λ-Model and Equilibrium Point Hypothesis References: 1.Latash M.L., Control of human movement, chapters 1-3, Human kinetics Publishers, Feldman A.G., Once more on the equilibrium-point hypothesis (λ-model) for motor control, Journal of Motor Behavior, 1986, Vol. 18, No. 1, 17-54

Candidate Variables (voluntary movement): Position or movement velocity; Jerk; Joint torque (forces) or torque change; Stiffness; EMG activity, etc. To control a movement, what parameters of the motor system are controlled by the CNS? Fact: All these variables describe voluntary movement at the level of motor execution! We are looking for a variable at another level of the motor control hierarchy: Its time changes would be controlled for all the variety of motor tasks All these are emergent properties of the system and cannot be directly specified by neural control levels!

Definition of Controlled Variable A signal that is supplied by one upper level of the motor control system to another independently of the current conditions of task execution Remark: Current conditions of task execution usually depend on external, and sometimes unpredictable, factors.  Non of the mentioned variables can be controlled. Example: posture change due to an unexpected load  When a subject occupy a position, subject’s MCS does not encode the position by itself, but rather encodes something different that implies this position in the given external conditions.

Based on the Bernsteinian approach: λ-Model and Equilibrium Point Hypothesis (Feldman, 1965) The model is based on the Mass-Spring models of muscle behavior! Force K1K1 K2K2 B T0T0 An isolated muscle model T 0 : active contractile element (increase in muscle force) Muscle force is a function of: - Muscle length (stretch reflex), (Static force) - Rate of length changes, (Dynamic force) - Excitation

Nonlinear behavior  : Muscle length at which the recruitment of  -MN starts Muscle Force-Length characteristics Observation: Change in the experimentally controlled descending signals led to nearly parallel transfers of the whole curve 1000 Resting length Length (cm) Force (N) (impulses / sec) 5 Invariant characteristics (ICs) Passive component Conclusion: λ appears to be the only parameter of the intact muscle force-length characteristic curve that is necessary to describe any effect of the descending signals! (Mono-parametric spring)

Regulation of stretch reflex thresholds An example: Posture-movement problem and its solution Postures are stabilized – a deviation from a posture evokes resistance tending to the body or limb back to the initial posture. Voluntary movement is an intentional deviation from the initial posture, e.g., gait initiation. How does the nervous system elicit movement without provoking resistance of posture stabilizing mechanisms to the deviation from the initial posture? A solution: Threshold control

Alpha-Gamma Coordination During Voluntary Contraction Length (cm) Force (N) (impulses / sec) 5 λ: Muscle length at which the recruitment of  -MN starts