Rotational osteotomy is commonly used for correction of the deformity in the orthopaedic practice, e.g. malunited fractures, congenital or developmental deformities. Many methods have been reported to determine the proposed correcting rotation angle. Among them a method proposed by Hoffer et al. requires two Kirschner wires or two Steinmann pins as guide of correction during operation [1]. However, surgeons usually find difficulty in correctly positioning these pins, especially when the planned correction angles are not round values (10°, 20°, 30°...). Another method by Lasserre et al. needs calculations and is inconvenient for use [2]. Fait et al. proposed a similar method that allows correction angle in steps (10°, 20°, 30°...), whereas it is unacceptable in an operation needing precise correction [3].

Čobeljić et al. recently published a method using a huge table of four printed pages [4]. Therefore surgeons can find the assumed correction chord distance in that table by attempted correction angle and bone diameter, and then perform the osteotomy. Such a method had a satisfactory precision and no sterilization is needed, except inconvenient to use a huge four-page table during the real practice.

We thus develop our method by summarizing the huge table into a small ruler with special scales. We also investigate the difference between Čobeljić et al. [4] and our methods. We hypothesize that if the difference is small, our method is comparable as that proposed by Čobeljić et al. [4] Thus our method can be more conveniently used for osteotomy in the clinical practice.

The four-page table proposed by Čobeljić et al. indeed is a sine function table [4]. The table presents the correction chord distance as number, thus it takes much printed space. In order to simply the application of such a huge table to find out the proper chord distance in an osteotomy operation, we find it simpler to just show the correction chord distance as the proposed real distance for operation using a ruler instead of checking the attempted value from such a huge table. Thus we tried to summarize this huge numeric table into a small ruler.

First we define the row elements of the numeric table as the angles for correction osteotomy while the column elements as average diameters of the bone to be operated. According to Čobeljić et al. [4], the numeric table is made of the formula.

t = 2r*sin(α/2)

where t means the chord distance for osteotomy; 2r means the average diameter of the bone; and α means the attempted osteotomy angle to be corrected during osteotomy.

The error of this method is due to mis-prediction of rotation radius, thus we build a computer model. We first get femur cross-section geometry data from CT (computer tomography) of pelvis below intertrochanter region. Then calculate the radius by method of Čobeljić et al., and then the actual distance from center of gravity to bondary. The differences are the cause of error. Then we calculate the error in percentage of these slices of CT (Fig. 1).

The average diameter is calculated by average of long and short axes of the bone (always ellipse in shape). In order to simply this calculation, we modify the formula.

t = 0.5*(4r)*sin(α/2)

where 4r means the sum of long axis and short axis, that is twice of 2r.

We designed such a ruler and investigated the difference in various situations about the effects of geometrical morphology of the femur on the chord distance.

Our method basically is an improvement of the application for previously published four-table method. By the aforementioned formula (2) we developed our ruler for application in the correction osteotomy opertation. The horizontal axis is the distance of 4r, and the vertical axis is t. The ruler is shown in Fig. 2. For the practical use, the surgeon can first make the osteotomy, and then measure the long and short axes of the bone ends. Thereafter the long axis (l) and short axis (s) can be marked on the ruler sequentially, and the chord distance for osteotomy can be read by the proposed correction angle (Fig. 3, 4). Then the surgeons can precisely rotate the bone to meet the proposed chord distance followed by secure fixation (Fig. 4). Such a chord distance was determined by real measurement instead of the radiogram data.

To justify our protractor, we first verify Čobeljić et al. method by computer model (Fig. 1). Totally eight CT slices, 1558 bourdary points are collected. The error, which is estimated by calculating difference between real distance from center of gravity to boundary and the estimated radius, the error is between -37% to 16% (mean ± SD = -6% ± 9%). We think it is acceptable for these operations.

Regarding the precision in the real practice, we afford an electrical version of our ruler in the real practice. The surgeon can magnify the ruler or on the computer screen to find out the final determined chord distance during an osteotomy procedure. Our invention is an image file, it can be printed in any size with propotional magnification. The magnification will not interfere its accuracy. In this study, we printed it as 5 cm-long size.

The rotational osteotomy is performed to correct the rotational deformity in the Orthopaedic practice, such as in the rotational deformity of the malunited fractures or to correct the excessive anteversion of proximal femur, etc. The clinical experience and comprehensive preoperative planning are important for the successful outcomes. Usually when we are doing rotational osteotomy, we must make the osteotomy perpendicular to the shaft, otherwise the rotational osteotomy may cause angulation. Furthermore, a convenient and precise apparatus may help much such a procedure and ensure a good expected result. Therefore we design such a ruler for the determination of the chord distance during a rotational osteotomy.

We verify our ruler at 49 mm diameter (2r), because this is the largest value mentioned in the table proposed by Čobeljić et al. [4] According to Formulas 1 and 2, the chord distance (t) is proportional to the diameter. If it works on the maximal diameter, it should also work on other diameter. We design this ruler and also measure the chord distance on the computer too. The original distance is in pixels and then is transformed to mm. Such a process can improve the precision.

The ideal condition of the osteotomy procedure is the femur with a circular geometry. Equations 1 and 2 show good precision when the cross-section of the bone ends is circular. However, the long bone is usually not circular and somewhat elliptical. For such bones with non-circular ends, the precision for such a correction osteotomy might be influenced by the location of the fixation region. It depends on fixation strategy. If the surgeon tries to fix the osteotomized bone at site with least curve change across bones, the chord distance would be smaller that is accompanied by a larger regional curvature, i.e., small regional radius (Figs. 5, 6). In such strategy, the surgeon should choose plate to fix the osteotomized bone. Because the curvature is different around each segment of ellipses, the chord distance is also different. If the surgeon tries to fix the osteotomized bone by the reference using the rotation center, the chord distance (t) is proportional to the distance to the center (Figs. 7, 8). In such strategy, the alignment is better than the previous one, and the surgeon should choose intra-medullary nail or locking plate to fix the osteotomized bone. These are sources of errors. Therefore for the real practice, we recommend the use of a pair of compasses to measure the determined chord distance. In our computer model, with center rotation strategy, most of the errors are between 2% to -15%. The error is acceptable in such operation.

Despite these uncorrectable errors, our ruler precision is equal to the previous published table method by Čobeljić et al. [4] We propose such a ruler for more convenient use in the operation practice. Such a ruler (Fig. 2) can be made of a paper or stainless steel, and then we can use it on operation table after sterilization.

We design a convenient ruler for application in the rotational osteotomy. Further clinical verification is warranted to justify it.