### Research volunteers

Male and female adult volunteers with ages between 21 and 50 years were selected by the doctors of the Department of Radiology of the Lumen Diagnostics Centre.

The inclusion criteria were volunteers without a history of ankle sprains and without CFL lesions, without fractures, congenital diseases, or orthopedic surgeries involving the ankle and foot. Cases where fracture of the CFL was detected in the volumetric acquisition of the images were excluded from the sample. The acquisition of volumetric isotropic images of the volunteers in the sagittal plane was performed. The images of these volunteers were reported and sent to the researchers (CAE 03556912.0.0000.5497).

### Procedures

The volumetric isotropic MR images of the 100 volunteers were first used to determine the dimensions of the CFL using the tools of the supervisory system of the Achieva Magnetic Resonance device. The measurements were performed 3 times by two technicians specializing in the musculoskeletal system.

Next, a computational model was developed that represents the CFL relative to the image plane and determines whether there is complete visualization of this ligament. The model can consider all of the dimensions of the ligament with the foot in the anatomical position and simulates the visualization of any orientation of the oblique transversal image plane.

To validate the computerized model, the CFL and its visualization were initially simulated considering the oblique transversal image plane at 35°. This technique was chosen because 35° is the CFL angle with the highest prevalence in the studied population. The CFL morphometric data from the volunteers were used for the simulation.

As follow, the images were acquired in oblique plane at 35° and the isotropies images from the 100 volunteers were reconstructed in the same image plane. The accuracy of image detection was obtained directly in the oblique plane at 35° and compared with the reconstructed images accuracy. This comparison was also accomplished with the simulated images using the C contingency test.

After validating the model, simulations were performed considering the oblique image plane at 36°, 37°, 38°, 39°, 40°, 41°, 42°, and 45°. The accuracy of detection was calculated to determine the best technique.

To test the method, reconstructions of the 100 volumetric isotropic images were performed in the oblique transversal plane at 38°, which was considered to be the most efficient by the simulator, and at the 45° angle used by many clinics. These images, without technical information, were evaluated at work stations by 2 Radiology Technicians specialized in Magnetic Resonance of the musculoskeletal system. The examiners analyzed the images and, in consensus, evaluated which images visualized the entire length of the CFL.

An analysis of agreement of the accuracy obtained across the various techniques was performed, both of the reconstructed images and of the simulations using the C contingency test. The reports from the doctors of the Lumen Diagnostic Centre were considered to be the gold standard.

#### Image bank

The images were acquired using a 3D volumetric isotropic proton density (PD) weighted turbo spin echo (PDW-TSE) sequence without fat saturation in the sagittal plane (TR/TE, 1000/30 ms; turbo factor 20; field of view 150 mm; thickness of voxel cut size (0.5)^{3}; matrix 300 × 250; number of excitations 2; and acquisition time 3 minutes and 10 seconds) (Figure
1a,
1b,
1c,
1d). An Achieva Magnetic Resonance device (Philips Medical System; Cleveland, OH, USA) was used with a “Sense Ankle Foot” bobbin with 8 (eight) channels for the transmission and reception of signals.

The volunteers were positioned in the supine position with the arms extended along the body, and the sequences were performed with free breathing. During the exams, the position of the foot relative to the ankle was maintained at an angle of 90°, using immobilizers and special foams to maintain an anatomical position.The 3D sagittal volumetric images of the 100 volunteers permitted multiplanar reconstructions. For these reconstructions, the multiplanar reconstruction (MPR) commands were used, followed by the orientation of the oblique transversal plane and then the line setting function to select an angle of 35°, 38° and 45° (Figure
2).

#### Ethical approval

Before to start this research with the specific, this research project was approved by the Ethics Committee advice in Research involving humans at the University of Mogi das Cruzes (CAAE-0151.0.237.000-10, process CEP/UMC-157/2010).

All participants were informed about the aims, and methodology of the study, as well as about the privacy of research subjects and confidentiality of their personal information, and institutional affiliations of the researcher.

#### Determination of the CFL measurements

Images were used in the volumetric sagittal plane to measure the average angle, length, and width of the CFL of each volunteer.To measure the angle, using the “Line Setting” tool with angle option, a straight line was traced in each image in the sagittal plane, parallel to the horizontal flat surface, and another line was traced parallel to the plane of the ligament investigated (Figure
3). After this command, the angle between these lines was calculated using the tools of the MR device.To measure the width of the CFL, a line was traced in the widest region of the ligament obeying the anatomical plane. The MR system tools permitted tracing and calculating the CFL width in mm (Figure
4).To measure the length of the CFL, the distal point of origin of the fibula and the point of insertion of the ligament on the calcaneus were marked. The value of the length between these two points was calculated using the MR device system tools (Figure
5).

#### Model for the simulation of the positioning of the CFL

The programming and graphic development module of MatLab® was used to simulate the limits of complete visualization of the calcaneofibular ligament (CFL) as a function of the angle of the image plane.The variable dimensions (length, width, and angle) are input into the model by the user. The application considers the CFL as a rectangle represented by continuous red lines. Initially, the central axis of the rectangle is aligned with the image plane, represented by a dotted blue line (Figure
6). The rectangle is rotated until its upper vertex coincides with the image plane, thus determining the maximum angular variation (β) that permits complete visualization of the CFL. The application indicates whether there was complete visualization for the CFL angle and the image plane angle, considering the width and the length of the ligament.

The image plane begins to be traced at the origin of the Cartesian system and ends at the coordinate X_{F} = 50 (the value chosen for graphical representation), with Y_{F} depending on the angular coefficient of the line (equation 1) that represents the image plane:

{\mathrm{Y}}_{\mathrm{F}}={\mathrm{X}}_{\mathrm{F}}*\mathrm{tangent}\left(\mathrm{\alpha}\right)

(1)

where: *α* = angle of the image plane.The dimensions of the rectangle (Figure
7) that represents the CFL are given by the following relationships:

{\mathrm{M}}_{\mathrm{X}}={\mathrm{X}}_{1}+\frac{\mathrm{length}}{2}

{\mathrm{X}}_{2}={\mathrm{X}}_{1}+\mathrm{lenght}

{\mathrm{M}}_{\mathrm{Y}}={\mathrm{M}}_{\mathrm{X}}\times tan\mathrm{\beta}

{\mathrm{Y}}_{1}={\mathrm{M}}_{\mathrm{Y}}-\frac{\mathrm{width}}{2}

{\mathrm{Y}}_{2}={\mathrm{Y}}_{1}+\mathrm{width}

The rectangle is rotated around the central point (M_{X}, M_{Y}) until it achieves the biometric position provided by the user. The matrix of rotation M is given by equation 9.

M=\left[\begin{array}{cc}\hfill cos\left(\beta \right)\hfill & \hfill -sen\left(\beta \right)\hfill \\ \hfill sen\left(\beta \right)\hfill & \hfill cos\left(\beta \right)\hfill \end{array}\right]

(9)

where: β = angle of maximum rotation of the CFL that permits complete visualization.

The “Processing” menu allows the user to choose the direction (clockwise or counter clockwise) of rotation of the CFL as a function of the image plane. The application calculates the new coordinates as a function of the ordinate axis (Y_{rot}), using equation 10.

{\mathrm{Y}}_{\mathrm{rot}}={\mathrm{M}}_{\mathrm{X}}*\mathrm{tangent}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{\beta}\right)

(10)

From Y_{rot}, it is possible to represent a right triangle from the center of the rectangle to Y_{rot}. Based on the right triangle, the hypotenuse and the opposite side can be calculated, and thus the angle of maximum rotation (clockwise and counter clockwise) of the representation of the CFL can be found. The expressions used in this phase are equations 11 and 12.

\mathrm{Hypotenuse}=\sqrt{{\left({\mathrm{M}}_{\mathrm{X}}-{\mathrm{X}}_{2}\right)}^{2}+{\left({\mathrm{M}}_{\mathrm{rot}}-{\mathrm{Y}}_{2}\right)}^{2}}

(11)

\mathrm{Opposite}\phantom{\rule{0.25em}{0ex}}\mathrm{side}={\mathrm{Y}}_{\mathrm{rot}}-{\mathrm{Y}}_{2}

(12)

As a result, the simulator shows the representation of the CFL (width and length), the angle of the image plane (α), the angle of the CFL (γ), the maximum angular variation as a function of the image plane (β), and whether complete visualization of this ligament occurred, as shown in Figure
8.

Another characteristic of the developed tool is the possibility of exporting the input and output data to a MS Excel® spreadsheet. This application also permits the printing of the graphical controls in conjunction with the data panels.