Table 3.

Constitutive laws for active muscle modeling (I).

References	Muscles	Geometries	Fiber architecture	Constitutive laws	Simulation	Validation
Martins et al. [35]	Brachialis	3D geometry from imaging data of the Visible Human Project	Fibers aligned in one direction	Active transversely isotropic, hyperelastic, and quasi-incompressible material (5 parameters, Abaqus UMAT routine)	Elongation	No
Johansson et al. [36]	Generic	Ideal geometries	Circularly directed and transversely orientated fibers	Active fiber-driven hyperelastic material	Isometric activation, isokinetic shortening, and stop quick release	Comparison with literature
Yucesoy et al. [37]	Generic	Ideal 3D geometries	Parallel fiber distribution	Active linked fiber-matrix mesh material	Activation, shear	Comparison with literature (muscle length-force characteristics)
Fernandez et al. [38]	Rectus femoris	1 patient, 3D geometries from MRI data	Bipennate fiber orientation	Active orthotropic material	Flexion	No
Blemker et al. [39]	Biceps brachii	Ideal geometries	Parallel fascicles with equal and unequal lengths, curved fascicles	Active fiber-reinforced composite with transversely isotropic material	Shortening	Measured length
d'Aulignac et al. [40]	Levator ani muscle	72-year-old female cadaver, 3D geometries from MRI data	Fibers aligned in one direction	Active transversely isotropic, hyperelastic, and quasi-incompressible material (5 parameters, Abaqus UMAT routine)	Deformation under pressure and muscle contraction	No
Tang et al. [41, 42]	Gastrocnemius	1 frog, 3D geometries from elliptical cross sections	Parallel fiber distribution	Active orthotropic material	Deformation in several planes	Measured deformation shape