Fascicle slack in computational musculoskeletal modelling

[Bas Van Hooren]

Hi,

Recent research found that slack can be present in both the fascicles and tendon/aponeurosis of the muscle-tendon unit and that the length at which slack is taken up can differ between both. I’m very interested in modelling the effects of slack on muscle fibre length changes during locomotion using OpenSim. For example, if slack is modelled, an increase in the distance between the attachment points of the muscle may not necessary represent active lengthening of the CE, but the uptake of slack. However, I’m not sure about the best way to model the effects of slack.

I’m currently thinking about two possibilities:
1. Simulating the electromechanical delay by providing the model with a time delay to account for slack (and tendon compliance). However, if I use this approach, then what should I use as value for tendon slack length? Should this be set to zero, since slack is already taken into consideration in the mechanical delay?
2. Providing the model with information about the muscle-tendon unit length at which the fascicles and tendon/aponeuroses fall slack. However, I wonder if the models assume that the fascicles and tendon/aponeuroses fall slack at the same length when a value is provided for tendon slack length? Or does the model assume there is never slack in the fascicles?

Bas

[Ross Miller]

Re: Fascicle slack in computational musculoskeletal modelling

Hi Bas,

A few thoughts:

(1) Unless the SEE is rigid, even when slack is not modeled an increase/decrease in the origin-to-insertion distance of a muscle will not necessarily indicate active lengthening/shortening of the CE. Loram has a nice paper on postural control where they refer to this as "paradoxical muscle movement" (http://www.ncbi.nlm.nih.gov/pubmed/15047776).

(2) Part of the difficulty in modeling something like slack with a Hill model is the disconnect between what the components of the Hill model actually are, and what they are often labeled and interpreted as. In my opinion it is not correct to refer to the components of the Hill model as "fibers" and "tendon" as is often done, or similarly to refer to its parameters as "optimal fiber length", "tendon slack length", etc. The CE/SEE in a Hill model account for many of the phenomena we attribute to fibers and tendon in real muscle, but they do this as a whole through their interactions: given an arbitrary excitation and arbitrary whole-muscle kinematics, accurately predict the output force. The CE/SEE are not (and are not intended to be) models of specific parts of real muscle on their own.

(3) A solution here to modeling slack in Hill models may be to include mass in the muscle model (or muscle mass in a musculoskeletal model, more specifically, e.g. http://www.ncbi.nlm.nih.gov/pubmed/20576268).

Edit to add an example of what I'm getting at with Thought #2 above:

Consider what happens if you stretch an inactive muscle with an external load (e.g. grab the origin with one hand and the insertion with your other hand and pull):

- In a real muscle, all bits of tissue with any elasticity will change length, fibers, tendon, everything.
- In a two-component Hill model (CC-SEC), only the CC changes length. The SEC stays isometric because it only changes length when the force produced by the CC changes, and the CC is inactive.
- The same situation appears if there is a parallel elastic component (PEC) parallel to both the CC and the SEC: the CC stretches, the PEC stretches, but the SEC stays isometric because the CC isn't expressing any force on it.
- The model matches reality a little better if we place the PEC within the CC, so that it's not in parallel with the SEC. In this case the SEC will stretch in response to an applied load with an inactive CC. However, the SEC is only qualitatively matching the reality of tendon in this case by coincidence: it's stretching because the force produced by the CC is changing, not because the external load is directly stretching the SEC.

Ross

[Jack Winters]

Re: Fascicle slack in computational musculoskeletal modelling

A few more thoughts to add to those of Ross:

(1) AV Hill's original idea, based on careful systematic study of muscle by multiple controlled methods, was that from a functional perspective there was lightly-damped spring in series with contractile machinery. In other words, there was series compliance within muscle tissue. This has stood the test of time - there are no "rigid pipes" along the chain of series myo-force transmission, including along the length of muscle fascicles as well as tendon. I am aware of no myo-proteins or functional myo-transmission complexes where the strain will not get to at least 1% over the range of physiological force (e.g., thick filaments & their cross bridges, thin filaments, z-disks, transmembrane force transmission via dystrophin-complex / integrin-complex, mixed-collagenous endo- and epi-mysium, collagenous tendon, etc). There are also 3D myo-effects that would functionally provide a functional series compliance. For high-force situations the series strain in tendon tends to be close to double that in muscle, but for lower everyday forces with sub-max recruitment I think the instant series compliance (and strain) may be more uniform (and mentioned this in various 1990s pubs). Thus attributing SEC to only tendon is a mistake, and the concept of a functional "slack length" is a bit problematic (i.e., it can dys-inform). One can get away with the rigid-muscle-extending-tendon approach when focused on mammalian limbs (e.g., human walking, arm reaching and hand manipulation) where there are long tendons, but it is a problem for most muscles where tendons are short or non-existent (e.g., human spinal and facial muscles, hearts, muscles in creatures such as fish, ...). In the 1960s & 70s pubs this CE length was often called the "hypothetical length" - it's a good perspective. And I prefer "virtual CE length" and SEC extensions. Of note is that as we study myo-proteins and myo-mRNA array data more fully and want to address roles for specific structural proteins, breaking down the SEC phenomena into its serial extensions becomes more important (e.g., muscular dystrophy).

(2) Our muscle modeling heritage of using "slack length" is a bit unfortunate. as such lengths are hard to measure (inherently error-prone). While considering mass might be helpful to some extent during a simulation, there is still the above problem. In terms of parameter values, I think we'd have been better off basing strategic lengths needed for models on small but specified preloads, as the biomechanics testing community has usually done since the 1970s in the soft connective tissue (e.g., ligaments, skin, ...) so as obtain more accurate data on tissue constitutive relations (and that can be better compared between labs). As the factor of safety for tendons (and presumably all structural myo-members in the series chain) is reasonably uniform (impressive from an engineering design perspective, one likely adaptively "tuned" via up/down-regulation of protein turnover transcription-translation processes), basing this preload on a small proportion of max isometric force would be helpful for improving models. But given the current databases, that ship has probably sailed.

Hope these quick thoughts are helpful,

Jack

Hi Bas,

A few thoughts:

(1) Unless the SEE is rigid, even when slack is not modeled an increase/decrease in the origin-to-insertion distance of a muscle will not necessarily indicate active lengthening/shortening of the CE. Loram has a nice paper on postural control where they refer to this as "paradoxical muscle movement" (http://www.ncbi.nlm.nih.gov/pubmed/15047776).

(2) Part of the difficulty in modeling something like slack with a Hill model is the disconnect between what the components of the Hill model actually are, and what they are often labeled and interpreted as. In my opinion it is not correct to refer to the components of the Hill model as "fibers" and "tendon" as is often done, or similarly to refer to its parameters as "optimal fiber length", "tendon slack length", etc. The CE/SEE in a Hill model account for many of the phenomena we attribute to fibers and tendon in real muscle, but they do this as a whole through their interactions: given an arbitrary excitation and arbitrary whole-muscle kinematics, accurately predict the output force. The CE/SEE are not (and are not intended to be) models of specific parts of real muscle on their own.

(3) A solution here to modeling slack in Hill models may be to include mass in the muscle model (or muscle mass in a musculoskeletal model, more specifically, e.g. http://www.ncbi.nlm.nih.gov/pubmed/20576268).

Edit to add an example of what I'm getting at with Thought #2 above:

Consider what happens if you stretch an inactive muscle with an external load (e.g. grab the origin with one hand and the insertion with your other hand and pull):

- In a real muscle, all bits of tissue with any elasticity will change length, fibers, tendon, everything.
- In a two-component Hill model (CC-SEC), only the CC changes length. The SEC stays isometric because it only changes length when the force produced by the CC changes length, and the CC is inactive.
- The same situation appears if there is a parallel elastic component (PEC) parallel to both the CC and the SEC: the CC stretches, the PEC stretches, but the SEC stays isometric.
- The model matches reality a little better if we place the PEC within the CC, so that it's not in parallel with the SEC. In this case the SEC will stretch in response to an applied load with in inactive CC. However, the SEC is only qualitatively matching the reality of tendon in this case by coincidence: it's stretching because the force produced by the CC is changing, not because the external load is directly stretching the SEC.

Ross

[Bas Van Hooren]

Re: Fascicle slack in computational musculoskeletal modelling

Ross and Jack,

Thank you for the responses!

Bas