Force-length property

Fig. 1 Force-length property of muscle a) fully activated force length properties...

In an ideal gas we considered the relations between the thermodynamic properties 5 and U, on the other hand, and the state variables P, V, and T of the substance. With an ideal elastomer we shall be concerned with the relation between U and 5 and the state variables force, length, and temperature. 

Durfee, W.K. and Palmer, K.I. Estimation of force activation, force-length, and force-velocity properties in isolated electrically stimulated muscle, IEEE Trans. Biomed. Eng. BME-41 205-216, 1994. 

Muscles provide the forces needed to make movement possible they transmit their forces to tendons, whose forces in turn cause rotation of the bones about the joints. Muscles, however, are not simple force generators the force developed by a muscle depends not only on the level of neural excitation provided by the central nervous system (CNS), but also on the length and speed at which the muscle is contracting. Thus, muscles are the interface between the neuromuscular and musculoskeletal systems, and knowledge of their force-producing properties is crucial for understanding how these two systems interact to produce coordinated movement. 

In the discussion below, the force-length and force-velocity properties of muscle are assumed to be scaled-up versions of the properties of muscle fibers, which in turn are assumed to be scaled-up versions of properties of sarcomeres. 

Modeling Contraction Dynamics. A. F. Huxley developed a mechanistic model to explain the structural changes at the sarcomere level that were seen under the electron microscope in the late 1940s and early 1950s. Because of its complexity, however, this (cross-bridge) model is rarely, if ever, used in studies of coordination. Instead, an empirical model, proposed by A. V. Hill, is used in virtually all models of movement to account for the force-length and force-velocity properties of muscle (Hill, 1938) (Fig. 6.21). 

Muscle contraction dynamics include the mechanical properties of muscle tissues and tendons, which are expressed as force-length and force-velocity relations. The activation dynamics include the voluntary and nonvoluntary (reflex) excitation signal and motor unit recruitment level in the muscle. It is well known that regardless of fatigue, the generated torque in each joint is dependent on muscle activation levels (MALs) and joint angle when in a stationary position. This was first observed by Tnman et al. 

Molecular Dynamics and Monte Carlo Simulations. At the heart of the method of molecular dynamics is a simulation model consisting of potential energy functions, or force fields. Molecular dynamics calculations represent a deterministic method, ie, one based on the assumption that atoms move according to laws of Newtonian mechanics. Molecular dynamics simulations can be performed for short time-periods, eg, 50—100 picoseconds, to examine localized very high frequency motions, such as bond length distortions, or, over much longer periods of time, eg, 500—2000 ps, in order to derive equiUbrium properties. It is worthwhile to summarize what properties researchers can expect to evaluate by performing molecular simulations ... 

Solution Properties. Typically, if a polymer is soluble ia a solvent, it is soluble ia all proportions. As solvent evaporates from the solution, no phase separation or precipitation occurs. The solution viscosity iacreases continually until a coherent film is formed. The film is held together by molecular entanglements and secondary bonding forces. The solubiUty of the acrylate polymers is affected by the nature of the side group. Polymers that contain short side chaias are relatively polar and are soluble ia polar solvents such as ketones, esters, or ether alcohols. As the side chaia iacreases ia length the polymers are less polar and dissolve ia relatively nonpolar solvents, such as aromatic or aUphatic hydrocarbons. 

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