A model of activity-dependent formation of cerebellar microzones

According to modern views of the cerebellum in motor control, each cerebellar functional unit, or microzone, learns how to execute predictive and coordinative control, based on long-term depression of the granule cell-Purkinje cell synapses. In the present paper, in light of recent experimental and theoretical studies on synaptic elimination and cerebellar motor learning, a model of the formation of cerebellar microzones by climbing fiber synaptic elimination is proposed. It is shown that competition for an activity-dependent supply of neurotrophic factor can reproduce the spatio-temporal characteristics of climbing fiber synaptic elimination. It is further shown that when this elimination is accurate, motor coordination can be acquired in an arm reaching task. In view of the results of the present study, several predictions are proposed. Received: 19 January 1998 / Accepted in revised form: 22 April 1998     

Examination of the λ equilibrium point hypothesis when applied to single degree of freedom movements performed with different inertial loads

 One of the theories of human motor control is the λ Equilibrium Point Hypothesis. It is an attractive theory since it offers an easy control scheme where the planned trajectory shifts monotionically from an initial to a final equilibrium state. The feasibility of this model was tested by reconstructing the virtual trajectory and the stiffness profiles for movements performed with different inertial loads and examining them. Three types of movements were tested: passive movements, targeted movements, and repetitive movements. Each of the movements was performed with five different inertial loads. Plausible virtual trajectories and stiffness profiles were reconstructed based on the λ Equilibrium Point Hypothesis for the three different types of movements performed with different inertial loads. However, the simple control strategy supported by the model, where the planned trajectory shifts monotonically from an initial to a final equilibrium state, could not be supported for targeted movements performed with added inertial load. To test the feasibility of the model further we must examine the probability that the human motor control system would choose a trajectory more complicated than the actual trajectory to control. Received: 20 June 1995 / Accepted in revised form: 6 August 1996     

Forming independent components via temporal locking of reconstruction architectures: a functional model of the hippocampus

The assumption is made that the formulation of relations as independent components (IC) is a main feature of computations accomplished by the brain. Further, it is assumed that memory traces made of non-orthonormal ICs make use of feedback architectures to form internal representations. Feedback then leads to delays, and delays in cortical processing form an obstacle to this relational processing. The problem of delay compensation is formulated as a speed-field tracking task and is solved by a novel control architecture. It is shown that in addition to delay compensation the control architecture can also shape long-term memories to hold independent components if a two-phase operation mode is assumed. Features such as a trisynaptic loop and a recurrent collateral structure at the second stage of that loop emerge in a natural fashion. Based on these properties a functional model of the hippocampal loop is constructed. Received: 18 March 1997 / Accepted in revised form: 30 June 1998     

A new explicit stability criterion for human periodic breathing<--RID="*"--><--ID="*" This research was supported by grants from DRED (96-920).-->

The aim of this paper is to carry out a stability analysis for periodic breathing in humans that incorporates the dynamic characteristics of ventilation control. A simple CO₂ model that takes into account the main elements of the respiratory system, i.e. the lungs and the ventilatory controller with its dynamic properties, is presented. This model results in a three-dimensional non-linear delay differential system for which there exists a unique equilibrium point. Our stability analysis of this equilibrium point leads to the definition of a new explicit stability criterion and to the demonstration of the existence of a Hopf bifurcation. Numerical simulations illustrate the influence of physiological parameters on the stability of ventilation, and particularly the major role of the dynamic characteristics of the respiratory controller. Received: 2 February 1999 / Revised version: 18 June 1999 / Published online: 23 October 2000     

On identification of Na+ channel gating schemes using moving-average filtered hidden Markov models

 Transitions between distinct kinetic states of an ion channel are described by a Markov process. Hidden Markov models (HMM) have been successfully applied in the analysis of single ion channel recordings with a small signal-to-noise ratio. However, we have recently shown that the anti-aliasing low-pass filter misleads parameter estimation. Here, we show for the case of a Na⁺ channel recording that the standard HMM do neither allow parameter estimation nor a correct identification of the gating scheme. In particular, the number of closed and open states is determined incorrectly, whereas a modified HMM considering the anti-aliasing filter (moving-average filtered HMM) is able to reproduce the characteristic properties of the time series and to perform gating scheme identification. Received: 11 February 1999 / Revised version: 18 June 1999 / Accepted: 21 June 1999     

Interaction of ON and OFF pathways for visual contrast measurement

We propose a novel model of visual contrast measurement based on segregated On and Off pathways. Two driving forces have shaped our investigation: (1) establishing a mechanism selective for sharp local transitions in the luminance distribution; (2) generating a robust scheme of oriented contrast detection. Our starting point was the architecture of early stages in the mammalian visual system. We show that the circuit behaves as a soft AND-gate and analyze the scale-space selectivity properties of the model in detail. The theoretical analysis is supplemented by computer simulations in which we selectively investigate key functionalities of the proposed contrast detection scheme. We demonstrate that the model is capable of successfully processing synthetic as well as natural images, thus illustrating the potential of the method for computer vision applications. Received: 5 June 1998 / Accepted in revised form: 12 May 1999     

Development of a biologically-based controlled growth and differentiation model for developmental toxicology

 A mathematical model is developed with a highly controlled birth and death process for precursor cells. This model is both biologically- and statistically-based. The controlled growth and differentiation (CGD) model limits the number of replications allowed in the development of a tissue or organ and thus, more closely reflects the presence of a true stem cell population. Leroux et al. (1996) presented a biologically-based dose-response model for developmental toxicology that was derived from a partial differential equation for the generating function. This formulation limits further expansion into more realistic models of mammalian development. The same formulae for the probability of a defect (a system of ordinary differential equations) can be derived through the Kolmogorov forward equations due to the nature of this Markov process. This modified approach is easily amenable to the expansion of more complicated models of the developmental process such as the one presented here. Comparisons between the Leroux et al. (1996) model and the controlled growth and differentiation (CGD) model as developed in this paper are also discussed. Received: 8 June 2001 / Revised version: 15 June 2002 / Published online: 26 September 2002 Keywords or phrases: Teratology – Multistate process – Cellular kinetics – Numerical simulation     

A model for learning human reaching movements

 Reaching movement is a fast movement towards a given target. The main characteristics of such a movement are straight path and a bell-shaped speed profile. In this work a mathematical model for the control of the human arm during ballistic reaching movements is presented. The model of the arm contains a 2 degrees of freedom planar manipulator, and a Hill-type, non-linear mechanical model of six muscles. The arm model is taken from the literature with minor changes. The nervous system is modeled as an adjustable pattern generator that creates the control signals to the muscles. The control signals in this model are rectangular pulses activated at various amplitudes and timings, that are determined according to the given target. These amplitudes and timings are the parameters that should be related to each target and initial conditions in the workspace. The model of the nervous system consists of an artificial neural net that maps any given target to the parameter space of the pattern generator. In order to train this net, the nervous system model includes a sensitivity model that transforms the error from the arm end-point coordinates to the parameter coordinates. The error is assessed only at the termination of the movement from knowledge of the results. The role of the non-linearity in the muscle model and the performance of the learning scheme are analysed, illustrated in simulations and discussed. The results of the present study demonstrate the central nervous system’s (CNS) ability to generate typical reaching movements with a simple feedforward controller that controls only the timing and amplitude of rectangular excitation pulses to the muscles and adjusts these parameters based on knowledge of the results. In this scheme, which is based on the adjustment of only a few parameters instead of the whole trajectory, the dimension of the control problem is reduced significantly. It is shown that the non-linear properties of the muscles are essential to achieve this simple control. This conclusion agrees with the general concept that motor control is the result of an interaction between the nervous system and the musculoskeletal dynamics. Received : 21 May 1996 / Accepted in revised form : 10 June 1997     

How honeybees make grazing landings on flat surfaces

 Freely flying bees were filmed as they landed on a flat, horizontal surface, to investigate the underlying visuomotor control strategies. The results reveal that (1) landing bees approach the surface at a relatively shallow descent angle; (2) they tend to hold the angular velocity of the image of the surface constant as they approach it; and (3) the instantaneous speed of descent is proportional to the instantaneous forward speed. These characteristics reflect a surprisingly simple and effective strategy for achieving a smooth landing, by which the forward and descent speeds are automatically reduced as the surface is approached and are both close to zero at touchdown. No explicit knowledge of flight speed or height above the ground is necessary. A model of the control scheme is developed and its predictions are verified. It is also shown that, during landing, the bee decelerates continuously and in such a way as to keep the projected time to touchdown constant as the surface is approached. The feasibility of this landing strategy is demonstrated by implementation in a robotic gantry equipped with vision. Received: 21 June 1999 / Accepted in revised form: 20 March 2000     

Impedance characteristics of a neuromusculoskeletal model of the human arm II. Movement control

The modulation of neuromusculoskeletal impedance during movements is analysed using a motor control model of the human arm. The motor control system combines feedback and feedforward control and both control modes are determined in one optimization process. In the model, the stiffness varies at the double movement frequency for 2-Hz oscillatory elbow movements and has high values at the movement reversals. During goal-directed two-degrees-of-freedom arm movements, the stiffness is decreased during the movement and may be increased in the initial and final phases, depending on the movement velocity. The stiffness has a considerable curl during the movement, as was also observed in experimental data. The dynamic stiffness patterns of the model can be explained basically by the α−γ coactivation scheme where feedback gains covary with motor control signals. In addition to the modulation of the gain factors, it is argued that the variation of the intrinsic stiffness has a considerable effect on movement control, especially during fast movements. Received: 14 October 1997 / Accepted in revised form: 18 May 1999     

Iterative manual control model of human operator

In this paper, we present an iterative manual control model of a human operator performing some repetitive task. Various aspects of the model are discussed in detail. Experiments have been done to study the human capability to perform the tasks by learning iteratively. Results of the experiments show the ability of the human operator to perform the tracking of a desired trajectory for some unknown non-linear system with quite reasonable accuracy during the iteration process. It is concluded that the human operator performs the repetitive task by modifying his control action using error and error rate in each iteration. During the modification, the human operator assigns different weights to the error and error rate in each iteration. These results can be implemented in designing more efficient iterative learning control algorithms. Received: 29 September 1998 / Accepted in revised form: 12 May 1999     

Self-organizing effects of spontaneous neural activity on the development of spinal locomotor circuits in vertebrates

Presented in this paper is a neural network model that can be used to investigate the possible self-organizing mechanisms occurring during the early ontogeny of spinal neural circuits in the vertebrate motor system. The neural circuit is composed of multiple types of neurons which correspond to motorneurons, Renshaw cells and a hypothetical class of interneurons. While the connectivity of this circuit is genetically predetermined, the efficacies of these connections – the synaptic s trengths – evolve in accordance with activity-dependent mechanisms which are initiated by the intrinsic, autonomous activity present in the developing spinal cord. Using Oja's rule, a modified Hebbian learning scheme for adjusting the values of the connections, the network stably self-organizes developing, in the process, reciprocally activated motorneuron pools analogous to those which exist in vivo. Received: 30 December 1996 / Accepted in revised form: 20 June 1997     

Simulating a neural cross-talk model for between-hand interference during bimanual circle drawing

Studies on drawing circles with both hands in the horizontal plane have shown that this task is easy to perform across a wide range of movement frequencies under the symmetrical mode of coordination, whereas under the asymmetrical mode (both limbs moving clockwise or counterclockwise) increases in movement frequency have a disruptive effect on trajectory control and hand coordination. To account for these interference effects, we propose a simplified computer model for bimanual circle drawing based on the assumptions that (1) circular trajectories are generated from two orthogonal oscillations coupled with a phase delay, (2) the trajectories are organized on two levels, “intention” and “motor execution”, and (3) the motor systems controlling each hand are prone to neural cross-talk. The neural cross-talk consists in dispatching some fraction of any force command sent to one limb as a mirror image to the other limb. Assuming predominating coupling influences from the dominant to the nondominant limb, the simulations successfully reproduced the main characteristics of performance during asymmetrical bimanual circle drawing with increasing movement frequencies, including disruption of the circular form drawn with the nondominant hand, increasing dephasing of the hand movements, increasing variability of the phase difference, and occasional reversals of the movement direction in the nondominant limb. The implications of these results for current theories of bimanual coordination are discussed. Received: 23 June 1998 / Accepted in revised form: 20 April 1999     

A holistic model for an internal representation to control the movement of a manipulator with redundant degrees of freedom

The paper proposes a model for the control of a multisegmented manipulator with redundant degrees of freedom. On the basis of an earlier model, the so-called MMC net, a simplified version is proposed here which has several advantages. First, it can easily be scaled up for the 3D case. Second, for the linear version a complete convergence proof is possible. Third, an easy way of implementing a damping parameter is shown. Fourth, the properties of the earlier model are unchanged, namely versatile control of the redundant system, immediate change from direct kinematics to inverse kinematics or any mixed control task, as well as robustness in the case of singularities. Received: 4 October 1997 / Accepted in revised form: 26 August 1998     

Jendrassik’s maneuver creates conditions for triggering involuntary stepping

The influence of the Jendrassik maneuver on the generation of the locomotor rhythmicity was studied under conditions of the “suspension” of legs in a horizontal plane. It was shown that during Jendrassik’s maneuver, passive movements of one limb trigger stepping with the participation of both limbs. The Jendrassik’s maneuver also notably facilitates the vibration-induced locomotion. The kinematics of the evoked stepping movements did not differ from the kinematics of the voluntary “air-stepping,” reciprocal electromyographic activity being observed in antagonistic muscles. It seems likely that the generation of cyclic movements during the Jendrassik maneuver occurs due to the activation of the same stepping automatism as in normal stepping. The experimental results suggest that an increase in the level of tonic readiness of the tonogenic CNS structures, which participate in realization of the locomotor program, is a necessary condition for the activation of the spinal mechanisms of the stepping generation.     

Impedance characteristics of a neuromusculoskeletal model of the human arm I. Posture control

The mechanical impedance of neuromusculoskeletal models of the human arm is studied in this paper. The model analysis provides a better understanding of the contributions of possible intrinsic and reflexive components of arm impedance, makes clear the limitations of second-order mass-viscosity-stiffness models and reveals possible task effects on the impedance. The musculoskeletal model describes planar movements of the upper arm and forearm, which are moved by six lumped muscles with nonlinear dynamics. The motor control system is represented by a neural network which combines feedforward and feedback control. It is optimized for the control of movements or for posture control in the presence of external forces. The achieved impedance characteristics depend on the conditions during the learning process. In particular, the impedance is adapted in a suitable way to the frequency content and direction of external forces acting on the hand during an isometric task. The impedance characteristics of a model, which is optimized for movement control, are similar to experimental data in the literature. The achieved stiffness is, to a large extent, reflexively determined whereas the approximated viscosity is primarily due to intrinsic attributes. It is argued that usually applied Hill-type muscle models do not properly represent intrinsic muscle stiffness. Received: 14 October 1997 / Accepted in revised form: 18 May 1999     

Simulation of gait and gait initiation associated with body oscillating behavior in the gravity environment on the Moon, Mars and Phobos

 A double-inverted pendulum model of body oscillations in the frontal plane during stepping [Brenière and Ribreau (1998) Biol Cybern 79: 337–345] proposed an equivalent model for studying the body oscillating behavior induced by step frequency in the form of: (1) a kinetic body parameter, the natural body frequency (NBF), which contains gravity and which is invariable for humans, (2) a parametric function of frequency, whose parameter is the NBF, which explicates the amplitude ratio of center of mass to center of foot pressure oscillation, and (3) a function of frequency which simulates the equivalent torque necessary for the control of the head-arms-trunk segment oscillations. Here, this equivalent model is used to simulate the duration of gait initiation, i.e., the duration necessary to initiate and execute the first step of gait in subgravity, as well as to calculate the step frequencies that would impose the same minimum and maximum amplitudes of the oscillating responses of the body center of mass, whatever the gravity value. In particular, this simulation is tested under the subgravity conditions of the Moon, Mars, and Phobos, where gravity is 1/6, 3/8, and 1/1600 times that on the Earth, respectively. More generally, the simulation allows us to establish and discuss the conditions for gait adaptability that result from the biomechanical constraints particular to each gravity system. Received: 15 February 1999 / Accepted in revised form: 9 October 2000     

A review of attempts to condition operantly alloprimate vocalizations

A central issue in the study of alloprimate vocalizations concerns the extent of the animal's control over vocalization production. Two competing models are the semanticity model which states that vocalizations contain an environmental referent, and the level-of-arousal model which states that vocalizations are an emotional product of differential internal states of arousal. One source of evidence bearing on this issue is the operant control of vocalizations by alloprimates. This paper presents a comprehensive review of 12 attempts to condition operantly alloprimate vocalizations. These 12 experiments are analyzed in terms of various subject and procedural variables, including the age, species and sex of the subject, and the type of task and reward used. The results of this analysis indicate the following: Primates are able to control their own vocal output with considerable success; species, age and sex variables place no restriction upon this ability. In addition, the appropriateness of the reinforcer influenced the success rate of the experiment. These results are interpreted as supporting evidence for the semanticity model of vocal production. Results are discussed in terms of an “ecologically-appropriate hypothesis.” This paper was first presented at the Rocky Mountain Psychological Association in April of 1984.     

A mode hypothesis for finger interaction during multi-finger force-production tasks

 Finger forces are known to change involuntarily during multi-finger force-production tasks, even when a finger's involvement in a task is not consciously changed (the enslaving effect). Furthermore, during maximal force-production (MVC) tests, the force produced by a given finger in a multi-finger task is smaller than the force generated by this finger in its single-finger MVC test (the force-deficit effect). A set of hypothetical control variables – modes – is introduced. Modes can be estimated based on individual finger forces during single-finger MVC tests. We show that a simple formal model based on modes with only one free parameter accounts for finger forces during a variety of multi-finger MVC tests. The free parameter accounts for the force-deficit effect, and its value depends only on the number of explicitly involved fingers. This approach offers a simple framework for the analysis of finger interaction during multi-finger actions. Received: 7 December 2001 / Accepted in revised form: 17 April 2002 Correspondence to: F. Danion (e-mail: danion@laps.univ-mrs.fr, Tel.: +33-491-172265, Fax: +33-491-172252)     

In one era and out the other

A guided tour through much of photosynthesis research as I saw it, 1936–2001, is presented here. For earlier perspectives, see Myers 1974 (Plant Physiol 54: 420–426) and 1996 (Photosynth Res 50: 195–208). This revised version was published online in June 2006 with corrections to the Cover Date.