This study was supported by a NATO-Science Fellowhip awarded by the Netherlands Organisation for Scientific Research (NWO) and by NIH grants HD07447 and AR41171.
 

Abstract - To determine the three-dimensional positions and orientations of axes of rotation for elbow flexion and forearm pro-supination, the flexion-extension and pro-supination movements were measured for five arms. Four right and one left arm were taken from four fresh cadavers. Movement was measured with an electromagnetic tracking system. Axes were found to be almost perpendicular (88.9 ± 5.1°) and crossed at 3.3 ± 0.8 mm. It is suggested that arm movements can be modelled with a two Degree-Of-Freedom model.

Biomechanical modelling of the upper extremity can play an important role in understanding the causes of upper extremity disorders and the corresponding treatment. Also, a biomechanical model can be used to get insight into more fundamental issues on motor control. Recently, a three-dimensional (3-D) model of the shoulder has been developed [1]. This model is based on morphological data that were collected in an extensive cadaver study [2]. However, this study did not embrace data for extension of the model to the elbow and the elbow function had to be modelled with a three Degree-of-Freedom (DOF) joint [1]. To improve the range of the model and allow for more accurate modelling of the function of the bi-articular arm muscles, the addition of a morphologically more realistic description of the arm was judged to be necessary. Since previous studies generally reported qualitative descriptions of elbow flexion axes [3,4,5,6] and forearm pro-supination axes [3,4,7], those data were not available from the literature. The aim of this project was to collect quantitative information on the 3-D orientations of rotation axes in the elbow and forearm.

Five upper extremities were harvested from four fresh specimen at the level of the scapula (four right, one left). Subsequently, the extremities were fastened onto a measuring table such that the scapula was fixed and the arm was fully free to move. Following fixation of 3-D electromagnetic sensors (Isotrack, Polhemus) on scapula, humerus, ulna and radius, the positions of local anatomical landmarks were digitized with an extra sensor, mounted with a stylus. The anatomical landmarks were at a later stage used for the definition of local orientation axes. Subsequently, each arm was moved through a selection of standard directions (elbow flexion-extension, forearm pro-supination and glenohumeral movements), during which the positions and orientations of each sensor were collected. A typical movement consisted of two cycles in which a joint was moved through its full range of motion. The sampling period was 15 seconds with a sampling frequency of Fs=10Hz.

Sensor data were used to determine the rotation axes for elbow flexion and pro/supination of the forearm. Estimations of the rotation axes were based on the Instantaneous Helical Axes (IHA) algorithms [8]. Prior to calculation of the instantaneous helical axes, for each sensor the position and angle time series were filtered with a cut-off frequency of 1.5 Hz. The angular velocity of each sensor was calculated using the method described by Woltring [9]. The Instantaneous Helical Axis was calculated for each time sample where the angular velocity of the distal segment, relative to the proximal segment was larger than 0.25 rad.s -1. To determine a mean helical axis and pivot, the optimal pivot point was calculated as sopt, as the mean 'pivot', closest to all Instantaneous Helical Axes in a least-squared sense [3]:

(1) where: , and  (2)

v = unit direction vector;

s = projection of the sensor origin onto the IHA.

Fig. 1 Typical example for IHA calculations for elbow flexion, represented in the measurement co-ordinate system. The X-Z plane roughly corresponds with the frontal plane. IHA are drawn with a length of 2 cm. Dots are data samples from the surfaces of humerus, ulna and radius. The two asterisks, connected with a dashed line, form the line EL-EM.

Fig. 2 Typical example for IHA calculations for forearm pronation, represented in the measurement co-ordinate system. The X-Z plane roughly corresponds with the frontal plane. IHA are drawn with a length of 2 cm. Dots are data samples from the surfaces of humerus, ulna and radius. The two asterisks, connected with a dashed line, form the line EL-US.

Analogous to the position vector, the optimal direction vector vopt wascalculated as the vector with the smallest angle between axes. For each specimen, these axes were subsequently expressed relative to a local co-ordinate system with its origin in the Epicondylus Medialis (EM) and its X-axis in the direction of the Epicondylu Lateralis (EL), and processus styloideus ulnaris (US) in the X-Y plane.

To allow for calculation of a mean axis over all five specimen, each arm was mathematically set in a theoretical anatomical position in which the long axes of the humerus and ulna both lie within the same plane, perpendicular to the elbow axis.. This position was obtained through a rotation of the humerus around the individual elbow axes, to the same plane as the ulna (Z=0). In this position, the elbow flexion angle is zero. The rotation to the theoretical anatomical positions was performed on all landmarks on the humerus: the Acromion (AC), EL and EM.

Figures 1 and 2 illustrate the helical axes as determined for elbow flexion and forearm pronation. The data are plotted in the measuring

co-ordinate system. IHA calculations showed fluctuations in position, but not as much in orientation. The mean smallest distances between the IHA axes and the optimal axes were generally well below 1 cm, while the mean absolute angle stayed below 2.6° (Table 1).

The individual optimal axes for flexion-extension and pro-supination are given in Table 1. These axes are expressed in the local ulnar system with the origin in EM and the local X-axis in the direction of EL, but with the arm in the originally measured (anatomical) position. In this position, the arm is in approximately 17.5° flexion. From the calculated error in Table 1, it can be seen that the pronation of the forearm appears to take place around a tighter axis than for elbow flexion. The kinematic flexion-extension axes deviate 6.0±2.6° from the axes through EM and EL. The pro-supination axis crosses the flexion-extension axis at 3.3 ± 0.8 mm and an angle of 88.9 ± 5.1°. This axis runs through the radial head and lies close to the anatomical landmarks EL (13.1±2.2 mm) and US (8.0±4.5 mm). The average distance to the center of the radial head was found to be 3.2±4.0 mm.

The mean elbow flexion-extension and forearm pro-supination axes have also been determined in the (theoretical) anatomical position where the elbow flexion angle is zero. Table 2 contains the average data for all five specimen. The data associated with the humerus (EL, AC, Huhe) have mathematically been transformed to a position in which the elbow angle is zero, which is the theoretical anatomical position. The data for AC and the estimated center of the humeral head indicate that the orientations of the humerus relative to the ulna was relatively constant over the five specimen. Obviously, this procedure still results in differences in position for the landmarks on humerus and ulna, since the specimen differ in build and in segment orientation.

The findings of this study confirm that the elbow-forearm complex can be modelled as a two DOF system. The orientations of the estimated elbow axes confirm previous qualitative observations that describe a flexion-extension axis as running through the centre of the trochlea and the capitulum humeri [3,4,5,6]. Also, the pro-supination axes measured in this study confirmed earlier descriptions [3,4,7] on an orientation of that axis through the center of the radial head and the most distal point on the ulna (which is approximated by US).

The results of this study are being implemented in a model of the shoulder and arm. First results indicate a good fit between in-vivo measured arm movements during wheelchair propulsion and kinematic model simulations.

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