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This book offers a succinct but comprehensive description of the mechanics of muscle contraction and legged terrestrial locomotion. It describes on the one hand how the fundamental properties of muscle tissue affect the mechanics of locomotion, and on the other, how the mechanics of locomotion modify the mechanism of muscle operation under different conditions.

Further, the book reports on the design and results of experiments conducted with two goals. The first was to describe the physiological function of muscle tissue (which may be considered as the “motor”) contracting at a constant length, during shortening, during lengthening, and under a condition that occurs most frequently in the back-and-forth movement of the limbs during locomotion, namely the stretch-shortening cycle of the active muscle. The second objective was to analyze the interaction between the motor and the “machine” (the skeletal lever system) during walking and running in different scenarios with respect to speed, step frequency, body mass, gravity, age, and pathological gait. The book will be of considerable interest to physiology, biology and physics students, and provides researchers with stimuli for further experimental and analytical work.

Inhaltsverzeichnis

Frontmatter

Muscle: The Motor

Frontmatter

Chapter 1. Experimental Procedures in the Study of Muscle Mechanics

Abstract
This chapter describes the laboratory procedures classically used to analyze the fundamental properties of muscular contraction. These procedures include the characteristics of the bath in which the specimen, isolated muscle or muscle fiber, is immersed during the experiment, its electrical stimulation and the setups used to record with a minimum of error the force exerted by muscle at a constant length (isometric contraction), during shortening against a constant load (isotonic contraction) and at a constant speed (isovelocity contraction). Isometric contractions at different muscle lengths allow the determination of the force-length relation, which will be described in Chap. 3. Isotonic contraction at a given length allows the determination of the force-velocity relation (Chap. 3) and can be attained mechanically on the whole muscle by means of an isotonic lever (whose physical principle and an example of the apparatus used are described) or electronically on a single muscle fiber and on a tendon-free fiber segment, by means of a feed-back system (isotonic release). An example is shown of the mechanical system (the Levin and Wyman ergometer) used to measure the work done by a muscle during an isovelocity contraction (Chap. 4). The physical response of a system to an action, i.e. the difference between input to a system (both mechanical and electrical) and output of the system, is analyzed with the aim to understand and minimize the distortion of the input signal and to define the ‘time constant’ of several trends of physiological processes reported in this book.
Giovanni Cavagna

Chapter 2. Functional Anatomy of Muscle

Abstract
This chapter describes the main anatomical structures giving skeletal muscle its striated appearance, the location of the “motor” and of other passive elastic elements within its functional unit, the half-sarcomere, which contains all the ingredients characterizing muscular contraction. It is shown that the length change of each myofibril equals the sum of the length change of all the sarcomeres set in series within the myofibril, whereas the force at the extremities of each myofibril equals the force exerted by each sarcomere. The contrary is true for the myofibrils set in parallel within the muscle fiber: the total force exerted by the fiber is the sum of the forces exerted by all myofibrils, whereas the length change of the fiber equals that of each myofibril. Series elastic elements transmitting the force exerted by the contractile component are located within the tendons whereas other elastic elements are located both in series and in parallel within the sarcomeres. Since these structures can shorten quickly without appreciable losses they are called undamped elastic elements and are essential for the storage and recovery of mechanical energy in the stretch-shortening cycle of muscle-tendon units. Other damped structures within the sarcolemma and the sarcomeres are not suitable for storage-recovery of mechanical energy, but have the function to contain and stabilize the actin-myosin filaments during sarcomere lengthening and contraction.
Giovanni Cavagna

Chapter 3. Measurements Made During or Starting from a State of Isometric Contraction

Abstract
This chapter describes experiments aimed to detect: (i) the interaction between “motor” and passive elastic structures during muscular contraction, and (ii) the basic characteristics of the “motor” function. The interaction between motor and elastic structures explains the time course of the force exerted by muscle in response to a single or a series of stimuli (twitch, clonus and tetanus). The characteristics of the motor are evidenced by two fundamental relations: the force-length relation, i.e. the force exerted by muscle tetanically stimulated at different lengths, and the force-velocity relation, i.e. the velocity of muscle shortening and lengthening, at a given length, against different loads. The force-length relation is shown both when the maximal isometric force is measured as a function of the length of the whole muscle and as a function of the length of the sarcomere. The trend of the force-length relation is explained on the basis of the different overlap between actin and myosin at the different sarcomere lengths. The changes of the force-velocity relation with muscle length and time delay since the beginning of stimulation are explained. The functional consequences of both force-length and force-velocity relations are evidenced. The iso-velocity force-length diagram is described and it is shown how it depends on the elastic and the contractile components of muscle at different velocities of shortening. Quick release experiments on a single muscular fiber allow determining the existence within each half sarcomere of an undamped and a damped structure whose force-length relations are described over the half-sarcomere length.
Giovanni Cavagna

Chapter 4. Measurements Made After Stretching the Contracting Muscle

Abstract
This chapter faces the problem to explain the origin of the additional amount of positive work done by a contracting muscle when it shortens immediately after being stretched, a condition that most often occurs during legged terrestrial locomotion. This task implied experiments made on the isolated muscle, on a single muscular fiber and on a tendon-free segment of the fiber. Initial experiments made on the whole muscle were unable to explain the whole amount of the extra work done after stretching with the release of elastic energy and suggested that the contractile component itself was in some way ‘enhanced’ by previous stretching. An enhancement of the contractile component was in fact subsequently suggested by a shift of muscle’s force-velocity relation and of the stress-strain relation of the undamped ‘elastic’ elements. Experiments made on a single fiber showed that after stretching: (i) the rate constant and the effect of temperature on the fast phase of stress relaxation are consistent with an energy transfer from the undamped to the damped structure within the sarcomeres, and (ii) shortening against the maximal isometric force takes place in four distinct phases similar to those measured after release from a state of isometric contraction. Experiments made on a tendon-free segment of the fiber showed that: (i) the above conclusions are not due to stress relaxation of the tendons, (ii) an energy transfer does occur after stretching between undamped and damped sarcomere structures, and (iii) muscle enhancement by stretch is not entirely due to sarcomere length inhomogeneity.
Giovanni Cavagna

Chapter 5. Muscle Thermodynamics

Abstract
This chapter explains the physical principles involved in the interpretation of the heat produced by muscle, i.e. the meaning of internal energy, enthalpy, entropy, free energy and efficiency. After a short description of the methods used to measure heat production on the isolated muscle specimen, this is divided into resting heat of the relaxed muscle, and initial heat developed during contraction with its components: (i) activation and maintenance heat during isometric contractions at different muscle’s lengths, (ii) shortening heat with its dependence on the applied load, (iii) the Fenn effect, i.e. the additional energy output during shortening, with its suggestive relationship between thermal and mechanical measurements, and (iv) the heat produced during stretching the contracting muscle at different velocities of lengthening. The heat produced after contraction, the relaxation heat, is shown to evolve on a much slower time scale than the initial heat with a trend that parallels that of oxygen consumption by muscle. Finally, muscular efficiency is defined in physical terms after the contraction-relaxation cycle, and distinguished from the improperly called ‘initial efficiency’ measured during shortening against different loads.
Giovanni Cavagna

Locomotion: Motor–Machine Interaction

Frontmatter

Chapter 6. External, Internal and Total Mechanical Work Done During Locomotion

Abstract
This chapter explains why and how the interaction between moving body and ground in legged terrestrial locomotion necessarily requires mechanical work to be done by muscles: external work to sustain the motion of the center of mass of the body relative to the surrounding and internal work to sustain the motion of the limbs relative to the center of mass. The procedure used to measure external work from the force exerted on the ground, measured by means of a force-platform, is described in detail with the errors it involves. The two basic mechanisms adopted in nature to minimize the metabolic energy expenditure due to external work performance, the pendular mechanism of walking and the bouncing mechanism of running, hopping and trotting, are introduced here and will be fully treated in Chaps. 7 and 8 respectively. The mechanical constraint causing execution of internal work in legged terrestrial locomotion is explained. The division of the total work in external plus internal is shown to be consistent with a physical principle (the Koenig’s theorem). The possibilities of error made in measuring internal work by a cinematographic procedure and total work as the sum of external plus internal work are discussed.
Giovanni Cavagna

Chapter 7. Walking

Abstract
This chapter describes the basic mechanism of walking in adult humans, in children during growth and in some animal species. This is done by measuring the changes in kinetic energy of forward motion and gravitational potential energy of the center of mass of the body during the step. These changes are in opposition of phase as in a pendulum with the result that the changes in the total mechanical energy of the center of mass, kinetic plus potential, and as a consequence the external work done to maintain locomotion, is conveniently reduced. The potential-kinetic energy exchange by this pendular mechanism is quantitatively measured (recovery) and found to attain a maximum at an ‘optimal’ walking speed similar to the speed where the external work per unit distance is at a minimum in humans, turkeys, rams, rhea and elephants. This ‘optimal’ speed is also similar to the speed where the metabolic energy expenditure was found to be at a minimum in adult humans; in children, it increases with age and equals the freely chosen walking speed; in parabolic flight maneuvers it increases with gravity. The recovery, measured at each instant within the step, is greater in load-carrying African women than in control subjects explaining their greater economy in carrying loads. The step frequency where the total, external plus internal, work is at a minimum is found to be related to the freely chosen step frequency. The mechanics of competition walking is analyzed and a method is shown evidencing anomalies of pathological gait.
Giovanni Cavagna

Chapter 8. Bouncing Gaits: Running, Trotting and Hopping

Abstract
This chapter describes the mechanism of running, hopping and trotting. In these gaits, opposite to walking, kinetic energy of forward motion and gravitational potential energies of the center of mass of the body oscillate in phase during the step. The step period is divided into ‘effective’ contact time, t ce, and aerial time, t ae, corresponding to a vertical force exerted on the ground greater respectively lower than body weight. At low running speeds and in trotting t ce = t ae, the rebound is on-off-ground symmetric, and the step frequency equals the resonant frequency of the bouncing system. At high running speeds and in hopping t ce < t ae, the rebound is on-off-ground asymmetric, and the step frequency is lower than the resonant frequency of the bouncing system. Furthermore, in all bouncing gaits (from turkeys to humans) the duration of the brake following impact on the ground is shorter than the duration of the subsequent push, i.e., t brake < t push, which is expression of a landing-takeoff asymmetry: hard landing-soft takeoff. The landing-takeoff asymmetry implies that the average force exerted during the brake, when the muscles are stretched, is greater than that exerted during the push when the muscles shorten. This means that very different machines (lever systems) comply with the basic characteristics of the motor (muscle), unchanged from frog to humans, to resist stretching with a force greater than that exerted during shortening. When the operation of the machine is reversed, as in backward running, the resulting soft landing-hard takeoff results in a decreased efficiency.
Giovanni Cavagna

Chapter 9. Effect of Speed, Step Frequency and Age on the Bouncing Step

Abstract
This chapter shows how the on-off-ground asymmetry and the landing-takeoff asymmetry of the rebound of the body change with running speed, step frequency and age. An increase in running speed causes an increase of the on-off-ground asymmetry and a decrease of the landing-takeoff asymmetry, suggesting that the length change of tendon versus that of muscle in the stretch-shorten cycle of muscle-tendon units increases with speed. At low and intermediate running speeds the freely chosen step frequency equals the resonant frequency of the bouncing system, coincides with the frequency minimizing the metabolic energy expenditure, but is lower than the frequency minimizing the mechanical power output, i.e. metabolic energy is saved by tuning step frequency to the resonant frequency even if this requires a greater mechanical power. At high running speeds a compromise is attained to minimize the aerobic power using longer leaps at a low step frequency within the limit set by the anaerobic-limited push-average power allowing these leaps. In children, as in adults, the freely chosen step frequency equals the natural frequency of the bouncing system up to ~11 km/h, although it decreases with age from 4 Hz at 2 years to 2.5 Hz above 12 years. Above ~11 km/h, the rebound becomes on-off-ground asymmetric in children as in adults. In the old subjects, on the contrary, the bounce is on-off-ground symmetric at all running speeds. The landing-takeoff asymmetry is greater in the oldest than in the youngest, qualitatively consistent with the more asymmetric force-velocity relation described in aged muscle.
Giovanni Cavagna

Chapter 10. Work, Efficiency and Elastic Recovery

Abstract
This chapter describes how speed, age, body mass and gravity affect work and efficiency during locomotion. In adult humans and in children the efficiency increases with running speed up to values well above the maximal efficiency of muscle contractile machinery suggesting elastic recovery. According to the spring-mass model of running, a reciprocal relationship is found between power spent against gravity and step frequency resulting in a lower external power in children; their higher step frequency however involves a greater internal power with the result that mass-specific power and efficiency are about the same as in adults. Similarly, in old subjects, a reduction of the vertical push during the running step causes, as in the youngest, a lower power spent against gravity, but a greater step frequency and internal power. The well known increase in efficiency of animal locomotion with increasing body mass is found to coincide with a decrease of elastic hysteresis in the stretch-shorten cycle during the rebound of running, trotting and hopping animals of different size. An increase in gravity causes a proportional increase of external work done by running humans and expands the range of speeds where the rebound is on-off ground symmetric. In sprint running the average power appears to be sustained by the contractile component at low speeds and, for an appreciable fraction, by elastic recovery at high speeds. The role of contractile component and elastic recoil is described during vertical jumps off both feet of different amplitude and under different simulated gravity values.
Giovanni Cavagna
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