Table 1.

Disc tissue properties used in the numerical model.

	NP	AF	CEP
Initial water content ${Ø}_0^{\mathrm{w}}$ (Water content: ${Ø}^w=({Ø}_0^w+e)/(1+e)$)	0.86 a	0.75 a	Normal:0.6 b, Calcified:0.45
Elastic constant λ (MPa)	0.02 c	0.2 c	0.1 d
Elastic constant µ (MPa)	0.015 c	0.15 c	0.2 d
Cell density (cells/mm3)	Normal:4000 e, Cell based therapy: 6000, 8000, 10000	9000 e	15000 e
Parameter for hydraulic permeability k = α1(Øw/Øs)b1	a1=0.00339 nm2 f, b1=3.24 f	a1=0.00044 nm2 g, b1=7.193 g	a1=0.0248 nm2 h, b1=2.154 h
Parameter for diffusivity $\frac{D^{\alpha }}{D_0^{\alpha }}=\mathit{\text{exp}}[a_2{(\frac{r_s^{\alpha }}{\sqrt{k}})}^{b_2}]$ α: ions and nutrient solutes	a2=1.25 nm i, b2=0.681 i	a2=1.29 nm i, b2=0.372 i	a2=1.29 nm i, b2=0.372 i

Where $r_s^{\alpha }$ is hydrodynamic radius of ions and nutrient solutes $(r_s^{+}=0.197\text{nm};r_s^{-}=0.142\text{nm};r_s^{\mathit{\text{oxy}}}=0.1\text{nm};r_s^{\mathit{\text{lac}}}=0.255\text{nm};r_s^{\mathit{\text{glu}}}=0.3\text{nm})$, $D_0^{\alpha }$ is diffusivity of ions and nutrient solutes in aqueous solution $(D_0^{+}=1.28\ast {10}^{-9}{m}^2/s,D_0^{-}=1.77\ast {10}^{-9}{m}^2/s,D_0^{\mathit{\text{oxy}}}=3.0\ast {10}^{-9}{m}^2/s,D_0^{\mathit{\text{lac}}}=1.28\ast {10}^{-9}{m}^2/s,D_0^{\mathit{\text{glu}}}=0.92\ast {10}^{-9}{m}^2/s)$.

^aYao and Gu, 2007.

^bRoberts et al., 1989; Setton et al., 1993.

^cYao and Gu, 2006.

^dMow et al., 2002; Yao and Gu, 2004.

^eMaroudas et al., 1975.

^fGu et al., 2003, from agarose gels.

^gGu and Yao, 2003, from porcine AF tissue.

^hMaroudas et al., 1975; Yao and Gu, 2004.

ⁱGu et al., 2004, from porcine AF tissue and agarose gels.