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Muscle and Limb Mechanics

George A. Tsianos, Gerald E. Loeb

10.1002/cphy.c160009

Source: Volume 7, Issue 2, April 2017

Published online: March 2017

Full Article on Wiley Online Library



ABSTRACT

Understanding of the musculoskeletal system has evolved from the collection of individual phenomena in highly selected experimental preparations under highly controlled and often unphysiological conditions. At the systems level, it is now possible to construct complete and reasonably accurate models of the kinetics and energetics of realistic muscles and to combine them to understand the dynamics of complete musculoskeletal systems performing natural behaviors. At the reductionist level, it is possible to relate most of the individual phenomena to the anatomical structures and biochemical processes that account for them. Two large challenges remain. At a systems level, neuroscience must now account for how the nervous system learns to exploit the many complex features that evolution has incorporated into muscle and limb mechanics. At a reductionist level, medicine must now account for the many forms of pathology and disability that arise from the many diseases and injuries to which this highly evolved system is inevitably prone. © 2017 American Physiological Society. Compr Physiol 7:429‐462, 2017.

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Figure 1. Figure 1. Basic architecture of a mammalian striated skeletal muscle fiber, consisting myofibrillar bundles of paracrystalline myofilaments organized into serially repeating sarcomeres. Action potentials traveling along the sarcolemma and invaginations called transverse tubules activate the contractile state by releasing calcium from terminal cisternae of the sarcoplasmic reticulum; relaxation occurs as calcium is pumped back into the sarcoplasmic reticulum. Varities of recently elucidated scaffold structures (not illustrated) maintain the highly regular alignment of all of these structures across the length and breadth of muscle fibers. Reprinted with permission (207).
Figure 2. Figure 2. Motor behaviors are the result of many complex physiological and mechanical processes that have limited experimental observability. The state of activation of muscles is often measured by electromyographical signals (EMG) reflecting action potentials along muscle fibers. The consequent kinetic (motive) processes that eventually affect the observable motion of the body and any forces applied to contacting objects depend, in turn, on the architecture, posture, and motion (spatial) of the musculoskeletal system. Reprinted with permission (207).
Figure 3. Figure 3. Coupling between muscle and limb mechanics. Neural signals from motoneurons in the spinal cord excite muscles that then generate force depending on the time course of musculotendon length (see Section “Muscle mechanics in the potentiated, nonfatigued state”). The musculotendon force then influences limb motion depending on the mechanics of the limb as well as the location and the pulling direction of the musculotendon force. The limb motion that results changes the musculotendon path depending on the musculoskeletal attachments within the limb and the physical constraints due to contact with neighboring bone/soft tissue. The musculotendon path determines both the musculotendon length, which has substantial effects on muscle mechanics, and musculotendon pulling direction, which has substantial effects on limb mechanics. Moreover, the limb motion, which results largely from musculotendon forces also modulates muscle mechanics through its effects on neural excitation of muscle through proprioceptor mediated input to the spinal cord and brain.
Figure 4. Figure 4. Tendon stiffness. The stress strain curve of a tendon is shown over a wide range of strains. As strain is increased past the slack length of the tendon, tensile stress begins to build in the tendon. As strain increases tendon stiffness increases so the effects of strain on stress grow stronger up until a point where stiffness plateaus (2%‐3%) and the sensitivity of stress to strain becomes maximal. Further increases in strain result in linear increases in stress up to a point (5%‐6%) where the tendon starts to experience irreversible damage and stress abruptly stops increasing in response to further strain and even starts decreasing for strains greater than about 7%. The experiment was performed on fresh cadaveric Achilles tendon from a 54 year woman at 37°C. Reprinted with permission (1).
Figure 5. Figure 5. Tetanic force‐length relationship. Muscle fiber tension as a function of sarcomere length is shown. When the muscle is stretched beyond the point of no overlap between thick and thin filaments (point A), tension is zero. As sarcomere length decreases, tension increases in proportion to the amount of myofilament overlap until it becomes maximal (point B). As sarcomere length decreases further (until point C), myofilament overlap increases but the number of crossbridges stay the same so tension does not change. Decreasing sarcomere length from this point leads to overlap of actin filaments from opposite sides of the sarcomere and tension decreases in proportion of this overlap until point D, where the force starts to decrease more steeply due to contact of the thick filament with the z discs and a passive restoring force in the opposite direction of active tension. This experiment was performed on intact single fibers from the semitendinosus muscle of the frog (Rana temporaria) at 4°C (132). Reprinted with permission (133).
Figure 6. Figure 6. Force‐length relationship at physiological firing rates (15, 30 pps) compared to tetanic (120 pps) in feline fast‐twitch muscle. (A and B) Typical isometric contractions. (C) Optimal length at physiological frequencies is substantially longer than the classical L0 defined at maximal tetanic activation when filament overlap is the only effect. (D) Effects of filament overlap were removed by normalizing curves to maximal activation at 120 pps, revealing dependence of activation on filament length as a result of unsaturated calcium diffusion kinetics. Reprinted with permission (40).
Figure 7. Figure 7. Scanning electron micrograph of the collagenous stroma that surrounds individual muscle fibers (long arrow), here removed by NaOH digestion; arrowhead points to perimysial bundles of thick collagen fibers that separate muscle fascicles. Reprinted with permission (305).
Figure 8. Figure 8. The total force (active plus passive) produced by a muscle depends on both its length (green line shows isometric force‐length relationship at velocity = 0) and velocity (red line shows force‐velocity relationship at optimal length = L0). For a supramaximally activated slow‐twitch muscle like feline soleus, this results in a complex surface that includes a negative slope region for a small range of muscle lengths above L0 (dashed circle).
Figure 9. Figure 9. Force‐velocity relationship/yield. At stimulation frequencies that generate near maximal isometric force (35 Hz), slow‐twitch muscle generates higher forces while lengthening and lower forces while shortening. For moderate stimulation frequencies (7 Hz), force decreases relative to isometric for both the lengthening and shortening conditions. For low frequencies (3 Hz), the lengthening muscle produces slightly higher forces than the isometric condition and shortening muscle produces slightly lower forces. The experiment was performed on feline soleus muscle at 37°C with intact nerve and blood supply. Groups of motoneurons were stimulated asynchronously to reproduce the smooth contractions observed in vivo for low frequencies of stimulation. Reprinted with permission (176).
Figure 10. Figure 10. Ca2+ activation of muscle. The effects of calcium concentration ([Ca2+]; pCa = −log([Ca2+]) on muscle fiber tension is shown. Force is generated once Ca exceeds some threshold. As Ca increases, its effects on tension become stronger up until a level of calcium that generates a moderate level of tension. Increasing Ca further leads to smaller effects of Ca on tension up until the point where tension saturates at high levels of Ca. Curve A and B were obtained using data from fibers in a different chemical environment [see (104) for more details]. The experiments were performed on single skinned muscle fibers from the frog at 0°C. Reprinted with permission (104).
Figure 11. Figure 11. Force‐frequency relationship at fascicle lengths from 0.8 to 1.2 L0 in feline fast‐twitch muscle. Naturally occurring firing rates are in the range 20 to 40 pps where the slope is steep. Reprinted with permission (40).
Figure 12. Figure 12. Effects of length on Ca2+ induced muscle activation. The active tension‐Ca2+ relationship is shown for different sarcomere lengths. If the only effect of length on tension is due to its effects on myofilament overlap then the tension‐Ca2+ relationship should scale similarly across all Ca2+ levels. This classical study shows, however, that as Ca2+ decreases from levels near maximal tension, tension at longer lengths decreases less than tension at shorter lengths, having near optimal overlap, and for low enough Ca2+ tension at suboptimal myofilament overlap even exceeds tension generated at optimal overlap. This indicates that stretching the muscle fiber facilitates muscle activation independent of the effects of myofilament overlap. The experiment was performed on single skinned muscle fibers from the toad (Xenopus laevis) at 0°C. Reprinted with permission (108).
Figure 13. Figure 13. Activation rise and fall times. (A) Rise times to half of the maximal force are shown for a wide range of muscle fascicle lengths and frequencies of stimulation. At low stimulus frequencies, rise time decreases with fascicle length and at high stimulus frequencies, the relationship is reversed. (B) Fall times from the end of stimulation after reaching a steady state force to the time at which force drops to half of the steady state value. Fall time increases with both fascicle length and stimulus frequency. The experiments were performed on feline caudofemoralis at 37°C with intact nerve and blood supply. Groups of motoneurons were stimulated asynchronously to reproduce the smooth contractions observed in vivo for low frequencies of stimulation. Reprinted with permission (49).
Figure 14. Figure 14. Sag. During constant frequency electrical stimulation of the fast‐twitch feline caudofemoralis muscle under isometric conditions at optimal length L0 in situ, force decreases substantially at 20 pps, less at 40 pps and not at all at the 60 pps tetanic frequency (timebase in ms; forces normalized to values at 133 ms for comparison of time course). Reprinted with permission (49).
Figure 15. Figure 15. Typical bipolar EMG recording configurations from a mixed muscle with regional stratification of early recruited, slow‐twitch muscle fibers versus late recruited, fast‐twitch muscle fibers. Reprinted with permission (207).


Figure 1. Basic architecture of a mammalian striated skeletal muscle fiber, consisting myofibrillar bundles of paracrystalline myofilaments organized into serially repeating sarcomeres. Action potentials traveling along the sarcolemma and invaginations called transverse tubules activate the contractile state by releasing calcium from terminal cisternae of the sarcoplasmic reticulum; relaxation occurs as calcium is pumped back into the sarcoplasmic reticulum. Varities of recently elucidated scaffold structures (not illustrated) maintain the highly regular alignment of all of these structures across the length and breadth of muscle fibers. Reprinted with permission (207).


Figure 2. Motor behaviors are the result of many complex physiological and mechanical processes that have limited experimental observability. The state of activation of muscles is often measured by electromyographical signals (EMG) reflecting action potentials along muscle fibers. The consequent kinetic (motive) processes that eventually affect the observable motion of the body and any forces applied to contacting objects depend, in turn, on the architecture, posture, and motion (spatial) of the musculoskeletal system. Reprinted with permission (207).


Figure 3. Coupling between muscle and limb mechanics. Neural signals from motoneurons in the spinal cord excite muscles that then generate force depending on the time course of musculotendon length (see Section “Muscle mechanics in the potentiated, nonfatigued state”). The musculotendon force then influences limb motion depending on the mechanics of the limb as well as the location and the pulling direction of the musculotendon force. The limb motion that results changes the musculotendon path depending on the musculoskeletal attachments within the limb and the physical constraints due to contact with neighboring bone/soft tissue. The musculotendon path determines both the musculotendon length, which has substantial effects on muscle mechanics, and musculotendon pulling direction, which has substantial effects on limb mechanics. Moreover, the limb motion, which results largely from musculotendon forces also modulates muscle mechanics through its effects on neural excitation of muscle through proprioceptor mediated input to the spinal cord and brain.


Figure 4. Tendon stiffness. The stress strain curve of a tendon is shown over a wide range of strains. As strain is increased past the slack length of the tendon, tensile stress begins to build in the tendon. As strain increases tendon stiffness increases so the effects of strain on stress grow stronger up until a point where stiffness plateaus (2%‐3%) and the sensitivity of stress to strain becomes maximal. Further increases in strain result in linear increases in stress up to a point (5%‐6%) where the tendon starts to experience irreversible damage and stress abruptly stops increasing in response to further strain and even starts decreasing for strains greater than about 7%. The experiment was performed on fresh cadaveric Achilles tendon from a 54 year woman at 37°C. Reprinted with permission (1).


Figure 5. Tetanic force‐length relationship. Muscle fiber tension as a function of sarcomere length is shown. When the muscle is stretched beyond the point of no overlap between thick and thin filaments (point A), tension is zero. As sarcomere length decreases, tension increases in proportion to the amount of myofilament overlap until it becomes maximal (point B). As sarcomere length decreases further (until point C), myofilament overlap increases but the number of crossbridges stay the same so tension does not change. Decreasing sarcomere length from this point leads to overlap of actin filaments from opposite sides of the sarcomere and tension decreases in proportion of this overlap until point D, where the force starts to decrease more steeply due to contact of the thick filament with the z discs and a passive restoring force in the opposite direction of active tension. This experiment was performed on intact single fibers from the semitendinosus muscle of the frog (Rana temporaria) at 4°C (132). Reprinted with permission (133).


Figure 6. Force‐length relationship at physiological firing rates (15, 30 pps) compared to tetanic (120 pps) in feline fast‐twitch muscle. (A and B) Typical isometric contractions. (C) Optimal length at physiological frequencies is substantially longer than the classical L0 defined at maximal tetanic activation when filament overlap is the only effect. (D) Effects of filament overlap were removed by normalizing curves to maximal activation at 120 pps, revealing dependence of activation on filament length as a result of unsaturated calcium diffusion kinetics. Reprinted with permission (40).


Figure 7. Scanning electron micrograph of the collagenous stroma that surrounds individual muscle fibers (long arrow), here removed by NaOH digestion; arrowhead points to perimysial bundles of thick collagen fibers that separate muscle fascicles. Reprinted with permission (305).


Figure 8. The total force (active plus passive) produced by a muscle depends on both its length (green line shows isometric force‐length relationship at velocity = 0) and velocity (red line shows force‐velocity relationship at optimal length = L0). For a supramaximally activated slow‐twitch muscle like feline soleus, this results in a complex surface that includes a negative slope region for a small range of muscle lengths above L0 (dashed circle).


Figure 9. Force‐velocity relationship/yield. At stimulation frequencies that generate near maximal isometric force (35 Hz), slow‐twitch muscle generates higher forces while lengthening and lower forces while shortening. For moderate stimulation frequencies (7 Hz), force decreases relative to isometric for both the lengthening and shortening conditions. For low frequencies (3 Hz), the lengthening muscle produces slightly higher forces than the isometric condition and shortening muscle produces slightly lower forces. The experiment was performed on feline soleus muscle at 37°C with intact nerve and blood supply. Groups of motoneurons were stimulated asynchronously to reproduce the smooth contractions observed in vivo for low frequencies of stimulation. Reprinted with permission (176).


Figure 10. Ca2+ activation of muscle. The effects of calcium concentration ([Ca2+]; pCa = −log([Ca2+]) on muscle fiber tension is shown. Force is generated once Ca exceeds some threshold. As Ca increases, its effects on tension become stronger up until a level of calcium that generates a moderate level of tension. Increasing Ca further leads to smaller effects of Ca on tension up until the point where tension saturates at high levels of Ca. Curve A and B were obtained using data from fibers in a different chemical environment [see (104) for more details]. The experiments were performed on single skinned muscle fibers from the frog at 0°C. Reprinted with permission (104).


Figure 11. Force‐frequency relationship at fascicle lengths from 0.8 to 1.2 L0 in feline fast‐twitch muscle. Naturally occurring firing rates are in the range 20 to 40 pps where the slope is steep. Reprinted with permission (40).


Figure 12. Effects of length on Ca2+ induced muscle activation. The active tension‐Ca2+ relationship is shown for different sarcomere lengths. If the only effect of length on tension is due to its effects on myofilament overlap then the tension‐Ca2+ relationship should scale similarly across all Ca2+ levels. This classical study shows, however, that as Ca2+ decreases from levels near maximal tension, tension at longer lengths decreases less than tension at shorter lengths, having near optimal overlap, and for low enough Ca2+ tension at suboptimal myofilament overlap even exceeds tension generated at optimal overlap. This indicates that stretching the muscle fiber facilitates muscle activation independent of the effects of myofilament overlap. The experiment was performed on single skinned muscle fibers from the toad (Xenopus laevis) at 0°C. Reprinted with permission (108).


Figure 13. Activation rise and fall times. (A) Rise times to half of the maximal force are shown for a wide range of muscle fascicle lengths and frequencies of stimulation. At low stimulus frequencies, rise time decreases with fascicle length and at high stimulus frequencies, the relationship is reversed. (B) Fall times from the end of stimulation after reaching a steady state force to the time at which force drops to half of the steady state value. Fall time increases with both fascicle length and stimulus frequency. The experiments were performed on feline caudofemoralis at 37°C with intact nerve and blood supply. Groups of motoneurons were stimulated asynchronously to reproduce the smooth contractions observed in vivo for low frequencies of stimulation. Reprinted with permission (49).


Figure 14. Sag. During constant frequency electrical stimulation of the fast‐twitch feline caudofemoralis muscle under isometric conditions at optimal length L0 in situ, force decreases substantially at 20 pps, less at 40 pps and not at all at the 60 pps tetanic frequency (timebase in ms; forces normalized to values at 133 ms for comparison of time course). Reprinted with permission (49).


Figure 15. Typical bipolar EMG recording configurations from a mixed muscle with regional stratification of early recruited, slow‐twitch muscle fibers versus late recruited, fast‐twitch muscle fibers. Reprinted with permission (207).
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Further Reading


MusculoSkeletal Modeling Software (MSMS) is a complete modeling package for creating models of musculoskeletal systems including muscle fiber-types, musculotendon architecture and proprioceptors, and interfacing them with control systems to view animations and to monitor internal state signals. MSMS is available as freeware through http://mddf.usc.edu. Its underlying models are described in more detail and compared to other modeling strategies in the following open publications:


Tsianos, G.A. and Loeb, G.E. Muscle Physiology and Modeling www.scholarpedia.org/article/Muscle Physiology and Modeling Scholarpedia, 8(10):12388, 2013.
Loeb, G.E. and Mileusnic, M. Proprioceptors and models of transduction www.scholarpedia.org/article/Proprioceptors_and_Models_of_Transduction Scholarpedia 10(5):12390, 2015.
Loeb, G.E. and Davoodi, R. Musculoskeletal mechanics and modeling Scholarpedia, 2016 (Under Review).


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Article Title: Muscle and Limb Mechanics
 

How to Cite

George A. Tsianos, Gerald E. Loeb. Muscle and Limb Mechanics. Compr Physiol 2017, 7: 429-462. doi: 10.1002/cphy.c160009