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)
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.
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).
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:
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:
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.
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.
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 |
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.
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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