The complex Young's modulus of skeletal muscle fibre segments in the high frequency range determined from tension transients

Stiffness measurements of muscle fibres are often based on application of a length change at one end of the muscle fibre and recording of the following tension change at the other end. In this study a method is developed to determine in the high frequency range (up to 40 kHz) the complex Young's modulus of skeletal muscle fibre as a function of frequency from the tension transient, following a rapid stepwise length change completed within 40 microseconds. For this purpose both a new mechanical moving part of the displacement generating system and a force transducer with a high natural frequency (70 kHz) had to be developed. In addition to stiffness measurements of a silk fibre to test the displacement generating system and the method of analysis, stiffness of skeletal muscle fibres in relaxed and rigor state have been measured. The complex Young's moduli of relaxed muscle fibres as well as muscle fibres in rigor state are frequency dependent. In both cases the complex Young's modulus increases smoothly with increasing frequency over a range of 250 Hz up to 40 kHz. The phase angles of the responses remained almost constant at a value of 0.3 radians for a fibre in rigor and 0.6 radians for a relaxed fibre. This leads to the conclusion that for muscle fibres in rigor state the recovery in the tension response to a step length change shows a continuous distribution of relaxation times rather than a few discrete ones. Results of our stiffness measurements are compared with results obtained from current viscoelastic models used to describe stiffness of muscle fibre in this frequency range.