# Roughness Digital Characterization and Influence on Wear of Retrieved Knee Components
## 1 Introduction  
Total knee replacement (TKR) is an elective surgical procedure in orthopedic surgery worldwide to relieve pain in patients with osteoarthritis and to improve function and restore a good quality of life for patients [1]. In general, TKR consists of three main components: a metal femoral part, a metal tibial plate, and a polyethylene tibial insert. A knee replacement may fail over time and may need a second surgery for a variety of issues. Evidence from previous studies demonstrates that a TKR can last, at most, 15-20 years [2]. It is known that the success and longevity of a knee implant is affected by the characteristics of patients such as age, weight, gender, and activity level [3, 4, 5, 6]. Surface damage and wear are the main threats to the long-term survival of a TKR [78]. Failure most commonly occurs due to fatigue and adhesive wear, which are responsible for the generation of micro particulate debris that, in turn, cause osteolysis around the replacements, ultimately leading to loosening and failure of the TKR [7, 8, 9]. The survival rate of total knee replacements (TKR) has been reported to increase along with the development of advanced technologies and operative techniques [10, 11, 12].  
Tribological aspects of knee components are strongly related to the surface conditions. For instance, the 3D distribution of roughness and the surface topography affect the joint effectiveness. Many tribological studies regarding knee implants were performed in vitro or in silico conditions [13, 14, 15, 16], as knee retrievals are difficult to find or are too damaged to be analyzed.  
In the case of in vitro studies, the femoral or tibial inserts undergo wearing cycles at dedicated simulators in laboratory conditions, trying to replicate general motion activities, whereas in silico studies involve computational analyses of knee virtual models. In vitro and in silico tribo-characterization of prostheses are surely useful but they are rarely as predictive as in vivo studies. Nevertheless, the advantage of in vitro and in silico analyses is that all the phenomena are repeatable.  
This study reports relevant damage mechanisms seen in retrieved metallic femoral components of total knee replacements accompanied with failure. Retrieved knee implants were obtained from the Register of Explant of Orthopedic Prostheses (REPO, IRCCS Istituto Ortopedico Rizzoli). To limit the effects of the prosthetic design on the roughness measurements, 18 prostheses of the same prosthetic model were selected to minimize possible confounding factors. Although most of the implants were removed due to infection, the surface analysis was essential to analyze the surface damage mode of a short-term implants. The aim of this paper is to perform a roughness characterization of the retrieved components to evaluate how changes and distribution of roughness are correlated between the medial vs. the lateral part and how the resulting digital topography can give insights about the wear behavior.  
The qualitative description of the severity and location of surface damage can explain the damage mechanism on the early-retrieved implants. The surface characterization was performed using a Hommel Werke rugosimeter to evaluate the surface roughness and the texture of these components in different locations over the lateral and medial areas. The rugosimeter allowed to acquire the target surfaces point by point. In addition, a Gaussian filter was involved as a digital method to reconstruct the 3D topography of the studied surfaces, which can be read as a 3D wear map, in terms of qualitative distribution considering the strict correlation with the roughness.