Computational modeling of RTSA facilitates estimation of muscle and joint loading, which is currently impossible to measure non-invasively in vivo. Modeling and simulation of RTSA has played a critical role in guiding implant positioning and surgical technique [19,20,21,22], prosthesis selection [23,24], implant design [25,26], and post-operative rehabilitation prescription [27,28]. To date, most modeling and simulation tools require high levels of expertise and are generally restricted to the research setting.

Biomechanical computer models are broadly categorized into three groups: rigid body models, finite element (FE) models, and multi-body models. Rigid body models characterize bones as non-deformable segments. Through simulating joint kinematics and internal and external forces, these models are used to investigate changes in muscle and joint function after RTSA [29,30]. The primary advantage of rigid body models is that they can run quickly and at a low computational cost. For example, shoulder muscle forces during upper limb elevation can be calculated in several minutes using a subject-specific rigid body model (Figure 1A) [28,31]; however, since deformation mechanics is neglected, the internal stresses and strains in the bone and implant cannot be accurately evaluated using this method. An important utility of rigid body models has been in their capacity to estimate the influence of arthroplasty on muscle moment arms, muscle and joint forces, and range of motion (ROM) at the shoulder, which are primary indicators of implant functional performance [21,23,24,29,30,31,32,33,34,35,36,37,38,39,40].

In contrast, FE models provide estimates of material deformation by discretization of structures into a finite number of elements, each element of which can be interrogated for load response such as stress, strain and displacement. This may reveal, for instance, how joint load is transmitted to bone via joint contact loading. The FE method has been used to investigate wear, component fixation, and joint stability after RTSA [41,42,43,44,45], which has aided in implant selection, intraoperative positioning, and fixation [20,44,46,47]. However, in contrast to rigid body models, FE model simulations can be computationally expensive. A FE model of the shoulder after RTSA, containing around half a million elements (Figure 1B), takes more than thirty minutes to run using a standard desktop computer [28].

Finally, multi-body musculoskeletal models input muscle and/or joint reaction force estimations from a secondary model simulation, typically derived from a rigid body model, into a FE analysis. This approach provides a basis for muscle and joint force prediction, as well as bone and implant deformation. Multi-body modeling has been used to assess the performances of different implant designs and surgical techniques in RTSA, with the capability to take into account accurate and physiologically meaningful boundary conditions [28,48,49,50,51].