Computational simulation of bone remodelling post reverse total shoulder arthroplasty - Liedtke, Helen (Centre for Research in Computational and Applied Mechanics (CERECAM), 2017)
Bone is a living material. It adapts, in an optimal sense, to loading by changing its density and trabeculae architecture - a process termed remodelling. Implanted orthopaedic devices can significantly alter the loading on the surrounding bone. In addition, these devices rely on bone ingrowth to ensure secure implant fixation. In this project, a computational model that accounts for bone remodelling is developed and used to elucidate the response of bone following a reverse shoulder procedure. The reverse shoulder procedure investigated here is for rotary cuff deficient patients. In this procedure up to 75 % complications are reported in some clinical series. It is therefore necessary, for the design of successful implants, to understand the loading environment to promote bone growth in the correct areas. The physical process of remodelling is modelled using continuum scale, open system thermodynamics whereby the density of bone evolves isotropically in response to the loading it experiences. The fully-nonlinear continuum theory is solved approximately using the finite element method. The finite element library AceGEN forms the basis for the implementation. Several benchmark problems were implemented to validate the code and demonstrate features of the theory. These include several one-dimensional problems, the classical two-dimensional femur benchmark, and a series of three-dimensional examples. The three-dimensional examples include different loading scenarios on a rectangular block, as well as the investigation of the ASTM testing procedure of the glenoid side prosthesis implanted in a polyurethane foam block. The results clearly demonstrate the adaptive behaviour of the bone density in response to the magnitude and duration of the loading. The numerical implementation is also shown to be robust. The remodelling of the scapula post reverse shoulder arthroplasty is then investigated. A statistical shape model of the scapula was obtained from collaborators in the Division of Biomedical Engineering at the University of Cape Town. The finite element model was used to determine the density distribution in the scapula prior to surgery. A virtual surgery was then performed. The resulting geometry provides the input for the pre-processing phase of the post reverse shoulder arthroplasty model. The loading conditions for the reverse shoulder were provided by collaborators in the Division of Biomedical Engineering and the Leon Root Motion Analysis Laboratory at the Hospital for Special Surgery in New York City. The maximal loading condition at 90° abduction is used as the input for the simulation. It was found that the density increases in the vicinity of the screws, where the maximum stresses are concentrated, however, bone resorption is observed directly below and adjacent to the implant. No conclusive statement can be made, however, as only one loading scenario is considered and calibration of the model against experimental results is still outstanding. A unique feature of the code is that the upper and lower bounds of the density do not have to be enforced directly, as done in most bone remodelling theories in the literature. Rather, the bounds of the density are naturally enforced by calibrating the mass flux for the problem at hand. This project lays out the groundwork for a sound remodelling code, which can serve as a predictive tool in the field of orthopaedics.