Shear wave imaging the active constitutive parameters of living muscles

Shear wave elastography (SWE) of human skeletal muscles allows for measurement of muscle elastic properties in vivo and has important applications in sports medicine and for the diagnosis and treatment of muscle-related diseases. Existing methods of SWE for skeletal muscles rely on the passive constitutive theory and have so far been unable to provide constitutive parameters describing muscle active behavior. In the present paper, we overcome this limitation by proposing a SWE method for quantitative inference of active constitutive parameters of skeletal muscles in vivo. To this end, we investigate the wave motion in a skeletal muscle described by a constitutive model in which muscle active behavior has been defined by an active parameter. An analytical solution relating shear wave velocities to both passive and active material parameters of muscles is derived, based upon which an inverse approach has been developed to evaluate these parameters. To demonstrate the usefulness of the reported method, in vivo experiments were carried out on 10 volunteers to obtain constitutive parameters, particularly those describing active deformation behaviors of living muscles. The results reveal that the active material parameter of skeletal muscles varies with warm-up, fatigue and rest. STATEMENT OF SIGNIFICANCE: Existing shear wave elastography methods are limited to imaging the passive parameters of muscles. This limitation is addressed in the present paper by developing a method to image the active constitutive parameter of living muscles using shear waves. We derived an analytical solution demonstrating the relationship between constitutive parameters of living muscles and shear waves. Relying on the analytical solution, we proposed an inverse method to infer active parameter of skeletal muscles. We performed in vivo experiments to demonstrate the usefulness of the theory and method; the quantitative variation of the active parameter with muscle states such as warm-up, fatigue and rest has been reported for the first time.