The Inuence of the Posterior Slope Angle and Posterior Condylar Offset in Posterior-Stabilized Total Knee Arthroplasty Was Analyzed From the Way of Constructing Flexion Gap

The purpose of this study was to compare the effects of two ways of establishing the exion gap on the exion angle and exion-extension motion after posterior-stabilized (cid:0) PS (cid:0) prosthesis. A way for the posterior slope angle (cid:0) PSA (cid:0) and posterior condylar offset (cid:0) PCO (cid:0) were greater than preoperative, another for less than preoperative. Materials and Methods They are grouped according to the way exion gaps are constructed. Data from 28 total knee arthroplasty (cid:0) TKA (cid:0) patients treated with propensity score match (PSM) were included. The difference of exion angle and exion-extension motion between the two groups was compared, and the inuence of PCO and PSA on the exion angle in the two ways was analyzed.


Introduction
The establishment of exion gap in TKA not only affects the stability of knee joint after surgery, but also affects the range of motion. The establishment of exion gap bony structure is mainly the construction of PSA and PCO. Studies [1] have proved that there is an anatomical correlation between them. In order to construct a good exion gap during the operation, it is also necessary to balance the relationship between them. More and more studies [2][3][4] analyze their in uence on exion together.
At present, prosthesis designers recommend conservative 3° low PSA osteotomy for PS prosthesis, but there is a lack of individualized treatment and systematic explanation, and clinical selection has been controversial [5,6].The studies [7,8] proved that the increase or decrease of PSA would lead to the increase or decrease of the exion gap.When the central osteotomy volume of the tibial plateau is consistent, the exion gap is not only related to the postoperative PSA, but also affected by the preoperative PSA. In other words, the increase or decrease of the postoperative PSA relative to the initial PSA will also lead to Page 3/15 the increase or decrease of the reconstructed exion gap.When the extension gap has been established and the PSA has been determined, it is common to ensure that there is no fracture of the anterior femoral cortex. Moving the osteotomy plate back and forth appropriately or adjusting the size of the prosthesis are common management methods, but the principle is to balance the exion gap by adjusting the PCO.
The exion gap can also be affected by soft tissue, but as a complement to good bone remodeling, osteotomy design is obviously more important. In theory, the simultaneous increase or decrease of PSA and PCO both can achieve a good bony balance in the exion gap. But which makes more reasonable?
What is the interaction between PSA and PCO in these two cases? This can also answer the question of whether uni ed low PSA osteotomy is reasonable at the present stage and whether individualized osteotomy should be established. Previous studies [9,10]generally only considered the single factor of PSA or PCO, and most did not consider the preoperative effect of both. With the deepening of cognition, it is more scienti c and rigorous to include the PCO and PSA of exion gap construction into the experiment and calculate the change amount to re ect the in uence on exion gap.

Patient inclusion criteria
From January 2019 to July 2019,patients with primary TKA were retrospectively examined by preoperative and postoperative lateral radiographs, and the values and changes of PSA and PCO were measured. Inclusion criteria were patients diagnosed with osteoarthritis, neutral or varus deformity less than 15°, and cartilage wear and pain requiring replacement. Patients with a history of knee surgery, fracture trauma, rheumatoid rheumatism, post-traumatic or suppurative arthritis of the knee, and abnormal muscle strength due to neurological diseases were excluded. A total of 36 cases of knee joints were enrolled, and 14 pairs were successfully matched after PSM treatment. The mean follow-up time was more than 1 year. None of the patients received revision surgery, and no serious complications required hospitalization.

Surgical and rehabilitation programs
The surgery was performed by a number of experienced surgeons. All knee surgeries were performed using PS knee prostheses(China, Ai-Kang, A3GT). The approach methods were median and patellar pararthrotomy, PSA lowering or raising standard osteotomy, and standard osteotomy of distal femur to establish expansion space. The posterior reference osteotomy was used and the exion gap was tested in the mold trial. According to the test results, the osteotomy plate was adjusted to establish the exion gap. After satisfactory remodeling of bony structure, the soft tissue should be ne-tuned, the articular surface of patella hyperplasia should be treated and denervated. The balance of exion and extension, force line establishment and patella trajectory were satisfactory. During hospitalization, passive functional exercise of knee joint was carried out uniformly. After discharge, the doctor instructed functional exercise and regular review.

Collected data
Page 4/15 The data of age, gender, body mass index (BMI), preoperative exion and extension activity were collected. The postoperative recovery was obtained through outpatient reexamination and follow-up. Postoperative exion angle was measured with protractor. Inspect whether there is patellofemoral joint bouncing, delayed knee extension weakness, pain in front of knee joint during exercise. The lateral radiographs of the knee were measured before and after the surgery, where the condyles and the prosthesis overlapped well. The PSA was assessed using the mean angles of the posterior tibial cortex (PTC) and the anterior tibial cortex (ATC) to the tibial plane ( Fig.1). This plain radiograph measurement proved to be well correlated with CT [11]. The measurement was completed by two professionals at an interval of 3 times within 1 week to take the average value. The data involved in this study were collected retrospectively and did not require the approval of an ethical statement.

Statistical analysis
Patients in the two groups were matched 1:1, the nearest neighbor method was used, and PSM were calculated according to age, gender, BMI and preoperative exion angle. The measurement data were tested by K-S to see if they were in line with normal distribution, and expressed as mean and standard deviation (SD). Counting data after pairing were analyzed by the McNemar test and expressed as percentage. Paired t test was used to analyze whether there was statistical difference in postoperative exion angle between groups. Wilcoxon signed rank sum test was used to analyze whether there was statistical difference in the grade data of exion and extension motion status between groups. In addition, univariate and multivariate linear regression analyses were performed for age, BMI, preoperative exion activity, PSA change, PCO change, and postoperative exion angle. The different effects of PSA change and PCO changes on knee exion angle were examined by considering the interaction between the variables. If there is no multivariate effect, the main effect is analyzed. The signi cance level for all analyses was set to P-0.05(bilateral). IBM SPSS 23 was used for all statistical analyses.

Results
Baseline data of patients after PSM are shown in Table 1 The correlation of PCO change value in the decrease group was signi cantly higher than that of other factors, but there was no statistical signi cance, which may be related to the sample size, and further study is needed. The number of patellofemoral joint bounce, delayed knee joint extension weakness and knee joint pain during postoperative exion and extension exercise was more in the decrease groups. Postoperative exion and extension motion grade data of the decrease group was better than the increased group (P =0.031)

Discussion
This experiment found that although the two construction methods recommended to retain the initial PCO, the two groups were different from each other in terms of the tightness of the exion gap. If the negative correlation between the increase of PCO and the exion angle is due to the tension of the exion gap, then why does the decrease of PCO become a negative effect when PSA decreases? This may be because the increase of PSA has an adverse effect on rollback, which weakens the advantage of PCO in delaying impact, and causes more tension in the exion gap and more pressure on the contralateral collateral ligament. The good rollback when PSA is reduced gives full play to the advantages of PCO retention. To better explain, we introduced cruciate-retaining CR prosthesis, which contrasted with PS rollback mechanism.

PSA, PCO and rollback in CR
In previous studies [12], the advantages of PCO recovery and PSA enhancement focus on the delay of impact. This theory has been widely recognized in CR prosthesis. Bellemans [13,9] found in their study that increasing PSA did indeed result in greater maximum exion before the tibial gasket impacted the posterior femur, with a 1.7° exion gain per degree of backward inclination. At the same time, PCO recovery was important because it also allowed greater exion before impact. However, the rollback of CR is better due to the presence of the posterior cruciate ligament (PCL), which ampli es the effects of PCO and PSA. PCL effectively prevents posterior dislocation of the tibial plateau and optimizes rollback without excessive release. Research [14] proved that the increase of PSA in Cr was conducive to rollback, so that the increasing advantages of PCO and PSA at this time could be better re ected, and the two were complementary in the exion gap. However, in PS, backward rolling is not as ideal as in CR, Banks [15] reported that CR had a greater posterior translation of the femur than PS during progressively increased activity.

PSA, PCO and rollback in PS
In PS prosthesis, the protective effect of PCL is lost and only depends on the interaction between the cam and the column to cause the backward roll. The increase of PSA not only cannot optimize the backward roll, but also has been proved many times to lead to abnormal forward roll. Piazza[16] show that the backward tilt of the tibial component shifts the interaction between the cam and the spine to a higher bending angle. As a result, the buckling angle increases and the range of action decreases, resulting in delay and shortage of backward roll. After computer simulation, Wang Zhi Wei [17] found that the increase of PSA delayed the cam binding by 38°, even much more than Piazza's delayed binding by 18°. Satoshi Hamai[18] directly compared the motion of PS and Cr when climbing stairs, and found that Cr showed good stability in the medium degree of exion due to the presence of PCL. In PS, there was abnormal femoral forward roll and posterior impact of the tibial column, and PSA was signi cantly larger in the cases that appeared. It is worth mentioning that the cam and the column are not engaged when rolling forward at medium exion angle. Piazza demonstrated that forward rolling occurred by simulating the change in cam-column contact with a high PSA. This may mean that anomalous forward roll caused by high PSA can occur in both cases when the cam is unengaged at a medium buckling angle and when the cam is engaged at a larger buckling angle. Ephrat Most [19] noted that reduced femoral rollback may be a limiting factor in knee reconstruction, and that the timing of cam post engagement must be combined with the joint geometry after TKA to enhance femoral rollback and increase the exion range of the knee. The increased PCO during insu cient rollback exerts additional pressure on the collateral ligaments and affects exion. In his study, Eisaku Fujimoto [20] raised the concern that too large PCO would make the exion gap too tight and affect the exion angle, and PCO should be properly repaired to achieve a better balance of the collateral ligament. In addition, it is necessary to consider that the exion gap after PCL removal is larger [7]. A larger PSA means a larger PCO to balance the exion gap, so the choice needs to be more careful. However, for the PSA decreasing group, the performance of backward roll would be better than that of the increasing group. In this case, the in uence of PCO was similar to the delayed impact in CR, and PCO retention became a favorable factor. Therefore, the opposite effect of PCO was caused in the two groups.
To sum up, in the PS prosthesis, the selection of PSA may require the rst guarantee of backward rolling, and then, according to the selected PSA, build a PCO that can delay the impact as much as possible without putting too much pressure on the collateral ligament. Roll-back optimization of PS is worthy of further study. From the practical point of view, conservative low PSA is suitable for most people. For a small number of individuals with small initial PSA, choosing 3° can avoid the occurrence of forward tilt. At the present stage, conservative low osteotomy may have optimization space, but it is relatively reasonable.

Differences in exion-extension movement
In addition, we also found that the patellofemoral joint bouncing, delayed knee extension weakness, pain in front of knee joint were more common in the increased groups than in the decrease group. We think this is related to increased pressure on the patellofemoral joint and a decrease in the extensor arm.
Reviewing previous mechanical studies [21][22][23], good rollback can directly reduce the pressure of femur on patella, increase the angle between the extensor arm and the action line between quadriceps and patella ligament, and reduce the pressure on patellofemoral joint. This can effectively relieve muscle weakness and preoperative knee pain after joint replacement and reduce wear and tear of the prosthesis. However, the increase of PSA leads to poor backward roll, and the reduction of moment arm is di cult to achieve. Meanwhile, the complementary increase of PCO in the exion gap is an adverse factor in patella pressure. [24] This may explain the higher incidence of patellofemoral joint bouncing, delayed knee extension weakness, and anterior knee pain in the increase group. At the same time, the increase of PSA has also been shown to lead to the excessive extension of the knee joint in the extension position, causing the femoral cam to impact the front of the tibial column, leading to the wear and deformation of the front column. [25] Hanjunlee[26] also suggests that care should be taken to match the tilt angle of the femur and tibia, as excessive extension could have a negative impact on the stability of the knee and quadriceps or hamstring fatigue. Therefore, from the perspective of exion and extension movement, it is not recommended to increase PSA and PCO to reconstruct the exion gap.

Limitations of the experiment
There are some limitations in this experiment. Firstly, the sample size of our study lost a lot due to the strict requirements on the type of prosthesis, lateral imaging data and PSM, but it was worth it for the scienti c nature of the experiment and the comparability of grouped samples. The regression analysis of the reduction group showed that PCO was the biggest in uencing factor of buckling angle, but it was limited by the sample size. The results were not statistically signi cant and require further study. Secondly, the retrospectively studied subjects were all Asian with PS prosthesis, which was not retro exed and had non-single radial xation platform. Whether the conclusions can be applied to other ethnic groups and prosthesis needs further study. Finally, there are bilateral operations in the data, and the exion angle may be affected by the operation on the other side.

Conclusion
Increasing the PSA and PCO to reconstruct the exion gap will cause problems with exion and extension motion. With regard to increasing the PSA expanded exion gap, increasing the PCO to make up will bring about the loss of exion angle, which may be due to the poor rollback caused by increasing the PSA. For the reconstruction method with reduced PSA, it may be more advantageous to keep the original PCO, which needs further study. It is suggested that it may be more reasonable to avoid excessive PSA and select appropriate PCO to reconstruct the exion gap in PS prosthesis.

Declarations Con ict of interest statement
On behalf of all authors, the corresponding author states that there is no con ict of interest.
Funding: Not applicable Con icts of interest/Competing interests: Not applicable In the case of PSA increase, the increase of PCO was negatively correlated with the postoperative exion angle.
Page 14/15 Figure 3 In the case of reduced PSA, the decrease of PCO was positively correlated with postoperative exion angle.