1 Introduction

Around-knee osteotomy (AKO) is a joint-preserving surgery for knee osteoarthritis that affects a single compartment. It is generally performed in young, active patients. Open-wedge high tibial osteotomy (OWHTO) is the standard procedure for medial knee osteoarthritis, achieving favorable clinical outcomes.¹ However, this technique may result in distal displacement of the tibial tuberosity and patella baja, potentially leading to reduced joint range of motion and concerns regarding patellofemoral arthrosis.^2,3 Consequently, in open-wedge distal tuberosity tibial osteotomy (OWDTO) reported by Gaasbeek,⁴ this problem is resolved by connecting the tibial tuberosity to the proximal bone fragment. OWDTO can suppress chondral degeneration of the patellofemoral joint.⁵ Furthermore, OWDTO is considered to have better clinical scores than OWHTO.⁶ However, it is considered less stable than OWHTO because the traction force exerted by the quadriceps tendon widens the osteotomy site. Previous clinical studies have shown that OWDTO is more prone to increased postoperative posterior tilt than OWHTO,⁷ and that bone union at the hinge site and sagittal cut are delayed.⁸ With AKO, the development of a locking plate enables robust initial fixation, and consequently facilitates rehabilitation through early weight-bearing.⁹ However, in OWHTO, 62.4 % of patients reported experiencing plate-related symptoms, such as skin irritation after surgery,¹⁰ and 52 % required implant removal.¹¹ Furthermore, the use of locking plates may make their removal difficult. Because a prolonged period before removal is a known risk factor for removal difficulties, it is desirable to perform removal as early as possible if necessary.^12,13 Both OWHTO and OWDTO undergo a bone healing process called “gap filling,” where the open area gradually closes from near the lateral hinge region. This makes it difficult to assess the healing condition using the conventional methods used for fractures, such as confirming the continuity of the callus and trabeculae. As gap filling progresses, the osteotomy site stabilizes; however, the relationship between the state of bone union and stability remains unclear. In OWHTO, prior studies on stability based on the degree of gap filling using finite element method analysis exist¹⁴; however, there are no reports on OWDTO. The results obtained for OWHTO cannot be directly applied to OWDTO, which is considered to be more unstable. Furthermore, in OWDTO, union may occur at the tibial tuberosity before gap filling (Fig. 1), and union at this site is expected to affect stability. In clinical practice, approximately half of the gap filled at the osteotomy site is used as the criterion for implant removal.¹⁵ Our institution also references this criterion and, so far, no clinical problems have arisen. However, there is no evidence that this hypothesis is valid. In this study, we analyzed the stability of the osteotomy site in OWDTO based on the progression of gap filling and descending cut union using the finite element method. We hypothesized that (1) the osteotomy site stabilizes with 50 % gap filling, and (2) stability differs depending on the presence or absence of descending cut healing.

Close

Fig. 1 State of union of the tibial tuberosity (a) A gap remains in the descending cut site, and fusion is incomplete. (b) Observed complete union.

Export to PPT

2 Material and methods

2.2

2.2 The model

A transverse cut was made along a line extending from a point 40 mm distal to the medial articular surface toward the center of the proximal tibiofibular joint. Then, a coronal osteotomy plane (descending cut) perpendicular to the transverse cut was created 10 mm posterior to the tibial tuberosity. The thickness of these osteotomy surfaces was set to 2 mm, considering the thickness of the bone saw used for osteotomy. The bone was separated by forming a mesh that included the osteotomy surface, yielding the respective shapes of the proximal and distal bone fragments. The hinge point was set 5 mm medial to the lateral cortex. The distal bone fragment model was rotated in the coronal plane until the distance between the medial cortices reached 10 mm, creating an OWDTO model (Fig. 2a). The proximal tibiofibular joint was reproduced by appropriately drawing its shape during Region of Interest (ROI) editing. Additionally, to replicate the state of the bone union, a cancellous bone model was created to interpose the proximal and distal bone fragments. First, a triangular prism-shaped cancellous bone model was created by using the osteotomy surfaces of the proximal and distal bone fragments as reference points. Using the mediolateral length of the distal end of the cancellous bone model as a reference, cancellous bone models illustrating different stages of bone union were created by cutting at positions 25 %, 50 %, 75 %, and 100 % from the lateral edge. No model placed was set as 0 % (Fig. 2b). For the tibial tuberosity area, we divided the cases into two patterns: those with and without bone union. We then analyzed a total of ten patterns created by combining these two patterns.

Close

Fig. 2 The created open-wedge distal tuberosity tibial osteotomy model and cancellous bone model for gap filling reproduction (a) A transverse cut was made along a line extending from a point 40 mm distal to the medial articular surface toward the center of the proximal tibiofibular joint and a coronal osteotomy plane (descending cut) perpendicular to the transverse cut was created at a position 10 mm posterior to the tibial tuberosity. The hinge point was set at a position 5 mm medial to the lateral cortex. The distal bone fragment model was rotated in the coronal plane until the distance between the medial cortices reached 10 mm. (b) Cancellous bone models of a triangular prism were created to reproduce gap filling.

Export to PPT

Each finite element model was composed of tetrahedral elements with four nodes and a side length of 4 mm. The number of elements and nodes for each model are listed in Table 1.

Table 1 Details of each model.

	Gap filling condition	Number of elements	Number of nodes
Without descending cut union	0 %	126,184	31,541
	25 %	136,875	33,627
	50 %	135,523	33,192
	75 %	142,299	34,513
	100 %	142,293	34,517
With descending cut union	0 %	132,994	32,963
	25 %	140,497	34,243
	50 %	141,733	34,479
	75 %	149,917	35,878
	100 %	151,177	36,182

3 Results

The distribution of von Mises stress without union of the descending cut is shown in Fig. 3. The stress was concentrated around the lateral hinge area, and the stress levels decreased as the gap filling progressed. Maximum von Mises stress decreased by 89.2 % from the model immediately after osteotomy (0 %) in the model with 50 % gap filling. Fig. 4 shows the stress distribution in the model with fused tuberosity. Compared with the model without fusion, the stress at the lateral hinge region was reduced. Furthermore, the medial side view confirmed that the stress was concentrated posterior to the osteotomy site of the tuberosity, indicating that the load was distributed at this site (Fig. 4b). The maximum stress for each gap filling, with and without the union of the descending cut, is shown in Fig. 5. When the tuberosity was fused, a reduction in maximum stress was observed: 66.7 % under gap filling 0 % conditions and 66.2 % under gap filling 25 % conditions. Fig. 6 shows the displacement of the osteotomy site under each condition. As the gap filling progressed, the displacement decreased. A noticeable decrease in displacement was observed in both the 0–25 % (22.020 mm–2.421 mm, 2.421 mm–1.466 mm) and 25–50 % (4.206 mm–1.108 mm, 1.466 mm–0.651 mm) ranges regardless of whether the descending cut was fused or not. However, displacement also differed depending on whether tuberosity fusion occurred. Under the gap-filling 0 % condition, displacement decreased by 87.9 %, whereas under the 25 % condition, it decreased by 65.1 %.

Close

Fig. 3 Maximum Mises stress at each stage of gap filling progression without descending cut fusion The tibia and fibula are observed in the posterior view. Stress is concentrated around the hinge region but decreases as the gap filling progresses.

Export to PPT

Close

Fig. 4 Maximum Mises stress at each stage of gap filling progression with descending cut fusion (a) Observation from the posterior reveals that stress at the lateral hinge region is reduced compared with cases without tibial tuberosity fusion. (b) Observed from the inside, the stress is concentrated at the fusion point of the descending cut (yellow arrow).

Export to PPT

Close

Fig. 5 Maximum Mises stress by gap filling progression with and without descending cut fusion When the tuberosity was fused, a reduction in maximum stress was observed: 66.7 % under gap filling 0 % conditions and 66.2 % under gap filling 25 % conditions.

Export to PPT

Close

Fig. 6 Maximum displacement by filling progression with and without descending cut fusion Displacement also decreased as gap filling progressed, similar to the stress. The decrease was particularly pronounced between 25 % and 50 %, when there is no healing of the descending cut. At gap filling levels of 0 % and 25 %, the presence or absence of healing in the descending cut resulted in a significant difference in displacement.

Export to PPT

4 Discussion

Finite element analysis is frequently used in various fields to evaluate stability and strength. Regarding AKO, there are reports on hinge position,²¹ graft placement,¹⁹ plate design,²² and the effects of additional screws.²⁰ To the best of our knowledge, this is the first study to analyze stability using the finite element method for each condition of gap filling and tuberosity union in OWDTO.

Brinkman reported that 90 % of the gap achieves consolidation by 1 year postoperatively, while recommending waiting one and a half years before removal²³; however, there is no explanation behind this reasoning. Considering that removal is necessary, delaying the procedure increases the risk of difficulty in removal. Therefore, removal should be performed as early as possible once sufficient stability to support the load is achieved.^12,13 Therefore, it is necessary to elucidate stability based on the state of fusion.

MacLeod²⁴ analyzed the stresses on plates according to the state of bone union by altering the material properties of the opening portion in OWHTO. Once it becomes a woven bone and attains a state evaluable by radiography, the study can be applied in actual clinical practice. However, distinguishing connective tissue from fibrous tissue is difficult, making it challenging to use for determining whether removal is possible. Furthermore, Berthe¹⁴ evaluated stresses for each gap filling in the OWHTO model, finding that a 25 % gap filling reduced stresses in the lateral hinge region by 91 %. While this study provides useful insights into stability based on the healing status after osteotomy, it remains unclear how stability is affected after plate removal because the analysis was conducted with the plates still in place.

Referring to reports from clinical practice, Kobayashi¹⁵ defined bone union in OWHTO when 40–60 % of the opening gap was filled, noting that 33 % met this criterion at 3 months and 83 % at 6 months. Furthermore, another report stated that, even in cases where plates were removed with 25–50 % gap filling, no changes were observed in X-rays after removal.¹⁰ As seen in these studies, in actual clinical practice, OWHTO considers gap filling of 25–60 % as judgement of bone union, leading to removal of the device. Even in the results from this OWDTO model, under loads simulating double-limb standing, the 50 % gap-filling model remained stable regardless of descending cut site healing. In contrast, at 25 %, the difference in stability based on the presence or absence of tuberosity union is significant. Therefore, when considering removal at approximately 25 %, it may be necessary to use tuberosity bone healing as a criterion in the decision.

Akasaki reported that nonunion of the tuberosity occurred in 13.3 % of cases in OWDTO.⁷ Determining whether removal is feasible in cases where fusion cannot be achieved at the tuberosity is difficult. In our study, when fusion of the tuberosity was not achieved, displacement was approximately 10 times greater at 0 % gap filling and approximately three times greater at 25 % gap filling. Similarly, the maximum von Mises stress was approximately three times higher under both conditions. In contrast, when gap filling exceeded 50 %, the difference becomes smaller. Therefore, in cases where descending cut healing is not achieved, it may be recommended to wait until gap filling reaches close to 50 % before removing the implants.

Surgical site infections occur in 1.93–18.0 % of cases with OWHTO, and 0.46–4.9 % of these are deep infections.^25,26 In cases of deep infection, implant removal may be necessary regardless of the healing status. However, we believe that the results of our study will help determine whether additional fixation methods, such as plaster cast immobilization or external fixation, are required in such situations.

This study had a few limitations. First, this evaluation was based on a single case; hence, the results may differ in other cases owing to variations in bone quality and the amount of correction. However, the CT data used were from a patient in their 60s without a diagnosis of osteoporosis, and the correction amount was a 10 mm-width correction, representing a common case of a patient undergoing OWDTO. Therefore, the results are considered relatively generalizable and applicable. Second, because CT scans using phantoms were not performed, it was difficult to evaluate the maximum breaking strength, which means that the load capacity that could be withstood under each condition could not be measured. Future studies should be conducted after data meeting the specified conditions have been prepared. Third, the analysis only considered loading conditions simulating double-limb standing weight-bearing and failed to evaluate movements such as squats. Analysis of these different load conditions will be necessary in the future.

5 Conclusion

In this study, when gap filling reached 50 %, both maximum stress and displacement decreased significantly compared with baseline, regardless of whether the descending cut had fused. Therefore, in cases where descending cut healing is not achieved, it may be recommended to wait until gap filling reaches close to 50 % before removing the implants. Furthermore, there was a significant difference in stability depending on whether the tibial tuberosity had fused, particularly when the gap filling was insufficient. Therefore, when considering removal at approximately 25 %, it may be necessary to use tuberosity bone healing as a criterion in the decision.

Consent to participate

Informed consent regarding the use of the data was obtained from the patient via a consent form.

CRediT author statement

Hiroya Akase: Methodology, Writing original draft; Nobuhiro Kaku: Writing - review & editing, Funding acquisition; Kensei Tanaka: Formal Analysis, Software; Masashi Hirakawa: Supervision.

Ethics approval and consent to participate

This study involved a computer simulation using computed tomography data; hence, it did not require ethical approval. Informed consent regarding the use of the data was obtained from the patient via a consent form.

Data statement

The dataset used in this study cannot be provided to other institutions without patient consent.

Funding

The publication fee of this study was supported by a research grant from Zimmer Biomet (no. ZBCS20250528008). The funder had no specific role in the conceptualization, design, data collection, analysis, decision to publish, or preparation of the manuscript.