“One should beware of mathematicians and all who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell” St Augustine, Bishop of Hippo, circa 400 A.D “To move things is all that Mankind can doFor such the sole executant is muscle, whether in whispering a syllable or in felling a forest” Charles Sherington, 1924 Optimization Principles in Motor Control1 Optimization Principles in Motor ControlProf. Dava J. NewmanJoseph H. SalehDepartment of Aeronautics and Astronautics Massachusetts Institute of Technology Optimization Principles in Motor Control2 Outline Review of Muscle Contraction From AP generation to contraction of fibers Muscle proprioceptors (spindles and Golgi tendons) Afferent and efferent axons The Muscle Simulink model Reflections on Models Optimization Principles in Motor Control Understanding the fundamental question in biomechanics Are all motor behavior optimal in some sense? Kinematic versus dynamic objective functions Pre-Programmed Muscle Response During Downward Jumps Optimization Principles in Motor Control3 Muscles: Effectors of the Motor System The major output of the elaborate information processing that takes place in our brain is the generation of a contractile force in our skeletal muscles. Muscle fasciculus Muscle fiber Myofibril Sarcomere Each muscle fiber is innervated by only one motor neuron, although each motor neuron innervates a number of muscle fibers The motor neuron and all the fibers it innervates is called a motor unit (the smallest functional unit controlled by the motor system) Optimization Principles in Motor Control4 Muscles: Effectors of the Motor System The number of muscle fibers innervated by one motor neuron is called the innervation ratio. The innervation ratio can vary between 10 and 2000 A low innervation ratio indicates a greater capacity for finely grading the muscle total force Optimization Principles in Motor Control5 Muscles: Effectors of the Motor SystemA simplified sequence from AP generation to muscular contraction Motor neuron fires an action potential It propagates down the motor axon until it reaches the neuro-muscular junction It triggers an AP in the muscle fiber This AP is propagated rapidly over the surface of the fiber and conducted into the myofibril by mean of the T-tubule system This in turn releases Ca+ from the Sarcoplasmic Reticulum (SR)-the SR serves as a store of Ca+ This in turn triggers the cyclic motion of Myosin heads, attaching and detaching on the Actin filaments, thus forming cross-bridges and generating the pulling force Ca+ are pumped back to the SR Optimization Principles in Motor Control6 Muscles: Effectors of the Motor System The force of contraction depends on the length of the muscle (length-tension relationship) The force of contraction also depends on the relative rates of movement of the Actin and Myosin filaments (tension-velocity relationship, Hills curve) Motor units are recruited in a fixed order from the weakest to the strongest (Henneman size principle): The weakest inputs recruit the slow units which generate the smallest force and are most resistant to fatigue. The fast fatigue- resistant are recruited next, followed by the fast fatigable units which generate the strongest force. Optimization Principles in Motor Control7 Muscles: Effectors of the Motor System Muscle Proprioceptors (spindles and Golgi tendons) There are different types of receptors which respond to light, sound, odor, heat, touch, pain, etc. The receptors which lead to conscious sensations are called exteroceptors, those which are not responsible for conscious sensation are called- primary in motor functions- are called proprioceptors Spindle organs Those are stretch receptors scattered deep within all muscles. They are usually attached in parallel with a muscle fiber, and therefore experience the same relative length change. Spindles give information about its length and rate of change of its length Golgi tendon They are found very close to the junction between tendon and muscle fibers. They are placed in series with the muscle fibers and respond to the tendon stretch which accompanies a muscle tension. Thus they are force transducers for the muscle. Optimization Principles in Motor Control8 Muscles: Effectors of the Motor System The nerve axons which run out of the spinal cord are called efferent, the ones that carry information to the cord are afferent Group I afferent fibers have large diameters therefore relatively high conduction velocities. They bring information from the spindle (Ia) and the golgi (Ib) to the cord The efferent which innervate the main muscle mass are the , and those that serve the intrafusal fibers within the spindles are called The stretch reflex, co-activation of -mn and -mn Op