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 do. For such the sole executant is muscle, whether in whispering a syllable or in felling a forest Charles sherington. 1924 Optimization principles in motor Control
“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 do…For such the sole executant is muscle, whether in whispering a syllable or in felling a forest” Charles Sherington, 1924 Optimization Principles in Motor Control 1
Optimization principles in motor control Prof Dava J. Newman Joseph h. saleh Department of Aeronautics and Astronautics Massachusetts Institute of Technology Optimization principles in motor Control
Optimization Principles in Motor Control Prof. Dava J. Newman Joseph H. Saleh Depart m ent of Aer onau tic s a n d Astr o nautics Ma s s achus e tts I n stitu te of T echnology O ptimization Princi ples in M otor Co ntrol 2
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 Control
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 Control 3
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 MyO 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 Control
Muscles: Effectors of the Motor System • The major output of the elaborate i nformation processing that takes place in o ur brai n i s the g e n erati o n of a con tractile force in our skeletal muscles. • Muscl e fasci c u lus – Muscle fib er • M y o fib ril – Sarcom ere • Each muscle fib e r is i n n ervated b y only one m otor neuro n, although each m otor n euron i n n ervates a numb e r of muscl e fib e rs • The m o t or ne u r on and al l the fiber s i t inne rvates i s cal l ed a m o t or u nit (the smal l est functional uni t contr o l l ed by the m o t o r system) O ptimization Princi ples in M otor Co ntrol 4
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 Control
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 g reater capacity for finely g rading the muscle total force O ptimization Princi ples in M otor Co ntrol 5
Muscles: Effectors of the Motor system A 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 Cat from the Sarcoplasmic Reticulum(SR)-the Sr serves as a store of cat+ 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 Cat* are pumped back to the sr Optimization principles in motor Control
Muscles: Effectors of the Motor System A simplified sequence from AP generation to muscular contraction • Motor neuron fir es an action potential • It propag ates down the m otor axon until i t reach e s the n euro-m u s cular junction • It triggers an AP in the m uscle fiber • This AP is propagated rapidly over the surface of the fiber and conducted into the myofi bril by mea n of t he T - tubule syst em • This in turn rel eases Ca++ from the Sarcoplasmic Reticulum (SR)-the SR serves as a store of C a++ • This in turn trigg ers the c y clic m otion of M yosin heads, attaching and detaching on the Actin filam ents, thus forming cross-bridges and gener ating the pulling force • C a++ are pumped back to the SR O ptimization Princi ples in M otor Co ntrol 6
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 Control
Muscles: Effectors of the Motor System • The force o f c ontractio n depends on the l e n g th o f the muscl e (l e ngtht e n sion relationship) • The force o f c ontractio n al so depe n d s o n th e rel a tive rat e s o f movem ent of t he Actin and Myosin filam e n ts (tension-vel o city relationship, Hill’s curve) • Motor u nits a re rec rui t ed i n a fixed order fr o m t he weake st t o the stro n gest (Hen n e m an size pri nci ple): The weakest i nputs recruit the slow units which generate the s mallest force a n d a re m ost re sistant to fati g u e. The fast fatigue - resist a nt a re recrui t ed next, fo l l owed by the fast fatigable units w hich gener a te the strongest force. O ptimization Princi ples in M otor Co ntrol 7
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 Control
Muscles: Effectors of the Motor System • Muscl e P ropriocep t ors (spind l es a n d G o l gi t end o n s) There are differ ent ty p es of receptors which r espond to light, sound, odor, heat, touch, pain, etc. The receptors which lead to conscious s ensations are called exteroc e p tors, those which are not responsible for conscious sensation are calledprimary in m otor functionsare c alled p roprio c e ptors – Spindle org ans Those a re stret ch receptors scatte r ed deep within all muscles. They a re usu ally attached in parallel with a muscle fiber, and therefore experience the sa me r elative length change. Spindles give information about its length and r ate of change of its length – Golgi tendon They are found very close to the junction b etween tendon and muscle fibers. They are placed in series with the muscle fib ers and respond to the tendon str etch which accompanies a m uscle tension. Thus th e y are force t ran s ducers for the muscle. O ptimization Princi ples in M otor Co ntrol 8
Muscles: Effectors of the Motor System The nerve axons which run out of the spinal cord are called efferer 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(la) and the golgi(Ib) to the cord The efferent which innervate the main muscle mass are the a and those that serve the intrafusal fibers within the spindles are called y The stretch reflex, co-activation of d-mn and y-mn Optimization principles in motor Control
Muscles: Effectors of the Motor System • The nerve axons which run out of the spi nal cord a re called efferent, the ones that carry information t o the c ord a re afferent • G r o up I a fferent fibers have l a r ge diameters t h e r e fo re rel a tivel y hi gh conducti on v e l ocities. They bri ng information fro m the spin dle (Ia) a n d the g o l gi (Ib) to th e co rd • The e fferent which innervate the m ain muscl e m ass are the α, and those that serve the intra fusa l fibers within the s pindles are called γ • The s tretch reflex, c o-acti vati o n of α-mn a nd γ-mn O ptimization Princi ples in M otor Co ntrol 9
Muscles: Effectors of the Motor System Stretch reflex stiffness Until recently, it was supposed that the tendon organ served as a sensor which turned off muscle activity (inhibited a-mn) when muscle force rose beyond safe levels Afferent activity from both spindles and golgi tendons balance in such a way that neither muscle force nor muscle length should be considered as controlled quantity, rather their ratio( the stiffness or change in force per change in length )appears to be fixed by the stretch reflex Optimization principles in motor Control
Muscles: Effectors of the Motor System Stret ch reflex st iffness • Until recent ly, it was s upposed that the tendon organ serve d as a sensor which turned off muscle activity (inhibited α-mn) when muscle force r ose b eyond safe lev e ls • Afferen t acti vity fr o m bo th spindles and Go lgi tendons b alance in such a way that n eith er muscle force nor muscle l e n gth shou ld be consi dered as c ontrolled quantity, rathe r their ratio (the stiffness or change in force per c h ange i n l e n g th) appea rs to be fixed b y t he s tret ch reflex O ptimization Princi ples in M otor Co ntrol 10