A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin–titin interaction

Although recent research emphasises the possible role of titin in skeletal muscle force enhancement, this property is commonly ignored in current computational models. This work presents the first biophysically based continuum-mechanical model of skeletal muscle that considers, in addition to actin–myosin interactions, force enhancement based on actin–titin interactions. During activation, titin attaches to actin filaments, which results in a significant reduction in titin’s free molecular spring length and therefore results in increased titin forces during a subsequent stretch. The mechanical behaviour of titin is included on the microscopic half-sarcomere level of a multi-scale chemo-electro-mechanical muscle model, which is based on the classic sliding-filament and cross-bridge theories. In addition to titin stress contributions in the muscle fibre direction, the continuum-mechanical constitutive relation accounts for geometrically motivated, titin-induced stresses acting in the muscle’s cross-fibre directions. Representative simulations of active stretches under maximal and submaximal activation levels predict realistic magnitudes of force enhancement in fibre direction. For example, stretching the model by 20 % from optimal length increased the isometric force at the target length by about 30 %. Predicted titin-induced stresses in the muscle’s cross-fibre directions are rather insignificant. Including the presented development in future continuum-mechanical models of muscle function in dynamic situations will lead to more accurate model predictions during and after lengthening contractions.