## 3 Knee FEA Workflow
### Pre-Processing
#### 3.1.3 Material Constitutive Models  
The constitutive models are chosen according to the objective of the study [59; 60; 61; 62], and the mechanical parameters should be selected to mimic real tissue behavior based on the experimental data. Cartilage. Articular cartilage can be described as a biphasic fibril-reinforced material. This tissue reacts differently under tensile and compressive forces. In addition, it exhibits a time-dependent behavior caused by two mechanisms: in compression, mainly due to fluid exudation, and in tension, mainly due to the viscoelasticity of the solid phase, particularly collagen fibrils. The simplest constitutive model defines this tissue as an isotropic homogeneous elastic material, indicating it mimics only one time-point from the stress-relaxation curve. As such, it should be used with caution to model only instantaneous and equilibrium tissue responses [63; 64]. For time-dependent behavior, cartilage has been modeled using solid viscoelastic [65; 66] and biphasic formulations [67; 68]. Biphasic models are based on poroelasticity theory, developed by [PERSON] [69], and mixture theory, developed by [PERSON] et al. [70; 71; 72]. Both theories consider a biphasic material composed of incompressible solid and fluid phases and lead to equivalent solutions [73]. There, the volumetric changes in tissue are explained by the net fluid flux through tissue boundaries. Subsequent cartilage models captured both relaxation mechanisms, with biphasic formulations including a viscoelastic solid phase [74; 75; 76; 77]. Further descriptions allow for modeling of the anisotropy caused by the collagen fibril network as well as the depth-dependent heterogeneities in water and the proteoglycan (PG) and collagen contents [78; 79; 80]. Finally, since PGs induce cartilage swelling due to negative charges, the most complex descriptions include swelling [81; 82] and triphasic [83; 84] models. The site-specific distributions of material constituents in cartilage may impact its mechanical response or serve as a measurement of tissue integrity. Researchers can use imaging techniques such as quantitative MRI (qMRI) to compute such distributions [85; 86; 87]. At the organ scale, [PERSON] et al. [86; 87] studied the effect of in vivo fixed charge density (FCD) distribution in knee cartilage under different loading conditions. To do so, they obtained the FCD distribution using \({}^{23}\)Na-MRI and used a fibril-reinforced poroviscoelastic with swelling effect formulation for cartilage and menisci. First, in [86], they compared the MRI-based tibial cartilage deformation before and after the standing period with the patient bearing half of their weight for 13 min statically. They concluded that using a subject-specific FCD content differs from using a constant value or a generic depth-dependent distribution from the literature. Second, in [87], they simulated the stance phase of the gait modeling combinations of different FCD contents and collagen network stiffnesses. Results showed that combining the lowest FCD content with the softest collagen network, as found in knee OA patients, resulted in a considerable reduction in cartilage mechanical capabilities. In addition to MRI-based solutions, ultrasound techniques can also estimate tissue characteristics in vivo, such as thickness and stiffness [88; 89; 90; 91], but quantifying other material properties such as permeability is still restricted to in vitro setups. Sometimes, the aim of the study can be reached with an intermediate complex material formulation. For instance, by using a biphasic transversely isotropic description, different authors were able to reproduce experimental cartilage stress-relaxation tests [92; 93; 94]. [PERSON] et al. [95] used a biphasic transversely isotropic model [60] to identify zones of knee cartilage susceptible to post-traumatic osteoarthritis. This demonstrated that constitutive models with this complexity level could simulate realistic responses of the tissue. Meniscus.