# Methodology of Multicriterial Optimization of Geometric Features of an Orthopedic Implant
## 1 Introduction  
In the modern world, an interdisciplinary approach is very important when solving engineering and medical issues, resulting in significant advances in medical technologies.  
The growing civilization is causing an increase of the number of injuries among citizens. In the case of athletes, it is caused by the increasing exploitation of the body, while for people leading a sedentary lifestyle, it is caused by lack of experience with sport. An increasingly frequent injury is the rupture of the Anterior Cruciate Ligament (ACL), which is located in the knee joint.  
The subject of this article is the optimal selection of the design features of the new implant used during the reconstruction of the anterior cruciate ligament. Such a reconstruction consists of inserting a graft (usually autogenous, e.g., a tendon) in place of the broken anterior cruciate ligament in the knee joint. The main problem during the surgery is the proper placement of the new graft in the bones of the knee joint and ensuring adequate fluid flow of blood and other body fluids in order to \"nourish\" it.  
The regenerative processes are responsible for the reconstruction of the bones in the body [1]. However, it is a slow process that depends on the patient's health, age, and individual characteristics.  
For the anterior cruciate ligament (ACL) reconstruction surgery to be successful, the graft inserted into the bone canals must grow in [2, 3, 4]. Prof. [PERSON] (the Medical Center Galen-Ortopedia in Biertu, Poland.) proposed the use of bioresorbable orthopedic implants to increase the probability of better fixation of the graft in the bone canals [5, 6]. The role of implant is to create a kind of \"scaffolding\" in the bone canal for the implanted graft, precisely anchoring it in the bone canal. Bioresorbable properties of the implant areexpected to accelerate the bone tissue ingrowth into the graft, so that the graft is properly stabilized and can take over the role of the anterior cruciate ligament in the knee joint [7]. The implant should be strong enough and allow the best blood perfusion, so that the graft and bone tissue will be properly \"nourished\", which will accelerate the growth of bone building cells into the graft.  
An orthopedic implant should have appropriate geometrical features (Figure 1) and dimension system so that it fulfills its function in the best possible way [8; 9].  
While orthopedic implant must include two different criteria, it is necessary to use multi-criteria optimization. Since a satisfactory mathematical model, which comprises both the problems of proper blood flow through the implant and the implant strength in case of overloads in a knee joint has not been developed yet, then Artificial Immune Systems from heuristic algorithms class will be used for the multicriterial optimization. The goal of the multicriterial optimization is to find an optimal solution due to the given criteria.  
In summary, the scientific goal of the work is to develop the methodology used for multi-criteria optimization of the geometric features of an orthopedic implant used for the reconstruction of the anterior cruciate ligament located in the knee joint. The implant should precisely fix the graft in the bone tunnel and accelerate the bone tissue ingrowth into the graft so that it can take over the role of a broken ligament.  
The aim of the research is to determine the optimal geometric features of implants in terms of two criteria, which are: the best possible use of the strength properties of the implant (with the limit on allowable stresses) and optimal blood saturation of the graft.  
The article describes the subject of the author's doctoral dissertation, the Promoter of which was Prof. [PERSON] (Silesian University of Technology).