# Development of a Generic Numerical Transtibial Model for Limb-Prosthesis System Evaluation
## 1 Introduction
In addition, the contact between soft tissue and the prosthesis is a complex interaction that depends on many factors, such as temperature, humidity, fit, etc., and is not constant as it is in a simulation. Due to all these limitations, numerical models are only an approximation of actual conditions, and the results should be treated accordingly. A substantial number of specific lower limb FE models have been developed in attempts to analyse the donning of the socket, stance phase, or even gait cycle. Although this may be accurate for a particular case, we cannot generalise the model to all patients, as the geometry of the limb and the material properties of the biological tissue vary considerably from case to case. Using a specific geometry to design a prosthetic component may lead to a solution that is only suitable for a given case [10]. In order to gain a more general insight into the biomechanical behaviour of the limb-prosthesis system, a generic geometry of the residual limb would be beneficial. Such a model could be used to compare different results relatively, and could support the development of a socket-liner system more objectively for general groups of patients [11]. Accurately capturing all biological components in a numerical model is challenging and often results in an unstable numerical model. Hence, it is necessary to reduce the complexity of the model, to ensure convergence and minimise computational costs [10]. One way to obtain the average geometry of a given biological component is through statistical shape modelling (SSM), where measurements are taken on a given population and then averaged [12]. Such an approach requires a sufficient amount of data and an accurate acquisition method for the model to be adequate, which can be time-consuming and costly. The detailed shapes of bones obtained with SSM are advantageous when comparing morphological differences between race, sex, age, lifestyle, etc. [13]. On the other hand, the specific details increase the computational cost significantly and reduce the numerical convergence of a complex biomechanical system. In order to analyse the bulk interaction between the residual limb and the prosthesis sufficiently, the morphological details should be reduced to such an extent that the model still reflects a typical biomechanical response. Based on the previous point, the generic transtibial model should be simple enough to ensure numerical convergence but still provide valid results in terms of contact pressure at the limb surface and relative deformation of the socket and liner, allowing an objective evaluation of the prosthetic's components [14]. To date, only a limited number of generic lower limb models have been developed that are currently outdated or highly simplified, and for which the results, therefore, cannot compete with today's advanced computer-aided technologies [11; 14; 15; 16; 17; 18; 19]. [PERSON] et al. developed a generic numerical transtibial limb model consisting of basic geometric shapes representing an average-sized limb [11]. The model was also used in later studies, where it was compared with experimental measurements and results from the literature [14; 15]. Due to the significant simplifications (linear elastic material models, basic geometric shapes, and simple boundary conditions), the overall biomechanical response of the model is questionable and can only be used as an initial assessment of the limb prosthesis system. On the contrary, the model developed in the current study uses nonlinear material models and complex boundary conditions, which represent more realistic scenarios; hence, more accurate biomechanical results could be obtained. Simplified 2D axisymmetric numerical models have also been used to analyse specific properties, such as friction and contact pressure at the limb-socket interface [16; 17; 18; 19]. Results have shown that such simplified and generic or quasigeneric models can be used to simulate specific biomechanical phenomena.