Predicting Leg Length Change After Valgus-Correcting Lateral Opening-Wedge Versus Medial Closing-Wedge Distal Femoral Osteotomy

Abstract

Background:

Distal femoral osteotomy (DFO) may be performed via either a lateral opening-wedge (LOW) or medial closing-wedge (MCW) osteotomy with meaningful clinical improvements; however, the effects of each DFO technique on leg length have not been well characterized.

Purpose:

To (1) validate a radiographic measurement technique to predict leg length changes after DFO and (2) compare the change in leg length after DFO for the LOW and MCW techniques.

Study Design:

Cohort study; Level of evidence, 3.

Methods:

Preoperative and postoperative full-length standing radiographs obtained from patients who underwent DFO at 1 of 2 academic medical centers were evaluated. The region on the medial (for LOW) or lateral (for MCW) distal femur cortex that would be the “hinge point” during DFO was identified on the radiographs. The distance from the center of the femoral head to the hinge point (A), the distance from the hinge point to the center of the talus (B), and the resultant angle (α) were measured. The equation presented within the text was used to plot the predicted leg length changes corresponding to the change in alpha angle produced by DFO. Comparisons were made between (1) the predicted and measured leg length changes after DFO and (2) the measured leg length change after LOW versus MCW osteotomies.

Results:

For both LOW (n = 10) and MCW (n = 10) osteotomies, the predicted leg length change was equivalent to the true change measured on postoperative radiographs (LOW: P = .16; MCW: P = .85). There was a mean lengthening of 0.85 mm (range, 0.5-1.3 mm) for every 1° of mechanical axis correction with LOW DFO, compared to a mean shortening of 0.45 mm (range, 0.1-1.4 mm) per 1° of MCW correction.

Conclusion:

Preoperative radiographic imaging can be used to predict leg length change after DFO with high reliability. Surgeons can expect approximately 0.85 mm of lengthening per 1° of DFO correction when performing LOW osteotomies, compared to 0.45 mm of shortening per 1° of correction for MCW osteotomies. However, the most accurate prediction results from patient-specific calculations.

A valgus-correcting distal femoral osteotomy (DFO) can be performed via 2 techniques: a lateral opening-wedge (LOW) osteotomy and a medial closing-wedge (MCW) osteotomy. Both techniques have demonstrated good survival rates (defined as requiring a revision or conversion to total knee arthroplasty), decreased risk of recurrent patellofemoral instability, reduction in pain, and improvement in all studied patient-reported outcome (PRO) scores for the knee.^4,9,11 Between these techniques, systematic reviews and meta-analyses have not shown a significant difference in terms of clinical outcomes or PROs. ² Small case series have looked at how leg length is affected by an LOW osteotomy, with one such study reporting a mean preoperative leg length discrepancy of −0.7 cm compared to −0.6 cm postoperatively, nonsignificantly increasing the length of the operative leg. ⁸ However, there is a lack of research comparing these leg length changes to those after MCW osteotomy. Additionally, no studies have presented a model for predicting the leg length changes that will occur after DFO of either technique. Given that limb length differences can lead to accelerated osteoarthritis of the shorter leg's knee, back pain, hip pain, and other issues, the ability to predict which technique can help prevent this pathology without a secondary procedure would be advantageous. ¹²

The purpose of this study was to (1) validate a radiographic measurement technique to predict leg length changes after valgus-correcting DFO and (2) compare the change in leg length after DFO for LOW and MCW techniques. We hypothesized that an LOW osteotomy would confer relative leg lengthening and that an MCW osteotomy would confer relative leg shortening.

Methods

After institutional review board approval by both institutions, a collaborative retrospective review was performed of patient clinical registries from 2 academic medical centers to query patients with valgus deformity who underwent DFO between September 2013 to June 2022. A data use agreement was executed between sites to allow for the sharing of de-identified plain radiographs for analysis. Patients with available full-length standing radiographs at both preoperative and postoperative time points were eligible for analysis. Patients whose radiographs lacked a visible sizing reference marker on either preoperative or postoperative radiographs were excluded to standardize subsequent radiographic measurements across all cases. Full-length leg radiographs were obtained with the patella as the landmark for anteroposterior orientation of the lower limb. Manual measurements were performed by 2 graders (T.J.E., E.C.H.) trained by the senior investigator (A.B.Y.) using a digital picture archiving and communication system.

Preoperative Radiographic Measurements

Full-length long leg radiographs were obtained with patients in a standardized standing position, ensuring equal weightbearing on both limbs. Radiographic acquisition was performed using a digital imaging system with a long cassette, capturing the entire lower extremity from the femoral head to the ankle joint in a single exposure. Limb positioning was standardized with the knees fully extended and the feet oriented forward to minimize rotational variance. After calibrating the standing radiograph using the reference marker, leg length was measured as the length of a straight line from the center of the femoral head to the center of the talus. ⁷

The region on the distal femoral cortex that would be the “hinge point” during DFO was identified. For LOW, the hinge point was selected on the medial cortex just superior to the proximal trochlea. For MCW, the hinge point was selected on the lateral cortex just superior to the proximal trochlea. The distance from the center of the femoral head to the hinge point was denoted as A. The distance from the same hinge point to the center of the talus was labeled B. The resultant angle at the hinge point was labeled α. The alpha angle was measured from the lateral side of the knee. The alpha angle was converted from radians to degrees by multiplying by 3.14/180 to fit into Equation 1. Figure 1 shows radiographic images obtained in a patient who received an LOW DFO with preoperative (Figure 1, A and B) and postoperative (Figure 1C) measurements performed.

Figure 1.

Method for estimating leg length change after valgus-correcting distal femoral osteotomy (DFO). (A) The hinge point (arrow) for the DFO (lateral opening-wedge in this patient) is identified, and the distance between the center of the femoral head and hinge point is marked as A. The distance between the hinge point and the center of the talus is marked as B. The angle subtended by lines A and B is marked as α. (B) Preoperative and (C) postoperative standing radiographs demonstrating that this patient experienced 7.93 mm of left lower extremity lengthening after an alpha angle change of 9.2°.

Using trigonometric principles, we utilized the law of cosines to calculate the starting leg length (SLL) on preoperative radiographs:

$$\mathrm{SLL}=\sqrt{(A^2+B^2-2\mathrm{ABcos}\left(\frac{\alpha ·3.14}{180}\right))}$$ (1)

Calculating Expected Leg Length Changes

Using the same measurements as above, we utilized the following equation to calculate the expected leg length change after osteotomy:

$$y=\sqrt{(A^2+B^2-2\mathrm{ABcos}(\frac{\alpha ·3.14}{180}+\frac{x·3.14}{180}))}-\mathrm{SLL}$$ (2)

Within this equation, y is the predicted leg length change (in millimeters) and x is the change in alpha angle as measured from the lateral side of the knee. Figure 2 demonstrates the graph plotted from Equation 2 for an example patient that can then be used to reveal the leg length change associated with an equivalent alpha angle correction achieved by either MCW or LOW osteotomy.

Figure 2.

A plot of Equation 2 demonstrating the expected differences in leg length changes after a lateral opening-wedge osteotomy versus a medial closing-wedge (MCW) osteotomy based on a 9.2° alpha angle correction for 2 patients. (A) In the top example, shortening follows MCW osteotomy, while (B) in the bottom example, initial lengthening is seen followed by shortening after the MCW osteotomy.

Surgical Osteotomy Technique

All osteotomies were performed by 1 of the 2 senior authors (A.B.Y., A.J.K.) using similar techniques.^1,3,6,10 Preoperatively, patients had valgus deformity, and the goal of treatment was to reestablish a neutral femorotibial mechanical axis. To start the osteotomy, guide pins were placed in the planned trajectory. For LOW osteotomy, this trajectory was started in the supracondylar region of the distal lateral femur and carried medially, and for MCW osteotomy, it was started in the distal medial femur and carried laterally. An oscillating saw was used to create a cut anteriorly, and an osteotome was used to perform the cuts posteriorly. All cuts were made to preserve approximately 1 cm of bone to the contralateral cortex, representing the “hinge point,” without disrupting the far cortex. A tricortical allograft from the distal tibia was configured in a doorstop configuration to hold the reduction in place and then fixed with a plate (ContourLock; Arthrex). The size of the bone allograft can be approximated by multiplying the tangent of the intended corrected angle (radians) by the width of the femur. ¹ Fluoroscopy was utilized to confirm each step (Figure 3).

Figure 3.

(A) Fluoroscopic image of a lateral opening-wedge distal femoral osteotomy with a tricortical allograft. Calculations are shown to determine the size of the bone wedge for an intended degree of correction (x). (B) Planned wedge resection of a medial closing-wedge distal femoral osteotomy with calculations to determine the size of the bone wedge to be removed for an intended degree of correction (x).

Validation and Statistical Analysis

Postoperative radiographs were utilized to measure the final leg length. Radiographs were calibrated and leg lengths were measured in an identical manner to that performed on preoperative radiographs. ⁷ The radiographic leg length change was calculated as the preoperative leg length measured on the preoperative radiograph subtracted from the leg length measured on the postoperative radiograph. A Shapiro-Wilk test was utilized to assess for normality of the data. The radiographic leg length change and predicted leg length change were then compared using the Wilcoxon matched-pair signed-rank test.

Simulated Comparison of Leg Length Changes Between LOW and MCW Osteotomies

For each patient, the predicted leg length changes at 5°, 10°, and 15° of alpha angle correction were calculated. The resulting values were then averaged to determine the length change that could be expected at these standard intervals of correction with an LOW or MCW DFO. Length changes at these 3 alpha angle intervals were compared between DFO techniques using Mann-Whitney U tests. All testing was 2-sided, and significance was set at P value <.05.

Results

Predicting Leg Length Changes

Ten patients were included for both LOW and MCW osteotomy length measurements for a total of 20 patients evaluated. The leg length after an LOW DFO was expected to increase 4.70 ± 2.48 mm (range, 1.93-9.31 mm) from baseline according to Equation 2. The true final leg length after LOW osteotomy as measured on postoperative radiographs was 5.10 ± 2.77 mm (range, 1.45 to 10.87 mm) longer than baseline. The mean difference in real leg length minus predicted leg length measured on postoperative radiographs after LOW DFO was 0.39 ± 0.71 mm (range, −0.48 to 1.68 mm), which was not found to be significant (P = .160).

For patients with an MCW osteotomy, the mean predicted leg length change was −2.60 ± 0.95 mm (range, −4.25 mm to −0.82 mm) as compared to the radiographic leg length change of −2.61 ± 1.25 mm (range, −4.56 mm to −0.50 mm). As before, the mean difference in real leg length minus predicted leg length measured on postoperative radiographs after MCW DFO was −0.01 ± 1.03 mm (range, −1.95 to 1.20), which was not found to be significant (P = .846).

Comparison of Length Changes Between DFO Techniques

The LOW DFO group had a mean leg lengthening of 5.10 ± 2.77 mm (range, 1.45-10.87 mm) compared to a mean leg shortening of 2.61 ± 1.25 mm (range, 0.50-4.56 mm) for MCW (P < .0001) (Figure 4).

Figure 4.

Box plot demonstrating that a lateral opening-wedge (LOW) osteotomy leads to leg lengthening, which is statistically different than the leg length shortening seen with medial closing-wedge (MCW) osteotomy (P < .0001).

The mechanical axis corrections in the MCW (8.05°± 3.19°; range, 3.75°-14°) and LOW (6.20°± 2.56°; range, 1.1°-10°) groups were equivalent (P = .226). Similarly, the mean alpha angle corrections were equivalent regardless of whether surgeons utilized an MCW (7.00°± 2.56°) or LOW (6.50°± 2.70°) (P = .541) technique (Figure 5).

Figure 5.

Box plots showing equivalent corrections of both mechanical axis and alpha angles in patients receiving medial closing-wedge (MCW) and lateral opening-wedge (LOW) osteotomies. DFO, distal femoral osteotomy.

For all patients, the mean mechanical axis correction (7.12°± 2.97°; range, 1.1° to 14°) was equivalent to the mean alpha angle correction (6.75°± 2.57°; range, 2.5 to 12°; P = .588). The mean difference between the mechanical axis and alpha angle corrections was 0.37°± 2.20° (range, −3.25° to 6°). The ratio of mechanical axis correction to alpha angle correction was 1.08:1.00. There was a mean lengthening of 0.84 mm (range, 0.18-1.59 mm) for every 1° of mechanical axis correction with LOW DFO, compared to a mean shortening of 0.50 mm (range, 0.07-1.14 mm) per 1° of MCW correction.

To determine the expected change in leg length at varying degrees of alpha angle correction, 5°, 10°, and 15° of correction were simulated for each patient (Table 1). Patients with an LOW osteotomy were estimated to have a mean leg lengthening of 3.77 mm at 5° of correction, 5.94 mm at 10° of correction, and 6.51 mm at 15° of correction. Conversely, patients with an MCW osteotomy were expected to experience a mean leg shortening of 1.43 mm at 5° of correction, 4.45 mm at 10° of correction, and 9.07 mm at 15° of correction. The difference in length changes between patients with MCW and LOW osteotomies was significant at each interval of correction angle (P < .0001 for all).

Table 1.

Estimated Mean Leg Length Change in 10 Patients Receiving LOW or MCW Osteotomy With 5°, 10°, and 15° of Alpha Angle Correction ^a

Osteotomy	Change in Alpha Angle
	5°	10°	15°
LOW	+3.77	+5.94	+6.51
MCW	−1.43	−4.45	−9.07

^aData are presented as mean leg length change (in mm). LOW, lateral opening-wedge; MCW, medial closing-wedge.

Discussion

The principal findings from the present study are 2-fold. First, standard lower extremity mechanical axis radiographs can reliably predict the leg length change produced by a varus-producing DFO via a series of reproducible measurements and a mathematical calculation that can be automated for routine clinical practice. Second, the study reports the most robust direct comparison to date of the changes in leg length rendered by LOW and MCW osteotomies. Whereas LOW osteotomies produce relative limb lengthening, the magnitudes of which increase with increasing degrees of deformity correction, MCW osteotomies produce relative limb shortening, the magnitudes of which change in a similar manner with increasing degrees of deformity correction.

Despite its potential clinical relevance, the impact of DFO on leg length has not been well characterized to date. In the lone study to directly measure leg length changes after DFO, Madelaine et al ⁸ reported on a cohort of 29 patients who underwent DFO for symptomatic genu valgum with an LOW technique. With a mean angular correction of 8.3°, the patient cohort demonstrated no statistically significant change in radiographic lower extremity limb length after DFO. ⁵ The authors concluded that DFO had “no effect on leg length.” In contrast, the present study identified small, statistically significant changes in leg length that varied according to both surgical technique and severity of angular correction. While both studies are limited in their sample size, the present analysis suggests a potential role for increased anticipation of leg length changes after DFO, particularly in patients with preexisting leg length discrepancies and in cases with larger planned correction of coronal plane malalignment.

To this purpose, the current study reports a reliable and accurate technique for estimating the magnitude and direction (ie, shortening or lengthening) of leg length change after DFO. In our validation study, the predictive tool matched the measured postoperative leg length change to 0.1 mm. This accuracy allows surgeons to converse about expected leg length changes with confidence. The measurements required to obtain the estimated leg length change are straightforward and clinically relevant. While a formal interrater and intrarater reliability assessment was beyond the scope of the present investigation, reliance on commonly measured radiographic parameters assures practitioners that they can adopt the technique with minimal difficulty. Previous literature has shown that mechanical axis deviation measurements have an interrater and intrarater reliability within 2°, which should be considered during surgical planning to ensure avoidance of overcorrection. ⁵ Moreover, while the mathematical formula presented may seem unwieldy, the predicted leg length changes shown in Table 1 may provide a rough estimation for most clinical purposes. Alternatively, this equation can be incorporated into existing web-based applications to determine patient-specific predictions for clinical practice. Additionally, once surgeons determine their planned degree of correction, simple trigonometry calculations can be performed to determine the correct size of the bone wedge, in millimeters.

Within our cohort, DFO performed with an LOW osteotomy resulted in minimal leg lengthening postoperatively, whereas an MCW resulted in minimal leg shortening. Clinical outcomes associated with both LOW and MCW techniques are both favorable and comparable. In a systematic review of 372 DFOs across 16 studies, Wylie et al ¹³ reported similar rates of surgical complications and conversions to total knee arthroplasty between techniques. Purported advantages of an LOW osteotomy include a simpler surgical dissection with reduced risk of neurovascular injury, the need to perform only a single bone cut, and easier capacity to titrate the magnitude of angular correction intraoperatively. ³ Alternatively, an MCW osteotomy affords direct bony apposition without the need for bone graft and may be preferable in patients with an increased risk for nonunion, such as in smokers. The clinical successes reported with both techniques indicate that surgeons may choose the procedure with which they have the most training, experience, and/or comfort. For many cases, the aforementioned attributes of LOW and MCW osteotomies may dictate which procedure is selected. Our study suggests that the magnitude of leg length change associated with both commonly used DFO techniques is relatively small. However, routine evaluation for preexisting leg length discrepancies may highlight particular patients in whom relative leg lengthening or shortening may be disfavored. In these patients, the present study offers data to counsel patients and, potentially, select a particular surgical technique. Specifically, an MCW osteotomy may be favorable in patients whose symptomatic lower extremity is longer than the contralateral limb and who are planned for a relatively large angular correction. Of note, some patients with a high degree of preoperative valgus may experience initial leg lengthening even with MCW osteotomy, as highlighted by the second patient in Figure 2. This occurs when the leg length increase seen from correcting the valgus alignment is greater than the length decrease that occurs from bone wedge removal. This highlights the value of our proposed equation in preoperative planning, as patients with valgus and leg length discrepancies may be candidates for only one technique, whereas in other patients acceptable leg length changes may be obtained with either technique.

Limitations

The study's findings must be considered within the context of its limitations. First, the sample size is relatively small, albeit comparable to those of prior studies evaluating DFOs. ² Given the limited number of patients qualifying for inclusion in this study, we did find that the groups were underpowered to detect significant differences in mechanical axis and alpha angle corrections between the LOW and MCW groups (26.2% and 6.8%, respectively). All radiographic parameters were measured manually, which confers some inherent measurement error. However, manual radiographic measurements for this specific purpose have previously been shown to be reliable with only minimal error. ⁸ Additionally, although the leg length radiograph protocol was standardized, there is some possibility for subtle variability in radiograph acquisition. It is our belief that usage of a calibration marker and experienced radiograph technologists following a specified protocol is the best available way to limit this variability. Finally, assessment of clinical outcomes was beyond the scope of the current investigation, and therefore no correlation between radiographic changes and clinical outcomes could be identified. Future work is necessary to determine whether a threshold magnitude of leg length discrepancy after DFO impairs postoperative clinical outcomes.

Conclusion

Preoperative radiographic imaging can be used to predict leg length change after valgus-correcting DFO with high reliability and accuracy. Surgeons can expect approximately 0.85 mm of lengthening per 1° of DFO correction when performing LOW osteotomies, compared to 0.45 mm of shortening per 1° of correction for MCW osteotomies. However, the most accurate prediction results from precise calculation for each individual patient.