Correlation between posterior offset of femoral condyles and sagittal slope of the tibial plateau

Abstract

The aim of this study was to address, in normal knees, the variability of posterior offset of femoral condyles and tibial slope, and the presence of any correlation between the two that might be needed to achieve an adequate joint motion in flexion. Magnetic resonance images of normal knees of 80 subjects, 45 males and 35 females, with a mean age of 38.9 years, were analysed. Measurements were performed by two independent observers using an imaging visualization software. The tibial slope averaged 8 and 7.7 °, on the medial and lateral sides, respectively (P = 0.2); the mean posterior offset of femoral condyles was 27.4 and 25.2 mm on the two sides, respectively (P = 0.0001). The variation coefficient of the condylar offset and tibial slope was 11.5 and 38%, respectively. In the medial compartment, a significant correlation was found between the femoral condylar offset and the tibial slope, while the same was not observed in the lateral compartment of the knee. Magnetic resonance imaging allows the assessment of tibial slope and femoral condylar offset in the medial and lateral side separately, taking into account any difference between the two compartments. The sagittal tibial slope exhibits a greater variability compared with the posterior offset of femoral condyles. The correlation found, in the medial compartment, between the tibial slope and femoral condylar offset suggests that the reconstitution of the proper morphology of the posterior part of the knee joint may be necessary to obtain a full range of motion in flexion after total knee replacement.

Introduction

A limited range of motion after total knee arthroplasty (TKA) may be responsible for unsatisfactory clinical outcomes, particularly in patients who need a high range of flexion due to cultural habits. However, an even worse condition is when knee flexion is below 110 °, which has been reported to be the necessary mobility for most activities of daily living (Kettelkamp et al. 1970; Laubenthal et al. 1972). When limited motion is due to excessive joint tightness in flexion, abnormal tensile and compressive stresses may occur, respectively, on the anterior and posterior portion of the implant, leading to early wear, micromotion and eventually loosening of the prosthesis (Laskin & Rieger, 1989; Bai et al. 2000).

The sagittal tibial slope is the inclination of the tibial plateaus in the sagittal plane. In healthy individuals, the anterior portion of tibial plateaus is usually higher than the posterior one, and the resulting sagittal inclination of tibial plateau is postero-caudally directed. The posterior femoral condyles are the portion of the femoral joint that articulate with tibial plateaus during the flexion of the knee. The distance between the most posterior portion of the condyles and the posterior diaphyseal cortex of femur is defined posterior condylar offset. Some authors suggested that, in TKA, the sagittal tibial slope and the posterior condylar offset may affect the range of motion in flexion in different ways (Bellemans et al. 2002; Massin & Gournay, 2006; Arabori et al. 2008; Malviya et al. 2009). An appropriate sagittal inclination of the tibial component may enhance the flexion space of the joint and prevent the knee from becoming too tight in flexion (Bellemans et al. 2002; Massin & Gournay, 2006; Arabori et al. 2008; Malviya et al. 2009). A proper restoration of preoperative offset of femoral condyles may increase the space between the posterior femoral cortex and the posterior border of the tibial plateau during knee flexion, thus reducing the risk of impingement between the two (Bellemans et al. 2002; Massin & Gournay, 2006; Arabori et al. 2008; Malviya et al. 2009). However, these assumptions were not substantiated by recent investigations, in which both sagittal tibial slope and posterior offset of femoral condyles were not found to be related to the range of motion of the knee in flexion (Arabori et al. 2008; Bauer et al. 2010).

Although several investigations have evaluated the influence of tibial slope and posterior condylar offset on knee flexion (Laskin & Rieger, 1989; Matsuda et al. 1999; Bellemans et al. 2005; Blaha et al. 2006; Hashemi et al. 2008; Malek et al. 2009), no study has analysed whether any relationship between the two exists in the normal knee. The present study was aimed at assessing, on magnetic resonance (MR) scans, the variability of the sagittal tibial slope and posterior offset of the femoral condyles, and evaluating whether any correlation exists between them. We hypothesized that, in order to achieve adequate joint motion and ligaments tension during the flexion of the knee, the degree of posterior tibial slope should be related to the posterior offset of femoral condyles. If this was the case we would expect that individuals with a marked sagittal inclination of the tibial plateaus concomitantly show a pronounced posterior offset of femoral condyle and vice-versa.

Materials and methods

Magnetic resonance scans of the knee of skeletally mature Caucasian subjects who complained of mild or moderate knee pain of recent onset were analysed. The exclusion criteria were: evidence of any abnormalities of the joint including degenerative changes in cartilage, menisci and subchondral bone; a history of traumas entailing injuries to cruciate ligaments or menisci, or osteochondral lesions; varus-valgus deformity; rheumatic diseases; aseptic necrosis of femoral or tibial condyles; and previous knee surgeries.

Potential candidates for the present investigation were selected, after the approval of the institutional review board and having obtained their informed consent, among 123 consecutive patients who underwent magnetic resonance imaging (MRI) of the knee in the 3 months before the beginning of the study. Forty-three patients who did not meet the inclusion criteria were excluded, leaving 80 patients eligible for the study. The sample size satisfied a power analysis conducted before the study, which revealed that a minimum of 40 subjects was needed to establish 90% power to protect against the undue acceptance of the null hypothesis. There were 45 males and 35 females, with a mean age of 38.9 years (range 16–64 years). The mean age was 37.3 years in the male group (range 14–70 years) and 40.7 years in the female group (range 15–62 years).

Magnetic resonance images included spin echo T1-weighted axial and sagittal sequences (TR: 450 ms; TE 12 ms; slice thickness 3 mm; Mx 256; 1.5 Tesla; SOMATOM, Siemens, Germany). The exam was conducted with the subjects in the supine position, the knee in extension and the lower limb in neutral rotation. Measurements were performed using OsiriX, an image display and visualization software (Pixmeo, Geneva, Switzerland; Macintosh platform, Apple, USA), which allows the measurement of linear values up to 0.1 mm and angular values up to 0.1 °. MRI were analysed by two orthopaedic surgeons who were blinded to the patients' data. The sagittal bone slopes of the medial and lateral tibial plateaus were measured in the first assessment of MR sequences. The posterior offset of medial and lateral femoral condyles was then measured in a second evaluation in which the examiner was blinded to the results of the tibial slope assessment.

Sagittal tibial slope

The sagittal anatomical axis of the tibia was first identified in a sagittal scan located in proximity to the tibial insertion of the posterior cruciate ligament and directed anteriorly in line with a perpendicular to the transepicondylar axis of the femur (Fig. 1A). On this sagittal scan, the sagittal tibial axis was identified, according to Hashemi et al. (2008), as a line connecting two points located 4–5 cm apart, at the proximal 1/3 and as distal as possible in the tibial shaft, respectively (Fig. 1B). To assess the slope of the medial and lateral tibial plateau, we selected two sagittal scans, parallel to the central sagittal slice previously identified, and located in the middle of the medial and lateral tibial plateau (Fig. 1A). Because the medial and lateral tibial plateau exhibit a concave and flat shape, respectively, the sagittal orientation of the medial plateau was assessed as a line tangent to the upper portion of the anterior and posterior bone profile, while the sagittal orientation of the lateral plateau was assessed as a line tangent to most of the superior bone profile. The angle between the tibial sagittal axis and each of these two lines was considered to be the bone slope of the medial and lateral tibial plateau, respectively (Fig. 1C).

Fig. 1.

Measurement of the tibial slope on MRI. (A) Axial scan depicting the projection of the transepicondylar axis (continuous line) and its perpendicular at the level of the posterior cruciate ligament insertion (dash–dot line), which represents the sagittal scan where the longitudinal axis was calculated. The dotted lines indicate the sagittal scans passing through the middle of the medial and lateral tibial plateau. (B, C) Sagittal scans showing the identification of the sagittal longitudinal axis of the tibia (B; arrowhead) and the measurement of the tibial slope (C).

Posterior offset of femoral condyles

To assess the posterior condylar offset, we selected a sagittal slice passing through the middle of the knee joint and the distal 1/3 of the femoral diaphysis. In the selected sagittal scan, the sagittal longitudinal axis of the femur was calculated by identifying two points located 5 cm apart, at the middle of the distal diaphyseal shaft (Fig. 2A). The sagittal longitudinal axis was then shifted posteriorly until it was tangent to most of the posterior femoral cortex. Once the posterior femoral cortex of reference was identified, it was translated medially, at the middle of the medial condyle, and laterally, at the middle of the lateral condyle, along the transepicondylar axis (Fig. 2B). To limit errors inherent to the selection of the sagittal scan where the posterior condyle had to be measured, the sagittal scan showing the largest circle fitting the peripheral border of the posterior condyle was selected from those passing through the middle portion of the condyle. The most posterior portion of the circle was then identified, and a line perpendicular to the posterior femoral cortex and passing through the most posterior point of the circle was considered as the posterior femoral offset of the medial and lateral condyle, respectively (Fig. 2C).

Fig. 2.

Measurement of condylar offset. (A) Sagittal scan depicting the identification of the sagittal longitudinal axis (arrow) and its translation to the posterior femoral cortex (arrowhead). (B) Axial scan showing the sagittal plane of (A) (dotted line) and its translation, along the transepicondylar axis (dash–dot line), to the middle of the medial and lateral condyles (continuous lines). (C) Sagittal scan showing the circle used to identify the largest posterior offset of femoral condyle. PFC, projection of posterior femoral cortex on the middle of the condyle; arrow, perpendicular to the posterior femoral cortex.

As the radii of femoral condyles were found to be related to the subject's height (Malek et al. 2009), their posterior offset was also reported as a ratio with respect to the diameter of the femoral diaphysis. The latter was calculated 5 cm proximally to the point where the posterior femoral offset was assessed.

To test the reliability of measurements, the sagittal tibial slope and the posterior offset of femoral condyles were calculated twice, the first time during the study and the second time 4 weeks after its completion. Intra- and inter-rater reliability were assessed using intra-class correlation coefficients.

Statistical analysis

Mean, 95% confidence intervals (CI) and standard deviation (SD) were computed for all measurement sets. The Lilliefors (Kolmogorov–Smirnov) normality test was performed for all the assessed variables. Student's t-test was performed to compare the medial and lateral tibial slope, the medial and lateral femoral offset, and differences between sexes. Paired t-tests were performed to test for differences between medial and lateral sides. Linear regression analysis was used to determine the relationships between the tibial slope and the posterior condylar offset. The variation coefficient was used to assess the variability of the sagittal tibial slope and posterior femoral offset in the population analysed. The level of significance was set at 0.05 for all t-tests and the correlation analysis. spss for Windows (version 9.0, SPSS, Chicago, IL, USA) was used for the statistical analysis.

Results

The sagittal tibial slope showed a normal distribution on the medial and lateral side. The mean slope was 8 and 7.7 ° on the two sides, the difference between them being not significant (P = 0.2) (Fig. 3). However, in six males (14%) and seven females (21%), the difference between the medial and lateral side exceeded 4 °. The inter- and intra-observer reliability was 0.88 and 0.94, respectively. On average, the medial tibial slope was 7.6 ° in males and 8.6 ° in females (P = 0.2), and the lateral tibial slope was 7.5 and 8 °, in males and females, respectively (P = 0.3) (Table 1).

Fig. 3.

Error bars showing mean and 95% CI values of tibial slope (left graph) and condylar offset (right graph).

Table 1.

Tibial slope, condylar offset and ratio condylar offset/femoral diaphysis

	Mean	SD	Range	95% CI	P-value
Tibial slope (medial)
Men	7.6 °	3.3	2–14.5 °	6.6–8.6 °	0.2
Women	8.6 °	2.6	2.6–12.9 °	7.7–9.5 °
Tibial slope (lateral)
Men	7.5 °	3.5	−1.8–14.4 °	6.4–8.6 °	0.3
Women	8 °	3.6	0.1–14.5 °	6.8–9.1 °
Condylar offset (medial)
Men (mm)	27.5	2.18	22–32	26.8–28.2	0.9
Women (mm)	27.2	2.06	23.3–40	25.8–28.6
Condylar offset (lateral)
Men (mm)	25.5	2.28	20–30	24.8–26.2	0.33
Women (mm)	24.8	3.85	20.1–40	23.4–26.2
Ratio condylar offset/diaphysis (medial)
Men	0.92	0.10	0.7–1.14	0.89–0.95	0.03
Women	0.99	0.17	0.7–1.5	0.93–1
Ratio condylar offset/diaphysis (lateral)
Men	0.86	0.12	0.6–1.1	0.82–0.90	0.19
Women	0.9	0.18	0.67–1.53	0.84–0.97

The posterior condylar offset showed a normal distribution on the medial and lateral side. The mean offset was 27.4 mm on the medial, and 25.2 mm on the lateral side (P = 0.0001) (Fig. 3; Table 1). In 37 subjects (47%) the difference between the medial and lateral condyle was > 2 mm, and in 20 (25%) it exceeded 4 mm. The mean posterior offset of the medial condyle was 27.5 mm in males and 27.2 mm in females (P = 0.9), while the mean offset of the lateral condyle was found to be, respectively, 25.5 and 24.8 mm (P = 0.33; Table 1).

The ratio posterior offset of femoral condyles/femoral diaphysis was, on average, 0.95 on the medial, and 0.88 on the lateral side (P = 0.002; Table 1). For the medial femoral condyle, the mean ratio was 0.92 in males and 0.99 in females (P = 0.03), while for the lateral condyle the values were 0.86 and 0.90, respectively (P = 0.19; Table 1). The inter- and intra-examiner reliability was 0.90 and 0.96, respectively.

There was no correlation between either age and degree of tibial bone slope or age and amount of offset of femoral condyles, both in males and females.

On the medial side, a significant correlation was found between the tibial slope and the offset of femoral condyles (Fig. 4), and between the former and the ratio posterior offset of femoral condyles/femoral diaphysis (r = 0.26; P = 0.02). That is, the greater the degree of the tibial slope, the larger the offset of the femoral condyle and its ratio with the femoral diaphysis. On the lateral side, no significant correlation was found between the degree of tibial slope and either the posterior offset of femoral condyles (Fig. 4) or the ratio posterior offset of femoral condyles/femoral diaphysis (r = 0.45; P = 0.69).

Fig. 4.

Graph showing the linear correlation analysis between the tibial slope and the posterior condylar offset in the medial compartment (left graph) and in the lateral compartment (right graph).

The subjects who had a marked tibial slope on the medial side (between 8 and 15 °) concomitantly showed a medial condylar offset significantly greater compared with the subjects with a mild to moderate (0–7.9 °) tibial slope. A similar correlation was not found on the lateral side (Fig. 5).

Fig. 5.

Histograms illustrating the mean posterior condylar offset in subjects with marked and mild–moderate tibial slope, in the medial compartment (left graph) and in the lateral compartment (right graph). Black columns represent the tibial slope; grey columns represent the posterior condylar offset. Y-axis indicates the entity of tibial slope in degrees (black columns) and that of posterior condylar offset in mm (grey columns).

Discussion

In this study we found that the sagittal tibial slope exhibits a greater variability compared with the posterior offset of femoral condyles. Furthermore, the posterior condylar offset differs significantly between the medial and lateral femoral condyles, while no significant difference emerged between the sagittal slope of medial and lateral tibial plateaus. A significant correlation was found between the tibial slope and the posterior offset of femoral condyles, but only in the medial compartment of the joint.

Controversial results have been reported on the influence of the sagittal tibial slope and posterior condylar offset on the range of motion in flexion after TKA (Bellemans et al. 2002, 2005; Massin & Gournay, 2006). However, in previous investigations the tibial slope and posterior condylar offset were assessed as separate entities, and the percentage of patients in whom their mutual relationship was restored after TKA was not analysed (Bellemans et al. 2002; Massin & Gournay, 2006; Arabori et al. 2008; Malviya et al. 2009; Bauer et al. 2010). In this study, we evaluated the tibial slope and condylar offset on MR scans using a high-resolution imaging software. Measurements were made separately on the medial and lateral side to identify differences between the two compartments that may not be detected on plain radiographs (Chiu et al. 2000; Jenny et al. 2005; Hudek et al. 2009). The tibial slope showed a variation coefficient of 34.5 and 41.6% on the medial and lateral side, respectively, the extreme values being −1.8 and 14.5 °, which implies that in a few subjects the tibial slope may be too extreme to be replicated in TKA. The posterior condylar offset exhibited a variation coefficient of 11 and 12% on the medial and lateral side, respectively. The difference between the two condyles was significant and > 4 mm in 25% of subjects.

The second objective of the study was to analyse whether the posterior condylar offset was related to the degree of sagittal tibial slope. We hypothesized that, as the condylar offset increases, the tibial slope should increase as well to avoid a tight knee in flexion and vice-versa. The results confirmed our hypothesis, but only partly. We found a significant correlation between the amount of posterior condylar offset and the degree of posterior tibial slope in the medial compartment, while a similar correlation was not observed in the lateral compartment. This finding, to our knowledge not previously reported, may be explained by the different anatomical features of the medial and lateral femoro-tibial joints. In the medial compartment, the concave shape of the tibial plateau along with the firm attachment of the medial meniscus to the tibia and the tight medial collateral ligament, render the femoro-tibial joint a rather constrained articulation. Therefore, a spatial correspondence between the posterior condylar offset and tibial plateau is needed to avoid an excessive joint tension, which would occur if a marked posterior offset was associated with a mild tibial slope, or an excessive joint laxity, which would occur in the opposite situation. However, in the lateral compartment a similar relationship may not be needed because the femoro-tibial joint exhibits a greater laxity due to the flat shape of the tibial plateau, the greater mobility of the lateral meniscus and the lower tension of the lateral collateral ligament compared with the medial one (Blaha et al. 2006). In addition, as the lateral femoral condyle rolls back during flexion due to the medial pivoting motion of the knee, femoro-tibial impingement is less likely to occur in the lateral compartment compared with the medial one (Nakagawa et al. 2000; Nakamura et al. 2010).

In TKA, the sagittal tibial cut may be performed as parallel as possible to the tibial slope of the operated knee (Catani et al. 2004; Massin & Gournay, 2006), or perpendicular to the sagittal mechanical axis of the tibia (Ecker et al. 1987; Bai et al. 2000). One of the potential clinical implications of our study is that, when using the former technique, the surgeon should attempt to replicate the preoperative femoral offset as much as possible to avoid an unbalanced knee in flexion. On the other hand, the perpendicular cut technique should be avoided in patients with a pronounced femoral offset, because it may expose to substantial risks of causing a tight joint in flexion.

This study has some limitations. We tried to reduce possible bias due to measurements performed on sagittal planes with different rotational alignment, as previously described. Nevertheless, this was achieved only partially on the femoral side, where the valgus orientation of femoral condyles, with respect to the femoral shaft, compels the measurement of posterior condylar offset to be performed in a different sagittal plane than that of the posterior femoral cortex. However, such a potential error should be limited, as the posterior condylar offset was calculated as the distance between a line, the tangent to the posterior femoral cortex, and a point, the most posterior point of the femoral condyle. Second, we analysed only normal knees, and the results may be different in arthrosic patients. However, in the medial compartment of the joint, where a closer relationship between femur and tibia was observed, degenerative changes occurring in varus knees rarely involve both the femoral condyle and tibial plateau to such an extent as to preclude a preoperative evaluation to be accomplished (Matsuda et al. 2004).

In conclusion, we believe that the knowledge of the normal anatomic relationship between the posterior femoral condyles and tibial plateaus is a necessary prerequisite to elucidate the role played by bony and soft tissue structures in balancing the knee joint during flexion. Our study has shown that the condylar offset is related to the sagittal slope of the tibial plateau, but only in the medial compartment of the knee. This finding might be due to the anatomic features of the knee joint, which entails a more constrained relationship between femur and tibia on the medial compartment than in the lateral one. Further investigations should assess whether, in the clinical setting, to take into account the relationship between the posterior condylar offset and the slope of tibial plateau may be helpful to obtain a painless knee with a full range of motion.

Authors' contributions

G.C. and P.S. worked on the design of the study and data interpretation. G.C. wrote the manuscript. F.R.R. and R.P. collected the data and collaborated to the analysis. R.M. worked on the statistical analysis and data interpretation. G.G. worked on the design of the study and data analysis.