i) light touch and vision, (ii) light touch, (iii) vision, and (iv) neither touch nor vision. For each subject and condition, the model of appropriate order was determined, and this model was characterized by the eigenvalues and coefficients of its autocovariance function. In most cases, postural-sway trajectories were similar to those produced by a third-order model with eigenvalues corresponding to a slow first-order decay plus a faster-decaying damped oscillation. The slow-decay fraction, which we define as the slow-decay autocovariance coefficient divided by the total variance, was usually near 1. We compare the stochastic structure of our data to two linear control-theory models: (i) a proportional–integral–derivative control model in which the postural system's state is assumed to be known, and (ii) an optimal-control model in which the system's state is estimated based on noisy multisensory information using a Kalman filter. Under certain assumptions, both models have eigenvalues consistent with our results. However, the slow-decay fraction predicted by both models is less than we observe. We show that our results are more consistent with a modification of the optimal-control model in which noise is added to the computations performed by the state estimator. This modified model has a slow-decay fraction near 1 in a parameter regime in which sensory information related to the body's velocity is more accurate than sensory information related to position and acceleration. These findings suggest that: (i) computation noise is responsible for much of the variance observed in postural sway, and (ii) the postural control system under the conditions tested resides in the regime of accurate velocity information. Received: 20 March 2001 / Accepted: 17 April 2002 Acknowledgements. We thank Tjeerd Dijkstra for bringing the slow-decay component of postural sway to our attention. Funding for this research was provided by National Institutes of Health grant R29 N35070–01A2, John J. Jeka, PI. Correspondence to: T. Kiemel (Tel.: +1-301-4056176, Fax: +1-301-3149358 e-mail: kiemel@glue.umd.edu)     

Development and analysis of a germline BAC resource for the sea lamprey, a vertebrate that undergoes substantial chromatin diminution

Over the last several years, the sea lamprey (Petromyzon marinus) has grown substantially as a model for understanding the evolutionary fundaments and capacity of vertebrate developmental and genome biology. Recent work on the lamprey genome has resulted in a preliminary assembly of the lamprey genome and led to the realization that nearly all somatic cell lineages undergo extensive programmed rearrangements. Here we describe the development of a bacterial artificial chromosome (BAC) resource for lamprey germline DNA and use sequence information from this resource to probe the subchromosomal structure of the lamprey genome. The arrayed germline BAC library represents ∼10× coverage of the lamprey genome. Analyses of BAC-end sequences reveal that the lamprey genome possesses a high content of repetitive sequences (relative to human), which show strong clustering at the subchromosomal level. This pattern is not unexpected given that the sea lamprey genome is dispersed across a large number of chromosomes (n ∼ 99) and suggests a low-copy DNA targeting strategy for efficiently generating informative paired-BAC-end linkages from highly repetitive genomes. This library therefore represents a new and biologically informed resource for understanding the structure of the lamprey genome and the biology of programmed genome rearrangement.