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* Fixed issue with expanded menu
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Probably a problem introduced when upgrading to the newest MyST parser
Copy file name to clipboardExpand all lines: Muscle_modeling/lesson5.md
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@@ -7,7 +7,7 @@ Muscle model is a description of how a muscle behaves under different
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operating conditions. There are two schools of thought within this area.
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- The first school pursues phenomenological models based on
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the classical work by *A.V. Hill*[^cite_hill-1938]. These models are usually based on
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the classical work by *A.V. Hill*[^cite_hill_1938]. These models are usually based on
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a description of a muscle as a contractile element in combination
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with a number of elastic elements. While these models make no attempt
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to directly model the microscopic mechanisms of muscle contraction,
@@ -16,7 +16,7 @@ operating conditions. There are two schools of thought within this area.
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efficiency.
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- The second school attempts to directly model the microscopic physical
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phenomena of cross bridge activity in muscle contraction. The origin
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of these models is usually attributed to *A.F. Huxley*[^cite_huxley-1957], and they lead
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of these models is usually attributed to *A.F. Huxley*[^cite_huxley_1957], and they lead
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to differential equations and consequently to much more
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computationally demanding models.
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@@ -48,7 +48,7 @@ for their parameters, and they also need fairly costly calibration steps to impr
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The following introduces the muscle models available in AnyBody. The simple (**AnyMuscleModel**) and the three-element (**AnyMuscleModel3E**) muscle models are the most commonly used ones in the AMMR, whereas the two-element (**AnyMuscleModel2ELin**) and the custom user-defined (**AnyMuscleModelUsr1**) models provide users with even more freedom to test, learn and benchmark muscle-tendon units.
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- `AnyMuscleModel`: This is the simplest conceivable muscle model, and it is the one we have used in the preceding lessons of this tutorial. The only required input to the model is the muscle's presumed isometric strength, F0, i.e. the force that the muscle can exert in a static condition at its optimal length. F0 is often believed to be proportional to the physiological cross sectional area of the muscle, and it is possible to find that dimension for most significant muscles in the human body from cadaver studies reported in the scientific literature. It is important to stress that the strength of this muscle model is independent of the muscle's current length and contraction velocity. It is known for a fact that muscles do not behave that way, but for models with moderate contraction velocities and small joint angle variations even this simple model will work reasonably well. Such has been shown to be the case for bicycling and gait. This model has a lesser need for calibration steps, which makes it beneficial to save effort while just preparing preliminary results for instance in a model ptorotyping phase.
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-`AnyMuscleModel3E`: This is a full-blown Hill model that takes parallel passive elasticity of the muscle, serial elasticity of the tendon, pennation angle of the fibers, and many other properties into account. The concepts for this model are adopted from [^cite_zajac-1989]. This model requires several physiological parameters that may be difficult to get or estimate for a particular muscle in a particular individual. Moreover, it applies non-linear force-length and force-velocity relationships, which means that the muscle vary strength depending on the length and contraction velocity. It also means and can loose its strength entirely and this calls for calibration of muscle parameters for each indivudualized model to match the muscle's working range to actual working range of the skeleton.
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-`AnyMuscleModel3E`: This is a full-blown Hill model that takes parallel passive elasticity of the muscle, serial elasticity of the tendon, pennation angle of the fibers, and many other properties into account. The concepts for this model are adopted from [^cite_zajac_1989]. This model requires several physiological parameters that may be difficult to get or estimate for a particular muscle in a particular individual. Moreover, it applies non-linear force-length and force-velocity relationships, which means that the muscle vary strength depending on the length and contraction velocity. It also means and can loose its strength entirely and this calls for calibration of muscle parameters for each indivudualized model to match the muscle's working range to actual working range of the skeleton.
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- `AnyMuscleModel2ELin`: This model is simpler multi-element model than the three-element model. It presumes that the muscle strength is proportional to its current length and contraction velocity. This means that the muscle gets weaker when its length decreases or the contraction velocity increases. In other words, the muscle strength is bilinear in the length and velocity space. The model also presumes that the tendon is linearly elastic and as such contains two elements: A contractile element (the muscle), and a serial-elastic element (the tendon). The rationale behind this model is that a muscle has a certain passive elasticity built into it. If the muscle it stretched far enough, the passive elasticity will build up force and reduce the necessity for active muscle force. This is in some cases equivalent to an increase of the muscle's strength. Notice, however, that this model has the significant drawback that the force can be switched off even if the muscle is stretched very far, while the true passive elasticity will always provide a force when it is stretched. While this model is simpler than the three-element model, it does not provide a more efficient workflow because calibration is typically also needed for this model. Therefore, this model is used less frequently for real applications, because it will be natural to consider the two previously described models when choosing will be between simplicity and accuracy.
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-`AnyMuscleModelUsr1`: This is a custom user-defined muscle model. The user is free to define the strength of the muscle as any explicit expression of muscle variables (e.g. isometric strength (F0), volume(Vol0) or PCSA, fiber length (Lf0)), kinematic measures (e.g. actual fiber length and velocity), and even time. This freedom implies that it is also the user's task to make the most reasonable relationship to muscle and kinematic parameters for instance to include when such paarmeters are affected by model scaling and calibration.
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