# Using Statistical Shape Models to Optimize TKA Implant Design
## 1 Introduction  
To restore good function of the knee joint, total knee arthroplasty (TKA) implants should fit well to each patient's anatomy. On the femoral side, a good fit of the component is crucial to obtain good kinematics and a stable knee joint. Overhang of the component can cause soft-tissue irritation [1, 2], while overstuffing of the patella can lead to anterior knee pain [3]. A good fit between the anterior shield and the trochlea is vital to restore satisfying patelltofemoral kinematics [4]. On the tibial side, sufficient bone coverage is important [5] while overhang should be avoided to prevent soft-tissue irritations [1, 6]. Several studies have outlined that implant designs do not fit well to some populations [7, 8, 9]. Finding a design that fits each patient well is indeed very challenging, as bone morphology greatly varies among patients. Besides ethnicity, other factors, such as gender and pathology, also influence the bone morphology. Before introducing a new implant to the market, implant manufacturers need to prove that the design fits well to the patient's anatomy. The norm for joint replacement implants ISO 21534 requires 'the suitability of the dimensions and shape of the implant for the population for which it is intended' be ensured. However, there is currently no clear guideline on how to best proceed. Currently the fit of implants is mainly assessed in the three following ways:  
Prototype or trial implants are placed intraoperatively on patients' bones [2, 10]. The main limitation is the restricted number of available bones. Additionally, the number ofimplant sizes that can be tested, the number of dimensions that can be measured intra-operatively, and the accuracy with which those measurements can be performed are limited. The most common method is the use of 2D or 3D medical images (radiographs, CT or MRI data) to collect specific dimensions on a specific population. For example several studies report the anteroposterior (AP) and mediolateral (ML) dimensions of the distal femur and proximal tibia obtained from medical images [7; 8; 9; 11; 12; 13; 14; 15]. These dimensions can then be compared to the implants' dimensions. This provides the first valuable information on the needed dimensions in an implant portfolio. However, it is limited to a few dimensions in specific areas of the implant. Moreover, it must be carefully considered whether the definition of the dimensions corresponds exactly to the analyzed implant dimension. For example, the location at which the AP dimension of the proximal tibia is measured to serve as a reference for the AP dimension of the tibial plate has to be considered with great care. Finally, 3D bone models generated from medical images can be used in different ways to evaluate the implant fit:  
A 'virtual implantation' enables the placement of implant components on 3D bone models. The fit can then be assessed by performing different measurements, such as overhang and underhang of the components. The challenge is to place the components in a clinically realistic way. In studies including a high volume of datasets, algorithms were developed to enable an automated placement of the components [16]. However, these algorithms cannot take individual specificities into account, which would influence the component placement during surgery. Furthermore, the quality of the virtual implantation is limited due to the lack of information on the soft tissue situation. Three-dimensional bone models can also be used to extract information about the 3D shape of relevant surfaces, such as the shape of the tibial plateau. For example Dai [17] provides a statistical description of the proximal tibia plateau, which can then be used to define the optimal contour of a tibial component. Finally, 3D bone models can be used to generate Statistical Shape Models (SSM) [18]. These models are created from many--typically over 100--bone models reconstructed from CT or MRI data of a given population.