Force-velocity property

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. 

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). 

For isokinetic exercise, in which the knee is made to move at a constant angular velocity, quadriceps force decreases as knee-extension speed increases. As the knee extends more quickly, quadriceps force decreases because the muscle shortens more quickly, and, from the force-velocity property, an increase in shortening velocity leads to less muscle force (see Fig. 6.4). As a result, ACL force also decreases as knee-extension speed increases (Figure 6.26), because of the drop in shear force applied to the leg by the quadriceps (via the patellar tendon) (Serpas et al., in press). 

In your AP Chemistry class you may have discussed the derivations for the equations that follow. The AP test does not have any questions that require depth of understanding of the physics of particle movement. You are required to be familiar with and comfortable using a few equations, and we will discuss their use. Their origins are a combination of experimental data and some basic physics involving the properties of gas particles, such as force, velocity, and acceleration. 

The test core technique has failed to find large-scale acceptance because of the unsatisfactory reproducibility of the results. The reasons for this may be due to differences in the force-velocity characteristics of the presses, as a result of which the recorded efforts and movements versus time largely reflect the properties of the equipment used rather than the properties of the material being tested. To achieve a better reproducibility of the test results the test must be carried out on equipment with calibrated metrological parameters. 

Sometimes in fluid mechanics we may start with these four ideas and the measured physical properties of the materials under consideration and proceed directly to solve mathematically for the desired forces, velocities, and so on. This is generally possible only in the case of very simple flows. The observed behavior of a great many fluid flows is too complex to be solved directly from these four principles, so we must resort to experimental tests. Through the use of techniques called dimensional analysis (Chap. 13) often we can use the results of one experiment to predict the results of a much different experiment. Thus, careful experimental work is very important in fluid mechanics. With the development of supercomputers, we are now able to solve many complex problems mathematically by using the methods outlined in Chaps. 10 and 11, which previously would have required experimental tests. As computers become faster and cheaper, we will probably see additional complex fluid mechanics problems solved on supercomputers. Ultimately, the computer solutions must be tested experimentally. 

The linear muscle model has the static and dynamic properties of rectus eye muscle, a model without any nonlinear elements. The model has a nonlinear force-velocity relationship that matches muscle data using linear viscous elements and the length tension characteristics are also in good agreement with muscle data within the operating range of the muscle. Some additional advantages of the linear muscle model are that a passive elasticity is not necessary if the equilibrium point Xe = —19.3°, rather than 15°, and muscle viscosity is constant that does not depend on the innervation stimulus level. 

In contrast, the information ratchet model [9], on which (18) and (19) are based, is consistent with microscopic reversibility for both the chemical and the mechanical processes. The shape of the curve described by (18) is governed by both the force dependence ofr and by the term q that parameterizes the relative likelihood of a forward ATP driven step vs a backward ATP-driven step. The force velocity curve is close to hyperbolic with a=l, but with a = 0, the velocity is nearly constant up to a force of slightly more than half the stopping force and then dramatically decreases to zero at the stopping force, and with a = 0.25 (not shown) the velocity is a nearly linearly decreasing function of the applied force up to Fstaii. The thermodynamic properties such as the step ratio, stoichiometry, efficiency, and stall force are independent of t. ... 

These equations are strikingly simple. Both the liquid s velocity and its flow rate are proportional to the driving force. This property is known as Poiseuille law. One can define a hydrodynamic conductivity, which is the ratio Q// and is inversely proportional to the viscosity p. The viscosity is an intrinsic property of the liquid (for a given force, the greater the viscosity, the lower the flow rate). However, this conductivity depends mainly on the thickness of the liquid film, actually varying as the cube of that thickness. A film twice as thick will support eight times the hydrodynamic flow. This is an important characteristic that comes up in most interface hydrodynamics problems, which are generally dominated by viscous friction. 

Since we are interested in cellular activities where several motors could be involved, a simplified mean-filed model emerge with the assumption that motors a) work independent of each other b) share the applied load equally. These equations are able to predict the transport properties of cargo particles such as their effective velocity and average run length. Two most important quantities that need to be mentioned here are the force-velocity relation and detachment rate of motor when a load is applied to the cargo. Several experiments have shown that velocity Vn(F) of a single motor in system of n bound motors decreases almost linearly with the force F applied against the motor movement. 

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. 

This procedure may be used unless the rate-dependence, load history-dependence, or deformation-hardening characteristics of the isolation system necessitate explicit consideration of their nonlinear and/or velocity-dependent force-deflection properties. 

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

The shear viscosity is an important property of a Newtonian fluid, defined in terms of the force required to shear or produce relative motion between parallel planes [97]. An analogous two-dimensional surface shear viscosity ij is defined as follows. If two line elements in a surface (corresponding to two area elements in three dimensions) are to be moved relative to each other with a velocity gradient dvfdx, the required force is... 

Basically, Newtonian mechanics worked well for problems involving terrestrial and even celestial bodies, providing rational and quantifiable relationships between mass, velocity, acceleration, and force. However, in the realm of optics and electricity, numerous observations seemed to defy Newtonian laws. Phenomena such as diffraction and interference could only be explained if light had both particle and wave properties. Indeed, particles such as electrons and x-rays appeared to have both discrete energy states and momentum, properties similar to those of light. None of the classical, or Newtonian, laws could account for such behavior, and such inadequacies led scientists to search for new concepts in the consideration of the nature of reahty. 

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