Methodology of Multicriterial Optimization of Geometric Features of an Orthopedic Implant
<p>Geometrical features of orthopedic implant.</p> "> Figure 2
<p>The method of modeling the femur model.</p> "> Figure 3
<p>Models of the femur and tibia.</p> "> Figure 4
<p>General algorithm of the immune system used.</p> "> Figure 5
<p>Through holes in implant concepts.</p> "> Figure 6
<p>Designation of parameters controlling the form and dimensions of through holes.</p> "> Figure 7
<p>An exemplary individual is saved with four items.</p> "> Figure 8
<p>The process of generating geometrical features of orthopedic implants.</p> "> Figure 9
<p>Defining a finite element mesh.</p> "> Figure 10
<p>Fixation and force application definition.</p> "> Figure 11
<p>Preparation of the model of the fluid volume in the implant.</p> "> Figure 12
<p>Determination of fluid inlet and outlet.</p> "> Figure 13
<p>Optimization using the Pareto function.</p> "> Figure 14
<p>Optimal geometrical characteristics of the implant selected by the immune algorithm using the objective function.</p> "> Figure 15
<p>Pareto-optimal individuals with Pareto front; k1—calculated value of the strength properties criterion; k2—calculated value of the blood perfusion criterion.</p> "> Figure 16
<p>Geometric features of Pareto-optimal individuals.</p> "> Figure 17
<p>Comparison of geometric features obtained with both methods for the FPI and FC implants.</p> "> Figure 18
<p>Applied force and implant fixation.</p> "> Figure 19
<p>Stress distribution in the implant.</p> "> Figure 20
<p>Distribution of deformation in the implant.</p> "> Figure 21
<p>Define a restraint site and apply forces to the femur.</p> "> Figure 22
<p>Stresses in the cortical bone tissue.</p> "> Figure 23
<p>Stress in spongy tissue and implant (scale change).</p> ">
Abstract
:1. Introduction
2. Materials and Methods
- 1.
- Method of developing a model of the bones of the knee joint;
- 2.
- Method of multi-criteria optimization of the geometric features of an orthopedic implant using the artificial immune system, the objective function, and the Pareto front;
- 3.
- Expert evaluation method based on forms.
2.1. Method of Developing a Model of the Bones of the Knee Joint
2.2. The Method of Multi-Criteria Optimization of the Geometric Features of an Orthopedic Implant with the Use of Artificial Immune System, the Objective Function, and the Pareto Front
- Learning;
- Remembering (and forgetting);
- Maintaining population diversity;
- Adapting to new situations.
2.2.1. The Method of Multi-Criteria Optimization with the Use of an Immune Algorithm
Implant Concepts
- External diameter—11 mm;
- Internal diameter—9 mm;
- Length—40 mm.
- D—The length of the through hole along the axis on the implant surface z—D ∈ [0.5, 3] mm;
- B—Through-hole width—B ∈ [1, 1.7] mm;
- —Distance between holes— ∈ [0.1, 10] mm;
- —The angle by which the through holes in the next row are offset from the previous row— ∈ [0, 30].
- The process of generating geometrical features of orthopedic implants, as shown in Figure 8;
- Determining the type and size of finite elements—SOLID187—1 mm (a solid element, 10-node, with 3 degrees of freedom, with translations in the direction of x, y, z, with a side length of 1 mm [19]). The size and type of the mesh have been selected prior to the optimization process and are not optimized with each new individual. FEM was selected with regard to the acceptable stress results and the simulation time Figure 9;
- Assignment of material properties;
- Automatic extraction of a restraint plane, receiving degrees of freedom of one of the planes (Figure 10);
- Automatic extraction of a plane to which an external force of 10 N has been applied (Figure 10);
- Calculation of implant stresses;
- Save results as text and model.
- CFX-Pre—define initial values (Figure 12);
- CFX-Solution—fluid flow calculation;
- CFX-Post—visualization and generation of fluid flow calculation results.
Criteria of Concept Evaluation—Strength
Criteria of Concept Evaluation—Blood Flow
Objective Function
Pareto Method
2.3. Expert Evaluation Method Based on Forms
3. Results
3.1. Simulation Results Using the Objective Function
3.2. Simulation Results Using the Pareto Method
3.3. Comparison of Both the Methods
3.4. Strength Verification
- Figure 19—stress results. A maximum stress of 1.66 MPa has been observed at the edge of one of the holes on the implant surface;
- Figure 20—results of implant deformation. The maximum deformation (equal to 8.8 × 10 mm) can also be observed at the edge of one of the holes at the bottom of the implant, oriented to the knee direction.
4. Discussion
- Method of production;
- Geometric form mold;
- Mold production;
- Price preparation of the implant;
- Implant manufacturing time;
- Product price;
- Method of sterilization;
- How the implant is implemented during surgery.
5. Conclusions
- 1.
- The methodology of multi-criteria optimization of geometric features was developed with the construction of a fully automatic environment for its implementation;
- 2.
- The multi-criteria optimization process was successful and the optimal (according to the given criteria) geometric features of an orthopedic implant for the reconstruction of the anterior cruciate ligament in the knee joint were selected;
- 3.
- The implementation of the multi-criteria optimization algorithm in the MATLAB® environment significantly simplified the optimization process;
- 4.
- The use of batch files for strength calculations and blood perfusion allowed to automate the optimization process;
- 5.
- The use of the Pareto method allows for a greater selection of Pareto-optimal solutions that can be applied, but it did not produce a better result, despite searching a much larger number of solutions;
- 6.
- Optimization using the objective function allows to obtain comparable results with optimization using the Pareto method, however, the computation time in the first case is much shorter;
- 7.
- A very important step in optimization is the appropriate selection of criteria and assigning them weights;
- 8.
- Verification of the geometrical characteristics of the implant after implementation in the femur model confirmed the possibility of using such a solution;
- 9.
- Verification of the implant model has shown that it will not be damaged during implantation.
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ACL | Anterior Cruciate Ligament |
DICOM | Digital Imaging and Communications in Medicine |
AIS | Artificial Immune System |
ANSYS APDL | Ansys Parametric Design Language |
ANSYS CFX | Ansys Fluid dynamics simulation |
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Mechanical Properties | Cortical Bone | Spongy Bone |
---|---|---|
Young’s module [MPa] | 17,000 | 300 |
Density [g/cm3] | 1.9 | 0.46 |
Poisson ratio | 0.3 | 0.3 |
Compressive strength [MPa] | 200 | 6 |
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Muzalewska, M. Methodology of Multicriterial Optimization of Geometric Features of an Orthopedic Implant. Appl. Sci. 2021, 11, 11070. https://doi.org/10.3390/app112211070
Muzalewska M. Methodology of Multicriterial Optimization of Geometric Features of an Orthopedic Implant. Applied Sciences. 2021; 11(22):11070. https://doi.org/10.3390/app112211070
Chicago/Turabian StyleMuzalewska, Małgorzata. 2021. "Methodology of Multicriterial Optimization of Geometric Features of an Orthopedic Implant" Applied Sciences 11, no. 22: 11070. https://doi.org/10.3390/app112211070