Muscle Mass and Energetics in Simulations

[Aaron Fox]

Hi All,

I am interested in running some simulations to test the effect of altered muscle mass, and the subsequent increase in strength, on muscle energetics during gait. Based on the equations presented in the Uchida et al. paper 'Stretching Your Energetic Budget: How Tendon Compliance Affects the Metabolic Cost of Running' it seems fairly straight forward that variable muscle mass can be incorporated into the energetics model and calculations of power consumption (equations 1 and 5 in the paper). The query I have is how the changes in muscle mass can be included in the musculoskeletal model during the simulation? I believe the muscle models are "mass-less" and hence there isn't a way to increase the mass of the muscle specifically. The added muscle mass could simply be incorporated into the segment(s) the muscle attaches too, however this is a somewhat crude way of doing it as it doesn't 100% reflect what is happening with changes to specific muscles, particularly if they are more localised to an area of the segment.

I'm hoping someone might be able to provide some direction to how this localised change in mass could be achieved in the model?

Thanks,

Aaron

[Ross Miller]

Hi Aaron,

You are correct that (most) of the muscle models, in OpenSim or elsewhere, do not include muscle mass in their contractile dynamics or in the equations of motion. The Millard2012Acceleration model has mass, which introduces an extra state for each muscle in the contractile dynamics, but this mass I think is not included in the equations of motion (also I believe this muscle model is still in a testing stage).

Adding individual muscle masses in the equations of motion is not terribly difficult to do, each one is essentially a "wobbling mass" and many models have used those, but it greatly increases the number of state variables in the model, two extra variables per muscle assuming 2nd-order dynamics. See Cole et al. (1996) for an example where this was done:

https://www.ncbi.nlm.nih.gov/pubmed/11415619

The easiest way I think is to just increase the segment masses accordingly, e.g. if glutmax mass increases by X then partition some fraction c*X onto the pelvis and the remainder (1-c)*X onto the thigh. You would have to do this manually, for example increasing the muscle mass parameters in the Umberger2010 energy probe will not change the segment masses. This would give you a place to start (the simplest approach) then you could get more complex later on (e.g. include mass in contractile dynamics and/or equations of motion) and see if it makes a difference.

Hope this helps,
Ross

[Aaron Fox]

Thanks for the response Ross!

Aaron

[Ross Miller]

This paper from Dinesh Pai may also be of interest:

https://www.ncbi.nlm.nih.gov/pubmed/20576268

[Adrian Lai]

Another paper of interest would be Ross and Wakeling (2016) Muscle shortening velocity depends on tissue inertia and level of activation during submaximal contractions.

http://rsbl.royalsocietypublishing.org/ ... 6/20151041