## 1 Introduction  
Ankle arthritis involves joint damage or severely worn cartilage [1]. End-stage ankle arthritis is characterized by bone-on-bone grinding of the joint surface after progressive wear of articular cartilage. This causes pain, loss of function and mobility, and severe limitation of daily activities [2, 3]. If conservative care (nonsteroidal anti-inflammatory drugs (NSAIDs) or other oral therapies, corticosteroid injections, or bracing) and alternative methods of pain control and management fail, there are two possible surgical treatments: ankle arthroresis (AA) and total ankle arthroplasty (TAA) [4]. Approximately 80.5 to 91.6% of patients with end-stage arthritis underwent AA in the 2000s; the rate fell to 54.6 through 70.7% in the 2010s. The respective rates for TAA were 9.0 to 19.5% and 29.3 to 45.4% [5, 6]. The rates of AA and TAA have fallen and increased, respectively, as people have sought to maintain a high quality of life against a background of lengthening lifespans [2, 5, 6]. However, the risk of implant complications remains higher after TAA than other lower limb arthroplasties, including total knee arthroplasty (TKA) and total hip arthroplasty (THA). The survival rate of TKA is 96.4 to 98.0% at 5 years and 89.3 to 92.9% at 15 years. For THA, the respective rates are 96.8 to 97.9% and 86.7 to 91.0% [7; 8; 9]. The TAA survival rate is similar to that of TKA and THA at 5 years (range, 90.4-96.0%), but lower at 15 years (range, 63.6-73.0%) [10; 11; 12]. Although various causes of revision were reported, such as malalignment, infection, bone stress fracture, polyethylene (PE) insert subluxation, deep infection, synthesize nonunion, and impingement [11; 12] a major cause of low survival is thought to be aseptic loosening caused by periprosthetic osteolysis [13; 14]. It is generally thought that periprosthetic osteolysis is caused by particles of polyethylene, which, stimulating a biological cascade, in turn enhance osteoclast activity [15; 16; 17]. The stress shielding effect caused by differences in material properties (i.e., the elastic modulus) between bone and implant is also a major reason for osteolysis [18; 19; 20]. Third- and fourth-generation TAA methods have improved TAA procedures and implant coatings [11; 21; 22; 23]. [PERSON] et al. reported that rounding of the surfaces and anterior flanges of the talar components of fourth-generation TAA systems reduced the subsidence caused by osteolysis [11]. [PERSON] et al. reported that the mobile bearing incorporated into third- and fourth-generation TAA systems reduced strain at the implant/bone interface and may also reduce osteolysis [22]. [PERSON] et al. reported that TAA, using a narrow PE insert, reduced edge loading and wear, which can cause osteolysis [23]. [PERSON] et al. reported that hydroxyapatite (HA) and porous coating of TAA components reinforced static interlocking and reduced the subsidence caused by osteolysis [21]. However, TAA still has various complications [11; 24]. A study by [PERSON] et al. indicated that the HA coating of TAA may cause extensive osteolysis [24]. Some studies reported the causative link between progression of degenerative lesions and postoperative deformity of the ankle joint, which includes alignment alternation and constrained inversion-eversion motion [25; 26; 27; 28]. Therefore, TAA designs that reduce the risk of osteolysis are needed. Many studies have aimed to improve TAA and reduce osteolysis [11; 22; 23], but few have considered the location and extent of osteolysis. As osteolysis is a progressive condition that needs early diagnosis, knowing the location and extent of osteolysis might be helpful [29]. Plus, bone remodeling theory suggests that the risk of osteolysis may be reduced if TAA applies sufficient stress to bone areas with low stress flow [18; 30; 31; 32]. Two-dimensional (2D) radiography and three-dimensional (3D) computed tomography (CT) data are available on the location and extent of osteolysis [15; 16; 29; 33; 34; 35; 36].