Estimation of musculoskeletal models from in situ measurements of muscle action in the rat hindlimb

Abstract

SUMMARYMusculoskeletal models are often created by making detailed anatomical measurements of muscle properties. These measurements can then be used to determine the parameters of canonical models of muscle action. We describe here a complementary approach for developing and validating muscle models, using in situ measurements of muscle actions. We characterized the actions of two rat hindlimb muscles: the gracilis posticus (GRp) and the posterior head of biceps femoris (BFp; excluding the anterior head with vertebral origin). The GRp is a relatively simple muscle, with a circumscribed origin and insertion. The BFp is more complex, with an insertion distributed along the tibia. We measured the six-dimensional isometric forces and moments at the ankle evoked from stimulating each muscle at a range of limb configurations. The variation of forces and moments across the workspace provides a succinct characterization of muscle action. We then used this data to create a simple muscle model with a single point insertion and origin. The model parameters were optimized to best explain the observed force-moment data. This model explained the relatively simple muscle, GRp, very well (R 2 >0.85). Surprisingly, this simple model was also able to explain the action of the BFp, despite its greater complexity (R 2 >0.84). We then compared the actions observed here with those predicted using recently published anatomical measurements. Although the forces and moments predicted for the GRp were very similar to those observed here, the predictions for the BFp differed. These results show the potential utility of the approach described here for the development and refinement of musculoskeletal models based on in situ measurements of muscle actions.

Transducer and base compliance alter the in situ 6 dof force measured from muscle during an isometric contraction in a multi-joint limb

“…We also considered the effects of varying attachment compliance when one endpoint dof (rotation along the mediolateral axis, (Yeo et al 2011) is released. In this situation, the dofs in the limb are matched with the dofs restrained by the transducer attachment.…”

“…Note that the ‘unbalanced’ stiffness considered in Figure 2F can also be achieved by scaling the force and moments differentially. For instance, for the rat hindlimb it is natural to use N/cm for the translational stiffness and N-cm/rad for the rotational stiffnesses (Yeo et al 2011). Consistent with this possibility, in our experiments we found that releasing a dof only minimally affected the measured forces and moments.…”

“…To illustrate the role of compliances in measuring muscle actions, we develop a rat hindlimb simulation based on our previous work (Yeo et al 2011). We simulate the actions of gracilis posticus (GP) at a single leg configuration (Figure 1).…”

“…The origin and insertion of GP was taken from Johnson et al, (2008), with origin on the hip (world coordinates, x=.01267, y=−.010403, z=−.00478m) and an insertion on the tibia (tibia coordinates of x=.0156, y=−.00452, and z=−.00378m). Peak muscle force was 2.3 N (Yeo et al 2011). Part C) Example of how the generalized 6 dof force at the ankle is displayed.…”

“…We performed this type of experiment in the rat hindlimb (Yeo et al 2011). We immobilized the pelvis and attached the limb to a 6-axis force transducer.…”