Table 1.

Overview of studies utilizing the kinematic growth theory to study G&R in the heart. Note that studies on organogenesis, e.g., [52,176] are not included. F_g is the inelastic growth deformation gradient; M_e is the elastic Mandel stress [177] ; λ denote fiber stretch, ϑ denote growth multipliers; f₀, s₀, and n₀ denote myocyte, sheet, and sheet-normal directions and E_• are strains in the respective direction; subscripts •_crit denote physiologial limit levels, subscripts •_hom denote homeostatic levels of the specific parameter; subscripts •_e denote values with respect to the elastic deformation gradient F_e; k(•) are growth scaling functions.

Model	Geometry and Material	Driving Factor	Growth Laws
Kroon et al. [38]	Truncated ellipsoid; transversely isotropic [178]	Deviation of myofiber strain $s=\sqrt{{\text{E}}_{\text{f}}+1}-1$ from its homeostatic level shom = 0.13	${\mathbf{\text{F}}}_{\text{g}}={\left[\beta \left(s-s_{\text{hom}}\right)\Delta t+1\right]}^{1/3}\mathbf{\text{I}},$ where β is a rate constant
Göktepe et al. [39]	Regularly shaped bi-ventricular model; isotropic material	Deviation from strain for eccentric growth ${\dot{\vartheta }}^{\parallel }=k^{\parallel }\left({\vartheta }^{\parallel }\right)\left(\frac{1}{{\vartheta }^{\parallel }}\lambda -{\lambda }_{\text{crit}}\right)$ Deviation from Mandel stress for concentric growth ${\dot{\vartheta }}^{\perp }=k^{\perp }\left({\vartheta }^{\perp }\right)\left(\text{tr}\left({\mathbf{\text{M}}}_e\right)-p_{\text{crit}}\right)$	Eccentric growth: Fg = I + [ϑ∥ − 1] f0 ⊗ f0 Concentric growth: Fg = I + [ϑ⊥ − 1] s0 ⊗ s0
Rausch et al. [44]	Regularly shaped bi-ventricular model; orthotropic Holzapfel–Ogden [106]	$\dot{\vartheta }=k\left(\vartheta \right)\left(\text{tr}\left(\mathit{\tau }\right)-p_{\text{crit}}\right),$ with τ the Kirchhoff stress tensor and pcrit the baseline pressure level	Fg = I + [ϑ − 1] s0 ⊗ s0
Klepach et al. [46]	Patient-specific LV; transversely isotropic Guccione [102]	Same as Rausch et al. [44]	${\mathbf{\text{F}}}_{\text{g}}=\vartheta {\mathbf{\text{f}}}_0\otimes {\mathbf{\text{f}}}_0+\frac{1}{\sqrt{\vartheta }}\left[\mathbf{\text{I}}-{\mathbf{\text{f}}}_0\otimes {\mathbf{\text{f}}}_0\right]$
Kerckhoffs et al. [47]	Thick-walled truncated ellipsoid; transversely isotropic Guccione [102]	Stimulus for axial fiber growth sl = max (Ef) − Ef,set, and radial fiber growth st = min (Ecross,max) − Ecross,set as differences between fiber strain Ef and maximum principal strain Ecross,max of the cross-sectional strain tensor: Ecross = [Es Esn; Esn En] and set-points •set	Transversely isotropic, incremental growth tensor, described by sigmoids and dependent on 10 parameters
Lee et al. [43]	Patient-specific LV; transversely isotropic Guccione [102]	$\dot{\vartheta }=k\left(\vartheta ,{\lambda }_{\text{e}}\right)\left({\lambda }_{\text{e}}-{\text{λ}}_{\text{hom}}\right)$	Fg = (ϑ − 1)f0 ⊗ f0 + I
Genet et al. [48]	Four-chamber human heart model; orthotropic Guccione [102]	$\dot{\vartheta }=\frac{1}{\tau }\langle \lambda -{\lambda }_{\text{crit}}\rangle ,$ where τ is a scaling parameter in time and 〈〉 Macaulay brackets	Eccentric growth: Fg = I + [ϑ − 1] f0 ⊗ f0 Concentric growth: Fg = ϑI + [1 − ϑ] f0 ⊗ f0
Witzenburg and Holmes [49]	LV treated as thin-walled spherical pressure vessel; time-varying elastance compartmental model	Same as Kerckhoffs et al. [47]	Same as Kerckhoffs et al. [47]
Del Bianco et al. [50]	Truncated ellipsoid; orthotropic Holzapfel–Ogden [106]	Local growth increments ϑn between cycles n and n + 1: ${\vartheta }^n=1+k({\displaystyle \prod _{i-1}^{n-1}{\vartheta }^i})\left[\text{tr}{\left({\mathbf{\text{M}}}_{\text{e}}\right)}_{\text{n}}-\text{tr}{\left({\mathbf{\text{M}}}_{\text{e}}\right)}_{\mathrm{hom}}\right]$	Same as Göktepe et al. [39] for eccentric growth
Peirlinck et al. [51]	Subject specific LV; orthotropic Holzapfel–Ogden [106]	${\dot{\vartheta }}^{\parallel }=\frac{1}{\tau }\langle {\lambda }_{\text{e}}-{\lambda }_{\text{crit}}\rangle ,{\dot{\vartheta }}^{\perp }=0,$ where τ is a scaling parameter and 〈〉 Macaulay brackets	Fg = ϑ∥ [f0 ⊗ f0] + ϑ⊥ [I − f0 ⊗ f0]