JOURNAL OF PHYSIOLOGY AND PHARMACOLOGY 2009, 60, Suppl 8, 65-68
www.jpp.krakow.pl
C. DUMONT1, R. PERPLIES2, J. DOERNER2, J. FANGHAENEL3, D. KUBEIN-MEESENBURG2,
M.M. WACHOWSKI1, H. NAEGERL2
MECHANISMS OF CIRCUMDUCTION AND AXIAL ROTATION
OF THE CARPOMETACARPAL JOINT OF THE THUMB
1Department of Trauma Surgery, Plastic and Reconstructive Surgery, University of Goettingen, Germany; 2Department
of Orthodontics, University of Goettingen, Germany; 3Department of Orthodontics, Preventive and Pediatric Dentistry,
Ernst-Moritz-Arndt University Greifswald, Germany
Osteoarthritis of the carpometacarpal joint of the thumb (CMCJ) is a frequent clinical problem. The aim of the study
was to discuss the mechanisms of circumduction and axial rotation of the CMCJ considering geometrical properties of
the articulating surfaces and the configuration of the muscle system acting over the CMCJ. 28 CMCJ from 7 female and
7 male corpses (age: 81 yrs (median), 53-91 yrs (interval), which did not show any sign of arthrosis, were investigated.
Contours in flexion/extension: in saddle point O, the contour of the proximal surface is stronger curved. For 23 of the
28 joints the contours showed an eye-catching difference. Contours in ab-/adduction: all 28 joints showed the respective
incongruity. Straight lines and their included angles: in both articulating surfaces, the angles between the straight lines
through the saddle point showed values which were close to 90°. Out of neutral position a small axial rotation (maximal
range: 3.5°) is possible without that the contact at the saddle points is changed. But, when one of the straight lines of the
proximal surface meets a respective straight line of the distal surface, the contact "point" is enlarged to a contact "line".
When the axial rotation is further increased, the contact "line" splits into two contacts "points", which are located at outer
areas of the articulating surfaces.
K e y w o r d s : osteoarthritis, saddle joint - physiological function, saddle point, circumduction, carpometacarpal joint
INTRODUCTION
Osteoarthritis (OA) of the carpometacarpal joint of the
thumb (CMCJ) is a frequent clinical problem and is present in
radiographs with a prevalence of about 33% in postmenopausal
women (1). This large prevalence of osteoarthritis (OA) is
attributed to the high contact pressures exposing the cartilage of
the CMCJ (2-6).
Anatomical findings
In the carpometacarpal joint (CMCJ) both articulating
surfaces are shaped like saddles (7-9). Under compressive joint
loads this unique geometric form is said to allow only small
contact areas between the articulating surfaces.
In ab/adduction the concavely shaped surface of the
trapezium articulates with the convexly shaped surface of the os
metacarpale I, but in flexion/extension, the now convexly shaped
trapezium with the now concavely shaped os metacarpale.
Incongruent curvatures of both surfaces were described at the
sides of ab- and adduction where joint spaces were found (9, 10)
partly filled with synovial foldings. In flexion/extension, the
articulating surfaces were said to be congruent (9). Surveying of
both articulating surfaces by stereophotogrammetry (SPG) and
approximation of the data of each surface by a single parametric
biquintic function revealed that the differences between both
empirical functions suggested a common incongruence of both
articulating surfaces (11).
Common geometric properties of saddle surfaces
At the saddle point the surface can be sectioned by two
planes which are perpendicular to each other so that (A). the
cutting edge of the planes coincides with the normal in the
saddle point, and (B). one line of intersection (k(z,x)) is
extremely concave and the other (k(y,z)) extremely convexa. At
all other points of the saddle the respective extreme curvatures
would be smaller. For the geometrical description it is
advantageous to take this main saddle point O as the origin of the
co-ordinate system, the normal in O as the z- axis, and the
direction of the extreme curvatures as y- or x-axis (Fig. 1). Other
planes which run through O and the z-axis produce lines of
intersection whose curvatures in O are between the curvatures of
the curves k(z,x) and k(y,z). Since the one curve is extreme
convex and the other extreme concave there are necessarily two
straight lines (curvature= 0) among the intersection lines. These
straight lines at the saddle point O can easily be located by
applying a straightedge to the saddle surface. The angle ρ
between both straight lines represents an important geometric
quantity to characterize a saddle surface.
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significance reached the 0.01 level. Hence, the centre of
curvature Mfp of the proximal contour lies more distal than that
of the distal surface (Mfd).
2. Contours in ab-/adduction
All 28 joints showed the respective incongruity (Fig. 2b).
The centres of curvature of the proximal surfaces were more
distal positioned than those of the distal surfaces.
3. Straight lines and their included angles
In both articulating surfaces, the angles between the straight
lines through the saddle point showed values which were close
to 90° (Table 1).
Table 1. The angles (ρp, ρd) were measured in the sector which
included the contour line of ab-/adduction.
Fig.1. Properties of saddle surfaces illustrated by the proximal
articulating surface in the CMCJ. k(z,x) = concave contour in the
plane of ab-/adduction: Rap = respective radius of curvature at the
saddle point O, Map = corresponding center of curvature. k(y,z) =
convex contour in the plane of flexion/extension: Rfp = respective
radius of curvature at the saddle point O, Mfp = corresponding
center of curvature. p1, p2 respective straight lines of the saddle
surface through the saddle point O. More details in the text.
Aims of the investigations
To discuss the mechanisms of circumduction and axial
rotation of the CMCJ considering geometrical properties of the
articulating surfaces and the configuration of the muscle system
acting over the CMCJ.
EVALUATION OF GEOMETRIC RELATIONS BETWEEN
THE TWO ARTICULATING SURFACES
Method
28 CMCJ from 7 female and 7 male corpses (age: 81 yrs
(median), 53-91 yrs (interval), which did not show any sign of
arthrosis, were investigated. They were preserved by a solution,
which largely keeps the articular and osseous structures relating to
stiffness and hardness (12) so that accurate-scale replicas could be
produced. The respective casts were sectioned in ab-/adduction and
in flexion/extension through the saddle point O in order to produce
the extremely curved contours k(z,x) and k(y,z). The two straight
lines in the saddle surfaces were sought out using a straightedge on
the plaster casts. The angles in between were measured.
Results
A common incongruity of both saddle surfaces could be
demonstrated also for the case that they contact each other in the
saddle points (neutral position, Fig. 2).
1. Contours in flexion/extension
In saddle point O, the contour of the proximal surface is
stronger curved (Fig. 2a): For 23 of the 28 joints the contours
showed an eye-catching difference, for five joints the
difference could not be resolved. Altogether the statistical
articulating surface
proximal
distal
variable
ρp/deg
ρd/deg
mean
86.6
90.1
SD
3.1
2.5
min
82.0
86.0
max
98.0
96.0
Nevertheless, the difference ∆ρ = (ρp-ρd) was clearly
significant (Student-test: ∆ρmean = -3.5°; SD=2.7°; t-value -6.72;
df=27; p<0.0001).
DISCUSSION
In guiding the joint motion the two articulating surfaces of
a diarthrose have biomechanically equal rights (13-15). Hence
out of neutral position, initial rotations can be performed around
the morphological defined center of curvature Mfd or Mfp or
simultaneously around both (flexion/extension, Fig. 2a), or
around the two centers (Mad, Map, Fig. 3b) of ab-/adduction.
These 4 kinematical degrees of freedom (4 DOF) are controlled
by eight muscles (4 muscles for flexion/extension and 4
muscles for ab-/adduction). Out of neutral position, a small
axial rotation is at first possible without that the contact at the
saddle points is changed (Fig. 3c), since the angles between the
straight lines of the saddle joints do not fit. Therefore, the
CMCJ has five as shown by the metacarpalphalangeal joint
(MCPJ) (15).
Muscular stabilization of axial rotation
In contrast to the MCPJ, in the CMCJ axial rotation can be
effectively stabilized by the muscular system. At first, out of
neutral position a small axial rotation (maximal range: 3.5°) is
possible without that the contact at the saddle points is changed
(Fig. 2c). But, when one of the straight lines of the proximal
surface meets a respective straight line of the distal surface, the
contact "point" is enlarged to a contact "line". When the axial
rotation is further increased, the contact "line" splits into two
contacts "points", which are located at outer areas of the
articulating surfaces. Thus the two bones (the trapezium and the
metacarpal bone) spiral apart and produce a dehiscence in the
center of the joint. Compressive joint forces in the two contacts,
which are produced by any combination of the 8 muscles,
counteract this dehiscence by producing an increasing
counteracting torque. This torque hinders further axial rotation
and/or spirals the joint back. Result: in the CMCJ axial rotation
can be essentially stabilized by the muscular apparatus in a
simple way: the muscles have to produce only a compressive
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Fig. 2. Contours of intersections through the CMCJ in
neutral position: the two articulating surfaces contact in
their main saddle points. a) y,z-plane = section plane of
flexion/extension; b) x,z-plane = section plane of ab/adduction; c) x,y-plane = section plane through the
straight lines of the proximal surface (p1, p2) and the
distal surface (d1, d2) running through the respective
saddle point. Full lines: contours of the distal
articulating surface. Dotted lines: contours of the
proximal articulating surface. The contours are true in
scale corresponding to the statistical mean. cv = convex,
cc = concave contours. Mfp, Mfd, Map, Mad = centres of
curvature of the respective contours in the saddle
points; Rfp, Rfd, Rap, Rad = respective radii of curvature.
Fig. 3. To the mechanism of circumduction. See details
in the text.
resultant force. This theory of stabilization mechanism of axial
rotation corresponds to the report of Cooney and Chao (16) that
the axial rotation in the CMCJ is always small under loads
during hand functions.
Circumduction
In vivo the musculature is able to guide the extended thumb
along a cone whose apex seems to lie in the CMCJ. In the course
of this motion the metacarpal bone does not rotate around its
long axis (no axial rotation). For that ab-/adduction und
flexion/extension have to occur simultaneously in an alternating
manner. Because ab-/adductions can be produced by rotations
around two independent axes (Mad, Map), it is possible that the
resulting instantaneous axis of ab-/adduction (IRAa) runs
through the common saddle point O (Fig. 3a). The same
procedure is possible in flexion (instantaneous axis: IRAf). In
both cases the angular velocities ω ij of the respective rotations
must then show distinct relations which are described by the
following formulae:
ω ap
Rad
ω fp
Rfd
ab-/adduction: - ____ = ____ ; flexion/extension: - ____ = ____
ω ad
Rap
ω fd
Rfp
The two instantaneous axes of ab-/adduction and
flexion/extension compose then to a resulting instantaneous axis
IRAres (Fig. 3b). The instantaneous motion is given by vector
addition of the vectors angular velocities:
ω f = ω f · ex and ω a = ω a · ey: ω res = ω a + ω f
When the 8 muscles operate in such a way that they accelerate
the metacarpal bone always perpendicularly to the vector of the
resulting angular velocity ω res, the resulting instantaneous axis
IRAres pivots around the saddle point O. The articulating surfaces
move in a rolling manner. In the simplest case the angular
velocities of ab-/adduction ω a and of flexion/extension ω f alternate
in phase-delayed harmonic time functions. Then the long axis of
the metacarpal bone moves on a cone-shaped shell without that
the bone carries out a rotation around its long axis. Precondition
for this mechanism is that the 8 muscles independently alter tonus
and length what physiologically possible as shown by many
investigations (17-23).
Note: Since the musculature, which stimulates the
circumduction, necessarily produces a compressive force, axial
rotation is stabilised and does hardly appear together with
circumduction.
Conflict of interests: None declared.
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R e c e i v e d : October 22, 2009
A c c e p t e d : December 18, 2009
Author's address: Prof. Dr. D. Kubein-Meesenburg,
Department of Orthodontics, University of Göttingen, Robert
Koch Str. 40, D-37099 Göttingen, Germany; E-mail:
[email protected]