Table 2 Details of the global material parameter set obtained by the inverse Finite-Element optimization of the spatial volume fractions in the framework of the computational model of cartilage.

From: Towards Patient-Specific Computational Modelling of Articular Cartilage on the Basis of Advanced Multiparametric MRI Techniques

 

Weighting parameters

Material model parameters

\({{\boldsymbol{w}}}_{{\bf{T1}}}^{{\boldsymbol{\xi }}}\)

\({{\boldsymbol{w}}}_{{\bf{T1}}{\boldsymbol{\rho }}}^{{\boldsymbol{\xi }}}\)

\({{\boldsymbol{w}}}_{{\bf{T2}}}^{{\boldsymbol{\xi }}}\)

\({{\boldsymbol{w}}}_{{\bf{T}}{{\bf{2}}}^{{\boldsymbol{\ast }}}}^{{\boldsymbol{\xi }}}\)

k 1

k 2

k 3

a 0

a 1

w

F (ξ = f)

0.41

0.42

0.16

0.01

0.6 MPa

50

25

0.35 MPa

5

0.3

CO (ξ = co)

0.31

0.12

0.11

0.46

  1. Weighting parameters (\({w}_{{\rm{Tx}}}^{\xi }\)) detail each qMRI parameter’s contribution to the collagen and fluid volume fractions and are to be read as follows: The fluid content of the tissue is primarily represented by T1 (41%) and T1ρ (42%), while the collagen content is primarily represented by T1 (31%) and T2* (46%). Six material model parameters complement the proposed constitutive model: k1, k3 and k3 are related to the biomechanical behaviour of collagen fibrils under tension, while a0 and a1 are associated with the stiffness and compressibility of the non-collagenous matrix. w describes the concentration of the collagen fibrils in their preferred direction.
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