A 3D-geometric model for the deformation of a transversally loaded muscle

Very recent measurements provided data on the ratio between the change in length of the active fibres and the lifting height of a mass compressing the muscle belly transversally to the direction of fibre contraction. In this study, we present additional data of the change in the third (unloaded) muscle dimension, extracted from the same contraction experiments. Using this data set for validation, we verify whether body models of two different geometries, cylindrical or ellipsoidal, can explain the three-dimensional deformation of a contracting muscle, when volume constancy is required as a constraint. Presetting the contractile length change and using this constraint, an additional equation is needed for model predictions. To that, we minimise the sum of the squared and weighted circumference length changes. With a specific set of the three penalty weights, it turns out that the ellipsoid model can explain the three-dimensional deformation. The set of penalty weights can also be interpreted as an anisotropic stiffness distribution of the connective tissue of the muscle belly. In various loading situations, our ellipsoidal model may help to predict the corresponding deformation scenarios or to calculate the stiffness distribution from measured load and deformation data.

► A muscle deforms in transversal direction during contraction.
► Using an ellipsoidal model, such deformations can be predicted.
► The model also predicts stiffness distributions within muscle tissue.
► It can be further used to calculate three-dimensional load scenarios in musculo-skeletal arrangements.