The Swing Angle of the Intramedullary Rod in the Canal During Medial Mobile-bearing Unicompartmental Knee Arthroplasty: a Finite Element Analysis Study

Background: To determine the swing angle of the intramedullary rod in the canal during medial mobile-bearing unicompartmental knee arthroplasty (UKA), we simulated the intramedullary localization process of mobile-bearing UKA via digital technology and analyzed the swing angle of the intramedullary rod swing in the canal through nite element analysis. Methods: Patients requiring mobile-bearing UKA in our department were prospectively selected. A three-dimensional femur model was established, and intramedullary rods of different lengths were inserted. The swing of the intramedullary rod in the canal was simulated, the angle of the moving rod was obtained, and the anatomic parameters of the femur were measured. Parson's correlation between the swing angle of the intramedullary rod and anatomical parameters of the femur were analyzed. Results: The longer the intramedullary rod, the smaller the swing range; this difference was statistically signicant (P<0.05). The maximum swing range of the same intramedullary rod was signicantly larger in the sagittal than in the coronal plane (P<0.05). Parson’s correlation analysis indicated that the isthmic diameter and femur length signicantly correlated with the 20-cm and 25-cm and 30-cm rod swing ranges, respectively. Conclusion: We proved that the longer the intramedullary rod, the smaller the swing angle in the femoral medullary canal. The femoral medullary canal diameter and femur length affect the swing angle; thus, in patients with a shorter femur length, we recommend 25-cm intramedullary rods.

[8] Additionally, despite positive results in Europe, the outcomes differ when applied to patients in Asian countries; for example, there is an increase in dislocation rate. [9,10] If the femoral component is optimally positioned, complications such as dislocation can be signi cantly reduced. [11,12] To avoid perforating the trochlea, most xed UKAs use the extramedullary technique when implanting the femoral component. [13,14] For a more accurate alignment of the femoral component, mobile-bearing UKA uses the intramedullary (IM) positioning method. [15] In the coronal plane, the femoral component should be aligned parallel to the femoral mechanical axis; additionally the angle between the femoral mechanical and anatomical (central axis of the IM canal) axes is about 7° . [16] Designers have created a new microplasty (MP) system in hopes of achieving a more accurate position [17,18]; it utilizes two kinds of IM rods, with lengths of 20-and 30-cm. It exhibits a certain range of swing within the IM canal, permitting a greater degree of error regarding distal femoral implant positioning.
We speculated that the accuracy of the IM technique in mobile-bearing UKA was related to the length of the IM rod, as well as the anatomical morphology of the femur. There is ongoing debate regarding the IM rod with respect to its usefulness. [19] In this study, a three-dimensional (3D) model of the femur and IM rods of different lengths were established using computed tomography (CT). The positioning errors for different rod lengths were obtained through nite element analysis, and correlations between the mathematical model of the femur and swing angle of the rods were evaluated.

Methods
Between January and October 2019, patients who underwent mobile-bearing UKA in our department were prospectively selected; Inclusion and exclusion criteria for mobile-bearing UKA were as de ned by Pandit et al. [20] Each patient underwent preoperative femoral CT using a 64-channel CT scanner (Somatom sensation 64; Siemens Healthcare, Erlangen, Germany).

3D model reconstruction
The femoral CT data (DICOM format, slice thickness: 0.625-mm) were imported into the Mimics software (Materialise NV, Leuven, Belgium) to reconstruct a 3D model of the femoral cortical bone; three IM rod models were established (Figure 1a

Model assembly
The coronal plane was de ned by three points; namely, the posteriormost points of the medial and lateral femoral condyles, and the greater trochanter. Subsequently, an anteromedial insertion point (1-cm anterior to the anteromedial corner of the intercondylar notch) was selected ( Figure 1d). The IM rod was inserted into the femur from the insertion point using 3-Matics 13.0 software (Materialise NV, Leuven, Belgium); the position of the rod was adjusted to ensure that it did not coincide with the cortex (Figure 1e). After optimizing and tting the surface using Geomagics 2014 software, the models were exported in IGES format. The assembled and optimized models were imported into ANSYS Workbench 19.1 software, and the display dynamics module was used for further analysis.

Measurement of the maximum swing angles of the three IM rods
Using the ANSYS Workbench 19.1 software, the maximum swing angles of the three IM rods were measured. First, the femoral cortex and rods were assumed to be rigid. The surface of femoral cortex was constrained ( Figure 2); 18 directional forces were then applied to the top of the rod (Figure 3a, b, c), with 20° between each direction. When the IM rod met the inner wall of the femur and stopped, the maximum moving distances of the rod were recorded. We visualized the moving range maps of the three kinds of IM rods' swing in the canal (Figure 3a, b, c). The maximum swing angle of the rods could be calculated ( Figure 3d).

Measurement of femoral anatomical parameters
Radius of the femoral curvature (RFC) Using the Mimics software to reconstruct the femoral bone marrow cavity model, the length was measured from below the small trochanter to the distal femoral expansion using the 'centerline' function to automatically reconstruct the centerline of the IM canal; the centerline was an approximate circular arc shape (Figure 4a). Referring to the method of Su et al., [21] the center line was t to a circle. The radius of the circle was the radius of the anterior arch of the femur.
Femur length (FL) FL was de ned as the distance between the uppermost point of the femoral head and lowermost point of the distal femoral condyle (medial femoral condyle), measured using the 3D model of the femur ( Figure  4c).

Femoral isthmic diameter (ID)
After using the 'best t diameter' function of the Mimics software to create the best t circle of each point of the center line in the canal, we selected the circle with the smallest radius. This circle was considered the isthmus and was measured in both the sagittal and coronal planes ( Figure 4c).

Femoral isthmus to insertion point distance (IPD)
This was de ned as the distance between the center of the best t circle of the femur isthmus and the insertion point of the distal femur ( Figure 4c).
All parameters were evaluated using the Kolmogorov-Smirnov test for normality. Paired t-tests were performed on the coronal and sagittal planes of the three IM rods in the femoral cavity; P<0.05 was considered statistically signi cant. Both Parson and Spearman correlation analyses were performed between the swing angle of the rods and anatomical parameters of the femur to obtain a corresponding correlation coe cient. All statistical analyses were performed using SPSS version 19 software (SPSS Inc., Chicago, Illinois).

Results
A total of 30 patients were enrolled in this study, with an average age of 64.1±10.6 years; detailed case data and measured femoral anatomical parameters are shown in Table 1. Both the length of the femur and distance from the isthmus to the opening point were signi cantly larger in male patients than in female patients; no differences were observed regarding other parameters.  We encountered ve cases in which the 30-cm IM rod could not be fully inserted into the femoral IM canal. The maximum swing range of the same IM rod was signi cantly larger in the sagittal plane than in the coronal plane (P<0.05; Table 2). In both planes, the longer the length of the rod, the smaller the swing range; this difference was statistically signi cant (P<0.05). Additionally, there was a signi cant correlation between the swing range of each rod in the two planes (Table 3). The length of the femur positively correlated with the swing range of the 30-cm medullary rod (Table 3); conversely, the 20-cm and 25-cm rods positively correlated with the inner diameter of the isthmus of the femoral marrow cavity. The correlation coe cients between the inner diameter and swing angle in the same plane were >0.6 (P<0.01).

Discussion
We found that the length of IM rod and anatomical shape of the femur affected the swing angle; the longer the rod, the smaller the swing angle. For the 20-cm and 25-cm rods, the most relevant factor for the swing angle was the isthmic diameter of the canal; conversely, for the 30-cm IM rod, femoral length was the most relevant factor.
IM positioning technology is widely used in TKA and UKA, and research on positioning accuracy during the procedures has always been a concern for surgeons. Burton et al. [22] reconstructed 20 models of the femur and built a model of the 20-cm IM rod used in mobile-bearing UKA. They found the mean rod orientation was 3.28±2.18° of exion and 2.58±2.08° of valgus. Kort et al. [23] used 10 lower limb cadavers to study the IM positioning accuracy of mobile-bearing UKA. They found that the short and long IM femoral rods may result in excessive exion alignment error of the femoral component.
To explore the in uence of the length of the IM rods on IM positioning accuracy during mobile-bearing UKA, we established three kinds of IM rod models (20-, 25-, and 30-cm), and simulated the process of the IM rods' swing in the femoral canal through nite element analysis; due to the irregular shape of the femoral medullary canal and presence of an anterior arch, methods based on manual measurement cannot determine contact between the rod and femoral cortex. Burton et al. [22] evaluated rod-canal interference using a collision detection algorithm, whereas we innovatively used the nite element method to resolve this problem. We calculated the maximum swing range of the rods in the sagittal and coronal planes; this method can more accurately obtain the maximum swing angle of the IM rods in two directions.
In the sagittal and coronal planes, the maximum swing angles were: 4.36±0.88° and 3.74±0.92° for the 20-cm rod; 2.47±0.74° and 1.64±0.48° for the 25-cm rod; and 1.01±0.51° and 0.79±0.48° for the 30-cm rod, respectively. This may be because the medullary canal is irregular, whereas the femur possesses curvature. The longer the IM rod, the greater the restriction on the inner wall of the femoral canal; thus, the smaller the swing angle. In femurs with a larger anterior arch radius and thin medullary canal, the 30-cm rod cannot be inserted completely.
To further explore the in uence of femoral anatomy on the swing angle of the IM rod swing in the canal, we measured a series of parameters, and analyzed the correlation between these parameters and the swing angle of each rod. The results show that for the 20-cm and 25-cm rods, the most relevant factor for the swing angle was the isthmic diameter of the IM canal; conversely, for the 30-cm IM rod, the femoral length was the most relevant factor (Table 3). In most cases, the tip of the 20-cm rod could not reach the femoral isthmus after insertion; conversely, the tip of the 25-cm rod was located near the isthmus ( Figure  5). Therefore, when the 20-cm and 25-cm rods swing in the medullary canal, the cortex will not block the body of the rod; only the end of the rod will come into contact with the inner wall of the canal, and can cover most, or even the entire medullary canal. The inner wall of the medullary canal is a smooth curve; thus, the inner diameter of the canal at the end of the rod relates to the inner diameter of the isthmus. Regarding the 20-cm and 25-cm rods, the most relevant factor for the swing angle was the isthmic diameter of the canal; the correlation coe cients were >0.6.
Previous studies of IM positioning during TKA demonstrate that the medullary rod tip approaches the isthmus with good positioning accuracy. [24,25] In some cases, such as in patients who had previously undergone total hip replacement, short rods could also be used [26]; our research also supports this view. The maximum swing of the IM canal using the 25-cm rod was 2.47±0.74° in the sagittal plane, and 1.64±0.48° in the coronal plane; this means that the maximum force line of the femoral prosthesis was 0.82° on the coronal surface. The maximum error range of the posterior inclination on the surface was 1.24°; for mobile-bearing UKA femoral prosthesis, this is su cient. Kang et al. [27] found that surgeons should avoid valgus malalignment in the femoral component, especially malalignment exceeding 9°.
Regarding the 30-cm rod, the tip extended signi cantly beyond the femoral isthmus ( Figure 5); this was particularly prominent in female patients with shorter femurs. The shorter the length of the patient's femur, the smaller the swing range in the IM canal. In short femurs with a narrow isthmus, the tip of the rod was in contact with the cortex of the front of the femur when inserting a 30-cm rod; therefore, it could not be inserted completely. During surgery, however, we did not nd this to be the case; we speculated that this discrepancy was due to the small diameter of the IM rod and slight deformation during advancement to adapt to the IM canal shape. During the operation, the medullary rod may penetrate the cortex, creating a risk of fracture. Moreover, when using a 30-cm rod, the tip is blocked by the anterolateral cortex of the femur; thus, its line of force is closer to the inner wall of the canal, deviating from the midline of the IM canal. Since women are known to have shorter femur lengths than men, using a 30-cm rod is not deemed suitable, as the positioning accuracy does not improve; rather, it imposes additional surgical risks.
There are some limitations to this study; rst, we used digital technology to simulate the intramedullary positioning process. While the femur was simulated as a long, hollow bone with a smooth inner wall, bone is composed of cortical and cancellous tissues; this likely caused errors during measurement of the IM rods' swing angle. Further clinical research is required to verify our results. Second, the sample size of this study was relatively small, which makes the accuracy of correlation analysis between the swing angle and femoral anatomical parameters biased.

Conclusions
We conclude that the longer the IM rod, the smaller the swing angle in the femoral medullary canal; the diameter of the femoral medullary canal and length of the femur also affect the swing angle. In patients with a shorter femur length, such as women, 30-cm IM rods may not be fully inserted; therefore, we recommend the use of a 25-cm IM rod.  Figure 1 3D models of the femur and intramedullary rods Computed tomography data were imported into the Mimics software to reconstruct 3D models of the femoral cortical bone (a, b); three IM rod models were established (c).The intramedullary rod was inserted into the femur from the insertion point (e), while the position of the rod was adjusted to ensure that it did not coincide with the cortex (f).

Figure 2
Finite Element model of the femur and intramedullary rod After meshing, the model was imported into the ANSYS software (a); 18 directional forces were applied to the top of the rod to obtain a moving range map (b).  Anatomical parameters of the femur were measured after the 3D models of the femoral cortical bone and canal were reconstructed The centerline of the medullary canal was established (a), and a circle was tted into the centerline of the medullary canal (b). Best t circles at each control point on the centerline were built, and the smallest circle was selected as the isthmus; the isthmic diameter in the coronal and sagittal planes were also measured (c).

Figure 5
Images of the three kinds of intramedullary rods inserted into the femoral medullary canal; (a) is in the coronal plane and (b) is in the sagittal plane.