16423JHST515J Space Biomedical l Engineering and Life Prof Dava Newman Early Ideas about Muscular Contraction Hippocrates thought that the tendons caused the body to move (he confused tendons with nerves, and in fact used the same word, neuron, for both) Aristotle compared the movements of animals to the movements of puppets and thought that the tendons played the role of the puppet strings, bringing about motion as they were tightened and released Muscles themselves were not credited with the ability to contract until the third century BC when Erasistratus suggested that the animal spirit flows from the head through the nerves to the muscle. He thought the nerves were hollow tubes, through which the muscles could be filled with pneuma, causing them to expand in breadth but contract in length, thus moving the joints. Actually, muscles don' t increase in volume as they contract! Jan Swammerdam in the early 1660s showed that muscle contracts without changing its volume. Using a frog muscle in a sealed air-filled glass and preserving the length of a nerve, the nerve was stimulated mechanically (pulling on it with a fine wire). A drop of water in the small tube should have risen if th muscle volume increased, but it did not. Extended to human muscles by francis Glisson in 1677(arm in a water filled rigid tube, sealed at the elbow) Most of what has been learned about muscle mechanics is from whole muscle removed from the animal. Many of the most important experiments being performed between 1910 and 1950 by A.V. Hill and his collaborators at University College, London. Isolated from muscle preparation(alive for several days in an oxygenated solution). When given a stimulus, the mechanical and thermal activation will not be synchronous at all points because the wave of electrical excitation is fairly slow(30-40 m/s in amphibian muscle) The fact that muscle is turned on electrically is very interesting 1
16.423J/HST515J Space Biomedical Engineering and Life Support Prof. Dava Newman Early Ideas about Muscular Contraction Hippocrates thought that the tendons caused the body to move (he confused tendons with nerves, and in fact used the same word, neuron, for both). Aristotle compared the movements of animals to the movements of puppets and thought that the tendons played the role of the puppet strings, bringing about motion as they were tightened and released. Muscles themselves were not credited with the ability to contract until the third century BC when Erasistratus suggested that the animal spirit flows from the head through the nerves to the muscle. He thought the nerves were hollow tubes, through which the muscles could be filled with pneuma, causing them to expand in breadth but contract in length, thus moving the joints. Actually, muscles don't increase in volume as they contract! Jan Swammerdam in the early 1660's showed that muscle contracts without changing its volume. Using a frog muscle in a sealed air-filled glass and preserving the length of a nerve, the nerve was stimulated mechanically (pulling on it with a fine wire). A drop of water in the small tube should have risen if the muscle volume increased, but it did not. Extended to human muscles by Francis Glisson in 1677 (arm in a water filled rigid tube, sealed at the elbow). Most of what has been learned about muscle mechanics is from whole muscles removed from the animal. Many of the most important experiments being performed between 1910 and 1950 by A.V. Hill and his collaborators at University College, London. Isolated from muscle preparation (alive for several days in an oxygenated solution). When given a stimulus, the mechanical and thermal activation will not be synchronous at all points because the wave of electrical excitation is fairly slow (30-40 m/s in amphibian muscle). The fact that muscle is turned on electrically is very interesting. 1
16423JHST515J Engineerng Prof Dava Newman b Figure 1. The experiment of Jan Swammerdam, circa 1663, showing that a muscle does not increase in volume as it contracts. A frog,s muscle(b)is placed in an air-filled tube closed at the bottom(a). When the fine wire() is pulled, the nerve is pinched against the support( d), causing the muscle to contract. The drop of water in the capillary tube (e)does not move up when the muscle contracts. From Needham(1971) Mechanical Events: Twitch and Tetanus The first mechanical event it is possible to measure following stimulation is not the development of force, but the resistance to an externally imposed stretch Even before the electrical action potential is over, about 3-5 msec after the stimulating shock, the contractile machinery feels stiffer to an external pull than it does when subjected to a similar pull without first being shocked There is latency for about 15 msec following the shock and the muscle produces no forceif stimulated under isometric constant length conditions). Finally, the muscle responds, and if it was given a single stimulus, it produces a single transient rise in tension TWitch The strength of the stimulus must be strong enough to depolarize the muscle membrane- otherwise nothing happens. Over a limited range above the threshold amplitude, the peak force developed in the twitch rises with the strength of the stimulus, as more muscle fibers are recruited into the force- generating enterprise. Once the majority of muscle fibers become active there are no further increases in force
16.423J/HST515J Space Biomedical Engineering and Life Support Prof. Dava Newman Figure 1. The experiment of Jan Swammerdam, circa 1663, showing that a muscle does not increase in volume as it contracts. A frog’s muscle (b) is placed in an air-filled tube closed at the bottom (a). When the fine wire (c) is pulled, the nerve is pinched against the support (d), causing the muscle to contract. The drop of water in the capillary tube (e) does not move up when the muscle contracts. From Needham (1971). Mechanical Events: Twitch and Tetanus The first mechanical event it is possible to measure following stimulation is not the development of force, but the resistance to an externally imposed stretch. Even before the electrical action potential is over, about 3-5 msec after the stimulating shock, the contractile machinery feels stiffer to an external pull than it does when subjected to a similar pull without first being shocked. There is latency for about 15 msec following the shock and the muscle produces no force (if stimulated under isometric = constant length conditions). Finally, the muscle responds, and if it was given a single stimulus, it produces a single transient rise in tension = TWITCH. The strength of the stimulus must be strong enough to depolarize the muscle membrane - otherwise nothing happens. Over a limited range above the threshold amplitude, the peak force developed in the twitch rises with the strength of the stimulus, as more muscle fibers are recruited into the forcegenerating enterprise. Once the majority of muscle fibers become active there are no further increases in force. 2
16423/HST515J Space Biomedical Engineering and Life Support Prof Dava Newman If a train of stimulations is given, the force has a steady magnitude with a little ripple at the stimulation frequency = Unfused Tetanus. As the frequency is raised, mean force rises and the ripple finally reaches a very low level (about 30 shocks per sec). Further increase in freq. produce no further increases in mean force TETANIC FUSION (mammalian muscle at body temp. 50-60 shocks per sec Tetanus fused tetanus Twitch Figure 2. Twitch and tetanus. When a series of stimuli is given, muscle force rises to an uneven plateau(unfused tetanus) which has a ripple at the frequency of stimulation. As the frequency is increased, the plateau rises and becomes smoother, reaching a limit as the tetanus becomes fused Tension-Length Curves: Passive and active Marey knew that somehow the elasticity of muscle must be one of the features that determine how the separate effects of a sequence of shocks coalesce in a tetanus. There are 2 separate elements of elastic behavior: one due to PASSIVE and one due to ACTIVE properties Passive properties: Force is recorded as the muscle is stretched to a number of constant lengths, with no stimulation. Curve gets progressively steeper with larger stretch, same reason that a piece of yarn gets stiffer as it's extended- fibrous elements which were redundant at low extension become tensed at high extension, thereby addin their spring stiffness in parallel The derivative of stress with respect to strain, do/dh, is shown to be a linearly increasing function of the stress(o=F/A)
16.423J/HST515J Space Biomedical Engineering and Life Support Prof. Dava Newman If a train of stimulations is given, the force has a steady magnitude with a little ripple at the stimulation frequency = Unfused Tetanus. As the frequency is raised, mean force rises and the ripple finally reaches a very low level (about 30 shocks per sec). Further increase in freq. produce no further increases in mean force = TETANIC FUSION (mammalian muscle at body temp. 50-60 shocks per sec). Figure 2. Twitch and tetanus. When a series of stimuli is given, muscle force rises to an uneven plateau (unfused tetanus) which has a ripple at the frequency of stimulation. As the frequency is increased, the plateau rises and becomes smoother, reaching a limit as the tetanus becomes fused. Tension-Length Curves: Passive and Active Marey knew that somehow the elasticity of muscle must be one of the features that determine how the separate effects of a sequence of shocks coalesce in a tetanus. There are 2 separate elements of elastic behavior: one due to PASSIVE and one due to ACTIVE properties. Passive properties: Force is recorded as the muscle is stretched to a number of constant lengths, with no stimulation. Curve gets progressively steeper with larger stretch, same reason that a piece of yarn gets stiffer as it's extended - fibrous elements which were redundant at low extension become tensed at high extension, thereby adding their spring stiffness in parallel. The derivative of stress with respect to strain, dσ/dλ, is shown to be a linearly increasing function of the stress ( σ = F/A) 3
16423JHST515J Space Biomedical Engineering and Life Support Prof Dava Newman a(+B) where n is the lagrangian strain when a muscle of rest length eo is stretched to a new length e Integratin ue-B where u is the constant of integration (rabbit heart muscle, many collagenous tissues -tendons, skin, resting skeletal muscle obey similar exponential relationships between stress and strain. No plausible derivation of this form from first principles has yet been given! When the muscle is tetanized, the tension at each length is greater than it was when the muscle was resting(some show a local max Developed tension(difference between the active(tetanized) and passive curves is greatest when the muscle is held at a length close to the length it occupied in the body. The maximum developed stress is almost a constant, about 2 kg/cm (in mammalian muscles taken from animals of a wide range of body sizes Noteworthy, because many other parameters(shortening speed, activity of enzymes controlling metabolic rate)are very different in animals and even between muscles. Cross-sectional area of muscle doesn' t have a unique meaning in muscle which tapers down into a tendon on either end, so divide the weight in grams by the length in centimeters(assuming muscle density -1 g/cm) Figure 3. Tension-length curves for frog satorius muscle at 0%C. The passive curve was measured on the resting muscle at a series of different lengths. The tetanized curve was measured at a series of constant lengths as the muscle was 4
16.423J/HST515J Space Biomedical Engineering and Life Support Prof. Dava Newman dσ 1 dλ = α(σ +β) where λ is the Lagrangian strain, o , when a muscle of rest length o is stretched to a new length 88 . Integrating, 2 σ = µeαλ − β where µ is the constant of integration (rabbit heart muscle, many collagenous tissues - tendons, skin, resting skeletal muscle obey similar exponential relationships between stress and strain. No plausible derivation of this form from first principles has yet been given! When the muscle is tetanized, the tension at each length is greater than it was when the muscle was resting (some show a local max.) Developed tension (difference between the active (tetanized) and passive curves) is greatest when the muscle is held at a length close to the length it occupied in the body. The maximum developed stress is almost a constant, about 2 kg/cm2 (in mammalian muscles taken from animals of a wide range of body sizes). Noteworthy, because many other parameters (shortening speed, activity of enzymes controlling metabolic rate) are very different in animals and even between muscles. Cross-sectional area of muscle doesn't have a unique meaning in muscle which tapers down into a tendon on either end, so divide the weight in grams by the length in centimeters (assuming muscle density ~ 1 g/cm3). Figure 3. Tension-length curves for frog satorius muscle at 0° C. The passive curve was measured on the resting muscle at a series of different lengths. The tetanized curve was measured at a series of constant lengths as the muscle was 4
16423JHST515J Space Biomedical Engineering and Life Prof Dava Newman held in isometric contraction. The rest length, lo, was the length of the muscle in he body. From Aubert et al. (1951) Gastrocnemius Tension Tension Developed Figure 4. Schematic force-length curves. The pennate-fibered gastrocnemius (left), with its short fibers and relatively great volume of connective tissue, does not show a local maximum in the tetanic length-tension curve. By contrast, the parallel-fibered sartorius(right) does show a maximum Conceptual Model of Muscle Stimulator Tensio Time component QQQ产 Figure 5.(a)Quick-release apparatus. When the catch is withdrawn, the muscle is exposed to a constant force determined by the weight in the pan. (b)The muscle is stimulated tetanically. Upon release of the catch, the muscle shortens 5
16.423J/HST515J Space Biomedical Engineering and Life Support Prof. Dava Newman held in isometric contraction. The rest length, lo, was the length of the muscle in the body. From Aubert et al. (1951). Figure 4. Schematic force-length curves. The pennate-fibered gastrocnemius (left), with its short fibers and relatively great volume of connective tissue, does not show a local maximum in the tetanic length-tension curve. By contrast, the parallel-fibered sartorius (right) does show a maximum. Conceptual Model of Muscle Figure 5. (a) Quick-release apparatus. When the catch is withdrawn, the muscle is exposed to a constant force determined by the weight in the pan. (b) The muscle is stimulated tetanically. Upon release of the catch, the muscle shortens 5