Spring–damper titin model improves the estimation of muscle forces during force enhancement measurements

Hill-type muscle models are a key component of large-scale inverse dynamic models. However, they do not accurately reproduce relevant characteristics of eccentric movements, such as force enhancement. This might be because the spring-like effect of titin is not incorporated. To investigate this, we added a spring-damper model to a Hill-type muscle model to represent titin's elastic and viscoelastic behaviour. Parameters not available in the literature were optimised using a leave-one-out cross-validation. Predictions of both the titin model and the standard model were validated against reference data from force enhancement experiments. We found that the model with titin predicts force enhancement significantly better than the standard titin-less model. Additionally, we were able to show that the model is also applicable to velocities it was not optimised for. Without requiring the complexity of detailed titin models the proposed model accurately predicts measured muscle forces. Due to its simplicity, the model can efficiently be incorporated into large-scale inverse dynamics models. As the model is based on general physiological principles, we expect its applicability to extend beyond the current conditions to a wide range of experimental settings, as already demonstrated for contraction velocities.