To develop a useful surgical navigation system, accurate determination of bone coordinates and thorough understanding of the knee kinematics are important. In this study, we have verified our algorithm for determination of bone coordinates in a cadaver study using skeletal markers, and at the same time, we also attempted to obtain a better understanding of the knee kinematics. The research was performed at the Medical Simulation Center of Tzu Chi University. Optical measurement system (Polaris® Vicra®, Northern Digital Inc.) was used, and reflective skeletal markers were placed over the iliac crest, femur shaft, and tibia shaft of the same limb. Two methods were used to determine the hip center; one is by circumduction of the femur, assuming it pivoted at the hip center. The other method was to partially expose the head of femur through anterior hip arthrotomy, and to calculate the centre of head from the surface coordinates obtained with a probe. The coordinate system of femur was established by direct probing the bony landmarks of distal femur through arthrotomy of knee joint, including the medial and lateral epicondyle, and the Whiteside line. The tibial axis was determined by the centre of tibia plateau localised via direct probing, and the centre of ankle joint calculated by the midpoint between bilateral malleoli. Repeated passive flexion and extension of knee joint was performed, and the mechanical axis as well as the rotation axis were calculated during knee motion. A very small amount of motion was detected from the iliac crest, and all the data were adjusted at first. There was a discrepancy of about 16.7mm between the two methods in finding the hip centre, and the position found by the first method was located more proximally. When comparing the epicondylar axis to the rotation axis of the tibia around knee joint, there was a difference of 2.46 degrees. The total range of motion for the knee joint measured in this study was 0∼144 degrees. The mechanical axis was found changing in an exponential pattern from 0 degrees to undetermined at 90 degrees of flexion, and then returned to zero again. Taking the value of 5 degrees as an acceptable range of error, the calculated mechanical axis exceeded this value when knee flexion angle was between 60∼120 degrees. The discrepancy between the hip centres calculated from the two methods suggested that the pivoting point of the femur head during hip motion might not be at the center of femur head, and the former location seemed closer to the surface of head at the weight bearing site. Under such circumstances, the mechanical axis obtained through circumduction of the thigh might be 1∼2 degrees different from that obtained through the actual center of femur head. During knee flexion, the mechanical axis also changed gradually, and this could be due to laxity of knee joint, or due to intrinsic valgus/varus alignment. However, the value became unreliable when the knee was at a flexion angle of 60∼120 degrees, and this should be taken into account during navigation surgery.
Clinical assessment of elbow deformity in children at present is mainly based on physical examination and plain X-ray images, which may be inaccurate if the elbow is not in fully supination; furthermore, the rotational deformity is even harder to be determined by such methods. Morrey suggested that the axis of rotation of the elbow joint can be simplified to a single axis. Based on such assumption, we are proposing a method to assess elbow deformity using rotational axis of the joint, and an optimized calculation algorithm is presented. The rotation axis of elbow in respective to the upper arm can be obtained from the motion tract of markers placed at the forearm. Cadaver study was done, in which three skeletal motion trackers were placed over both the anterior aspect of humerus, as well as distal ulna. Osteotomy was created at the supracondylar region of humerus through lateral approach, and the bone fragments were stabilized with a set of external skeletal fixator, leaving the soft tissue intact. The amount of deformity was created manually by adjusting the position of the distal fragment via skeletal fixator. Ultrasound 3D motion tracking system from Zebris® was used in this study, and the program was developed under the Matlab environment. Cycles of passive elbow flexion/extension motion were carried out for each set of deformity. The data were initially transformed to humerus coordinate, and since the upper arm was not absolutely stationary, its influence on the measured position of ulna was adjusted. With this adjusted data, a best fit plane that would include most of the ulna positions ( Fresh frozen cadaver study was conducted in the Medical Simulation Center at Tzu-Chi University. After adjustment of the raw data to eliminate the influence of humerus motion, the ulna motion could be narrowed down from a band of 10mm to 3mm, with a significant smaller standard deviation. The rotation axis was obtained by the normal vector to the best fit plane. Two different approaches were attempted to find the plane. In the first method, the plane was obtained via least square method from the adjusted ulna positions, and the second method found the plane via RANSAC method. Calculations were repeated several times for each method, and the results showed a variation of 5 degrees in the first method and about 2 degrees in the second method. Rotational axis can be used to define the 3-dimensional deformity of elbow joint; however, it is difficult to obtain such axis accurately due to hypermobility and multi-directional motion of the shoulder joint. In this study, we have developed another method to assess the elbow deformity using motion analysis system instead of the conventional image studies, and this may be applicable clinically if the facility becomes more accessible in the future. (This research was supported by the project TCRD-TPE-99-30 granted by the Buddhist Tzu-Chi General Hospital, Taipei Branch).
