## 3 Search Results
### Quantities of Interest
\begin{table}
\begin{tabular}{c l} \hline \hline
**Research paper** & \multicolumn{1}{c}{**Indirect contact models**} \\ \hline [PERSON]. [PERSON] et al. [38] & Bone remodelling and bone ringworth were simulated based on the theory of continuum damage mechanics. Interface damage or interface repair was modelled by changing tissue stiffness (i.e., bounding degrees) defined based on mechanical stimuli (e.g., relative displacement at the interface). The bonded/debended process was implemented using thin elements that connect the bone and implant with frictionless contact between the surfaces. \\ \hline \multirow{2}{*}{[PERSON]. [PERSON] et al. [48]} & Two models were used to simulate osseogenization. In the first model, the mechano-regulatory model and diffusion analysis described in [70] were used for the differentiation of MCS into fibroblasts, chondrocytes, and osteoblasts. The new tissue type was predicted for each element, and the effective material properties were assigned based on [70]. The second model used a modified tissue differentiation algorithm that allowed a change from immature bone to mature bone and the reverse change (bone resorption). \\ \hline [PERSON] et al. [50] & Bone ringworth was simulated using a linear elastic bioactive interface layer. An evolution rule for osseogenization based on normal pressure and relative motion was considered to change the tissue stiffness. \\ \hline \multirow{2}{*}{[PERSON] et al. [47]} & A lattice model that represents a space for the extracellular matrix and cells was considered for the tissue differentiation algorithm. Cells can proliferate, migrate, and differentiate according to the mechanoengineering algorithm proposed in [43], which also included the growth of the capillaries. Oxygen concentration and two mechanical stimuli, shear strain and fluid/solid velocity, were used for the differentiation of MCS into fibroblasts, chondrocytes, and osteoblasts. Oseongization was implemented considering a bone-immediate interface layer of 1 mm thick preoperative tissue of prostatic elements. \\ \hline \multirow{2}{*}{[PERSON] et al. [35]} & A uniform layer of 0.75 mm (corresponding to three layers of porous coating thickness in the Pozbrain implant) was created around the implant to represent the formation of granulation tissue. This layer was assumed to be fully bonded by the implant and the bone. \\ \hline \multirow{2}{*}{[PERSON] et al. [35]} & Tissue differentiation algorithm based on the mechano-regulation theory from [PERSON] et al. [17]. The tendency for ossification was represented by the osteogenic index \(T\), dependent on the element stress at the acute cycle. A low value of 1 denotes the tendency to form from tissue. The Index was mapped onto a range of material properties, considering an interpolated value of the Young's modulus of the materials. Values were averaged over 10 iterations to avoid rapid changes in tissue type from one reaction to the next. Convergence was obtained after about 50 iterations or when the change in tissue type between two successive iterations in every element in the layer was less than 5%. \\ \hline \multirow{5}{*}{[PERSON]. [PERSON] et al. [28]} & Bone ringworth simulated by activating spring elements based on micromotion (less than 40)\(\mu\)m gave (smaller than 500 \(\mu\)m). \\  & local stresses (less than 25 MPa). De-bonding (spring elements calculated) occurred when local bone stresses exceeded 25 MPa. \\ \cline{1-1}  & Friction implant-tube contact (coefficient was 0.5 or 0.88 for different materials of the stem). \\ \cline{1-1}  & The spring stiffness was defined as the summation of the adjacent bone elements’ Young’s modulus was multiplied by 1/3 of the corresponding element face area (each face had three nodes connected to it), divided by the original spring length (equal to the gap between implant and bone node). \\ \cline{1-1}  & Bone remodelling was simulated on for the cases with the best bone ingrowth performance. Adaptive bone theory was used [73]. \\ \hline \multirow{5}{*}{[PERSON]. [PERSON] et al. [26]} & The bone-implant interface was modelled with a surface-based contact model with the penalty method (the stem is the master surface and the bone is the slave). \\ \cline{1-1}  & Bone remodelling was simulated using an optimisation process that computes the evolution of volume fraction (0 void; total density corresponding to cortical bone) at each point based on strain energy density values. \\ \cline{1-1}  & Cusoogregation was simulated by changing the stiffness of computer elements included between the bone and the stem based on a relative displacement criteria described in [31]. Oseseongization increases when the contact is achieved (normal contact force -1) and the tangential displacement is less than a threshold value. If these conditions were not verified, the initial contact conditions (contact with friction 0.3 if the surface is coated and frictionless contact for uncoated surfaces). Fully counterintegration was modelled with glued contact. De-bounded was also possible for high levels of stress (contact pressure > 0.8 MPa) and shear stress > 35 MPa). \\ \hline \multirow{5}{*}{[PERSON] et al. [52]} & An interface layer made of solid elements is considered between the bone and implant surfaces, with the initial constitutive behaviour described by the Drucker-Prager plasticity model [75]. Oseongization is simulated considering the evolution of bone mineral density as a function of the mechanical stimuli (micromotions and strain energy density) interface stiffness, ability to carry tensile loads, and the limit until sliding occurs, which increases with ongoing mineralization. \\ \cline{1-1}  & \multicolumn{1}{c}{} \\ \end{tabular}
\end{table}