Overview of morphological parameters for modelling of the human shoulder and arm

The Mayo-study (1993-1997)

 

H.E.J. Veeger

 

 
 


(to overview of all available data)

 

Acknowledgments

This project was partially sponsored through a Nato Science fellowship for H.E.J. Veeger, awarded by the Netherlands Organisation for Scientific Research and by NIH grants HD07447 and AR41171.

These data have been made available for non-commercial use only. In any other case, previous contact with the authors is necessary. Any use of these data should be accompanied with proper reference to the source. It is suggested to use the following reference when referring to these data: Veeger HEJ., Yu B, An KN, Rozendal RH (1997) Parameters for modeling the arm. J. Biomechanics 30(6); 647-652.

The authors would also appreciate notification of the use of these data by e-mail (H_E_J_Veeger@fbw.vu.nl), which address can also be used for suggestions for improvement of these pages.


Abstract

To enable the development of a musculoskeletal model of the upper extremity, geometry parameters, as well as axes of rotation, were collected on four fresh specimens. Following the estimation of mass and moments of inertia on the basis of antrhopometric measurements, four right arms and one left arm were severed from the specimens, keeping the scapulohumeral region fully intact. After fixation of the scapula on a measuring table, electromagnetic sensors (Isotrack, Polhemus) were fixed onto the humerus, ulna and radius. Subsequently, each arm was moved in a selection of standard directions in the glenohumeral, humeroulnar and ulnoradial joint and movements of sensors were recorded. With the collected data, the mean axes of rotation for elbow flexion and for pronation, as well as the rotation center for the glenohumeral joint were estimated. In the following phase, the positions of all relevant attachment sites and structures were digitized, relative to their local sensor. Origins and insertions were calculated as either points or lines, in a global (anatomical) orientation. Also, a selection of muscle parameters was collected (length, mass, volume).
 


Table of contents (this document)

      1. Abstract
      2. Introduction
      3. Methods
      4. Data description
      5. Discussion
      6. References

 



 

Introduction

In a previous study (Veeger et al, 1991; Van der Helm et al, 1992), morphological parameters were collected for modelling of the shoulder mechanism. This study did not include the arm musculature that crosses the elbow or the orientation of the elbow flexion/extension axis. A recent survey on human musculotendinous parameters by Yamaguchi et al (1990) revealed that the literature on upper extremity parameters was far from complete. To extend the biomechanical model of the upper extremity as described earlier (Van der Helm, 1994) down to the wrist, a morphological study was undertaken that would generate the data necessary for such an extension.

The research project that is described here, comprised three major goals. These research goals were:

Methods

Five upper extremities (four right and one left arm) were taken from four fresh specimen. After the collection of descriptive antropometry for estimation of segment mass and moments of inertia on the intact specimens, the upper extremities severed from the thorax wall by disarticulation of the clavicle and cutting the thoracoscapular and thoracohumeral muscles and without removing the skin. This dissection thus left all scapulohumeral and more distal muscles intact. Special sensor seats had been developed to hold 3Space electromagnetic sensors. These seats were fixed on the spine of the scapula and the shafts humerus, ulna and radius, In doing so, it was tried to inflict a minimum of damage to the soft tissues. Following this, the exarticulated arms were mounted with the dorsal side of their scapulae and their spines against a perspex measuring board, such that the arm was free to abduct and ante/retroflex.


Position and Orientation data were collected with a magnetic position and orientation tracking system (3Space Isotrak System). The system setup used in this experiment, consisted out of the System Electronics Unit, a source and four sensors. According to manufacturer specifications, the magnetic tracking system has a static position accuracy of 6.4 mm RMS and an angular accuracy of 1.5° RMS, with position resolution of 3.3 mm an angular resolution of 0.7°;. The magnetic tracking system has been extensively tested for its usefulness in biomechanical analyses of human movement. It has been found to be quite accurate and easy to use (An et al, 1988). The 3Space System was used in two modes: as a static digitizer, to measure anatomical landmarks and insertion sites; and as a dynamic position recording system, to measure the relative movements of scapula, humerus, ulna and radius. In the latter mode, data were collected with a sample frequency of 10 Hz, and a maximum sample period of 15 seconds.

The data collection procedure consisted of four separate steps:
 

1. Measurement of reference positions.

For each specimen 3Space sensors were fixed onto the humerus, ulna and radius. To enable control on the fixation of the scapula, a sensor was also positioned on the scapular spine. After fixation of the scapula onto the measuring board, the relative orientations of the sensors were determined in the 'anatomical' position. In this position, the arm hung vertically downward, and the forearm was brought in the anatomical position, which for some of our specimen appeared to be the maximal supination position. Due to the fixation of the scapula to the measuring board, the scapula was in a position in which the scapular plane was oriented in the global Xg-Zg plane, with the spine of the scapula close to parallel to the Xg-axis.

 

2. Measurement of passive motion

Passive motion was also measured on the intact specimen, and consisted of a series of arm- and elbow movements along the main axes. Each motion was performed by the experimenter, and was thus a passive joint motion. As the experimenter moved the arm, the orientations and positions of sensors on all four segments were recorded with the 3Space system (Fs= 10Hz). Each data collection was repeated thrice. Recordings on the glenohumeral joint comprised ab/adduction, flexion/extension and endo/exorotation. For the humeroulnar and radioulnar joints recordings were made of elbow flexion and pro/supination. In addition, a set of combined movements were recorded, in which simultaneous rotations around all joint axes occurred.

 

3. Local measurement of origins, insertions and geometric shapes

Following dynamic recordings, all five specimen were dissected down to the separate segments. In doing so, muscles were taken off their insertions and joints were exarticulated. However, great care was taken to leave the sensor mounts untouched. On each segment (scapula, humerus, ulna and radius), all relevant anatomical landmarks, insertions and morphological shapes were digitised, relative to their own local sensor. These data, in combination with the data from phase 1, allow us to reconstruct the positions of the locally measured structures in the anatomical position. Table 1 is a listing of anatomical landmarks and their definitions, as measured on all specimens.
 

Table 1

Abbreviation

Definition of bony landmark

AC

Most cranial point on the acromioclavicular joint

AA

Angulus Acromialis

TS

Trigonum Spinae

AI

Angulus Inferior

EM

Epicondylus Medialis Humeri

EL

Epicondylus Lateralis Humeri

OL

Olecranon

US

Processus Styloideus Ulnae

RS

Processus Styloideus Radii

 

4. measurement of muscle characteristics

Each dissected muscle was weighed and its volume was determined. Muscle weight was determined with the muscle as much as possible cleaned from fat. Weighing was performed on a scale with an accuracy of 0.1 grams. Muscle volume was measured through the immersion method and could be performed with an accuracy of 1 ml. Tendons were included in the measuring process. Also determined were estimates for their tendon and belly lengths, as well as the fibre angles. These estimates had to be obtained directly on the dissection table, with the use of a slide measure and a goniometer.

Belly length was defined as the distance from the most proximal musculotendinous connection to the most distal one. When manifest, the proximal and distal tendon lengths were measured from the same musculotendinous connections to their relative attachments. Tendon diameter was estimated by measurement of the tendon circumference at the roundest part of the tendon. Fibre angles were found to be difficult to determine and are, for this reason, reported in 15° intervals.

For each specimen, the body dimensions necessary for the calculation on inertia parameters tor the upper arm, forearm and hand were measured. Segment mass, mass position was determined with the use of the regression equations published by Clauser et al (1969). The center of mass positions were defined relative to their proximal landmarks. Segment moments of inertia were determined based on the equations published by Hinrichs (1985), but could also be expressed based on Yeadon & Morlock (1989). The total inertia tensor is expressed as one moments of inertia about one of the transverse principal axes and a moment of inertia about the longitudinal principal axis of each segment.

Within the global reference system all landmarks, origins and insertions of muscles were expressed as a point or a line. The x-, y- and z-co-ordinates are expressed as functions of the variable t. The general relationship between x-, y- and z-coordinates is given as:

X= A(1)*t0+A(2)*t1

Y= B(1)*t0+B(2)*t1

Z= C(1)*t0+C(2)*t1

For all origins and insertions, the highest order for the t-value was chosen to be either zero or one. A zero-order polynomial thus represents a point, while a first order polynomial represents a line-shaped insertion-site. For each coordinate the parameters of the function were estimated separately, using a combined least squares criterion. See for an extensive description of this procedure Van der Helm et al (1992). The decision on the order of fit was based upon the estimated error. A mean error of more than 1 cm for the zero-order polynomial indicated the choice for a first-order fit. Higher order fits were decided to be impractical. Exception to this is the definition of the Bicipital Sulcus. The Sulcus was modelled as a second-order line. Other relevant morphological structures have been modelled as a sphere (Glenoid, Humeral Head) or a cylinder (ulna at the level of M. Pronator Quadratus, radius at the level of M. Biceps Brachii and M. Supinator). To estimate a minimum moment arm in extension for M. Brachialis and in flexion for M. Triceps, the elbow was modelled as a cylinder through the Trochlea Humeri. Analogous to previous publications (Van der Helm et al, 1992), data were fitted to the geometrical shapes with the use of an iterative Gauss-Newton method.

The data on passive joint movement that were collected in phase 2, were used for the calculation of joint rotation axes. Prior to the calculation of instantaneous helical axes, all position and angle data were filtered with a cut-off frequency of 1.5 Hz. For the angle data all elements of the orientation matrices were filtered. This avoided filtering errors due to sign changes as would have occurred when the Euler angles had been filtered. The angular velocity of the sensors was calculated following Woltring (1991). Linear velocity was calculated with the use of a five-point differentiating filter (Lees, 1980).

For the humeroulnar and radioulnar rotation axes, rotation axes were calculated with the use of the Instantaneous Helical Axis (IHA) algorithms as published by Woltring (1990). Followed by the calculation of a mean axis through the calculation of the pivot point a, described by Woltring (1990) and the optimal direction vector.
 

 

Discussion

The data in this study have been used for modelling of the upper extremity. As such, they are far from complete: not all upper-extremity muscles are included and neither are the data on the muscle-tendon complex. However, these data do also include 3-D information on the rotation axes for three joints. The data are thus thought to be a useful extension of the earlier published data (Veeger et al, 1991; Helm et al, 1992).

The data in this study can be used for the calculation of moment arms, but care should be taken to avoid calculation errors that would result from modelling the muscles as a straight-line, as has been stated by several authors (Fick, 1911; Amis et al, 1979; An et al, 1981). Calculation of the moment arm for M. Brachialis in full elbow extension would, for instance, lead to an extensor torque for that muscle. However, the data set given here, allow for correction by using the geometrical shapes for the definition of contact areas around which the relevant muscles are wrapped. In the example of the Brachialis, this contact area can be derived from the cylinder fit through the trochlea humeri. Also, from the cylindrical fit, it can be derived that the minimum moment arm for M. Brachialis will be equal to the estimated radius for that cylindrical fit. In specimen #4, the radius was for instance 1.33 cm.

For modelling purposes, the rotation centre of the humeral head has been positioned in the centre of a sphere, describing the glenoid (Van der Helm et al, 1989). This choice was based on the results of spherical fits through both humeral and scapular articular surfaces, as well as on earlier literature. Poppen & Walker (1976) described the centre of rotation as lying close to the centre of the humeral head. A recent comparison of the positions of the kinematic rotation centre and the midpoints of the spheres indicated only marginal and insignificant differences (Veeger et al (submitted)). See the Figure below.
 

The calculations of the axis of rotation for elbow flexion-extension has indicated that elbow flexion did not really occur around a very tight hinge joint. Although part of the deviation will be the consequence of the high sample frequency, and thus the small angular rotation intervals (Lange et al, 1990), the finding as such has also been described by Fick (1911) and Morrey & Chao (1976). Fick (1911), on the basis of data by Fischer (1885), described the mean elbow axis as a collection of axes that run through one central point, located in the centre of the capitulum humeri. When the movement of the axis was subsequently projected on a plane at the level of the medial epicondyle, the positions of its piercing point was shown to vary in the order of millimetres. However, the difference in movement direction between the two specimens studied, was considerable and no general displacement pattern of the axis could be found.

The helical axis estimations in this study indicated a tight axis of rotation for pro/supination. The axis appears to run through the radial head and the distal end of the ulna. For our five specimen the mean absolute distance between the estimated axis of rotation and the centre of the radial head was found to be 0.32 cm (range 0.19 - 0.99 cm). In a recent study on the axis of rotation of the forearm, Hollister et al (1994) demonstrated that the axis of rotation of the forearm is constant and independent of elbow position.

Although Physiological Cross Sectional Area (PCSA) is an important parameter for modelling, we originally chose not to include the estimated PCSA. Motivation for this is that different definitions are being used for PCSA. For example, PCSA has been measured directly on fresh specimen (Weber, 1851), directly on embalmed specimen (Veeger et al, 1991), embalmed on the basis of volume and muscle length (Basset, 1983; Wood et al, 1989), on volume and bundle length (Basset, 1983; Howell et al, 1986), or on the basis of Coons surfaces (Wood et al, 1989). The data in the anthropometry section allow for the calculation of PCSA with either the use of muscle volume, or muscle weight and muscle length. The, not extremely accurate, estimation of pennation also allows for the inclusion of this parameter (see Yamagushi et al, 1990). However, based on comments by the reviewers a table for the calculation of PCSA related to specimen #4 was added to the paper (Veeger et al, 1997).

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