The Effect of Sagittal Plane Inclination on Posterior Tibial Slope in Medial Open Wedge HTO – Experimental Study With a Square Column Model-Sang

Background: Medial open-wedge high tibial osteotomy (MOWHTO) is an effective and safe treatment method in medial osteoarthritis of knee. However, it may accompany unintended change of posterior tibial slope (PTS). Several factors are known to cause PTS change after MOWHTO. However, there is a lack of research on the sagittal plane osteotomy inclination (SPOI). The purpose of this study was to evaluate that SPOI affected the change in PTS. The hypothesis was that parallel SPOI causes no PTS change after MOWHTO. Methods: A square model with a was by two and A series of was on a through using and an a and The was into perpendicular The was increased was in sagittal


Background
Medial open-wedge high tibial osteotomy (MOWHTO) is an effective and safe treatment method in medial osteoarthritis of knee [1][2][3]. It is for correction of coronal varus deformity. However, it may accompany unintended sagittal changes. It is already well known that posterior tibial slope (PTS) increases after medial OWHTO [4]. Unintended sagittal changes such as increase of PTS may in uence knee kinematics and stability in the sagittal plane [5,6].
Several studies have been conducted to nd the cause of unintended change in PTS after medial OWHTO [2,[7][8][9]. Known causes are incomplete posterior cut [7], improper gap ratio [8], and inappropriate hinge position [2,9]. However, there is a lack of study on the effect of sagittal plane osteotomy inclination (SPOI) on increase in PTS. Only one study reported that SPOI is correlated with PTS after medial HTO [10].

Precondition establishment
To analyze the effect of SPOI on PTS, a square column model with a 10°posterior slope was produced ( Fig. 1). The value of the posterior slope 10° was set based on the average value reported [11]. Using this square column model, a virtual surgery was performed and the changes were measured. First, this process was performed with 3D programs. Then a 3D printer was used to make a real square column model and the changes were measured.
The reasons for requiring a square column model are as follows. First, it is di cult to accurately measure the structural changes after MOWHTO due to complexity of proximal tibia. Therefore, it is necessary to accurately measure and analyze even small changes through simple structuring. Second, even simplifying the complex structure of the proximal tibia does not damage its relationship. There may be a difference in the amount of variation between the complex structure of the proximal tibia and the simpli ed structure, but the relationship does not change.
The reason to be analyzed through experiments rather than through actual surgery is as follow. The actual surgery cannot be performed perfectly at all times, so confounding variables may occur. Therefore, experiments are needed to apply accurately the known cause such as complete posterior cut and true lateral hinge position.

Virtual simulation using two 3D programs
The Autodesk® Maya® software (Autodesk, San Jose, CA, USA) and the Rhinoceros® software (McNeel, Seattle, WA, USA) were used for virtual simulations. Thissoftware's have already been used in many medical papers as tools for 3D modeling and simulation [12][13][14].
The simulation was conducted as follows. First, a virtual square column model with a 10° posterior slope was produced. Second, the SPOI was divided into 4 types: parallel SPOI plus 10° (SPOI: 20°), parallel SPOI (SPOI: 10°), perpendicular SPOI (SPOI: 0°), and perpendicular SPOI minus 10° (SPOI: -10°) ( Fig. 1). The known elements, complete posterior cut and true lateral hinge position, were applied. The correction angle was increased by 5°from 0° to 30°. The change of posterior slope was measured in sagittal plane. 3. Actual simulation using a 3D printer, a testing machine and a measurement system Using a 3D printer (Objet 24, Stratasys Inc., Israel),foursquare column models with a 10° posterior slope were produced. The four types of SPOI were produced by different angles of jig attached to four square column models (Fig. 2). A jig is required to attach a square column model to a testing machine. The axis The purpose of this study was to evaluate the effect of SPOI on the change in PTS. The hypothesis was that parallel SPOI causes no PTS change after MOWHTO. of coronal correction or rotation is lateral hinge in MOWHTO. In experiments using a testing machine, the axis of coronal correction or rotation is lateral hinge too. The rotation of the square column model occurs around lateral hinge. The central axis of jig is lateral hinge. Therefore, the sagittal plane angle of the jig is SPOI.
The correction angle was increased by 5°from 0° to 30° using a testing machine MTS 858 Bionix(MTS system Corp., MN, USA) (Fig. 2). The change of posterior slope was measured using a MicroScribe™ system (Revware Systems, Inc., USA). The reported accuracy of the device is ± 0.05mm [14]. To measure the change of posterior slope with a MicroScribe™ system, two holes were made in advance in the square column model. The anterior end point of the posterior slope is point A and posterior end point is point B (Fig. 2). These two points were reconstructed with a slope line using Rhinoceros software. Using this software, the change of posterior slope was determined as the angle (Fig. 2).
Previous studies have recommended that the osteotomy line in the sagittal plane be parallel to the PTS in MOWHTO [15][16][17]. Miller et al. [18] stated that they maintained the osteotomy line parallel to the PTS in MOWHTO to avoid inadvertent alteration of the native PTS. Amendola et al. [19] suggested that parallel osteotomy line is needed because not parallel osteotomy to PTS but perpendicular osteotomy to the tibia sagittal axis would create a very thin bony fragment posteriorly. However, there is still insu cient as a scienti c rationale to support parallel osteotomy line.
To provide adequate scienti c evidence, we attempted to interpret the results of this study mathematically (Fig. 4). However, the distance from OP line changed from x1 to x1' and the angle changed from θ1 to θ1 + θ. After correction, the position of P2 in the posterior view changed to P2'. The value of r2 is the same. However, the distance from the OP line changed from x2 to x2' and the angle changed from θ2 to θ2 + θ. The 10°p osterior slope of the square column model can be described by the height of P1 and P2 in the sagittal view. As described above, the height of P1 is x1 and the height of P2 is x2 for the OP line. After correction with θ angle, the height of P1' is x1' and the height of P2' is x2'. Then, x1, x2, x1', x2' can be formulated as follows.
If θ1 and θ2 are the same value, the changing values from x1 and x2 to x1' and x2' are the same. Therefore, posterior slope is the same. If θ1 and θ2 are different values, the changing values are different. Therefore, posterior slope is changed. After all, in order forθ1 and θ2 to be the same value, it should be a parallel SPOI.
Lee et al. [10] reported that only 12.9% of patients were parallel and 87.1% of patients had anteriorinclined osteotomy (AIO) despite trying to do parallel osteotomy. In this paper, the changes in PTS after surgery were signi cantly correlated with sagittal osteotomy inclination. Therefore, they concluded that surgeons should make all efforts to perform parallel osteotomy. Although the result is similar with our result in that PTS was maintained in the parallel SPOI, there is a difference in the direction of the PTS change. Our results showed a decrease in PTS in perpendicular SPOI similar to the AIO group while Lee et al. [10] reported that PTS was increased in the AIO group. This difference may come from the hinge position. The AIO group may have the increased PTS by posterolateral hinge position.
Akamatsu et al. [20] reportedthat there was no signi cant difference between the sagittal osteotomy plane angle and the change in PTS while the AP hinge position ratio were signi cantly correlated with the change in PTS. This result is inconsistent with our results. However, they could not control the effect of hinge position in the analysis of the association between the sagittal osteotomy plane angle and the change in PTS. This may obscure the relationship. It is thought that consideration for the effect of hinge position is needed to evaluate the effect of SPOI on the change in PTS.
This study had some limitations that be considered. First, it was an experimental study using a square column model with two 3D programs and a 3D printer. Therefore, it is different from the proximal tibia. However, as described above, even though the complex structure of the proximal tibia is simpli ed to a square column model, the relationship between the variables we want to observe is not compromised. Rather, it is possible to analyze accurately the relationship between SPOI and PTS. However, due to the difference in structure, the difference in the amount of change may occur. Therefore, in the proximal tibia, the amount of change in PTS may be greater than the result of this experiment. Second, this study has no consideration for soft tissue around the knee. Therefore, the results may vary due to the effect of soft tissue in MOWHTO. Third, although our results show the changes in PTS by SPOI, the differences of PTS may not seem to be clinically signi cant. However, the change in PTS was evaluated only in lateral hinge position. If SPOI is increased in the posterolateral hinge position, the change in PTS can be greatly increased. Therefore, further model study is need to demonstrate the effect of SPOI on the change of PTS by hinge positions.
Although there were several limitations, this square column model study has an advantage in that other factors affecting the PTS can be completely controlled in measuring the change of PTS. Thus, our study shows the relationship between the change in PTS and SPOI excluding other related factors of PTS.

Conclusion
In this study, SPOI affected the change in PTS and PTS was maintained in the parallel SOPI. It seems that parallel SOPI in MOWHTO is necessary to prevent the change in PTS. In the further study, it is need to demonstrate the effect of SPOI on the change of PTS by hinge positions.