Computerized Assessment of Excessive Femoral and Tibial Torsional Deformation by 3D Anatomical Landmarks Referencing K. Subburaj1, B. Ravi1 and M.G. Agarwal2 1
OrthoCAD Network Research Centre, Indian Institute of Technology Bombay, Mumbai, India 2 Department of Surgical Oncology, Tata Memorial Hospital, Mumbai, India
Abstract — Bone torsional deformity is excessive anatomical or axial twist of proximal portion with respect to distal. Accurate, simple, and quick measurement of torsional deformities at preoperative stage is clinically important for decision making in prosthesis design and surgery planning. Commonly used 2D methods for assessing excessive torsion use radiographic images or a set of slices of CT/MR images. The slices representing reference axes of distal and proximal portion are superimposed; the angle between the axes provides a measure of torsion. Representing 3D anatomical landmarks and reference axes in a 2D transverse slice or projected radiographic image leads to inaccurate and inconsistent values. Owing to the complex 3D shape of bones (ex. femur and tibia), there is a need for 3D model based assessment methods with little or no human intervention. Excessive torsion in the tibia and femur affects the procedure of total knee replacement. We present an automated methodology for assessing excessive torsional deformation of femur and tibia bone based on 3D anatomical landmarks based referencing. Reconstructed 3D bone model from a set of CT scan images using tissue segmentation and surface fitting is used in this methodology. Anatomical landmarks on femur and tibia bone are automatically identified based their shape and predefined landmarks spatial adjacency matrix. The identified 3D anatomical landmarks and computed functional and reference axes (femur: neck axis, condylar axis, and long axis; tibia: tibial plateau axis, long axis, and malleolus axis) are used for measuring torsional deformation, using 3D shape reasoning algorithms. The methodology has been implemented in a software program and tested on five sets of CT scan images of lower limb. The computerized methodology is found to be fast and efficient, with reproducible results. Keywords — anatomical landmarks, femoral torsion, tibial torsion, torsional deformities, virtual surgery planning
I. INTRODUCTION Anatomically deformed femur and tibia (secondary to trauma, congenital defects, prior surgery, etc) give significant challenges to orthopaedic surgeons [1]. This also changes the loading pattern [2] owing to the altered functional axes and distorted anatomic landmarks. Bone torsional deformity can be defined as the excessive anatomical or axial twist of proximal portion with respect to distal one. In case of femur (F), it is a projected angle of femur neck
axis and femur condylar line on a plane, which is perpendicular to the longitudinal axis of the bone. This is measured as femoral anteversion or retroversion according to nature of the twist. In tibial bone, tibial torsion is measured as twist of the tibial plateau axis with respect to distal tibia malleolus line. Torsional deformation has been studied, both in vivo and in dry bone, using a variety of techniques by various researchers. This leads to a wide range of reported femoral and tibial torsion values. The most accurate technique of assessment is by measuring the angle formed by the pins inserted in bone to represent the axes required to measure. However, this method cannot be used in vivo. The next best methods are based on diagnostic medical images, which give a good representation of the underlying anatomy [3]. In image based (2D) studies, various sources of images are used such as x-ray [4], ultrasonic [5], CT [6,7,3], and MRI [8]. In 3D studies, Kim et al [7] studied the femoral anteversion on a set of dry bones using CT data. The fundamental axes (neck axis, long axis, and condylar line) are estimated semi-automatically from the extracted edge coordinates. Liu et al [9] used interactively located landmarks on a digitized model for tibial torsion assessment. In summary, estimating deformities is important in anatomical understanding for performing virtual surgery planning. 2D methods of measuring torsion using images suffer from inherited issues in various stages, such as (i) orientation of patient (ii) inexact abduction, flexion, and rotation of hip while scanning, (iii) selecting reliable 3D anatomical landmarks, and (iv) choosing best slice representing reference axis. It is difficult to estimate and represent complex 3D reference axes in a x-ray image or CT slice. There is a poor consensus concerning the optimal techniques for their clinical assessment [10]. Researchers have used varieties of axes and reference landmarks in measuring torsion with no established standard in defining them. None of the available methods are suitable for automatic assessment of anatomical deformations. Owing to the complex 3D shape of bones, there is a need for a 3D assessment method, which is simple, reliable, robust, and suitable for use in busy clinical environment.
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II. MATERIALS AND METHODS A. Computerized Methodology Our objective is to accurately measure the torsional deformation of long bones of the lower limb. Each step of the proposed methodology is as follows:
Condylar line of the tibia (CLT) is defined as a line connecting MP and LP landmarks on the tibial plateau. Malleolus Line (TML): A line connecting medial malleoli (MM) on tibia and lateral malleoli (LM) on fibula.
Algorithm: Assessment of torsional deformities Input: A set of CT scan images of the lower limb Output: Torsional deformation of the long bones Procedure: Step 1: Reconstruct 3D bone models from CT images Step 2: Identify the required anatomical landmarks Step 3: Compute medial axis of the long bones Step 4: Segment the medial axis for computing axes Step 5: Compute reference axes from the landmarks Step 6: Measure torsional deformation by reference axes The reference axes and centers which are needed to assess the torsional deformation are given in table 1. Table 1 Reference axes Axis
Terms
Axis
Terms
FNA Femoral Neck Axis
TML Tibial Malleolus Line
CLF Condylar Line of Femur
CLT
Condylar Line of Tibia
LAF Longitudinal Axis of Femur
LAF
Longitudinal Axis of Tibia
B. Reference Axes Anatomical Landmarks: The required anatomical landmarks (Fig. 1) in computing reference axes include, on femur bone: medial and lateral epicondyles (ME and LE), most distal point of each (medial and lateral) condyle (MC and LC), and greater and lesser tronchater (GT and LT); on tibia bone: medial and lateral intercondylar tubercles (spines) (MT and LT), most medial and lateral points of tibial plateau (MP and LP), and medial and lateral malleolus (MM and LM). Anatomical landmarks are localized and identified based on their intrinsic geometric characteristics and spatial-adjacency (Fig. 4). It employs curvature derivatives (curvature gradient, peaks, ridges, pits, and ravines), as well as topology (relative position) of identified landmark regions [12]. Centre of the Femur Head (CFH): The femur head is approximated into sphere from a set of profiles of the cortical bone extracted from CT images. These edge profiles are approximated to circular shape before used as a reference for fitting the sphere. Centre of sphere referred as the centre femur head. Condylar Lines: Condylar line of the femur (CLF) is defined as a connecting line between MC and LC landmarks.
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Fig. 1 Required anatomical landmarks on (a) proximal femur, (b) distal femur, (c) proximal tibia, and (d) distal tibia
Longitudinal or Anatomical Axis: This axis passes through the middle of the bone structure rather than connecting only end points. To compute LAF, we used medial axis [12] of middle long portion (5/8) of the femur. The steps are Step 1: Orient and divide the femur model into sections Step 3: Compute medial axis for each section Step 4: Collect the medial points of the long section Step 5: Fit a best curve for localizing the axis The same procedure is applied for computing longitudinal axis of tibia (LAT) also. Femoral Neck Axis: Medial axis of the top division (1/4) of the femur is used to establish the femoral neck axis (FNA). This is carried out by identifying a junction in medial axis. C. Measurement of Torsional Deformation Femoral Torsion: Three reference axes (FNA, CLF, and LAF) are required in computing femoral torsion. Due to the complex orientation, FNA and CLF are projected on a plane perpendicular to the LAF. The angle formed between these projected lines measured as femoral torsional angle (Fig. 2).
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were imported in DICOM format, followed by filtering and bony tissue segmentation; the 3D bone surface model is reconstructed in a lab-built 3D reconstruction software program. The reconstructed model's accuracy range with respect to the original model was 0.65 to1.95 mm [11] Anatomical landmarks are identified on this triangulated surface model before dividing it for medial axis computation. Both landmarks (Fig. 4) and medial axis (Fig. 5) are used in establishing reference axes as explained in section II-B. Since the identified landmarks are on bone rather on body surface, errors caused by skin movement and patient’s position during data acquisition are minimized. Each anatomical landmarks is referred in terms of the relative coordinates with respect to the coordinate system established for the corresponding bone. The anatomical landmarks are identified with the accuracy range of 2 to 6 mm [12]. Once the reference axes are established, measurement of torsional deformation is carried out as per the methods de-
Fig. 2 Method of measuring femoral torsion Tibial Torsion: Three reference axes (CLT, TML and LAT) are required in computing tibial torsion. TML and CLT are projected on a plane perpendicular to the LAT. The angle formed between these projected lines is measured as tibial torsional angle (Fig. 3).
Fig. 4 Identified anatomical landmarks of femur and tibia bone
Fig. 3 Method of measuring tibial torsion III. IMPLEMENTATION AND RESULTS The results are presented here for a knee reconstructed from a set of 496 CT scan image slices (pixel size was 0.782 mm and slice thickness was 2 mm). The CT images
Fig. 5 Medial axis for reference axis (a) complete model, (b) for determining femur neck axis, and (c) for longitudinal axis of the femur
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scribed in section II-C. Figure 6a and 6b show the measurement of the femoral and tibial torsion with reference axes and landmarks respectively. The measured femoral torsion was 12.80 (anteversion) and tibial torsion was 22.120.
Further work includes verification of reproducibility and accuracy with more data. We plan to use the measured deformation values in virtual surgery planning of total knee replacement and implant fixation analysis.
ACKNOWLEDGMENT This work is a part of an ongoing project in OrthoCAD Network Research Centre at IIT Bombay in collaboration with Non-Ferrous Materials Technology Development Centre, Hyderabad and Tata Memorial Hospital, Mumbai, supported by the Office of the Principal Scientific Adviser to the Government of India, New Delhi.
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Fig. 6 Measurement of femoral and tibial torsion
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Three sets of CT scan images were used in verifying the effectiveness of the proposed methodology. The measured femoral and torsional deformation angle are verified with respect to the angle obtained by manually placed reference axes on the same 3D reconstructed bone models. The deviation observed in femoral torsion was 1.980 to 3.130 and in tibial torsion was 2.120 to 2.890. Even though the sample lot is low in numbers to establish the relations, the results and accuracy obtained establish the superiority of the 3D based approach.
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IV. CONCLUSIONS
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This article presents a new methodology for assessing torsional deformities of long bones (femur and tibia) of the lower limb. The method ensures repeatability by the characterized anatomical landmarks (bone) and established reference axes (medial axis and landmarks referencing). The method offers automated, fast, and non-invasive measurement of torsional deformation. It works well where nonimaging methods (laser scanning and palpation) do not work; when anatomical landmarks are on bone rather on body surface. For example on obese patients, the required anatomical landmarks on legs are often not distinguishable from the surrounding subcutaneous fat.
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Dr. Bhallamudi Ravi Indian Institute of Technology Bombay Powai Mumbai India
[email protected]
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