# Methodology of Multicriterial Optimization of Geometric Features of an Orthopedic Implant
## Materials and Methods
### Method of Developing a Model of the Bones of the Knee Joint
#### 2.2.1 The Method of Multi-Criteria Optimization with the Use of an Immune Algorithm  
The clonal selection algorithm was selected from immune systems methods. A general algorithm of the immune system is shown in Figure 4.  
The optimization process has been implemented in the MATLAB(r) environment. The ANSYS APDL software was used for strength calculations, the ANSYS CFX software was used for fluid flow calculations. Each software has been prepared for fully automatic calculations. running a Matlab program, automatically running batch files for strength and fluid flow calculations, which automatically returned the results to the main function, where the immune algorithm has been continued. \begin{table}
\begin{tabular}{c c c} \hline
**Mechanical Properties** & **Cortical Bone** & **Spongy Bone** \\ \hline Young’s module [MPa] & 17,000 & 300 \\ Density [g/cm\({}^{3}\)] & 1.9 & 0.46 \\ Poisson ratio & 0.3 & 0.3 \\ Compressive strength [MPa] & 200 & 6 \\ \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of the bone tissue of the femur. Implant Concepts  
The optimization process has changed the size and arrangement of the through holes (Figure 5), which regulated the rate of blood perfusion. The segment of a hollow tapered cylinder has been selected in the earlier research. When oozing blood through the implant, the described shape ensures an adequate blood supply to the transplant, with the least possible rinsing of the bone-forming cells already embedded in the graft and implant. Figure 4: General algorithm of the immune system used. Figure 5: Through holes in implant concepts. The dimensions of the implant are closely related to the humans anatomical characteristic and the surgical instruments. Ultimately, a typology of geometric forms of orthopedic implants should be made, differing in the external and internal diameter of the implant and its length. In the described work, specific size of an orthopedic implant has been selected (after consultation with a doctor):  
* External diameter--11 mm;
* Internal diameter--9 mm;
* Length--40 mm. The material that has been selected for this work is LATI LatI Latiega B01 F1 Bio-Polymer [18]. The through-holes on the implant surface have been described by parameters that are closed in the following compartments (Figure 6):  
* \(D\)--The length of the through hole along the axis on the implant surface \(z\)--\(D\in\) [0.5, 3] mm;
* \(B\)--Through-hole width--\(B\in\) [1, 1.7] mm;
* \(Oddd\)--Distance between holes--\(Oldd\in\) [0.1, 10] mm;
* \(Thxy\)--The angle by which the through holes in the next row are offset from the previous row--\(Thxy\in\) [0, 30 deg]. These ranges have been defined to maintain the feasibility of the geometrical features of the implant and the desired strength properties. The immunological algorithm generates each individual, specifying its characteristics from the interval describing the holes on the implant surface. An exemplary individual is saved with four items Figure 7.  
Each individual generated by the immunological algorithm is a separate set of geometrical features of the implant, the parameters of which must be transferred to the script written in APDL and the stresses occurring in it must be calculated for each individual. That is why it was so important to parameterize and automate the calculation process of strength properties. Module that calculates the stresses in the implant  
In the script for the Mechanical APDL environment for strength calculations, the following was specified:  
Figure 6: Designation of parameters controlling the form and dimensions of through holes. Figure 7: An exemplary individual is saved with four items  
Fluid flow calculating module  
For blood perfusion calculations, in the Mechanical APDL language, a negative of the implant body has been made, which is a model of the volume of fluid flowing through the implant (Figure 11).