# Development of a Generic Numerical Transtibial Model for Limb-Prosthesis System Evaluation
## 1 Introduction  
An estimated 30 major lower limb amputations per 100,000 people are performed in Europe, most of which are transtibial (below the knee) [1]. It is predicted that the number of amputations will increase in the coming years due to increasing life expectancy and the associated increase in vascular disease and diabetes [2]. After lower limb amputation, patients are usually provided with prostheses to restore mobility and for their successful reintegration into social life. Prostheses are designed and manufactured in hospitals and rehabilitation centres by orthopaedic technicians according to the patient's abilities and the condition of the residual limb [3]. One of the most important parts of the prosthesis is the socket (with or without a liner), allowing the user to move as normally as possible and ensuring adequate safety. A challenging task is to rectify the socket to provide a comfortable fit between the limb and the socket. The residual limb is not designed for the stresses that occur during standing and walking. Therefore, designing and producing a socket that distributes the load optimally, providing stability and safety, is a significant challenge. The current process for socket manufacturing is time-consuming and relies on prosthetists' knowledge, experience, and skills to shape a socket properly [3]. During the first year after the amputation, the user has to visit the prosthetist on average nine times to modify the prosthesis for an improved fit [4]. The predominant approaches to socket design are the total surface bearing (TSB) and specific surface bearing (SSB) methods, with the patella tendon bearing (PTB) predominating [2]. The main difference between the above approaches is that, in the case of SSB,the aim is to transfer loads to the less sensitive sites that can withstand higher stresses, such as the patellar tendon in the case of PTB. On the other hand, TSB sockets aim to distribute the load as evenly as possible over the entire surface of the limb. The TSB method has become widespread in recent years, with the advent of silicone liners that distribute contact pressure over larger areas and help reduce stress concentrations in the residual limb. Silicone liners also adhere to the skin and provide a high coefficient of friction (CoF), which is beneficial for the load transfer between the limb and the prosthesis [5]. Usually, all socket variants are combined with either elastomeric or foam liners, which cushion the load further and provide sufficient friction between the skin and the socket. The use of FEM in prosthetics has accelerated the development of the socket-liner system by analysing the results in terms of stresses, contact pressures, displacements, deformations, etc., effectively [6]. In vivo testing and measurement are time-consuming and costly, demanding a handful of physical prototypes. Therefore, virtual models are beneficial for initial design evaluation and provide insights into results that are otherwise difficult to obtain. Not only the design but also various materials can be compared for a better understanding of the outcome without the need to produce a physical prosthesis. Recent trends in computer-aided technologies led to a proliferation of numerical models in prosthetics [7; 8]. Despite the complex geometry of the residual limb and nonlinear material properties of biological tissue, significant improvements have been made in recent decades [9]. Therefore, the numerical results should be used to analyse and evaluate socket-liner systems to further optimise fit, comfort, stability, and safety. However, the limitations of FEM should be considered when developing the numerical model and evaluating the results. The nonlinear models used to represent biological tissue are homogeneous and time-independent and therefore do not consider muscle activation or changes in soft tissue over time.