J. Biomechanics Vol. 25, No.6, pp. 591-607, 1992. Printed in Grea:t Britain
0021-9290/92 S5.00 +.00 Pergamon Press Ltd
CURVATURE CHARACTERISTICS AND CONGRUENCE OF THE THUMB CARPOMETACARPAL JOINT: DIFFERENCES BETWEEN FEMALE AND MALE JOINTS G. A. ATESHIAN,* M. P. ROSENWASSERt and V. C. Mowt *Department of Mechanical Engineering, Columbia University, New York, NY 10027, U.S.A., tDepartment of Orthopaedic Surgery, Columbia-Presbyterian Medical Center, New York, NY 10032, U.S.A. and tOrthopaedic Research Laboratory, Departments of Mechanical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10032, U.S.A. Abstract-Three-dimensional geometric models of the articular surfaces of the thumb carpometacarpal (CMC) joint were constructed using precise data obtained from stereophotogrammetry (SPG). It was demonstrated that by using a least-squares surface-fitting technique, the SPG data on the surface can accurately be described by a single parametric biquintic spline function. From this mathematical description, curvature maps of the surfaces were calculated for 13 CMC joints (eight females, average 64 yr old, five males, average 70 yr old). The surface geometry ofeach joint was analyzed, comparisons were made between trapezial and metacarpal surfaces of the joint and differences determined between males and females. With regard to joint surface areas, the female trapezium is significantly smaller than that of the metacarpal. The shape of the female trapezial surface is also fundamentally 'different from that of males. No gender-related difference exists regarding the shape of the metacarpal surface. Congruence of the two opposing articular surfaces was defined by their relative principal curvatures. From these definitions, congruence in the radioulnar and dorsovolar anatomic directions, as well as the global congruence of the joint, were calculated. Most CMC joints were found to be more congruent along the radioulnar direction than the dorsovolar direction and, globally, female joints were found to be less congruent than male joints. The concept ofjoint congruence has played a central role in a number of hypotheses relating to the etiology ofCMC joint osteoarthritis (OA), although conflicting hypotheses do exist. The precise quantitative findings of this study may lead to an improved understanding of CMC joint OA, and perhaps explain its prevalence in the female population over 55.
INTRODUCflON The prevalence of osteoarthritis (OA) at the thumb carpometacarpal (CMC) joint (Kelsey, 1982; Lawrence et al., 1966) has led many investigators to hypothesize that degenerative changes are attributable to the high loads transmitted across the joint (Chao et aI., 1976; Chao and An, 1978; Cooney and Chao, 1977) and to the specific shape of this joint (Aune, 1955). The biomechanics literature contains many studies on the relationship between the geometric form of joint surfaces and load transmission across the articular surfaces (e.g. Scherrer et al., 1979; Ahmed and Burke, 1983; Ahmed et al., 1983; Brown and Shaw, 1983, 1984; Brown et al., 1988; Carter and Wong, 1988; Huberti and Hayes, 1984; Huiskes and Blankevoort, 1990). The literature also contains numerous studies on the relationships between the development of OA and the geometric form of joint surfaces, and cartilage histomorphologic appearance, particularly those from the lower extremities (e.g. Bullough, 1981; Bullough and Jagannath, 1983; Mankin et al., 1971; Mankin, 1982; Sokoloff, 1969). Figure l(a) shows the CMC joint location at the base of the thumb; Figs l(b) and l(c) show the commonly described saddle-shaped anatomy of the metacarpal and trapezial surfaces. These saddle-shaped surfaces Received in final form 29 July 1991.
have attracted considerable attention and discussion in relation to the predisposition of this joint to OA (Kapandji, 1981; Kuczynski, 1974, 1975; Napier, 1955; Pieron, 1973; Smith and Kuczynski, 1978). Because the metacarpal bone is relatively long in comparison with its cross section, it functions mechanically as a cantilevered structure [Fig. l(a)]. It has been estimated that the loads applied across this joint during strong grasp can reach as high as 120 kgf (1180 N) (Chao et al., 1976; Chao and An, 1978; Cooney and Chao, 1977). It is also hypothesized that positions such as pinch and grasp tend to bring the saddle surfaces of the trapezium and metacarpal into an incongruent contacting position. This incongruence results in a reduction in contact areas and, thus, an increase in contact stresses under unchanged applied loads. Such decreases in contact areas and increases in contact stresses are believed to be responsible for the development of focal lesions frequently observed in the dorsoradial and volar-ulnar regions of the CMC joint (Eaton and Glickel, 1987; Koebke, 1983; Pelligrini, 1991). It is generally believed that, under chronic conditions, these high stresses will cause focal cartilage lesions and CMC joint OA (Aune, 1955; Eaton and Littler, 1969; Eaton and Glickel, 1987). Based on clinical observations (Aune, 1955; Eaton 'and Littler, 1973; Menon, 1983; North and Rutledge, 1983; Smith and Kuczynski, 1978), differing opinions have been advanced as to which types ofjoint contour
591
592
G. A.
ATESHIAN
may predispose the CMC joint to OA. North and Rutledge (1983) quantified the contour changes by simple anthropometric measurements of 77 embalmed, elderly cadaver specimens. From these measurements, they found that the trapezial surface tends to be flatter in women and in joints with early degenerative changes. Thus, these investigators suggested that some forms ofthe trapezium, such as those with shallow articular surfaces, may predispose the CMC joint to the development of OA. Other authors have also suggested that natural joint incongruency (as opposed to incongruency induced by ligamentous laxity) is the major factor causing CMC joint OA. Napier (1955) has noted certain types of articular surface incongruency from gross anatomic dissection studies. Thomas (1977), Koebke (1983), Menon (1983), and Eaton and Glickel (1987) all have suggested that rotation of the CMC joint, even without ligamentous insufficiency, may lead to joint incongruency with focal stress peaks on the dorsoradial and volar-ulnar regions of the joint. Strong inferences have been made that these focal high-contact-stress regions are the regions of cartilage erosion leading, eventually, to clinically manifested CMC joint OA. In the present study, we plan to determine the global and subtle variations in CMC joint anatomy using the method of stereophotogrammetry (SPG). Our technique for developing mathematical reconstructions of CMC joint surfaces using precise anatomic data from our SPG system (Ateshian et al., 1991) is based on standard principles of analytical photogrammetry (Ghosh, 1979), and on concepts developed by Scherrer and Hillberry (1979), and by
et
at.
Huiskes et al. (1985) for diarthrodial joints. We analyze the mathematical reconstructions of the CMC joint surfaces using differential geometry (Beck et aI., 1986; Mortenson, 1985). These measuremet1ts and calculations provide precise and quantitative data with which we may distinguish one specimen from another,and perhaps a means to develop a classification scheme to catalogue various CMC joint surfaces. We also present a quantitative measure of joint congruence and discuss its role in joint contact mechanics. Results will be presented in the context of gender differences and relation to thumb CMC joint OA.
MATERIALS AND ·EXPERIMENTAL METHODS
Eight female (average 64 yr old) and five male (average 70 yr old) fresh frozen human hands were thawed for 12 h at 25°C and radiographed and clinically staged for osteoarthritic disease using the grading technique described by Eaton and Glickel (1987). Subsequently, the thumb CMC joints were dissected to expose the articular surfaces for SPG analysis. Our SPG method, which was described previously (Ateshian et al., 1991; Huiskes et al., 1985), is summarized here. In this method, the trapezium and metacarpal were each placed inside the workspace of a precision calibration frame. The joint surfaces were positioned such that the radioulnar and dorsovolar directions were consistently aligned with the coordinate axes of a laboratory-fixed coordinate system. A fine grid was projected on the articular cartilage surface to provide a network of recognizable object
Metacarpal
Thumb
...... volar
vi X/iX\XsQiill?!i XF! ..".
~-
_
-,....:.... ...
__ ulnar
radiai :.-----:... C ) ) : .... .... dorsal -/
)
Trapezium (a)
(b) Fig. l(a, b).
Fig. 1. (a) The carpometacarpal joint at the base of a right thumb. (b) The saddle-shaped trapezial and metacarpal articular surfaces. Frequent occurrence of OA at this joint has led to many hypotheses about its form and function. (c) Typical thumb CMC joint specimen (trapezium is on the right).
593
v.
~
'0
V
Greatest -150 concavity
-100
-50
50 0
100
150
(c)
Fig. 8(a-
0021-9290/92 S5.00 +.00 Pergamon Press Ltd
CURVATURE CHARACTERISTICS AND CONGRUENCE OF THE THUMB CARPOMETACARPAL JOINT: DIFFERENCES BETWEEN FEMALE AND MALE JOINTS G. A. ATESHIAN,* M. P. ROSENWASSERt and V. C. Mowt *Department of Mechanical Engineering, Columbia University, New York, NY 10027, U.S.A., tDepartment of Orthopaedic Surgery, Columbia-Presbyterian Medical Center, New York, NY 10032, U.S.A. and tOrthopaedic Research Laboratory, Departments of Mechanical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10032, U.S.A. Abstract-Three-dimensional geometric models of the articular surfaces of the thumb carpometacarpal (CMC) joint were constructed using precise data obtained from stereophotogrammetry (SPG). It was demonstrated that by using a least-squares surface-fitting technique, the SPG data on the surface can accurately be described by a single parametric biquintic spline function. From this mathematical description, curvature maps of the surfaces were calculated for 13 CMC joints (eight females, average 64 yr old, five males, average 70 yr old). The surface geometry ofeach joint was analyzed, comparisons were made between trapezial and metacarpal surfaces of the joint and differences determined between males and females. With regard to joint surface areas, the female trapezium is significantly smaller than that of the metacarpal. The shape of the female trapezial surface is also fundamentally 'different from that of males. No gender-related difference exists regarding the shape of the metacarpal surface. Congruence of the two opposing articular surfaces was defined by their relative principal curvatures. From these definitions, congruence in the radioulnar and dorsovolar anatomic directions, as well as the global congruence of the joint, were calculated. Most CMC joints were found to be more congruent along the radioulnar direction than the dorsovolar direction and, globally, female joints were found to be less congruent than male joints. The concept ofjoint congruence has played a central role in a number of hypotheses relating to the etiology ofCMC joint osteoarthritis (OA), although conflicting hypotheses do exist. The precise quantitative findings of this study may lead to an improved understanding of CMC joint OA, and perhaps explain its prevalence in the female population over 55.
INTRODUCflON The prevalence of osteoarthritis (OA) at the thumb carpometacarpal (CMC) joint (Kelsey, 1982; Lawrence et al., 1966) has led many investigators to hypothesize that degenerative changes are attributable to the high loads transmitted across the joint (Chao et aI., 1976; Chao and An, 1978; Cooney and Chao, 1977) and to the specific shape of this joint (Aune, 1955). The biomechanics literature contains many studies on the relationship between the geometric form of joint surfaces and load transmission across the articular surfaces (e.g. Scherrer et al., 1979; Ahmed and Burke, 1983; Ahmed et al., 1983; Brown and Shaw, 1983, 1984; Brown et al., 1988; Carter and Wong, 1988; Huberti and Hayes, 1984; Huiskes and Blankevoort, 1990). The literature also contains numerous studies on the relationships between the development of OA and the geometric form of joint surfaces, and cartilage histomorphologic appearance, particularly those from the lower extremities (e.g. Bullough, 1981; Bullough and Jagannath, 1983; Mankin et al., 1971; Mankin, 1982; Sokoloff, 1969). Figure l(a) shows the CMC joint location at the base of the thumb; Figs l(b) and l(c) show the commonly described saddle-shaped anatomy of the metacarpal and trapezial surfaces. These saddle-shaped surfaces Received in final form 29 July 1991.
have attracted considerable attention and discussion in relation to the predisposition of this joint to OA (Kapandji, 1981; Kuczynski, 1974, 1975; Napier, 1955; Pieron, 1973; Smith and Kuczynski, 1978). Because the metacarpal bone is relatively long in comparison with its cross section, it functions mechanically as a cantilevered structure [Fig. l(a)]. It has been estimated that the loads applied across this joint during strong grasp can reach as high as 120 kgf (1180 N) (Chao et al., 1976; Chao and An, 1978; Cooney and Chao, 1977). It is also hypothesized that positions such as pinch and grasp tend to bring the saddle surfaces of the trapezium and metacarpal into an incongruent contacting position. This incongruence results in a reduction in contact areas and, thus, an increase in contact stresses under unchanged applied loads. Such decreases in contact areas and increases in contact stresses are believed to be responsible for the development of focal lesions frequently observed in the dorsoradial and volar-ulnar regions of the CMC joint (Eaton and Glickel, 1987; Koebke, 1983; Pelligrini, 1991). It is generally believed that, under chronic conditions, these high stresses will cause focal cartilage lesions and CMC joint OA (Aune, 1955; Eaton and Littler, 1969; Eaton and Glickel, 1987). Based on clinical observations (Aune, 1955; Eaton 'and Littler, 1973; Menon, 1983; North and Rutledge, 1983; Smith and Kuczynski, 1978), differing opinions have been advanced as to which types ofjoint contour
591
592
G. A.
ATESHIAN
may predispose the CMC joint to OA. North and Rutledge (1983) quantified the contour changes by simple anthropometric measurements of 77 embalmed, elderly cadaver specimens. From these measurements, they found that the trapezial surface tends to be flatter in women and in joints with early degenerative changes. Thus, these investigators suggested that some forms ofthe trapezium, such as those with shallow articular surfaces, may predispose the CMC joint to the development of OA. Other authors have also suggested that natural joint incongruency (as opposed to incongruency induced by ligamentous laxity) is the major factor causing CMC joint OA. Napier (1955) has noted certain types of articular surface incongruency from gross anatomic dissection studies. Thomas (1977), Koebke (1983), Menon (1983), and Eaton and Glickel (1987) all have suggested that rotation of the CMC joint, even without ligamentous insufficiency, may lead to joint incongruency with focal stress peaks on the dorsoradial and volar-ulnar regions of the joint. Strong inferences have been made that these focal high-contact-stress regions are the regions of cartilage erosion leading, eventually, to clinically manifested CMC joint OA. In the present study, we plan to determine the global and subtle variations in CMC joint anatomy using the method of stereophotogrammetry (SPG). Our technique for developing mathematical reconstructions of CMC joint surfaces using precise anatomic data from our SPG system (Ateshian et al., 1991) is based on standard principles of analytical photogrammetry (Ghosh, 1979), and on concepts developed by Scherrer and Hillberry (1979), and by
et
at.
Huiskes et al. (1985) for diarthrodial joints. We analyze the mathematical reconstructions of the CMC joint surfaces using differential geometry (Beck et aI., 1986; Mortenson, 1985). These measuremet1ts and calculations provide precise and quantitative data with which we may distinguish one specimen from another,and perhaps a means to develop a classification scheme to catalogue various CMC joint surfaces. We also present a quantitative measure of joint congruence and discuss its role in joint contact mechanics. Results will be presented in the context of gender differences and relation to thumb CMC joint OA.
MATERIALS AND ·EXPERIMENTAL METHODS
Eight female (average 64 yr old) and five male (average 70 yr old) fresh frozen human hands were thawed for 12 h at 25°C and radiographed and clinically staged for osteoarthritic disease using the grading technique described by Eaton and Glickel (1987). Subsequently, the thumb CMC joints were dissected to expose the articular surfaces for SPG analysis. Our SPG method, which was described previously (Ateshian et al., 1991; Huiskes et al., 1985), is summarized here. In this method, the trapezium and metacarpal were each placed inside the workspace of a precision calibration frame. The joint surfaces were positioned such that the radioulnar and dorsovolar directions were consistently aligned with the coordinate axes of a laboratory-fixed coordinate system. A fine grid was projected on the articular cartilage surface to provide a network of recognizable object
Metacarpal
Thumb
...... volar
vi X/iX\XsQiill?!i XF! ..".
~-
_
-,....:.... ...
__ ulnar
radiai :.-----:... C ) ) : .... .... dorsal -/
)
Trapezium (a)
(b) Fig. l(a, b).
Fig. 1. (a) The carpometacarpal joint at the base of a right thumb. (b) The saddle-shaped trapezial and metacarpal articular surfaces. Frequent occurrence of OA at this joint has led to many hypotheses about its form and function. (c) Typical thumb CMC joint specimen (trapezium is on the right).
593
v.
~
'0
V
Greatest -150 concavity
-100
-50
50 0
100
150
(c)
Fig. 8(a-
