Table 6.

Constitutive laws for active muscle modeling (IV): special case of facial muscles.

References	Muscles	Geometries	Fiber architecture	Constitutive laws	Simulation	Validation
Gladilin et al. [56]	20 facial muscles	1 healthy subject, 3D geometries from MRI data	Fiber tangent interpolation using B-spline	Active fibrous material with heuristic model construction	Facial mimics (happiness, disgust)	No
Röhrle and Pullan [57]	Masseter	3D geometries from the Visible Human Project	Parallel fiber distribution using anatomical-based approximation	Active hyperelastic, incompressible, and transversely isotropic material (9 constants)	Mastication	Comparison with literature
Beldie et al. [22]	20 facial muscles	1 patient, 3D geometries from MRI data	Parallel fiber distribution in a single direction	Active, quasi-incompressible, transversely isotropic, and hyperelastic material (13 parameters) (UMAT LS-DYNA)	Maxillofacial surgery	In vivo postsurgery data (skin envelop)
Nazari et al. [58]	10 paired facial muscles	1 subject, 3D geometries from CT data	Curvature-driven cable elements	Active transversely isotropic material (ANSYS)	Dynamic orofacial movements	Measured velocity profile and the acoustic signal
Wu et al. [26]	20 facial muscles	1 healthy subject, 3D geometries from MRI data	Fiber angle interpolation by piecewise linear functions	Active heterogeneous force-drivenhyperelastic material	Facial expressions	Skin deformation from the structured-light scanner
Fan et al. [59]	2 paired zygomaticus major	1 healthy subject, 3D geometries from MRI data	Parallel fiber distribution in muscle mean-line direction	Active transversely isotropic, hyperelastic, and quasi-incompressiblematerial (5 parameters) (VUMAT Abaqus)	Facial mimics	In vivo MRI-based displacement