## 2 Materials and Methods  
### Computational Model of the Intact Knee Joint  
This study was performed using an entirely validated FE model of the knee joint, developed in our prior studies [22; 23; 24; 25] from computed tomography (CT) and magnetic resonance imaging (MRI) of the left knee joint of a 37-year-old healthy male volunteer [26]. The manual segmentation had an accuracy of 0.1 mm. The combination process for the reconstructed CT and MRI models was via positional alignment of each model using commercial software, Rapidform (version 2006; 3D Systems Korea, Seoul, Korea). The image data were then imported into Mimic 17.0 image processing software (Materialise Ltd., Leuven, Belgium) to obtain the geometry for the three-dimensional (3D) model generation of all structures. The initial graphics exchange specification (IGES) files exported from Mimic were imported into Unigraphics NX software (version 7.0; Siemens PLM Software, Torrance, CA, USA) to generate solid models for each femur, tibia, fibula, patella, and soft-tissue segment. The solid models were then imported into Hypermesh software (version 8.0; Altair Engineering, Troy, MI, USA) to create an FE mesh. The FE mesh analysis was conducted through the use of ABAQUS (version 6.11; Simulia, Providence, RI, USA) (Figure 1a).  
All bones except the tibia were assumed to be rigid, whereas the tibia was considered to be transversely isotropic in this model because it is stiffer than soft tissue, with minimal effect on the current research [27]. The constitutive laws for the cortical and trabecular bones of the tibia were assumed [28; 29]. The cortical bone was regarded as transversely isotropic. Its mechanical properties were applied as follows: \(E_{1}=E_{2}=11.5\) GPa, \(E_{3}=17\) GPa, \(\
u_{12}=0.51\), and \(\
u_{23}=\
u_{13}=0.31\). We took the third axis to be parallel to the anatomical axis of each bone. The trabecular bone was regarded as a linear isotropic material. The material properties were applied as follows: \(E=2.13\) GPa and \(\
u=0.3\)[28; 29]. The articular cartilage was assumed to be a linear elastic and isotropic material because a simple compressive and time-independent load was applied to the knee joint. Its mechanical properties were a modulus of 15 MPa and a Poisson ratio of 0.47 [30]. The menisci were assumed to be of a transversely isotropic, linearly elastic, homogeneous material. Their moduli were 120 MPa in the circumferential direction and 20 MPa in the axial and radial directions. The Poisson ratios of the menisci were 0.2 in both the circumferential and radial directions and 0.3 in the axial direction [31]. To represent the meniscal attachments, each meniscal horn was bonded to the bone through the use of linear spring elements (SPRINGA element type) with a total stiffness of 2000 N/mm [32]. In addition, the major ligaments were modeled through the use of nonlinear and tension-only spring elements [33; 34]. The interfaces between the bones and cartilage were modeled as fully bonded. The contacts between the femoral cartilage and meniscus, the meniscus and tibial cartilage, and the femoral cartilage and tibial cartilage were applied to both the medial and lateral sides, resulting in six contact pairs [22]. Contact was defined using a penalty-based method with a weight factor. As a result, contact forces were defined as a function of the penetration distance of the master into the slave surface.  
Figure 1: The validated 3D finite element (FE) model for (**a**) the intact knee joint and (**b**) the fixed-bearing uni-compartmental knee arthroplasty (UKA) used in this study.