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. 66 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 67 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). 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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]

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