A computational model for the modulation of the prepulse inhibition of the acoustic startle reflex

The acoustic startle reflex (ASR), a defensive response, is a contraction of the skeletal and facial muscles in response to an abrupt, intense (> 80 db) auditory stimulus, which has been extensively studied in rats and humans. Prepulse inhibition (PPI) of ASR is the normal suppression of the startle reflex when an intense stimulus is preceded by a weak non-starting pre-stimulus. PPI, a measure of sensory motor gating, is impaired in various neuropsychiatric disorders, including schizophrenia, and is modulated by cognitive and emotional contexts such as fear and attention. We have modeled the fear modulation of PPI of ASR based on its anatomical substrates and taking into account data from behaving rats and humans. The model replicates the principal features of both phenomena and predicts underlying neural mechanisms. In addition, the model yields testable predictions.     

A mathematical model of the optokinetic reflex

The role of the optokinetic reflex (OKR) is that of cooperating with the vestibulo-ocular reflex (VOR) in the task of image stabilization on the retina during head rotations in a stationary visual surround. Since the dynamics of VOR was already well established, it has been possible to make a broad estimation of what the dynamics of OKR should be in order to obtain the performances observed in normal subjects. A mathematical model of OKR has been presented, and the experimental results obtained by Raphan et al. (1977) in the monkey and by Collins et al. (1970) in man were used to validate the model and to obtain a precise estimation of its parameters.Work supported by CNR, Special Project on Biomedical Engineering, grant No. 78.00512.86     

A model of quick phase generation in the vestibuloocular reflex

The vestibuloocular reflex of the cat was studied during step and sinusoidal head velocity stimuli. A model is presented which simulates the observed slow phase and quick phase behavior. The model is constructed to be compatible with neurophysiological observations of the behavior of neurons in the pons. Emphasis is placed on the amplitude and timing of quick phases which are active orienting movements that drive the eyes into the direction of turning. It is proposed that quick phases, like saccades, are generated by a local feedback loop in the pons which rapidly drives the eyes to a point in the orbit specified by a vestibular signal. It is suggested that two internal signals specify the eye positions at which quick phases start and end. The statistics of the fluctuations of these signals was measured and correlation between them was discovered and incorporated in the model.     

A large-scale model of some spinal reflex circuits

This paper reports the development of a large-scale model of some spinal reflex circuitry, useful for studying the dynamic interactions among neuronal populations during simple behaviors. The included populations and properties of the neurons and terminals were derived from the literature, mainly on cat spinal cord. The model was conceived as a symmetrical controller of a pair of antagonistic muscles, within the behavioral domain of the stretch and Golgi-tendon-organ reflexes, and was scaled to include realistic numbers of motoneurons. Inputs to the model were fiber populations providing random synaptic drive to some of the populations and sensory stimuli appropriate for the reflexes. The resulting model contained roughly 2300 neurons in six pairs of populations. The total number of connections in the model was about 600 000, and individual postsynaptic potentials were small (0.1–0.6 mV). Model responses were calibrated by examination of their ability to reproduce known aspects of the reflexes. Published algorithms were used to construct the environment, which is easily expandable, in terms of membrane channels, neuronal geometry, and synaptic properties. The system was built to combine a system-level perspective of spinal circuitry with the single-unit perspective common in electrophysiological investigation. It provides a computational tool for system-level investigations of spinal cord similar to the tools available at the level of membrane currents. Received: 16 May 1997 / Accepted in revised form: 2 October 1997     

A distributed control model for the air-righting reflex of a cat

A multisegment, multijoint model of a falling animal is presented to examine the effectiveness of a two-stage control scheme in a zero-momentum self-righting maneuver. The model contains a much larger number of degrees of freedom than is required to execute a self-righting maneuver and is thus capable of providing multiple solutions for the same task. The decentralized control scheme is designed to achieve gross turning in minimum time and to maintain a steady orientation relative to gravity after the turn has been achieved. The scheme is able to determine the sequence of steps necessary to execute the motor task and also incorporates learning features. Results from various simulations are presented and their implications discussed. Received: 26 June 1995 / Accepted in revised form: 30 June 1998     

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     

A model of the central and reflex inhibition of inspiration in the cat

An attempt is made to summarize the results obtained in previous work from this and other laboratories on the steady state and transient relationships between the mechanical and neural events in breathing and their precise timing in the breathing cycle at different blood chemical demands for ventilation and at different body temperatures, and to fit these results into a functional and realistic model of the bulbo-pontine inspiratory off-switch mechanisms. The experimentally based requirements for the model are briefly described and listed. After a presentation of the model in qualitative terms its functional properties are considered quantitatively and compared with the performance of the real, biological system. This has been achieved by assuming some simple mathematical approximations for the activities of the introduced physiological parameters and their chemical “drive” dependence. The gaps in our present knowledge are pointed out and some key experiments suggested. The proposed model is consistent with the main conclusions reached in previous work from this laboratory that there are three neural submechanisms which are mainly responsible for the effects of increased CO₂ on ventilation: 1) a rise in the inspiratory off-switch threshold, 2) an increased rate of rise of the centrally generated inspiratory activity that projects to the off-switch mechanism (and to the spinal respiratory motoneurons), and 3) the vagal volume feed-back. Of these 1) and 2) are mainly responsible for the increase in tidal volume, whereas the vagal volume feed-back is mainly responsible for the increase in respiratory rate. The comparison between the model behaviour and experimental data suggest that the slight CO₂ sensitivity of the pulmonary stretch receptors recently reported on, has to be taken into account. The model studies have suggested the increase in respiratory rate with increased temperature may be due either to an increased rate of rise of inspiratory activity or to a decreased off-switch threshold, or both in combination. The mechanism controlling the expiratory durations are briefly discussed.     

Experimental study of displays in contralateral acoustic reflex auditory stimulation

The results of an experimental study of manifestations of the acoustic reflex with contralateral auditory stimulation at a frequency of 1 kHz are presented, and the principal possibility and informativeness of its use for diagnosing the diseases of the organ of hearing are demonstrated. The principal difference of the developed approach is the use of polyharmonic signal for measuring acoustic reflex manifestations during contralateral stimulation, which allows accelerating the examination procedure.     

A model of the compression of acoustic information in neuronal networks

A model for processing of acoustic information in neuron networks has been proposed. The model takes into account the final rate of transfer of electric signal along the nerve fibers. The model indicates a possibility for the existence of a mechanism of compression of the input wide frequency band signal that retains its energetic parameters (in a certain limit). The model allowed to create a very efficient synthesizer of repellent acoustic signals that may be used to manage the bird behavior and regulate their numbers.     

A dynamical model for reflex activated head movements in the horizontal plane

 We present a controls systems model of horizontal-plane head movements during perturbations of the trunk, which for the first time interfaces a model of the human head with neural feedback controllers representing the vestibulocollic (VCR) and the cervicocollic (CCR) reflexes. This model is homeomorphic such that model structure and parameters are drawn directly from anthropomorphic, biomechanical and physiological studies. Using control theory we analyzed the system model in the time and frequency domains, simulating neck movement responses to input perturbations of the trunk. Without reflex control, the head and neck system produced a second-order underdamped response with a 5.2 dB resonant peak at 2.1 Hz. Adding the CCR component to the system dampened the response by approximately 7%. Adding the VCR component dampened head oscillations by 75%. The VCR also improved low-frequency compensation by increasing the gain and phase lag, creating a phase minimum at 0.1 Hz and a phase peak at 1.1 Hz. Combining all three components (mechanics, VCR and CCR) linearly in the head and neck system reduced the amplitude of the resonant peak to 1.1 dB and increased the resonant frequency to 2.9 Hz. The closed loop results closely fit human data, and explain quantitatively the characteristic phase peak often observed. Received: 15 April 1996 / Accepted in revised form: 1 July 1996     

A numeric study of the noise-induced tremor in a mathematical model of the stretch reflex

A mathematical model of the stretch reflex for the cat soleus muscle is presented. The time-delay differential equations of the model are solved using the fourth-order Runge-Kutta algorithm, introducing a Gaussian-noise term to simulate the environmental noise. The muscle response dynamics are then studied under various levels of average muscle activation. Finally, the feasibility of explaining the so-called physiological tremor from the properties of the stretch reflex mechanisms is discussed by comparing our results with reported experimental evidence.     

A new chromosome model

We present a new model of the three-dimensional structure of chromosomes. With DNA and protein staining it could be shown by high-resolution scanning electron microscopy that metaphase chromosomes are mainly composed of DNA packed in "chromomeres" (coiled solenoides) and a dynamic matrix formed of parallel protein fibers. In the centromeric region, the chromomeres are less densely packed, giving insight into the matrix fibers. We postulate that chromosome condensation is achieved by the binding of solenoids to matrix fibers which have contact sites to one another and move antiparallel to each other. As condensation progresses, loops of solenoids accumulate to form additional chromomeres, causing chromosomes to become successively shorter and thicker as more chromomeres are formed. For sterical reasons, a tension vertical to the axial direction forces the chromatids apart. The model can simply explain the enormous variety of chromosome morphology in plant and animal systems by varying only a few cytological parameters. Primary and secondary constrictions and deletions are defined as regions devoid of chromomeres. Even in the highly condensed metaphase, all genes would be easily accessible.     

A new biophysical method to determine the gain of the acoustic trachea in bushcrickets

A method is described for measuring the gain (i.e., the change of amplitude and phase angle) for sounds that propagate to the internal surface of the tympana in ears working as pressure difference receivers. The gain of the acoustic trachea has been measured in two similarly sized and closely related species of bushcrickets, in which the acoustic spiracles and tracheae differ markedly in size. The amplitude part of the gain is much larger in the species with the larger acoustic spiracle, whereas the phase part is very similar in the two species. The method is compared with other methods, which in the past have been used for estimating the gain of sound pathways inside animal bodies.