2.2. Decomposition of the total deformation gradient tensor

The model was developed to account for the kinematics of the growth of a spherical tumor seed surrounded by healthy tissue based on the decomposition of the total deformation gradient tensor F (Skalak et al., 1996; Ambrosi et al., 2002):

where F_e is the elastic component of F used to account for interactions with the normal tissue, and F_g was assumed to be an isotropic tensor that accounts for tumor growth due to cancer cell proliferation. The growth tensor F_g was defined by an associated growth stretch ratio λ_g as follows (Roose et al., 2003; Kim et al., 2011; Stylianopoulos et al., 2013; Mpekris et al., 2015):

while the elastic component F_e is determined by rearranging Eq. (1).