G. C. Y. Peng1, T. C. Hain2 and B. W. Peterson1,2
1Department of Biomedical Engineering, 2Northwestern University Medical School NUMS Physiology M211, 303 E. Chicago Ave., Chicago, IL 60611l
Abstract-- We have developed a horizontal plane head movement model to explore the interactions of the vestibulocollic (VCR) and cervicocollic (CCR) reflexes during trunk perturbations. The model was constructed utilizing parametric identification with homeomorphic data. Control systems analyses enabled us to explain complex frequency response characteristics and assign functionality to neck reflexes. (Modified from Proc IEEE Eng Med Bio Soc, 2031-2032, 1995)
The vestibulocollic reflex (VCR) is a neural reflex that activates neck muscles when head motion is sensed by the vestibular organs in the inner ear. The cervicocollic reflex (CCR) is thought to be a neck stretch reflex driven by neck proprioceptive input. Due to the nature of the reflexes, both reflexes operate under closed loop control, and utilize spatial (VCR) and body (CCR) coordinate systems. It is well known that the VCR and CCR produce neck muscle activation in response to perturbations of the trunk across a wide range of frequencies [1-4]. The closed loop frequency response of compensatory head movement (head movement with respect to trunk) exhibits 2nd order system behavior at frequencies above 1Hz; however, a peculiar phase peak centered around 1 Hz can't be explained readily [3, 4].
In addition to complex frequency characteristics, very little is known of the functional significance of these reflexes. By integrating neurophysiological, musculoskeletal, and kinematic information into a homeomorphic model (homeomorphic = following human structures), we were able to apply a quantitative approach to understanding this complex system.
Figure 1 displays a block diagram of our 4th order lumped-parameter model for horizontal plane head and neck movement. The passive head plant was modeled with a 2nd order underdamped mechanical system, with parameters taken from biomechanical measurements in humans [5-7]. The reflexes were modeled with transfer functions based on open loop animal EMG measurements [1,2]. The EMG output from the reflexes were passed through a low pass filter, approximating muscle contraction dynamics , to produce neck torque input for the head plant
The parameter limits of the reflex plants were set by the ranges of transfer function fits from the open loop studies [1,2]. The mean values for tIA, tC, tMS1 tMS2 are very similar to physiological time constants found in the peripheral processing of the VCR and CCR [9, 10]. Although tCNS1 and tCNS2 are not physiologically defined, the same lead-lag terms were previously implicated in the central pathways from the vestibular nucleus to the neck motorneurons .
The input-output configuration of the model is drawn to illustrate the signal flow for compensatory head movements. Passive inertial, VCR and CCR contributions to neck torque (head torque with respect to the trunk) are summed to provide input to the passive head plant. Output from the head plant describes the movement dynamics of the compensatory head response to an input perturbation of the trunk. The feedback paths were constructed to provide the proper coordinate frame input for the VCR and CCR.
The closed loop transfer function for the system in figure 1 is described by, where P(s) represents the passive head plant as a function of the complex Laplacian operator, s. The characteristic equation in the denominator incorporates dynamics from the plant and both reflexes. Since inertial and VCR components appear in the feedforward path, their sum results in a complex conjugate zero in the transfer function. Combined with the complex conjugate pole in the denominator, the reciprocal effects produce two opposing resonant peaks in the gain, and a phase peak centered between the natural frequencies of the complex zeros and poles.
The CCR plant acts a negative feedback controller, affecting only the characteristic equation. Since KCCR is assigned a very small number, it mainly increases the amount of damping in the complex pole. The system is 4th order because of the lags in the VCR transfer function.
A linearized transfer function of this closed loop feedback system was determined by perturbing the system around the zero state operating point in which the torques and angular velocities are zero. The frequency response was generated and presented in terms of neck movement gain and phase in relation to the trunk movement in space. Perfect compensation produced a gain of 0dB and a phase of -180°.
Figure 2 displays a brief summary our simulations. The passive plant (OL) produces a frequency response of an underdamped system with a 5 dB resonance peak around 2 Hz. The passive head has near perfect compensation above resonance. When only the CCR is added as negative feedback to the passive plant (CL-CCR), the amount damping is increased slightly, decreasing the resonance peak and phase lag. The VCR produces a greater influence on the passive head (CL-VCR). At low frequencies (0.01-0.5 Hz) the VCR pushes the gain and phase towards compensation but never reaches complete head stabilization. At mid-frequencies (0.5-1 Hz) the VCR controller effectively merges with the passive head create the 40 dB/decade rise of the 2nd order zero, or equivalently the 40 dB/decade fall of the 2nd order pole. At higher frequencies, it is also involved in decreasing the amplitude of the resonant peak, bringing the head closer to critically damped. When both reflex controllers are added to the system (CL), the separate closed loop responses (CL-CCR and CL-VCR) are summed, producing essentially a damped CL-VCR response.
Although tCNS1 and tCNS2 are not homeomorphically defined, they have a strong influence on the system response. Increasing tCNS1 increases the amount of damping at each of the resonant peaks. Simulations showed that effects of KVCR and tCNS2 complement each other. For example, decreases in KVCR required a proportional decrease in tCNS2 in order to maintain the same frequency response. The closed loop simulation (CL) fits the experimental data reasonably well. The best fit parameters, listed in figure 1, caused the VCR to be approximately 9 times stronger than the CCR.
This model has shown that the VCR dominates the compensatory head movements from 0-1 Hz, creating the rising portion of the characteristic phase peak. The CCR is mainly effective above 1 Hz, and with passive head behavior, produces the falling slope of the phase peak. Functionally, the VCR improves the low frequency neck response, activating the neck muscles to better compensate for the unpredictable trunk movement. Both the VCR and CCR increase damping during high-energy motion when damping is needed to prevent injury.
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