Electro-mechanical delay in Hill-type muscle models

In this study, we investigated to which extent Hill-type muscle models can explain the electro-mechanical delay (EMD). The EMD is a phenomenon that has been well examined in muscle experiments. The EMD is the time lag between a change in muscle stimulation and the subsequent measurable change in muscle force. A variety of processes as, e.g., signal conduction and interaction of contractile and elastic muscle structures contribute to the EMD. The relative contributions of the particular processes have not been fully unveiled so far. Thereto, we simulated isometric muscle contractions using two Hill-type muscle models. Their parameters were extracted from experiments on the cat soleus muscle. In agreement with literature data, predicted EMD values depend on muscle-tendon complex (MTC) length and increase when reducing MTC lengths. The highest EMD values (28 and 27 ms) occur at the lowest MTC length examined (78% of optimal length). Above optimal MTC length, we find EMD saturation (2 ms) in one model. In the other model, the EMD slightly re-increases up to 9 ms at the highest length examined (113% of optimal length). The EMD values predicted by the two models were then compared to EMD values found in the same experiments from which the muscle parameters were extracted. At optimal MTC length, the EMD values, mapping ion release and visco-elastic interactions, predicted by both models (3.5 and 5.5 ms) just partly account for the measured value (15.8 ms). The biggest share (about 9 ms) of the remaining 11 ms can be attributed to signal conduction along the nerve and on the muscle surface. Further potential sources of delayed force generation are discussed.