## 2 Materials and Methods  
To investigate individual cellular model parameters of cartilage regeneration, a mechano-biological tissue-differentiation model that included theoretical descriptions of cellular processes was used according to a previous validation method [17]. This model has been employed to simulate the major aspects of normal conditions and cartilage regeneration [17; 18]. Mechano-regulation processes are driven by the mechanical environment in the vicinity of the cell. A computational approach, such as finite element (FE) modeling, enables the evaluation of the mechanical stimuli within the extracellular matrix of a regenerating tissue. In this study, a cartilage defect within the knee joint was investigated using a poroelastic FE model. Briefly, the entire callus was assumed to consist of granulation tissue at the beginning of the stimulation regimen. Generally, once the subchondral bone is penetrated, MSCs invade the defect in the bone marrow. Given this, the stem cells were assumed to originate from the perigosteum, outer cortical surface and medullary canal in a previous study [18]. This method was applied to generate the first phenomenological model. In the second model, adipose synovium-derived MSCs were used for cartilage defect implantation because we have had successful clinical experience with this approach [19; 20; 21]. To simulate the diffusion of stem cells throughout the callus, a diffusion coefficient was selected to predict 99% stem cell coverage at six weeks after implantation [12]. After this, the differentiation of the granulation tissue in a given element towards the fibrous tissue, cartilage or bone was determined by the stimulus factor (S) according to Equation (1):  
\[S=\frac{\gamma}{a}+\frac{v}{b} \tag{1}\]  
where \(\gamma\) is the octahedral shear strain, \(\
u\) is the fluid velocity and a (3.75%) and \(b\) (3 \(\mu\)m/s) are the scaling factors for each stimulus. Based on the mechano-regulation theory, \(S>3\) is predicted as fibrous connective tissue, \(1<S<3\) indicates cartilage, \(0.53<S<1\) indicates immature woven bone, \(0.01<S<0.53\) indicates mature woven bone and \(0<S<0.01\) indicates bone resorption [4; 12; 13; 18; 19; 22]. Poroelastic material properties were updated according to a rule of mixtures based on the concentration of cells in a given element (\(n_{c}\)), the volume fractions (\(\varphi_{j}\)) and material properties of the granulation tissue and \(j\) types of differentiated tissues in that element. For example, [PERSON]'s modulus (E) for a given element was calculated according to Equation (2):  
\[\mathrm{E}=\frac{\left(n_{c}^{max}-n_{c}\right)}{n_{c}^{max}}E_{ granulation}\ +\frac{n_{c}}{n_{c}^{max}}\sum_{j=1}^{n_{l}}E_{j}\varphi_{j} \tag{2}\]where \(n_{c}^{max}\) is the maximum number of cells that can occupy any single element and \(Ej\) is Young's Modulus of the \(j\)th differentiated tissue. The volume fraction \(\varphi_{j}\) of a given type of differentiated tissue was evaluated as the fraction of the last ten iterations for which this particular differentiated tissue type was predicted in the element. This enabled the material properties to change gradually and prevented instability in the algorithm [23]. Material property was calculated for each element by this formula using a custom FORTRAN script. The two poroelastic FE models were developed to simulate in vivo mechanical conditions within knee joint OA mechano-regulation under different loading conditions. The first phenomenological axi-symmetric FE model of the knee was created, which included a meniscus, femoral condyle and articular cartilage layer to validate this approach (Figure 1). The pore fluid pressure was adjusted to zero at free. The meniscus and the cartilage surface could not penetrate each other in the axial direction. However, the surfaces were allowed to slide relative to each other. The cartilage defect size and depth were set at 5 mm each. Complete integration was assumed between the repair tissue and normal tissue.