Introduction

The extensor mechanism of the knee includes the quadriceps muscle and tendon, the patella, and the patellar ligament [1]. It is believed that increased lateralization of the tibial tuberosity, represented by the tibial tuberosity (TT)–trochlear groove (TG) distance (Fig. 1), is a factor predisposing to patellofemoral instability. The likely outcome is the malalignment of extensor mechanism of the knee [2], and patellofemoral pain, a common musculoskeletal complaint [3].

Fig. 1
figure 1

The TT–TG distance of the right knee. The distance between the tibial tuberosity (TT) and the trochlear groove (TG) defines the alignment of the extensor mechanism of the knee (3D CT image was rendered with InVesalius 3.0. beta 2 software, Renato Archer Information Technology Centre)

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To quantify the extent of lateralization, axial computed tomography (CT) is used. Axial CT images showing the center of the tibial tuberosity on the one hand and the center of the trochlear groove on the other are routinely superimposed.

In measuring the TT–TG distance, three lines are drawn [1, 4–7].

The first line passing through the visually approximated positions of the most posterior points of the femoral condyles is called the posterior intercondylar line. The anatomy of the posterior parts of the femoral condyles is usually symmetric and stable [8]. The posterior intercondylar line is therefore a reliable reference line in measuring the TT–TG distance. Some of the close synonyms are: the posterior femoral condylar line [4], the posterior bicondylar line [5], the posterior condylar line [6], and the bicondylar line [7].

The other two lines are vertical to the posterior intercondylar line. The first line passing through the visually approximated position of the most anterior point of the tibial tuberosity is called the TT line [6]. The second line passing through the visually approximated position of the most posterior point of the trochlear groove is called the TG line [6]. The horizontal distance between the TT line and the TG line is called the TT–TG distance [4–7]. A TT–TG distance value greater than 20 mm and patellofemoral pain are perceived as probable indications for knee surgery [7].

The objective of this study was to compare the positions of the TG line and the vertical midline of the pericondylar rectangle on axial CT.

Materials and methods

Materials

A retrospective pilot study was conducted in February and March 2011 at the Clinical Institute of Diagnostic and Interventional Radiology of the Zagreb University Hospital Center in Croatia. Given the retrospective study design, the patients’ written informed consent was not deemed necessary, although the Declaration of Helsinki as revised at the 59th World Medical Association General Assembly in Seoul 2008 was closely followed where applicable.

From the group of consecutive patients that had musculoskeletal CT imaging during the period of this study, 14 knees in 9 patients (7 women, 2 men, mean age 32.22 ± 12.98 years), 4 unilateral and 5 bilateral, were included. Inclusion criteria were as follows: patellofemoral pain, a normal trochlear angle (124°–145°) [7], and no medical record of prior knee surgery.

Methods

The CT positioning protocol was: supine position and quadriceps muscles relaxed with knees in full anatomical extension. The CT imaging protocol was: 43–50 mA, 130 kV, and 2-mm slice thickness at bone window setting (width= 1,500, center = 450). The CT measuring protocol will be described in detail. Below is an introduction to some of the concepts in geometry utilized in the study.

Basic geometry concepts

In Euclidean plane geometry (Euclid, 325–265 BC), a rectangle is a quadrilateral with four vertices at right angles (90°). The horizontal sides of a rectangle are the lower and the upper horizontal side. The vertical sides of a rectangle are the left and the right vertical side. The opposite sides of a rectangle are of the same length. Since they are also parallel, a rectangle is a parallelogram. Moreover, a rectangle has two midlines: the horizontal midline passing through the midpoints of the vertical sides and the vertical midline passing through the midpoints of the horizontal sides.

In Cartesian analytic geometry (Renatus Cartesius alias René Descartes, 1596–1650), the numerically expressed position of a point in a two-dimensional space is called a coordinate. The rectangular coordinate system consists of the horizontal x-axis (the abscissa) and the vertical y-axis (the ordinate) at right angle (90°) to each other, dividing the two-dimensional space into four quadrants (marked by convention with Roman numerals I, II, III, and IV in counter-clockwise order). The intersection of the rectangular coordinate axes is the origin of coordinates (the coordinate 0). A horizontal distance of a point from the origin of coordinates is the x-coordinate. A vertical distance of a point from the origin of coordinates is the y-coordinate. The coordinates make ordered pairs (x, y).

The CT measuring protocol

The CT measuring protocol is schematically summarized in Fig. 2.

Fig. 2
figure 2

The CT measuring protocol. a The pericondylar rectangle located in the first quadrant of the Cartesian rectangular coordinate system. b The CT measuring protocol of the left knee. RA Roman arch, TG trochlear groove line, TT tibial tuberosity line, TT–TG tibial tuberosity–trochlear groove distance, VM vertical midline of the pericondylar rectangle, asterisk visually approximated position of the most posterior point of the trochlear groove. Orientation box: A anterior, L lateral, M medial, P posterior

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Initially, a sequence of axial CT images was obtained. From this a single axial CT image was taken as a reference. The “reference cut” was the axial CT image with a fully recognizable intercondylar groove shaped as a Roman arch, hence displaying the midtrochlear region [5, 7]. It should be noted that the antero-posterior diameter of the Roman arch was approximately one third of the antero-posterior diameter of the femoral condyles [7].

The pericondylar rectangle was drawn with vertices ABCD in counter-clockwise order. The horizontal sides of the pericondylar rectangle ABCD were the lower (AB) and the upper (CD) horizontal side. Notice that the lower horizontal side (AB), passing through the visually approximated positions of the most posterior points of the femoral condyles, was the posterior intercondylar line. The vertical sides of the pericondylar rectangle ABCD were the left (AD) and the right (BC) vertical side.

To ensure that the axial CT image depicts the midtrochlear region, the antero-posterior diameter of the Roman arch was one third of the length of the vertical sides (AD and BC).

Subsequently, the trochlear angle was measured. The value of the trochlear angle between 124° and 145° [7] indicated a normal, groove-shaped midtrochlear region—the center of the trochlear groove—and the respective axial CT image was included in the study.

The pericondylar rectangle ABCD was located in the first quadrant of the Cartesian rectangular coordinate system. Point A was the origin of coordinates.

Depending on the visually approximated position of the most posterior point of the trochlear groove, the position of the TG line varied solely in the horizontal direction (left–right).

In measuring the TT–TG distance, the TG line is always vertical. Therefore, the horizontal distance between any of the points on the TG line and the origin of coordinates was equal. The horizontal distance of a point from the origin of coordinates, as stated previously, is the x-coordinate. Thus, the x-coordinate of the TG line, the length of DE, was measured.

The vertical midline of the pericondylar rectangle was the line passing through the midpoints of the horizontal sides. However, only the length of AB was measured. The x-coordinate of the vertical midline, the length of AF, was calculated as half the length of AB. In addition, the length of AB varied with condylar morphology.

Duplicate measurements of the lengths of DE (DE1 and DE2) and AF (AF1 and AF2), at 2-week intervals, are shown in Table 1.

Table 1 Trochlear angles and the positions of the TG line (DE1 and DE2) and the vertical midline (AF1 and AF2) of the pericondylar rectangle on axial CT, obtained at 2-week intervals
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Statistical analysis

Statistical analysis was performed with MedCalc Software (version 12.0., Mariakerke, Belgium). A p value <0.05 was considered statistically significant. Although the Kolmogorov–Smirnov test could not reject the normality of the data, because of the small sample size [9], the non-parametric Wilcoxon signed rank test for matched pairs was employed to evaluate the difference between medians. Bland–Altman plots [10] were drawn and the single measure of intraclass correlation coefficient (ICC), with a two-way random model and an absolute agreement type, was calculated to analyze the agreement between matched pairs with 95% confidence intervals (CI). Finally, the coefficient of variation (CV) for duplicate measurements was obtained to assess the relative variation.

Results

The results of the statistical analysis are shown in Table 2. There were no statistically significant differences between matched pairs. Also, 95% of differences showed less than 1.96 standard deviation (SD) on the Bland–Altman plots (Fig. 3). According to Landis and Koch [11], substantial agreement was found between the positions of the TG line and the vertical midline of the pericondylar rectangle at 2-week intervals (ICC = 0.688 and 0.670 respectively), with almost perfect agreement of duplicate measurements (ICC = 0.975 and 0.998 respectively). Much less relative variation was observed with regard to the vertical midline (mean = 38.893, SD = 0.475, CV = 1.22% and mean = 39.304, SD = 0.135, CV = 0.34% respectively).

Table 2 The positions of the TG line (DE1 and DE2) and the vertical midline (AF1 and AF2) of the pericondylar rectangle on axial CT, obtained at 2-week intervals and statistically analyzed as matched pairs for differences and agreements
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Fig. 3
figure 3

The positions of the TG line (DE1 and DE2) and the vertical midline (AF1 and AF2) of the pericondylar rectangle on axial CT, obtained at 2-week intervals and statistically analyzed as matched pairs for agreement using Bland–Altman plots

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Discussion

This retrospective pilot study showed that there was no statistically significant difference between the position of the TG line and the vertical midline of the pericondylar rectangle on axial CT: they were identical.

An interesting point to highlight is that in drawing the vertical midline of the pericondylar rectangle, the trochlear morphology was circumvented.

Trochlear dysplasia is the most frequent condition in patellofemoral instability [12]. Consequently, when the midtrochlear region is not remotely groove-shaped (Fig. 4), the visual approximation of the position of its most posterior point is quite impossible. It can be difficult to decide where to draw the TG line [13, 14]. Since different observers yield different results, this might have a serious bearing on the value of the TT–TG distance. Saudan and Fritschy [15] have suggested that one of the reasons for increased interobserver variability in measuring the TT–TG distance was the labeling of the TG point in the case of major trochlear dysplasia. The corresponding literature seems fairly scarce and few authors have tried to provide a viable solution. Yet, the pericondylar rectangle method implies that drawing the vertical midline instead of the TG line could objectify the measurement of the TT–TG distance in the case of major trochlear dysplasia.

Fig. 4
figure 4

Major trochlear dysplasia of the right knee in three different subjects. The a shallow, b flat or c bumpy midtrochlear region (arrows) makes the visual approximation of its most posterior point on axial CT quite impossible

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The main limitation of this retrospective pilot study, apart from the possible selection bias due to design itself, was a small sample size, which made it less able to detect a true difference (type II [β] error). Nevertheless, as this was the first study of its kind, the results could primarily serve as a starting point in estimating the relevant statistical parameters needed for broader studies in the future.