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A Chondral Modeling Theory Revisited
J. theor. Biol. (1999) 201, 201}208 Article No. jtbi.1999.1025, available online at http://www.idealibrary.com on
A Chondral Modeling Theory Revisited MARK W. HAMRICK* Department of Anthropology & Division of Biomedical Sciences, Kent State ;niversity, Kent, OH 44242, ;.S.A. (Received on 13 January 1999, Accepted on 17 September 1999)
The mechanical environment of limb joints constantly changes during growth due to growthrelated changes in muscle and tendon lengths, long bone dimensions, and body mass. The size and shape of limb joint surfaces must therefore also change throughout post-natal development in order to maintain normal joint function. Frost's (1979, 1999) chondral modeling theory proposed that joint congruence is maintained in mammalian limbs throughout postnatal ontogeny because cartilage growth in articular regions is regulated in part by mechanical load. This paper incorporates recent "ndings concerning the distribution of stress in developing articular units, the response of chondrocytes to mechanically induced deformation, and the development of articular cartilage in order to expand upon Frost's chondral modeling theory. The theory presented here assumes that muscular contraction during post-natal locomotor development produces regional #uctuating, intermittent hydrostatic pressure within the articular cartilage of limb joints. The model also predicts that peak levels of hydrostatic pressure in articular cartilage increase between birth and adulthood. Finally, the chondral modeling theory proposes that the cell}cell and cell}extracellular matrix interactions within immature articular cartilage resulting from mechanically induced changes in hydrostatic pressure regulate the metabolic activity of chondrocytes. Site-speci"c rates of articular cartilage growth are therefore regulated in part by the magnitude, frequency, and orientation of prevailing loading vectors. The chondral modeling response maintains a normal kinematic pathway as the magnitude and direction of joint loads change throughout ontogeny. The chondral modeling theory also explains ontogenetic scaling patterns of limb joint curvature observed in mammals. The chondral modeling response is therefore an important physiological mechanism that maintains the match between skeletal structure, function, and locomotor performance throughout mammalian ontogeny and phylogeny. ( 1999 Academic Press
1. Introduction The role of mechanical factors in determining the shape of limb joint surfaces early in skeletal morphogenesis is rather limited since a normal articular topography will appear even if the adjacent joint surface is absent (Thorogood, 1983) or if limb paralysis is induced (Ruano-Gil et al., * E-mail: [email protected] 0022}5193/99/230201#08 $30.00/0
1978). These and other previous studies (e.g. Fell & Canti, 1934; Murray & Selby, 1930; Mitrovic, 1982) support the hypothesis that the initial shape of the cartilaginous anlagen is determined by positional information assigned during pattern formation (Wolpert, 1969, 1978; Carter, 1987; Craig et al., 1987). Recent work indicates that early patterning of the limb joint surfaces is strongly in#uenced by growth factors expressed in the joint interzone, such as the bone ( 1999 Academic Press
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morphogenetic proteins (BMPs) and growth and di!erentiation factors (GDFs; Francis-West et al., 1999). Once the joint cavity is formed and the shape of the joint determined the articular units expand as chondrocytes deposit cartilage matrix and also undergo mitosis (Haines, 1947; Hinchli!e & Johnson, 1983). The latter process is responsible for most of the pre-natal growth seen in the articular ends of long bones and in the bones of the wrist and ankle (Hamrick, 1999). Cartilage growth in articular units is accompanied by growth-related changes in the size and shape of muscles, tendons, and bony levers (Carrier, 1983; Herring, 1994). These growthrelated changes yield related modi"cations in the mechanical advantages of muscles at joints, the potential forces generated by skeletal muscles at joints, and the relative speeds of limb segment movement at joints (Hurov, 1991). The forces acting on a limb joint are often greater than several times body mass (Paul, 1980), yet joint contact areas are typically relatively small, only of the order of several square centimeters in the larger limb joints of humans (Ahmed & Burke, 1983). Articular cartilage is therefore highly stressed (Mow et al., 1989). The articular surfaces of a growing joint must, in order for the locomotor system to function e!ectively, follow a developmental trajectory that maintains both a normal pattern of joint movement and an acceptable stress distribution within the articular cartilage throughout post-natal ontogeny. Joint incongruities resulting from deviations in this growth trajectory will produce very high contact pressures between the articular surfaces. These high contact pressures lead to articular surface wear by reducing #uid "lm lubrication (Frankel et al., 1971; Mow et al., 1989). Furthermore, joint incongruities produce small contact areas between articular surfaces which generate abnormally high mechanical stresses leading to joint failure in the form of degenerative joint disease (Radin & Paul, 1970, 1971; Mow et al., 1989). Thus, for a joint to remain functional during growth, the articular surfaces must be (1) large enough so that the maximum stresses in the joint do not frequently exceed an acceptable level and (2) curved in such a way that the major forces crossing the joint during movement remain normal to the articular surfaces.
How, after formation of the joint cavities, do limb joints maintain congruence and a normal kinematic pathway as the magnitude and direction of forces imparted upon the limb joints change due to growth-related changes in soft tissue morphology, bone dimensions, and body mass? Frost (1979, 1994, 1999) proposed a chondral modeling theory to explain the mechanisms by which &&a growing joint surface2tend[s] toward that shape which eliminates incongruous "t under the patterns of load and motion imposed by neuromotor anatomy and function'' (Frost, 1979, p. 187). Frost's theory was based upon the assumption that cartilage growth will cease in a region bearing excessive compressive load and increase in adjacent regions in order to increase the bearing area. Thus, the direction of cartilage growth and alignment of cartilage layers will always re#ect the magnitude and direction of prevailing loads at the articular surface. Finite element models of stress distribution in developing articular units (Carter & Wong, 1988, 1990) indicate that it is not compressive loading per se that in#uences the growth response of epiphyseal cartilage. Rather, it is the relative magnitude, frequency, and distribution of hydrostatic pressure that regulate the metabolic activity of chondrocytes. Frost's theory was non-speci"c regarding the role of particular tissue layers in the modeling process. Moreover, it provided few speci"c details as to how mechanotransduction might regulate articular cartilage growth and development. The goal of this paper is to expand upon Frost's original theory to further explicate the mechanisms that facilitate functional integration in the developing mammalian locomotor system. The theory presented here is similar to Frost's in that it is speci"c to mammals, it refers only to modeling during post-natal development, and it underscores the importance of mechanotransduction in regulating articular cartilage growth. The theory presented here di!ers from Frost's in that it makes explicit predictions regarding ontogenetic change in limb joint shape, speci"es the magnitudes and frequencies of joint loads that stimulate chondral modeling, and considers age-related changes in the loading environment of articular cartilage.
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2. The Theory The chondral modeling theory presented here predicts that (1) peak levels of hydrostatic pressure in articular cartilage increase between birth and skeletal maturity because articular cartilage thickness decreases, force generation increases, and relative joint size decreases, (2) the articular cartilage of growing mammals responds to this ontogenetic increase in joint stress by a process of chondral modeling*chondrocyte division and cartilage matrix synthesis in response to changes in the tissue's mechanical environment, (3) hydrostatic pressure in the range of 1}10 MPa at a frequency of 1}4 Hz stimulates chondrocyte division and matrix synthesis, and (4) an equilibrium state is established soon after cartilage growth is stimulated under a given load and local tissue deposition will not be initiated again by mechanotransduction unless the range of hydrostatic pressure exceeds the level at which equilibrium was reached. Chondral modeling is argued in this paper to be an important mechanism of skeletal adaptation during post-natal development because the mechanical stresses on articular cartilage are likely to increase between birth and adulthood for the following four reasons. First, levels of hydrostatic pressure in pre-natal articular cartilage are expected to be quite low given that the limbs are suspended in amniotic #uid and are not subjected to weight-bearing loads. Second, ossi"cation centers form in the ends of long bones of mammals and in the short bones of the carpus
and tarsus prior to weaning (Hamrick, 1999). Therefore, as endochondral ossi"cation progresses in the articular regions of juvenile mammals the articular cartilage becomes thinner relative to the overall size of the joint. Articular cartilage stress, expressed as force per unit area, will therefore increase because the relative crosssectional area of the cartilage is decreasing. Third, force generation during locomotion is known to actually increase with age in many mammals (Carrier, 1996). In the case of humans, joint loads can increase over 20 times between birth and skeletal maturity (Burr, 1997). Finally, relative joint size may actually decrease during growth. Human infants, for example, possess joint diameters that are larger, relative to body size, than those of adults (see Fig. 6.12 in Williams, 1995). Newborn and juvenile rats also possess joint diameters that are larger, relative to body size, than those of adult rats (Table 1). These data suggest that joint stress will increase with age in these species because the weightbearing surface of the joint will be smaller, relative to body size, in adults than in younger animals. It is, however, expected that more precocial mammals (e.g., jackrabbits; Carrier, 1983, 1995) having a relatively greater capacity for locomotor acceleration as juveniles should also have relatively larger joint surface areas as juveniles. In vitro studies using controlled loading of isolated cartilage plugs indicate that dynamic, intermittent hydrostatic pressure generated by compressive loads applied to hyaline cartilage
TABLE 1 Joint diameters relative to body length in a mixed cross-sectional sample of laboratory rats. Mean values are separated from standard deviations by commas. Results of Kruskal}=allis tests are shown in brackets. Body length is measured from the base of the skull to the base of the tail
Age* Newborns (n"4) Juveniles (n"4) Adults (n"4)
(Humeral head diameter/ body length)]100 [H"9.17, P"0.01]
(Femoral head diameter/ body length)]100 [H"10.05, P(0.01]
3.8, 0.30 4.4, 0.29 2.7, 0.05
3.3, 0.16 3.7, 0.09 2.8, 0.08
* Newborns are 1}12 h post-parturition, juveniles are 20 post-natal days of age, and adults are '90 post-natal days of age.
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stimulates chondrocyte division and proliferation (Urban, 1994). Additional in vitro studies of isolated chondrocytes also demonstrate that mechanically induced chondrocyte deformation stimulates cartilage matrix synthesis (Smith et al., 1996; Lee & Bader, 1997; Takahashi et al., 1997; Urban, 1994). Speci"cally, hydrostatic pressure in the range of 1}10 MPa at a frequency of 1}4 Hz stimulates chondrocyte division and matrix synthesis, whereas chondrocyte metabolism is inhibited by loads that are either static, infrequent, weak ((1 MPa; Takahashi et al., 1997), or excessive ('10 MPa; Lee & Bader, 1997; Smith et al., 1996; Takahashi et al., 1997; Wong et al., 1997). Dynamic loading and changing levels of hydrostatic pressure are thought to induce chondrocyte mitosis by either releasing transforming growth factor-beta (TGFb) that is &&tied up'' within the extracellular matrix or directly stimulating TGFb expression by chondrocytes (Archer, 1994; Takahashi et al., 1997). Elevated matrix synthesis observed after loading appears to be a response to mechanically induced cartilage matrix degradation (Archer, 1994). The magnitudes and frequencies of applied hydrostatic pressure which were observed in the aforementioned experiments to stimulate chondrocyte division and matrix synthesis represent normal physiological levels*human knee joint articular cartilage exhibits and average resting hydrostatic pressure of 0.2 MPa that rises to 4}5 MPa during walking (Urban, 1994). Hydrostatic pressure in the range of 5}50 MPa alters cell morphology and generally inhibits chondrocyte activity (Urban, 1994; Wong et al., 1997). When these variables are plotted graphically, a growth response curve is generated which illustrates the general metabolic response of hyaline cartilage to mechanical load (Fig. 1). Rubin & Lanyon (1984a, 1987) have emphasized the importance of load frequency and periodicity in stimulating bone modeling and remodeling. Figure 1 indicates that the same requirements exist for growing cartilage. Secondary ossi"cation centers form in mammalian long bones prior to a major pre-pubertal growth spurt (Hamrick, 1999). In order for the limb joints to increase in surface area at the same rate as either body mass or body length, cartilage between the articular surfaces and the secondary ossi"cation centers must proliferate at the same
FIG. 1. Proposed relationship between cartilage growth and stress distribution in articular units depicted as a growth response curve. Compression applied to an articular surface produces hydrostatic pressure (dilatational stress) which up-regulates cartilage growth. The model assumes that such growth will be inhibited once these dilatational stresses become excessive. It also assumes that dilatational stresses must be dynamic and intermittent in order to stimulate chondrocyte division and cartilage matrix synthesis. Finally, it assumes that an equilibrium condition will be reached soon after growth is stimulated under a given loading state. Continued local tissue deposition will not occur again unless the range of hydrostatic pressure exceeds the level of the equilibrium state; however, systemic growth will probably continue under the regulation of circulating growth factors.
rate. Cartilage growth in developing joints involves chondrocyte division, proliferation, hypertrophy, and matrix synthesis (Hinchli!e & Johnson, 1983). The lining of joint cavities lacks perichondrium and so chondrocytes must proliferate in articular regions by mitosis of resident cells. Immature limb joint cartilages show increasing cell size, decreasing collagen content, and increasing proteoglycan content with increasing depth away from the articular surface (Hunziker, 1992; Archer et al., 1996). The anisotropy of growing articular cartilage suggests that hydrostatic pressure must vary throughout the articular cartilage of a joint loaded in compression. Wong et al. (1997) found that, in adult articular cartilages, axial strains are indeed higher in the upper-half of the tissue. Moreover, the level of axial strain is inversely correlated with the biosynthetic activity of adult chondrocytes.
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FIG. 2. Distribution of hydrostatic pressure within the mitotic annulus of two articular units under compressive loading. Darker shading indicates areas of higher hydrostatic pressure as predicted from "nite element modeling by Carter & Wong (1988). Note that zones of high hydrostatic pressure occur in those areas loaded during articular contact. The two graphs shown below the three joints indicate that as the joint passes through a single cycle of movement, hydrostatic pressure changes in di!erent ways in two di!erent regions. The chondral modeling response is therefore also expected to vary between these two regions according to di!erences in the magnitude and distribution of hydrostatic pressure.
Mankin (1962) and Archer et al. (1994) observed that most articular cartilage growth in immature mammals occurs in a mitotic annulus, or band, located in the upper-half of the tissue depth. The observed responses of chondrocytes to compressive loading, axial strain, and hydrostatic pressure suggest that, in an immature joint under compressive loading, chondrocyte division and cartilage matrix synthesis within this mitotic annulus will respond in both negative and positive feedback modes. High levels of hydrostatic pressure in frequently loaded regions will temporarily inhibit the metabolic activity of chondrocytes, whereas lower levels of hydrostatic pressure in adjacent regions, as well as in the same region immediately before and after pressure levels peak, would be expected to stimulate chondral modeling (Fig. 2). Furthermore, #uid #ow within the cartilage induced by mechanical deformation is expected to have a positive e!ect on cartilage growth and metabolism because it aids in moving nutrients through the extracellular #uid to growing chondrocytes (Mow et al., 1984; Lanyon & Rubin, 1985). Frequently #uctuating levels of hydrostatic pressure would also
inhibit the progression of ossi"cation (Carter & Wong, 1988, 1990), possibly by maintaining the metabolic activity of hypertrophic chondrocytes and thereby suppressing calci"cation (Hunziker, 1992). The model assumes that an equilibrium state will be established soon after growth is stimulated under a given load. Mechanotransduction will not induce local tissue deposition again unless the range of hydrostatic pressure exceeds the level at which equilibrium was reached; however, systemic growth will probably continue under the regulation of circulating growth factors. 3. Discussion The goal of this paper is to present a chondral modeling theory that incorporates new information in order to explain previously unexplained facts. The "rst of these unexplained phenomena is related to the general role of mechanical factors in limb joint morphogenesis. Ogden (1980, p. 167) stated that &&postnatally, joint motion and joint reaction forces are extremely consequential to the "nal adult joint contours'' and Frost (1999,
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p. 168) has argued that &&chondral modeling determines the curvature, shape, congruence and smoothness of a joint's articular surfaces''. The speci"c ways in which joint movement and loading in#uence the shape of developing articular surfaces have, however, remained unclear. Evidence from "nite element models of stress distribution in articular cartilage, in vitro studies of load distribution in cartilage explants, and in vitro studies of chondrocyte metabolism in response to mechanical perturbation together suggest that mechanotransduction (Moss, 1997) is an important determinant of limb joint growth and form. Speci"cally, chondrocyte proliferation and di!erentiation in growing articular cartilage requires cell}cell and cell}extracellular matrix interactions induced by mechanical stimuli (Cancedda et al., 1995). The regulation of cartilage growth by mechanical load is therefore a primary mechanism by which extrinsic factors in#uence limb joint morphogenesis. Furthermore, the chondral modeling response is an important process that enables developing articular units to adapt to changes in their mechanical environment during growth. The second unexplained observation addressed in this paper is related to observed scaling patterns of limb joint curvature values in mammals. Limb excursion angles have been observed to decrease with increasing body size in mammals in order to maintain similar levels of peak bone stress during locomotion (McMahon, 1975; Biewener, 1983; Rubin & Lanyon, 1984b; Biewener et al., 1986). Observations on limb kinematics in developing mammals show that infants and juveniles are characterized by highly #exed limb positions whereas subadults and adults exhibit more extended limb postures (Langworthy, 1925; Hurov, 1991). The model presented in this paper suggests that if limb excursion angles decrease with age and increasing body mass in growing mammals then limb joint curvature values should also be expected to decrease. Hindlimb stride length increases with increasing body size in mammals so that stride frequency decreases in proportion to (body mass)~0.14 (Heglund et al., 1974; Pennycuick, 1975). Decreasing stride frequency is not expected to in#uence the rate of chondral modeling
since the chondrocytes are responding to load level di!erentials within the tissue rather than overall frequency of loading per unit time. Low ranges of angular excursion experienced at a joint throughout ontogeny would be expected to generate relatively low levels of hydrostatic pressure in the most anterior and posterior regions of a joint (Fig. 2). The rates of chondroctye division and matrix synthesis within the mitotic annulus in these regions should be quite high since levels of hydrostatic pressure are #uctuating but not excessive. In contrast, the more central region of each articular unit would experience levels of hydrostatic pressure that are frequently above growth-stimulating levels. Modeling would therefore be expected to proceed at a relatively slower rate in this heavily loaded region. Eventually, this pattern of growth would increase the bearing area of the articular surface and thereby average loads across the joint by decreasing the degree of anteroposterior curvature of each condyle. This prediction of the model ia borne out by data showing that knee joint curvature values decrease with age and increasing
FIG. 3. Bivariate plot of logged normalized knee joint curvature values against logged femoral length values for a mixed cross-sectional growth series of 15 post-natal Didelphis virginiana individuals. Curvature is measured in the sagittal plane on the distal articular surface of the femur and is calculated following Biewener (1983) and Hamrick (1996). The sample includes animals ranging in age from 60 days (approximately pouch exit; Hamrick, 1999) to adulthood. Note that joint curvature values decrease post-natally with increasing age and size. y-intercept"5.11; slope"!0.20; r"0.78; p"0.001.
CHONDRAL MODELING THEORY
body size during post-natal development in the didelphid marsupial Didelphis virginiana (Fig. 3). The model may also explain Frost's (1999) observation that joint curvatures decrease during growth, more so in normal than in paralysed limbs. These preliminary results suggest that ontogenetic scaling patterns of limb joint curvature values in mammals may result from the action of local, extrinsic biophysical processes acting in concert with systemic, intrinsic growth factors. A similar explanation has been proposed by Van der Meulen & Carter (1995) to account for both intra- and inter-speci"c scaling patterns of diaphyseal dimensions in mammals. The importance of mechanical factors in regulating chondroosseous development underscores the need for analyses which examine covariances among constituent musculoskeletal elements during growth (Hall, 1990; Herring, 1994; Smith, 1994). This type of research program is necessary in order to elucidate the mechanisms that preserve the match between post-cranial structure, function, and locomotor performance throughout mammalian ontogeny and phylogeny (Galis, 1996). I am grateful to Drs D. Carrier, M. J. Ravosa, C. Owen Lovejoy, and an anonymous reviewer for providing helpful comments on the manuscript. Dr. J. Marcinkiewicz generously donated specimens of Rattus. Funding for this research was provided by National Science Foundation Grant IBN-9603808. REFERENCES AHMED, A. M. & BURKE, D. L. (1983). In vitro measurement of static pressure distribution in synovial joints. I. Tibial surface of the knee. J. Biomech. Engng 105, 216. ARCHER, C. W. (1994). Skeletal development and osteoarthritis. Ann. Rheum. Dis. 53, 624}630. ARCHER, C. W., MORRISON, H. & PITSILLIDES, A. (1994). Cellular aspects of the development of diarthrodial joints and articular cartilage. J. Anat. 184, 447}456. ARCHER, C. W., MORRISON, H., BAYLISS, M. T. & FERGUSON, M. (1996). The development of articular cartilage: II. The spatial and temporal patterns of glycosaminoglycans and small leucine-rich proteoglycans. J. Anat. 189, 23}35. BIEWENER, A. (1983). Allometry of quadrupedal locomotion: the scaling of duty factor, bone curvature, and limb orientation to body size. J. Exp. Biol. 105, 147}171. BIEWENER, A., SWARTZ, S. & BERTRAM, J. (1986). Bone modeling during growth: dynamic strain equilibrium in the chick tibotarsus. Calc. ¹iss. Int. 39, 390}395.
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BURR, D. B. (1997). Muscle strength, bone mass, and agerelated bone loss. J. Bone. Min. Res. 12, 1547}1551. CANCEDDA, R., CANCEDDA, F. & CASTAGNOLA, P. (1995). Chondrocyte di!erentiation. Int. Rev. Cytol. 159, 265}358. CARRIER, D. R. (1983). Postnatal ontogeny of the musculoskeletal system in the black-tailed jack rabbit (¸epus californicus). J. Zool. 210, 27}55. CARRIER, D. R. (1995). Ontogeny of jumping performance in the black-tailed jackrabbit (¸epus californicus). Zool. 98, 309}313. CARRIER, D. R. (1996). Ontogenetic limits on locomotor performance. Physiol. Zool. 69, 467}488. CARTER, D. R. (1987). Mechanical loading history and skeletal biology. J. Biomech. 20, 1095}1109. CARTER, D. R. & WONG, M. (1988). The role of mechanical loading histories in the development of diarthrodial joints. J. Orthop. Res. 6, 804}16. CARTER, D. R. & WONG, M. (1990). Mechanical stresses in joint morphogenesis and maintenance. In: Biomechanics of Diarthrodial Joints (Mow, V. C., Radcli!e, A. & Woo, S. L. Y., eds), pp. 155}174. New York: Springer-Verlag. CRAIG, F., BENTLEY, G. & ARCHER, C. (1987). The spatial and temporal pattern of collagens I and II and keratan sulphate in the developing chick metatarsophalangeal joint. Development 99, 383}391. FELL, H. B. & CANTI, R. B. (1934). Experiments on the development in vitro of the avian knee joint. Proc. R. Soc. ¸ond. 116, 316}327. FRANCIS-WEST, P., PARISH, J., LEE, K. & ARCHER, C. (1999). BMP/GDF-signalling interactions during synovial joint development. Cell ¹iss. Res. 296, 111}119. FRANKEL, V. H., BURSTEIN, A. H. & BROOKS, D. B. (1971). Biomechanics of internal derangement of the knee. J. Bone Jt Surg. 53A, 945}962. FROST, H. M. (1979). A chondral modeling theory. Calc. ¹issue Intl. 28, 181}200. FROST, H. M. (1994). Perspectives: a vital biomechanical model of synovial joint design. Anat. Rec. 240, 1}18. FROST, H. M. (1999). Joint anatomy, design, and arthroses: Insights of the Utah paradigm. Anat. Rec. 255, 162}174. GALIS, F. (1996). The application of functional morphology to evolutionary studies. ¹rends Ecol. Evol. 11, 124}129. HAINES, R. W. (1947). The development of joints. J. Anat. 81, 33}55. HALL, B. K. (1990). Bone, Vol. 6. Bone Growth 2 Mechanical Factors, Skeletal Components and Consequences. Boca Raton, FL: CRC Press. HAMRICK, M. W. (1996). Articular size and curvature as determinants of carpal joint mobility and stability in strepsirhine primates. J. Morphol. 230, 113}127. HAMRICK, M. W. (1999). Development of epiphyseal structure and function in Didelphis virginiana (Marsupiala, Didelphidae). J. Morphol. 239, 283}296. HEGLUND, N. C., TAYLOR, C. R. & MCMAHON, T. A. (1974). Scaling stride frequency and gait to animal size: mice to horses. Science 186, 1112}1113. HERRING, S. W. (1994). Development of functional interactions between skeletal and muscular systems. In: Bone (Hall, B. K., ed.), Vol. 9 pp. 165}191. Boca Raton: CRC Press. HINCHLIFFE, J. R. & JOHNSON, D. R. (1983). Growth of cartilage. In: Cartilage, (Hall, B. K., ed.), Vol. 2, pp. 255}295. New York: Academic Press.
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HUNZIKER, E. B. (1992). Articular cartilage structure in humans and experimental animals. In: Articular Cartilage and Osteoarthritis (Kuettner, K., Schleyerbach, R., Peyron, J. & Hascall, V.), pp. 183}199. New York: Raven Press. HUROV, J. R. (1991). Rethinking primate locomotion: what can we learn from development? J. Motor Behav. 23, 211}218. LANGWORTHY, O. R. (1925). The development of progression and posture in young opossums. Am. J. Physiol. 74, 1}13. LANYON, L. & RUBIN, C. (1985) Functional adaptation in skeletal structures. In: Functional
RADIN, E. & PAUL, I. (1970). Does cartilage compliance reduce skeletal impact loads? Arth. Rheum. 13, 139}144. RADIN, E. & PAUL, I. (1971). Response of joints to impact loading. Arth. Rheum. 14, 357}362. RUANO-GIL, D., NARDI-VILARDAGA, J. & TEJEDO-MATEU, A. (1978). In#uence of extrinsic factors on the development of the articular system. Acta Anat. 101, 36}44. RUBIN, C. & LANYON, L. (1984a). Regulation of bone formation by applied dynamic loads. J. Bone Jt Surg. 66, 397}402. RUBIN, C. & LANYON, L. (1984b). Dynamic strain similarity in vertebrates: an alternative to allometric limb bone scaling. J. ¹heor. Biol. 107, 321}327. RUBIN, L. & LANYON, L. (1987) Osteoregulatory nature of mechanical stimuli: function as a determinant for adaptive remodeling in bone. J. Orthop. Res. 5, 300}310. SMITH, K. K. (1994). Integration of craniofacial structures during development in mammals. Am. Zool. 36, 70}79. SMITH, R., RUSK, S., ELLISON, B., WESSELLS, P., TSUCHIYA, K., CARTER, D., CALER, W., SANDELL, L. & SCHURMAN, D. (1996). In vitro stimulation of articular chondrocyte mRNA and extracellular matrix synthesis by hydrostatic pressure. J. Orthop. Res. 14, 53}60. TAKAHASHI, K., KUBO, T., KOBAYASHI, K., IMANISHI, J., TAKIGAWA, M., ARAI, Y. & HIRASAWA, Y. Hydrostatic pressure in#uences mRNA expression of transforming growth factor-beta 1 and heat shock protein 70 in chondrocyte-like cell line. J. Orthop. Res. 15, 150}158. THOROGOOD, P. (1983). Morphogenesis of cartilage. In: Cartilage (Hall, B. K., ed.), Vol. 2, pp. 223}254. New York: Academic Press. URBAN, J. (1994). The chondrocyte: a cell under pressure. Br. J. Rheum. 33, 901}908. VAN DER MEULEN, M. C. H. & CARTER, D. R. (1995). Developmental mechanics determine long bone allometry. J. theor. Biol. 172, 323}327. WILLIAMS, P. L. (1995). Gray's Anatomy, 38th edn. London: Churchill Livingstone. WOLPERT, L. (1969). Positional information and the spatial pattern of cellular di!erentiation. J. theor. Biol. 25, 1}47. WOLPERT, L. (1978). Pattern formation in biological development. Sci. Am. 239, 154}164. WONG, M., WUETHRICH, P., BUSCHMANN, M., EGGLI, P. & HUNZIKER, E. (1997). Chondrocyte biosynthesis correlates with local tissue strain in statically compressed adult articular cartilage. J. Orthop. Res. 15, 189}196.
A Chondral Modeling Theory Revisited MARK W. HAMRICK* Department of Anthropology & Division of Biomedical Sciences, Kent State ;niversity, Kent, OH 44242, ;.S.A. (Received on 13 January 1999, Accepted on 17 September 1999)
The mechanical environment of limb joints constantly changes during growth due to growthrelated changes in muscle and tendon lengths, long bone dimensions, and body mass. The size and shape of limb joint surfaces must therefore also change throughout post-natal development in order to maintain normal joint function. Frost's (1979, 1999) chondral modeling theory proposed that joint congruence is maintained in mammalian limbs throughout postnatal ontogeny because cartilage growth in articular regions is regulated in part by mechanical load. This paper incorporates recent "ndings concerning the distribution of stress in developing articular units, the response of chondrocytes to mechanically induced deformation, and the development of articular cartilage in order to expand upon Frost's chondral modeling theory. The theory presented here assumes that muscular contraction during post-natal locomotor development produces regional #uctuating, intermittent hydrostatic pressure within the articular cartilage of limb joints. The model also predicts that peak levels of hydrostatic pressure in articular cartilage increase between birth and adulthood. Finally, the chondral modeling theory proposes that the cell}cell and cell}extracellular matrix interactions within immature articular cartilage resulting from mechanically induced changes in hydrostatic pressure regulate the metabolic activity of chondrocytes. Site-speci"c rates of articular cartilage growth are therefore regulated in part by the magnitude, frequency, and orientation of prevailing loading vectors. The chondral modeling response maintains a normal kinematic pathway as the magnitude and direction of joint loads change throughout ontogeny. The chondral modeling theory also explains ontogenetic scaling patterns of limb joint curvature observed in mammals. The chondral modeling response is therefore an important physiological mechanism that maintains the match between skeletal structure, function, and locomotor performance throughout mammalian ontogeny and phylogeny. ( 1999 Academic Press
1. Introduction The role of mechanical factors in determining the shape of limb joint surfaces early in skeletal morphogenesis is rather limited since a normal articular topography will appear even if the adjacent joint surface is absent (Thorogood, 1983) or if limb paralysis is induced (Ruano-Gil et al., * E-mail: [email protected] 0022}5193/99/230201#08 $30.00/0
1978). These and other previous studies (e.g. Fell & Canti, 1934; Murray & Selby, 1930; Mitrovic, 1982) support the hypothesis that the initial shape of the cartilaginous anlagen is determined by positional information assigned during pattern formation (Wolpert, 1969, 1978; Carter, 1987; Craig et al., 1987). Recent work indicates that early patterning of the limb joint surfaces is strongly in#uenced by growth factors expressed in the joint interzone, such as the bone ( 1999 Academic Press
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morphogenetic proteins (BMPs) and growth and di!erentiation factors (GDFs; Francis-West et al., 1999). Once the joint cavity is formed and the shape of the joint determined the articular units expand as chondrocytes deposit cartilage matrix and also undergo mitosis (Haines, 1947; Hinchli!e & Johnson, 1983). The latter process is responsible for most of the pre-natal growth seen in the articular ends of long bones and in the bones of the wrist and ankle (Hamrick, 1999). Cartilage growth in articular units is accompanied by growth-related changes in the size and shape of muscles, tendons, and bony levers (Carrier, 1983; Herring, 1994). These growthrelated changes yield related modi"cations in the mechanical advantages of muscles at joints, the potential forces generated by skeletal muscles at joints, and the relative speeds of limb segment movement at joints (Hurov, 1991). The forces acting on a limb joint are often greater than several times body mass (Paul, 1980), yet joint contact areas are typically relatively small, only of the order of several square centimeters in the larger limb joints of humans (Ahmed & Burke, 1983). Articular cartilage is therefore highly stressed (Mow et al., 1989). The articular surfaces of a growing joint must, in order for the locomotor system to function e!ectively, follow a developmental trajectory that maintains both a normal pattern of joint movement and an acceptable stress distribution within the articular cartilage throughout post-natal ontogeny. Joint incongruities resulting from deviations in this growth trajectory will produce very high contact pressures between the articular surfaces. These high contact pressures lead to articular surface wear by reducing #uid "lm lubrication (Frankel et al., 1971; Mow et al., 1989). Furthermore, joint incongruities produce small contact areas between articular surfaces which generate abnormally high mechanical stresses leading to joint failure in the form of degenerative joint disease (Radin & Paul, 1970, 1971; Mow et al., 1989). Thus, for a joint to remain functional during growth, the articular surfaces must be (1) large enough so that the maximum stresses in the joint do not frequently exceed an acceptable level and (2) curved in such a way that the major forces crossing the joint during movement remain normal to the articular surfaces.
How, after formation of the joint cavities, do limb joints maintain congruence and a normal kinematic pathway as the magnitude and direction of forces imparted upon the limb joints change due to growth-related changes in soft tissue morphology, bone dimensions, and body mass? Frost (1979, 1994, 1999) proposed a chondral modeling theory to explain the mechanisms by which &&a growing joint surface2tend[s] toward that shape which eliminates incongruous "t under the patterns of load and motion imposed by neuromotor anatomy and function'' (Frost, 1979, p. 187). Frost's theory was based upon the assumption that cartilage growth will cease in a region bearing excessive compressive load and increase in adjacent regions in order to increase the bearing area. Thus, the direction of cartilage growth and alignment of cartilage layers will always re#ect the magnitude and direction of prevailing loads at the articular surface. Finite element models of stress distribution in developing articular units (Carter & Wong, 1988, 1990) indicate that it is not compressive loading per se that in#uences the growth response of epiphyseal cartilage. Rather, it is the relative magnitude, frequency, and distribution of hydrostatic pressure that regulate the metabolic activity of chondrocytes. Frost's theory was non-speci"c regarding the role of particular tissue layers in the modeling process. Moreover, it provided few speci"c details as to how mechanotransduction might regulate articular cartilage growth and development. The goal of this paper is to expand upon Frost's original theory to further explicate the mechanisms that facilitate functional integration in the developing mammalian locomotor system. The theory presented here is similar to Frost's in that it is speci"c to mammals, it refers only to modeling during post-natal development, and it underscores the importance of mechanotransduction in regulating articular cartilage growth. The theory presented here di!ers from Frost's in that it makes explicit predictions regarding ontogenetic change in limb joint shape, speci"es the magnitudes and frequencies of joint loads that stimulate chondral modeling, and considers age-related changes in the loading environment of articular cartilage.
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2. The Theory The chondral modeling theory presented here predicts that (1) peak levels of hydrostatic pressure in articular cartilage increase between birth and skeletal maturity because articular cartilage thickness decreases, force generation increases, and relative joint size decreases, (2) the articular cartilage of growing mammals responds to this ontogenetic increase in joint stress by a process of chondral modeling*chondrocyte division and cartilage matrix synthesis in response to changes in the tissue's mechanical environment, (3) hydrostatic pressure in the range of 1}10 MPa at a frequency of 1}4 Hz stimulates chondrocyte division and matrix synthesis, and (4) an equilibrium state is established soon after cartilage growth is stimulated under a given load and local tissue deposition will not be initiated again by mechanotransduction unless the range of hydrostatic pressure exceeds the level at which equilibrium was reached. Chondral modeling is argued in this paper to be an important mechanism of skeletal adaptation during post-natal development because the mechanical stresses on articular cartilage are likely to increase between birth and adulthood for the following four reasons. First, levels of hydrostatic pressure in pre-natal articular cartilage are expected to be quite low given that the limbs are suspended in amniotic #uid and are not subjected to weight-bearing loads. Second, ossi"cation centers form in the ends of long bones of mammals and in the short bones of the carpus
and tarsus prior to weaning (Hamrick, 1999). Therefore, as endochondral ossi"cation progresses in the articular regions of juvenile mammals the articular cartilage becomes thinner relative to the overall size of the joint. Articular cartilage stress, expressed as force per unit area, will therefore increase because the relative crosssectional area of the cartilage is decreasing. Third, force generation during locomotion is known to actually increase with age in many mammals (Carrier, 1996). In the case of humans, joint loads can increase over 20 times between birth and skeletal maturity (Burr, 1997). Finally, relative joint size may actually decrease during growth. Human infants, for example, possess joint diameters that are larger, relative to body size, than those of adults (see Fig. 6.12 in Williams, 1995). Newborn and juvenile rats also possess joint diameters that are larger, relative to body size, than those of adult rats (Table 1). These data suggest that joint stress will increase with age in these species because the weightbearing surface of the joint will be smaller, relative to body size, in adults than in younger animals. It is, however, expected that more precocial mammals (e.g., jackrabbits; Carrier, 1983, 1995) having a relatively greater capacity for locomotor acceleration as juveniles should also have relatively larger joint surface areas as juveniles. In vitro studies using controlled loading of isolated cartilage plugs indicate that dynamic, intermittent hydrostatic pressure generated by compressive loads applied to hyaline cartilage
TABLE 1 Joint diameters relative to body length in a mixed cross-sectional sample of laboratory rats. Mean values are separated from standard deviations by commas. Results of Kruskal}=allis tests are shown in brackets. Body length is measured from the base of the skull to the base of the tail
Age* Newborns (n"4) Juveniles (n"4) Adults (n"4)
(Humeral head diameter/ body length)]100 [H"9.17, P"0.01]
(Femoral head diameter/ body length)]100 [H"10.05, P(0.01]
3.8, 0.30 4.4, 0.29 2.7, 0.05
3.3, 0.16 3.7, 0.09 2.8, 0.08
* Newborns are 1}12 h post-parturition, juveniles are 20 post-natal days of age, and adults are '90 post-natal days of age.
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stimulates chondrocyte division and proliferation (Urban, 1994). Additional in vitro studies of isolated chondrocytes also demonstrate that mechanically induced chondrocyte deformation stimulates cartilage matrix synthesis (Smith et al., 1996; Lee & Bader, 1997; Takahashi et al., 1997; Urban, 1994). Speci"cally, hydrostatic pressure in the range of 1}10 MPa at a frequency of 1}4 Hz stimulates chondrocyte division and matrix synthesis, whereas chondrocyte metabolism is inhibited by loads that are either static, infrequent, weak ((1 MPa; Takahashi et al., 1997), or excessive ('10 MPa; Lee & Bader, 1997; Smith et al., 1996; Takahashi et al., 1997; Wong et al., 1997). Dynamic loading and changing levels of hydrostatic pressure are thought to induce chondrocyte mitosis by either releasing transforming growth factor-beta (TGFb) that is &&tied up'' within the extracellular matrix or directly stimulating TGFb expression by chondrocytes (Archer, 1994; Takahashi et al., 1997). Elevated matrix synthesis observed after loading appears to be a response to mechanically induced cartilage matrix degradation (Archer, 1994). The magnitudes and frequencies of applied hydrostatic pressure which were observed in the aforementioned experiments to stimulate chondrocyte division and matrix synthesis represent normal physiological levels*human knee joint articular cartilage exhibits and average resting hydrostatic pressure of 0.2 MPa that rises to 4}5 MPa during walking (Urban, 1994). Hydrostatic pressure in the range of 5}50 MPa alters cell morphology and generally inhibits chondrocyte activity (Urban, 1994; Wong et al., 1997). When these variables are plotted graphically, a growth response curve is generated which illustrates the general metabolic response of hyaline cartilage to mechanical load (Fig. 1). Rubin & Lanyon (1984a, 1987) have emphasized the importance of load frequency and periodicity in stimulating bone modeling and remodeling. Figure 1 indicates that the same requirements exist for growing cartilage. Secondary ossi"cation centers form in mammalian long bones prior to a major pre-pubertal growth spurt (Hamrick, 1999). In order for the limb joints to increase in surface area at the same rate as either body mass or body length, cartilage between the articular surfaces and the secondary ossi"cation centers must proliferate at the same
FIG. 1. Proposed relationship between cartilage growth and stress distribution in articular units depicted as a growth response curve. Compression applied to an articular surface produces hydrostatic pressure (dilatational stress) which up-regulates cartilage growth. The model assumes that such growth will be inhibited once these dilatational stresses become excessive. It also assumes that dilatational stresses must be dynamic and intermittent in order to stimulate chondrocyte division and cartilage matrix synthesis. Finally, it assumes that an equilibrium condition will be reached soon after growth is stimulated under a given loading state. Continued local tissue deposition will not occur again unless the range of hydrostatic pressure exceeds the level of the equilibrium state; however, systemic growth will probably continue under the regulation of circulating growth factors.
rate. Cartilage growth in developing joints involves chondrocyte division, proliferation, hypertrophy, and matrix synthesis (Hinchli!e & Johnson, 1983). The lining of joint cavities lacks perichondrium and so chondrocytes must proliferate in articular regions by mitosis of resident cells. Immature limb joint cartilages show increasing cell size, decreasing collagen content, and increasing proteoglycan content with increasing depth away from the articular surface (Hunziker, 1992; Archer et al., 1996). The anisotropy of growing articular cartilage suggests that hydrostatic pressure must vary throughout the articular cartilage of a joint loaded in compression. Wong et al. (1997) found that, in adult articular cartilages, axial strains are indeed higher in the upper-half of the tissue. Moreover, the level of axial strain is inversely correlated with the biosynthetic activity of adult chondrocytes.
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FIG. 2. Distribution of hydrostatic pressure within the mitotic annulus of two articular units under compressive loading. Darker shading indicates areas of higher hydrostatic pressure as predicted from "nite element modeling by Carter & Wong (1988). Note that zones of high hydrostatic pressure occur in those areas loaded during articular contact. The two graphs shown below the three joints indicate that as the joint passes through a single cycle of movement, hydrostatic pressure changes in di!erent ways in two di!erent regions. The chondral modeling response is therefore also expected to vary between these two regions according to di!erences in the magnitude and distribution of hydrostatic pressure.
Mankin (1962) and Archer et al. (1994) observed that most articular cartilage growth in immature mammals occurs in a mitotic annulus, or band, located in the upper-half of the tissue depth. The observed responses of chondrocytes to compressive loading, axial strain, and hydrostatic pressure suggest that, in an immature joint under compressive loading, chondrocyte division and cartilage matrix synthesis within this mitotic annulus will respond in both negative and positive feedback modes. High levels of hydrostatic pressure in frequently loaded regions will temporarily inhibit the metabolic activity of chondrocytes, whereas lower levels of hydrostatic pressure in adjacent regions, as well as in the same region immediately before and after pressure levels peak, would be expected to stimulate chondral modeling (Fig. 2). Furthermore, #uid #ow within the cartilage induced by mechanical deformation is expected to have a positive e!ect on cartilage growth and metabolism because it aids in moving nutrients through the extracellular #uid to growing chondrocytes (Mow et al., 1984; Lanyon & Rubin, 1985). Frequently #uctuating levels of hydrostatic pressure would also
inhibit the progression of ossi"cation (Carter & Wong, 1988, 1990), possibly by maintaining the metabolic activity of hypertrophic chondrocytes and thereby suppressing calci"cation (Hunziker, 1992). The model assumes that an equilibrium state will be established soon after growth is stimulated under a given load. Mechanotransduction will not induce local tissue deposition again unless the range of hydrostatic pressure exceeds the level at which equilibrium was reached; however, systemic growth will probably continue under the regulation of circulating growth factors. 3. Discussion The goal of this paper is to present a chondral modeling theory that incorporates new information in order to explain previously unexplained facts. The "rst of these unexplained phenomena is related to the general role of mechanical factors in limb joint morphogenesis. Ogden (1980, p. 167) stated that &&postnatally, joint motion and joint reaction forces are extremely consequential to the "nal adult joint contours'' and Frost (1999,
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p. 168) has argued that &&chondral modeling determines the curvature, shape, congruence and smoothness of a joint's articular surfaces''. The speci"c ways in which joint movement and loading in#uence the shape of developing articular surfaces have, however, remained unclear. Evidence from "nite element models of stress distribution in articular cartilage, in vitro studies of load distribution in cartilage explants, and in vitro studies of chondrocyte metabolism in response to mechanical perturbation together suggest that mechanotransduction (Moss, 1997) is an important determinant of limb joint growth and form. Speci"cally, chondrocyte proliferation and di!erentiation in growing articular cartilage requires cell}cell and cell}extracellular matrix interactions induced by mechanical stimuli (Cancedda et al., 1995). The regulation of cartilage growth by mechanical load is therefore a primary mechanism by which extrinsic factors in#uence limb joint morphogenesis. Furthermore, the chondral modeling response is an important process that enables developing articular units to adapt to changes in their mechanical environment during growth. The second unexplained observation addressed in this paper is related to observed scaling patterns of limb joint curvature values in mammals. Limb excursion angles have been observed to decrease with increasing body size in mammals in order to maintain similar levels of peak bone stress during locomotion (McMahon, 1975; Biewener, 1983; Rubin & Lanyon, 1984b; Biewener et al., 1986). Observations on limb kinematics in developing mammals show that infants and juveniles are characterized by highly #exed limb positions whereas subadults and adults exhibit more extended limb postures (Langworthy, 1925; Hurov, 1991). The model presented in this paper suggests that if limb excursion angles decrease with age and increasing body mass in growing mammals then limb joint curvature values should also be expected to decrease. Hindlimb stride length increases with increasing body size in mammals so that stride frequency decreases in proportion to (body mass)~0.14 (Heglund et al., 1974; Pennycuick, 1975). Decreasing stride frequency is not expected to in#uence the rate of chondral modeling
since the chondrocytes are responding to load level di!erentials within the tissue rather than overall frequency of loading per unit time. Low ranges of angular excursion experienced at a joint throughout ontogeny would be expected to generate relatively low levels of hydrostatic pressure in the most anterior and posterior regions of a joint (Fig. 2). The rates of chondroctye division and matrix synthesis within the mitotic annulus in these regions should be quite high since levels of hydrostatic pressure are #uctuating but not excessive. In contrast, the more central region of each articular unit would experience levels of hydrostatic pressure that are frequently above growth-stimulating levels. Modeling would therefore be expected to proceed at a relatively slower rate in this heavily loaded region. Eventually, this pattern of growth would increase the bearing area of the articular surface and thereby average loads across the joint by decreasing the degree of anteroposterior curvature of each condyle. This prediction of the model ia borne out by data showing that knee joint curvature values decrease with age and increasing
FIG. 3. Bivariate plot of logged normalized knee joint curvature values against logged femoral length values for a mixed cross-sectional growth series of 15 post-natal Didelphis virginiana individuals. Curvature is measured in the sagittal plane on the distal articular surface of the femur and is calculated following Biewener (1983) and Hamrick (1996). The sample includes animals ranging in age from 60 days (approximately pouch exit; Hamrick, 1999) to adulthood. Note that joint curvature values decrease post-natally with increasing age and size. y-intercept"5.11; slope"!0.20; r"0.78; p"0.001.
CHONDRAL MODELING THEORY
body size during post-natal development in the didelphid marsupial Didelphis virginiana (Fig. 3). The model may also explain Frost's (1999) observation that joint curvatures decrease during growth, more so in normal than in paralysed limbs. These preliminary results suggest that ontogenetic scaling patterns of limb joint curvature values in mammals may result from the action of local, extrinsic biophysical processes acting in concert with systemic, intrinsic growth factors. A similar explanation has been proposed by Van der Meulen & Carter (1995) to account for both intra- and inter-speci"c scaling patterns of diaphyseal dimensions in mammals. The importance of mechanical factors in regulating chondroosseous development underscores the need for analyses which examine covariances among constituent musculoskeletal elements during growth (Hall, 1990; Herring, 1994; Smith, 1994). This type of research program is necessary in order to elucidate the mechanisms that preserve the match between post-cranial structure, function, and locomotor performance throughout mammalian ontogeny and phylogeny (Galis, 1996). I am grateful to Drs D. Carrier, M. J. Ravosa, C. Owen Lovejoy, and an anonymous reviewer for providing helpful comments on the manuscript. Dr. J. Marcinkiewicz generously donated specimens of Rattus. Funding for this research was provided by National Science Foundation Grant IBN-9603808. REFERENCES AHMED, A. M. & BURKE, D. L. (1983). In vitro measurement of static pressure distribution in synovial joints. I. Tibial surface of the knee. J. Biomech. Engng 105, 216. ARCHER, C. W. (1994). Skeletal development and osteoarthritis. Ann. Rheum. Dis. 53, 624}630. ARCHER, C. W., MORRISON, H. & PITSILLIDES, A. (1994). Cellular aspects of the development of diarthrodial joints and articular cartilage. J. Anat. 184, 447}456. ARCHER, C. W., MORRISON, H., BAYLISS, M. T. & FERGUSON, M. (1996). The development of articular cartilage: II. The spatial and temporal patterns of glycosaminoglycans and small leucine-rich proteoglycans. J. Anat. 189, 23}35. BIEWENER, A. (1983). Allometry of quadrupedal locomotion: the scaling of duty factor, bone curvature, and limb orientation to body size. J. Exp. Biol. 105, 147}171. BIEWENER, A., SWARTZ, S. & BERTRAM, J. (1986). Bone modeling during growth: dynamic strain equilibrium in the chick tibotarsus. Calc. ¹iss. Int. 39, 390}395.
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BURR, D. B. (1997). Muscle strength, bone mass, and agerelated bone loss. J. Bone. Min. Res. 12, 1547}1551. CANCEDDA, R., CANCEDDA, F. & CASTAGNOLA, P. (1995). Chondrocyte di!erentiation. Int. Rev. Cytol. 159, 265}358. CARRIER, D. R. (1983). Postnatal ontogeny of the musculoskeletal system in the black-tailed jack rabbit (¸epus californicus). J. Zool. 210, 27}55. CARRIER, D. R. (1995). Ontogeny of jumping performance in the black-tailed jackrabbit (¸epus californicus). Zool. 98, 309}313. CARRIER, D. R. (1996). Ontogenetic limits on locomotor performance. Physiol. Zool. 69, 467}488. CARTER, D. R. (1987). Mechanical loading history and skeletal biology. J. Biomech. 20, 1095}1109. CARTER, D. R. & WONG, M. (1988). The role of mechanical loading histories in the development of diarthrodial joints. J. Orthop. Res. 6, 804}16. CARTER, D. R. & WONG, M. (1990). Mechanical stresses in joint morphogenesis and maintenance. In: Biomechanics of Diarthrodial Joints (Mow, V. C., Radcli!e, A. & Woo, S. L. Y., eds), pp. 155}174. New York: Springer-Verlag. CRAIG, F., BENTLEY, G. & ARCHER, C. (1987). The spatial and temporal pattern of collagens I and II and keratan sulphate in the developing chick metatarsophalangeal joint. Development 99, 383}391. FELL, H. B. & CANTI, R. B. (1934). Experiments on the development in vitro of the avian knee joint. Proc. R. Soc. ¸ond. 116, 316}327. FRANCIS-WEST, P., PARISH, J., LEE, K. & ARCHER, C. (1999). BMP/GDF-signalling interactions during synovial joint development. Cell ¹iss. Res. 296, 111}119. FRANKEL, V. H., BURSTEIN, A. H. & BROOKS, D. B. (1971). Biomechanics of internal derangement of the knee. J. Bone Jt Surg. 53A, 945}962. FROST, H. M. (1979). A chondral modeling theory. Calc. ¹issue Intl. 28, 181}200. FROST, H. M. (1994). Perspectives: a vital biomechanical model of synovial joint design. Anat. Rec. 240, 1}18. FROST, H. M. (1999). Joint anatomy, design, and arthroses: Insights of the Utah paradigm. Anat. Rec. 255, 162}174. GALIS, F. (1996). The application of functional morphology to evolutionary studies. ¹rends Ecol. Evol. 11, 124}129. HAINES, R. W. (1947). The development of joints. J. Anat. 81, 33}55. HALL, B. K. (1990). Bone, Vol. 6. Bone Growth 2 Mechanical Factors, Skeletal Components and Consequences. Boca Raton, FL: CRC Press. HAMRICK, M. W. (1996). Articular size and curvature as determinants of carpal joint mobility and stability in strepsirhine primates. J. Morphol. 230, 113}127. HAMRICK, M. W. (1999). Development of epiphyseal structure and function in Didelphis virginiana (Marsupiala, Didelphidae). J. Morphol. 239, 283}296. HEGLUND, N. C., TAYLOR, C. R. & MCMAHON, T. A. (1974). Scaling stride frequency and gait to animal size: mice to horses. Science 186, 1112}1113. HERRING, S. W. (1994). Development of functional interactions between skeletal and muscular systems. In: Bone (Hall, B. K., ed.), Vol. 9 pp. 165}191. Boca Raton: CRC Press. HINCHLIFFE, J. R. & JOHNSON, D. R. (1983). Growth of cartilage. In: Cartilage, (Hall, B. K., ed.), Vol. 2, pp. 255}295. New York: Academic Press.
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HUNZIKER, E. B. (1992). Articular cartilage structure in humans and experimental animals. In: Articular Cartilage and Osteoarthritis (Kuettner, K., Schleyerbach, R., Peyron, J. & Hascall, V.), pp. 183}199. New York: Raven Press. HUROV, J. R. (1991). Rethinking primate locomotion: what can we learn from development? J. Motor Behav. 23, 211}218. LANGWORTHY, O. R. (1925). The development of progression and posture in young opossums. Am. J. Physiol. 74, 1}13. LANYON, L. & RUBIN, C. (1985) Functional adaptation in skeletal structures. In: Functional
RADIN, E. & PAUL, I. (1970). Does cartilage compliance reduce skeletal impact loads? Arth. Rheum. 13, 139}144. RADIN, E. & PAUL, I. (1971). Response of joints to impact loading. Arth. Rheum. 14, 357}362. RUANO-GIL, D., NARDI-VILARDAGA, J. & TEJEDO-MATEU, A. (1978). In#uence of extrinsic factors on the development of the articular system. Acta Anat. 101, 36}44. RUBIN, C. & LANYON, L. (1984a). Regulation of bone formation by applied dynamic loads. J. Bone Jt Surg. 66, 397}402. RUBIN, C. & LANYON, L. (1984b). Dynamic strain similarity in vertebrates: an alternative to allometric limb bone scaling. J. ¹heor. Biol. 107, 321}327. RUBIN, L. & LANYON, L. (1987) Osteoregulatory nature of mechanical stimuli: function as a determinant for adaptive remodeling in bone. J. Orthop. Res. 5, 300}310. SMITH, K. K. (1994). Integration of craniofacial structures during development in mammals. Am. Zool. 36, 70}79. SMITH, R., RUSK, S., ELLISON, B., WESSELLS, P., TSUCHIYA, K., CARTER, D., CALER, W., SANDELL, L. & SCHURMAN, D. (1996). In vitro stimulation of articular chondrocyte mRNA and extracellular matrix synthesis by hydrostatic pressure. J. Orthop. Res. 14, 53}60. TAKAHASHI, K., KUBO, T., KOBAYASHI, K., IMANISHI, J., TAKIGAWA, M., ARAI, Y. & HIRASAWA, Y. Hydrostatic pressure in#uences mRNA expression of transforming growth factor-beta 1 and heat shock protein 70 in chondrocyte-like cell line. J. Orthop. Res. 15, 150}158. THOROGOOD, P. (1983). Morphogenesis of cartilage. In: Cartilage (Hall, B. K., ed.), Vol. 2, pp. 223}254. New York: Academic Press. URBAN, J. (1994). The chondrocyte: a cell under pressure. Br. J. Rheum. 33, 901}908. VAN DER MEULEN, M. C. H. & CARTER, D. R. (1995). Developmental mechanics determine long bone allometry. J. theor. Biol. 172, 323}327. WILLIAMS, P. L. (1995). Gray's Anatomy, 38th edn. London: Churchill Livingstone. WOLPERT, L. (1969). Positional information and the spatial pattern of cellular di!erentiation. J. theor. Biol. 25, 1}47. WOLPERT, L. (1978). Pattern formation in biological development. Sci. Am. 239, 154}164. WONG, M., WUETHRICH, P., BUSCHMANN, M., EGGLI, P. & HUNZIKER, E. (1997). Chondrocyte biosynthesis correlates with local tissue strain in statically compressed adult articular cartilage. J. Orthop. Res. 15, 189}196.