Modeling the human knee for assistive technologies

Abstract

In this paper, we use motion capture technology together with an EMG-driven musculoskeletal model of the knee joint to predict muscle behavior during human dynamic movements. We propose a muscle model based on infinitely stiff tendons and show this allows speeding up 250 times the computation of muscle force and the resulting joint moment calculation with no loss of accuracy with respect to the previously developed elastic-tendon model. We then integrate our previously developed method for the estimation of 3-D musculotendon kinematics in the proposed EMG-driven model. This new code enabled the creation of a standalone EMG-driven model that was implemented and run on an embedded system for applications in assistive technologies such as myoelectrically controlled prostheses and orthoses.

Fig. 1

Schematic view of the EMG-driven model structure. RRA-generated experimental joint moments are used during the model calibration only (see Section II-C). After calibration, the model only needs EMG signals and IK-generated joint angles to determine muscle force and the resulting muscle-generated joint moments.

Fig. 2

Scaled musculoskeletal model is used to obtain musculotendon length ℓ^mt nominal values for each muscle corresponding to discrete combinations of lower limb joint angles ϑ. The ℓ^mt nominal values are then used to compute the coefficients for a multidimensional cubic spline function per muscle which is used to generate ℓ^mt values as a function of joint angles. Moment arm values as a function of joint angles are obtained by differentiating the ℓ^mt spline function with respect to the joint angle of interest.

Fig. 3

First test. The MTU force estimated using the elastic-tendon model (EHM) and the infinitely stiff-tendon model (SHM) is compared for all MTUs as described in Section III. The square of the Pearson product moment correlation coefficient (R²) between EHM and SHM force is reported for each MTU where names are defined as in Section II-C.

Fig. 4

First test. Values of (a) tendon strain and (b) fiber length variation averaged over the entire duration of all dynamic trials for all subjects. (c) Ensemble average of the experimental KFE moment (reference) is compared to that estimated using the infinitely stiff-tendon muscle model (SHM) and to that estimated using the elastic-tendon muscle model (EHM). The standard deviation of the ensemble average of the reference KFE moment is represented by the dotted lines and the shaded area. Reference moments were obtained using RRA (see Section II-B). MTU names are defined as in Section II-C.

Fig. 4

First test. Values of (a) tendon strain and (b) fiber length variation averaged over the entire duration of all dynamic trials for all subjects. (c) Ensemble average of the experimental KFE moment (reference) is compared to that estimated using the infinitely stiff-tendon muscle model (SHM) and to that estimated using the elastic-tendon muscle model (EHM). The standard deviation of the ensemble average of the reference KFE moment is represented by the dotted lines and the shaded area. Reference moments were obtained using RRA (see Section II-B). MTU names are defined as in Section II-C.

Fig. 4

First test. Values of (a) tendon strain and (b) fiber length variation averaged over the entire duration of all dynamic trials for all subjects. (c) Ensemble average of the experimental KFE moment (reference) is compared to that estimated using the infinitely stiff-tendon muscle model (SHM) and to that estimated using the elastic-tendon muscle model (EHM). The standard deviation of the ensemble average of the reference KFE moment is represented by the dotted lines and the shaded area. Reference moments were obtained using RRA (see Section II-B). MTU names are defined as in Section II-C.

Fig. 5

Second test. The percentage variation of the KFE moments is estimated as described in Section III. The upper standard deviation is graphed to quantify the maximum KFE moment variation.