| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1 Department of Orthodontics and Craniofacial Developmental Biology, Hiroshima University Graduate School of Biomedical Sciences, 1-2-3 Kasumi, Minami-ku, Hiroshima 734-8553, Japan; and 2 Department of Functional Anatomy, Academic Center for Dentistry Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands;
*corresponding author, etanaka{at}hiroshima-u.ac.jp
Abstract Introduction (I) Nature of Loading Applied to the TMJ Disc (A) ELASTICITY UNDER VARIOUS LOADINGS (B) VISCOELASTICITY (a) Stepwise loading (b) Cyclic loading (II) Biomechanical Properties of the Disc Related to its Composition and Organization (A) COLLAGEN (B) PROTEOGLYCANS (C) TISSUE FLUID (III) Biomechanical Behavior of the Disc (A) ELASTIC CONSTANTS (a) Tensile modulus (b) Compressive modulus (c) Shear modulus (B) VISCOELASTIC PROPERTIES (a)Quasi-static behavior (i) Stress relaxation (ii) Creep (b) Dynamic behavior (IV) Adaptive Changes of the Disc (A) AGE (B) TRAUMA AND PATHOLOGY (V) Concluding Remarks REFERENCES
| Abstract |
|---|
 Top Next |
|---|
Key words. Stress and strain, viscoelasticity, elastic modulus
| Introduction |
|---|
|
TopPreviousNext |
|---|
The articular surfaces of the TMJ are highly incongruent. Due to this incongruence, the contact areas of the opposing articular surfaces are very small. When joint loading occurs, this may lead to large peak loads, which may cause damage to the cartilage layers on the articular surfaces. The presence of a fibro-cartilaginous disc in the joint is believed to prevent these peak loads (Tanne et al., 1991; Scapino et al., 1996), since it is capable of deforming and adapting its shape to that of the articular surfaces. These deformations ensure that loads are absorbed and spread over larger contact areas. In addition, the shape of the disc and the area and location of its contact areas with the articular surfaces change continuously during jaw movement to adapt to the changing geometry of the articular surfaces of the mandible and temporal bone. As a result, there will be a continuous change in the magnitude and location of the deformations that occur. For example, according to the work of Beek et al. (2001b), when loading occurs in the jaw-closed position, the deformations in the disc are spread throughout the entire intermediate zone, while translation of the condyle in the forward direction to obtain a protrusive or open jaw position leads to a concentration of the deformation in the lateral part of the disc. This suggests that certain areas of the disc are more heavily loaded than other areas.
The magnitude of the deformation and resulting stress of the disc is primarily determined by the nature of the applied loads and by the biomechanical properties of the disc, such as stiffness and strength. An understanding of these properties is important for several reasons. First, they determine the role of the disc as a stress-distributing and load-absorbing structure (Nickel and McLachlan, 1994; Beek et al., 2001a). Therefore, the properties of the disc will also influence the stresses and strains that occur in the cartilage layers on the bone surfaces. These stresses and strains are of critical importance for adaptation and wear. For example, mechanical stress affects the proteoglycan synthesis in the disc (Carvalho et al., 1995), resulting in an adaptation of stiffness. Second, precise information on the biomechanical properties of the disc is required to develop suitable joint simulation models, with which the distribution of stress and strain in the structures of the joint can be estimated. In the last decade, several three-dimensional finite element models of the joint have been developed (Korioth et al., 1992; Tanaka et al., 1994, 2001c; Nagahara et al., 1999; Beek et al., 2000). However, thus far, the available models do not include all relevant properties, such as the shock-absorbing capabilities of the disc. Finally, information on the biomechanical properties of the disc is indispensable for the development of replacement materials for TMJ prostheses.
In this paper, the fundamental concepts of the biomechanical behavior of the TMJ disc are reviewed. The review is divided into four parts. The first part introduces some basic definitions and the general physical properties of soft tissues, to facilitate comprehension of the later parts, in which the biomechanical behavior of the TMJ disc is discussed. Part 2 relates this behavior to the composition and organization of the disc, such as its collagen fiber and proteoglycan contents. In part 3, the biomechanical properties of the disc, including elastic modulus and viscoelasticity, are summarized. Finally, in part 4, adaptive changes of the disc in relation to its biomechanics are discussed.
| (I) Nature of Loading Applied to the TMJ Disc |
|---|
|
TopPreviousNext |
|---|
). Obviously, during natural loading of the joint, combinations of these basic types of the disc loading do occur. During compressive loading, the disc becomes shorter in the loading direction; during tensile loading, it is stretched in the loading direction; and during shear loading, one boundary surface of the disc moves parallel to an adjacent surface. During every type of loading, the disc undergoes a deformation, while internal forces are produced within the tissue. The amount of deformation is quantified by the amount of strain, which is defined as the change in length per unit of original length. The internal forces are quantified by the amount of stress, which is defined as force per unit area in Pa (1 Pa = 1 N/m2).
|
). The curve has both elastic and plastic deformation regions. If the structure is not loaded beyond the elastic region, it will return to its original shape once the load is released. If the structure is loaded up to its plastic region, it will not return to its original shape when the load is released. After plastic deformation, the stress will cause permanent damage of the tissue. In the elastic region, a toe region and a transition zone can be distinguished (Fung, 1981; Li et al., 1983), which are more or less arbitrarily divided by the so-called critical point (Tanne et al., 1991; Tanaka et al., 2000). The toe region can be considered as the physiologic range of stress and strain in which the tissue normally functions (Fung, 1981). Beyond the toe region, in the transition zone, the tissue usually will have a large reserve of strength before it ruptures and fails. The physiologic range can be very different for various connective tissues (mesentery, 100-200%; skin, 40%; tendon, 2-5%; Fung, 1981). The physiologic range of the disc is reported to be approximately 4% (canine, tensile strain; Teng et al., 1991).
|
For evaluation of the basic biomechanical characteristic of a tissue, the elastic modulus or Young’s modulus E is commonly calculated. This modulus is defined as the slope of the elastic region (almost linear part) of the stress-strain curve. The tensile and compressive moduli are a measure of the ability of the tissue to resist deformation in the direction of the applied load. These are defined as E = 
/
, where is the stress and is the strain. The shear modulus G is a measure of the ability of the tissue to resist shear stress in a particular plane. It is defined as G = 
/
, where is the shear stress and is the shear strain. Here, the shear strain is the displacement in the direction of the applied force per original thickness (Fig. 1
). In general, the shear modulus tends to be 1/3 to 1/2 of the value of the tensile or compressive modulus.
When the disc is compressed or stretched in one direction, not only will it deform in that direction (primary strain), but it will also become thicker or thinner, respectively, in a direction perpendicular to it (secondary strain). Poisson’s ratio is a measure of the ability of a structure to resist deformation in a direction perpendicular to that of the applied load. Poisson’s ratio (v) is defined as v = y/x, where y is the secondary strain and x is the primary strain. Because the volume does not increase upon loading, the Poisson’s ratio is less than 0.5.
The elastic constants of a tissue (elastic modulus, shear modulus, and Poisson’s ratio) describe the relationship between a load placed on the tissue and the resulting deformation within the elastic range. If the elastic constants have the same values in different loading directions, the tissue is called isotropic. For an isotropic material E, G and v are related as:
 |
However, the elastic constants are generally not equal in all directions. This directional dependency is called anisotropy.
(B) VISCOELASTICITY
The disc exhibits not only elastic but also viscous characteristics. The combination of these effects is called viscoelasticity, i.e., if the disc is subjected to a constant force or deformation, its response varies over time. This results in a characteristic stress-strain behavior when the disc is loaded, i.e., a rapid deformation upon load application, followed by a time-dependent creep or stress-relaxation phase of increasing deformation or reducing stress (Fig. 3). Creep is defined as the strain over time with constant stress; stress-relaxation is the decrease of stress in time with constant strain. Here, the viscoelastic properties are mainly the result of fluid flow through and out of the disc. Immediately after loading occurs, the small permeability of the collagen network impedes instantaneous fluid flow through the collagen network. With time, the load causes the fluid to be driven away from the loaded site, through pores in the collagen network (Scapino et al., 1996). This fluid flow also explains another feature of viscoelasticity, i.e., that the biomechanical behavior of the tissue is dependent on the strain rate and on the time after stress application. For instance, when the strain and stress are applied rapidly, the slope of the stress-strain curve will be steeper than when they are applied slowly.
|
). The parameters obtained from these tests provide valuable information on the tissue behavior as a function of time and are of great importance for our better understanding of mechanical properties of the disc, such as energy dissipation and stress absorption. In a stress-relaxation test, a stepwise deformation with a specific strain level is applied to a specimen, and this strain level is kept constant until the stress reaches an almost steady level. From this test, the relaxation time and the relaxed modulus are obtained. The relaxation time is defined as the time in which the steady level of stress is reached. One calculates the relaxed modulus by dividing the stress value after relaxation, i.e., the relaxed stress, by the specified strain. In a creep test, a certain amount of stress is applied instantaneously and kept constant, and the time-dependent changes of strain are observed. In a restoration test, the stress and strain are observed after removal of the loading. The remaining deformation is called residual strain.
In a viscoelastic material, the stress-strain curve during loading is essentially different from that during unloading, and this feature is called hysteresis (Fig. 3). The area enclosed by the stress-strain curves during loading and unloading is a measure of the amount of energy dissipation. The lower the energy, the more elastic the response of the tissue. The hysteresis energy may dissipate as heat or in the drag of the fluid that is exuded and absorbed during loading and unloading, respectively.
There are many physical models to represent viscoelastic behavior during creep and stress relaxation. In these models, the elastic behavior is usually represented by a spring with an elastic constant. The spring produces a resistance which is proportional to the applied force and determines the stress level after stress-relaxation. The viscous behavior is represented by a dashpot with a viscous constant. Although the dashpot exhibits resistance to stress at the onset of stress application, the resilient force disappears gradually. Of the many available models, the following three models are commonly used (Fig. 4). Maxwell’s model is a serial combination of a linear spring and a dashpot and is used to characterize restoration and hysteresis after stress removal (Fung, 1969). Voigt’s model is a parallel combination of a linear spring and a dashpot and is used to characterize creep features (Fung, 1969). Kelvin’s model is a combination of Maxwell’s and Voigt’s model and has been applied to characterize both creep and stress-relaxation behavior (Fung, 1969). The relationship between stress and strain at a particular time is formulated as + 
= ER( + 
) where and are time constants, and ER is the relaxed modulus after stress-relaxation; the time constant is a measure of the relaxation time. These parameters are commonly used in studies describing the viscoelastic properties of the disc.
|
Under cyclic loading, the disc will quickly settle into a steady-state response. Usually, this steady state is achieved in fewer than 10 cycles (Beek et al., 2001a). Sometimes, there is also some slow secondary creep of the steady-state cycle. However, this is generally negligible compared with the differences in response over the first few cycles of loading. The sizes of the hysteresis loops of the stress-strain curves may change dramatically during the first few cycles of loading and unloading. This is called pre-conditioning (Fung, 1972). Cycle tests of connective tissue specimens at a constant strain rate and at moderate strain levels will show repeatable stress-strain relationships within 7 to 10 cycles of pre-conditioning. The hysteresis loop during loading and unloading, at a constant rate after pre-conditioning, will remain essentially unchanged.
Due to the viscoelastic behavior of the disc, the stress response to a cyclic strain is, in general, out of phase, and the phase difference between the stress and strain is somewhere between 0 and 90°. The schematic representation of the relationship between stress and strain, with a sinusoidally varying stress, for a perfectly elastic material, a viscoelastic material, and a perfectly viscous liquid is shown in Fig. 5. If the material is perfectly elastic (Hookean body), the strain is exactly in phase with the stress, which implies that the phase difference is 0°. If the material is perfectly viscous (Newtonian fluid), the strain is 90° out of phase with stress. For viscoelastic materials, the phase angle 
is somewhere in between 0 and 90°. The complex dynamic modulus E* can be determined experimentally by the application of a sinusoidal strain (Murata et al., 2000). The modulus E* consists of a real part, the storage modulus E', and an imaginary part, the loss modulus E'', shown vectorially in Fig. 5. The magnitude of the complex modulus |E*| is determined by |E*| = /. With the phase angle , the storage and loss moduli, E' and E'', are determined by
|
 |
where E' = |E*| cos, E'' = |E*| sin, i = 
- 1, and tan = E''/E' is the loss tangent. E' describes the elastic deformation under stress and is directly proportional to the energy storage in a cycle of deformation. E'' denotes the viscous deformation and is proportional to the average dissipation or loss of energy as heat in a cycle of deformation. In addition, the tangent of the phase angle () between stress and strain, i.e., the loss tangent (tan), is a measure of the ratio of energy loss to energy stored during cyclic deformation. For a tissue with a high value of the loss tangent, the viscous behavior is stronger than the elastic behavior. In such a tissue, the energy used for its deformation is dissipated as heat and causes changes in the inner structure by movement of fluid.
| (II) Biomechanical Properties of the Disc Related to its Composition and Organization |
|---|
|
TopPreviousNext |
|---|
(A) COLLAGEN
The collagen fibers maintain the shape of the disc, while elastin restores shape during unloading (Scapino et al., 1996). Collagen fibers commonly exhibit waviness ("crimping"). The functional significance of this crimping can be seen in the stress-strain curve (Fig. 2). When a tension is applied to the disc, the first effect is to straighten the crimp, and that accounts for the initial toe region of the curve (Stegenga et al., 1991; Berkovitz, 2000). Thus, the initial toe region reflects a high compliance and corresponds to the straightening of the crimping without any lengthening of the collagen fibers (Gathercole and Keller, 1991). Beyond this initial phase, the collagen fibers begin to extend and become load-bearing. Furthermore, the small permeability of the collagen network impedes interstitial fluid flow through this network (Mow et al., 1984, 1993). Therefore, the loads acting on a cartilaginous structure as the disc are initially transmitted by a pressurization of the incompressible fluid without much deformation of the collagen network (Soltz and Ateshian, 1998). Nonetheless, fluid flow through the collagen network leads to a gradual transfer of the load from the fluid to the collagen fibers. When further loaded, the collagen network deforms, and water is squeezed out of the disc while the orientation of the collagen fibers is re-arranged (Mow et al., 1986; Woo, 1986). The movement of fluid out of the disc and the re-arrangement of the collagen fibers are reversible when the disc is not deformed beyond the physiologic strain range. Even application of significant long-term stresses beyond the physiologic strain range introduces but minor changes in fiber waviness and alignment within the disc (Scapino et al., 1996). This enables the disc to adapt its shape continuously to fit in the space between the opposing articular surfaces and to distribute loads suitably in the TMJ. Collagen gives the disc much of its tensile stiffness and strength.
The thin surface layers of the disc have an architecture different from that of the thick inner layer (Fig. 6). In the superior and inferior surface layers, the collagen fibers are more or less perpendicularly arranged in an antero-posterior and medio-lateral direction (Minarelli et al., 1997). In the inner layer, the orientation of collagen fibers varies markedly in different regions of the disc. The fibers run primarily antero-posteriorly in the intermediate zone and medio-laterally in the anterior and posterior bands. The antero-posterior fibers from the intermediate zone are interlaced with the medio-lateral fibers in both bands (Teng and Xu, 1991). In the central region of the bands, the fibers from the intermediate zone flare superiorly and inferiorly and turn medially and laterally, merging structurally with those of the bands (Mills et al., 1994; Scapino et al., 1996). In the medial and lateral regions of the disc, near the condylar poles, the antero-posterior fibers of the intermediate zone are attached tightly to the poles of the condyle (Teng and Xu, 1991). As a result of these differences in collagen fiber orientation, regional differences and anisotropy in the mechanical properties of the disc can be expected.
|
Proteoglycans are enmeshed in the network of collagen fibers and are virtually immobile. Proteoglycan molecules possess a high viscosity and a large molecular size that reduce their capacity to diffuse through the collagen network, thus resulting in the retention of large amounts of water (Muir, 1973). The result is a stiff viscoelastic material surrounding the collagen fibers. Because of their molecular structure, proteoglycans are ideally suited to resist compressive loadings. Proteoglycans can indirectly modulate the stiffness of the collagen network, since an increase in proteoglycan concentration leads to an increase in the osmotic pressure, which in turn affects the synthesis of collagen (Muir, 1981).
In the disc, the large proteoglycans and the related chondroitin sulfate are preferentially localized in the central area of the intermediate zone and in the anterior and posterior bands (Mills et al., 1988; Nakano et al., 1993; Nakano and Scott, 1996; Mizoguchi et al., 1998). It has therefore been suggested that these parts of the disc encounter heavy compressive loading during function and may be responsible for maintaining the resilience of the disc (Nakano and Scott, 1996). The small proteoglycans, decorin and biglycan, are mainly found in the lateral and medial parts of the intermediate zone and are present in lesser amounts in the central part of the intermediate zone and in the anterior and posterior bands (Scott et al., 1995; Mizoguchi et al., 1998). The expression of decorin mRNA in tendon is promoted by tensile stress (Robbins and Vogel, 1994). Consequently, the distribution of decorin may reflect the distribution of tensile stress in the disc. Decorin can also interact with type I collagen and cause small increases in fibrillar diameter (Scott et al., 1995). This is in line with the observation that the collagen fibrils in the decorin-rich peripheral region of the disc are the thickest (Kuc and Scott, 1994). These biochemical findings for the proteoglycan concentration in different areas of the disc are consistent with results obtained from mechanical tests (see Part III).
(C) TISSUE FLUID
The tissue fluid is a viscous gel and contains mostly water. This fluid can move both inside and through the surface layer of the disc. The collagen and proteoglycans are dispersed in the fluid, making the cartilage a microporous material with a certain permeability. The amount of permeability is particularly significant for compression, since the mechanical response of the disc will depend on it (Beek et al., 2001b). A low permeability means that any substantial exchange of fluid between the inside and outside of the disc must take place over a substantial period of time (e.g., minutes) compared with the physiological loading cycle (1 sec). As a consequence, the disc will maintain its stiffness under compression. In case of a high permeability, a rapid exchange of fluid is possible, which results in a substantial decrease of stiffness.
| (III) Biomechanical Behavior of the Disc |
|---|
|
TopPreviousNext |
|---|
Another problem when the results of various studies are compared is that different tests (for example, compression and tension) have not been performed on the same specimen. Also, as mentioned before, the relationship between stress and strain for the disc is non-linear and time-dependent. For example, the tensile modulus of the porcine disc is about 27 MPa at a strain rate of 0.5 mm/sec, whereas it is about 83 MPa at a rate of 500 mm/sec (Beatty et al., 2001). Thus, when data on elastic moduli are evaluated, consideration should also be given to the strain rate, the magnitude of the applied strain, and the measuring time. In addition, because of structural differences within the disc, the location of the loading and its direction and type (tension, compression, shear) are major factors for determining its elastic properties.
(a) Tensile modulus
The tensile modulus is mainly dependent on the orientation of collagen fibers, because they can resist tension only in the direction parallel to their orientation. As mentioned in Part II, the intermediate zone of the disc consists mainly of antero-posteriorly oriented fibers. Therefore, the tensile modulus and tensile strength of the intermediate zone are larger in the antero-posterior direction than in the medio-lateral direction (Beatty et al., 2001; Tanne et al., 1991; Teng et al., 1991). For example, the tensile modulus of the porcine disc was 76.4 MPa in the antero-posterior direction, whereas it was 3.2 MPa in the medio-lateral direction (strain rate, 500 mm/min; Beatty et al., 2001). Because in the anterior and posterior bands, the collagen fibers run mainly medio-laterally, they have a relatively large tensile modulus and strength in the medio-lateral direction, although no data for the antero-posterior direction are available because of their short antero-posterior length. Interestingly, the antero-posterior tensile moduli of the central and lateral regions of the intermediate zone differ (Tanne et al., 1991; Tanaka et al., 2001a). This suggests differences in collagen fiber distribution between the two regions. In addition, in the bovine disc, the tensile moduli in the lateral and medial regions are higher than those in the central region (Tanaka et al., 2001a), whereas in the canine disc (Tanne et al., 1991), the reverse is true (Table). This difference may be dependent on the difference in masticatory patterns between cattle and dogs. As mentioned above, the dog exhibits mainly chopping strokes during mastication, which may be primarily associated with loadings in the central region. Cattle exhibit lateral translatory movements, as in humans, which may be associated with a shift of the loading to the lateral side of the intermediate zone (Beek et al., 2000).
|
). The possible explanation for this regional difference is that the large chondroitin-sulfate proteoglycans and the related chondroitin sulfate are preferentially localized in the central region of the intermediate zone and in the anterior and posterior bands (Mizoguchi et al., 1998). During compression, these proteoglycans with large molecules may interfere with the flow of fluid out of the disc, resulting in an increase of the compressive modulus. In the medial and lateral regions of the intermediate zone, the major GAG is dermatan sulfate, which is related to the small proteoglycans, decorin and biglycan (Nakano and Scott, 1996). In these regions, the interference of fluid flow is assumed to be lower than in the chondroitin-sulfate-rich regions, resulting in smaller values of compressive modulus and strength. The compressive modulus of the disc is generally considered to be smaller than its tensile modulus. There are only two studies available in which this has been demonstrated by means of the same experimental protocol and material (bovine disc: Tanaka et al., 2001a; del Pozo et al., 2002). In these studies, the tensile modulus ranged between about 22 and 26 MPa, and the compressive modulus between 14 and 17 MPa. The possible explanation for the larger tensile modulus is that the elasticity of the disc is more dependent on the collagen fibers than on the proteoglycans. During tension, the stiffness is primarily due to the resistance produced by the collagen fibers. During compression, the collagen fibers are probably slack, which makes them less effective in resisting compressive stress.
(c) Shear modulus
Investigation of shear properties in synovial joints is of particular interest, because shear stress can result in fatigue, damage, and deformation of cartilage (Spirt et al., 1989; Zhu et al., 1993, 1994). Therefore, data on the shear modulus might contribute to a better understanding of secondary tissue damage.
It is very likely that shear stresses occur during loading of the disc, because the articular surfaces that compress the disc are not parallel. As a result, not all areas of the disc are deformed in the same direction, leading to local shear. Another reason why shear stress occurs in the disc is its non-homogeneous structure. Its inner layer consists mainly of antero-posterior running collagen fibers and the "leaflet-like" proteoglycans (Kuc and Scott, 1994; Nakano and Scott, 1996), whereas the superior and inferior surface layers consist mainly of antero-posteriorly and medio-laterally running collagen fibers and small proteoglycans (Nakano and Scott, 1996; Minarelli et al., 1997). Therefore, these layers are considered to have different biomechanical properties (Nakano and Scott, 1996; Mizoguchi et al., 1998), which might lead to shear stress. This is supported by the results of a finite element study, in which a relatively large shear stress was predicted in a disc consisting of three layers (Tanaka et al., 1994).
With respect to the shear modulus of the disc, thus far, only one study has been published, in which the shear modulus of the intermediate zone of the human disc (strain rate, 0.02 mm/sec) was evaluated (Lai et al., 1998). It appeared that in the central region the shear modulus (about 1.0 MPa) was lower than in the lateral and medial regions (about 1.75 MPa). It has been reported that the shear stress in cartilage is very sensitive to the frequency and direction of the loading and to the amount of compressive strain (Mow et al., 1992). Therefore, the shear behavior of the disc should also be considered as a non-linear, anisotropic, and time-dependent behavior. Future studies need to examine the effects of dynamic shear properties on the disc.
(B) VISCOELASTIC PROPERTIES
(a)Quasi-static behavior
(i) Stress relaxation
When the disc is compressed with a constant strain, it shows a time-dependent stress relaxation (Fig. 7). The produced stress decreases markedly during the initial 5 to 30 sec, after which it levels off to a steady low, but not zero, level (Scapino et al., 1996; Tanaka et al., 1999; del Pozo et al., 2002). The relaxation time of the disc ranges from 3 to 45 sec, and the relaxed stress ranges between ca. 5 and 50% of the initial stress (Fontenot, 1985; Tanaka et al., 1999; del Pozo et al., 2002). These large variations in relaxation time and relaxed stress are due to a dependency of the applied stress level; when large amounts of stress are applied, the curve shows a relatively long relaxation time and a large relaxed stress. These findings indicate that the movement of fluid out of the disc under loading is relatively slow and not proportional to the fluid pressure. Because of this relatively long relaxation time, the loaded disc becomes relatively stiff when it is cyclically loaded—during, for example, chewing and speaking (Beek et al., 2001a).
|
After stress relaxation, a biomechanical equilibrium will eventually occur, which implies a balance between the applied stress and the resistance to this stress in the disc. Before relaxation, a high initial stress acting on the disc is distributed through the whole disc. More than 50% of the initial stress is dissipated. This behavior implies that the disc functions as a stress absorber and a stress distribution material. Without the dissipation of strain energy, storage of excessive strain energy can lead to breakage of the disc and other components of the TMJ (Fontenot, 1985; Teng and Xu, 1991; Nickel and McLachlan, 1994; Tanaka et al., 1999; del Pozo et al., 2002).
(ii) Creep
The creep curves of the disc (Fig. 8) show a marked increase in strain during the initial few seconds, followed by a slow increase, reaching an almost steady level after 3-10 min (compression, Kuboki et al., 1997; tension, Tanaka et al., 2001a). Creep time is longer in compression (more than 10 min; Kuboki et al., 1997) than in tension (3 min; Tanaka et al., 2001a). These findings indicate that fluid flow within and out of the disc is slower during compression than during tension. Creep time appears not to be dependent on loading region (central, lateral, and medial regions of the intermediate zone; Tanaka et al., 2001a) or stress level (10 N, 20 N, and 30 N; Kuboki et al., 1997; 1.0 MPa and 1.5 MPa; Tanaka et al., 2001a). During tension, the initial response to the load is due to stretching of the collagen crimping within the toe region, and the secondary response is due to the elongation of the collagen network and the squeezing of fluid against internal stress. Fluid flow through the network is nonetheless possible, which leads to a gradual transfer of the load from the fluid to the collagen network. This finding also indicates that stress distribution occurs in the disc. Changes in the shape of the disc reduce the amount of stress concentration and probably decrease the progression of injury (Tanaka et al., 2001a).
|
) exhibit a marked decrease in strain during the first 5 sec, and the decrease in strain ceases after a few minutes. This feature indicates that some of the energy used to deform the disc is not released immediately after unloading occurs, and that the return of fluid from outside the disc and the recovery to its original shape are relatively slow (Beek et al., 2001a). The residual strain after creep could be an important factor for the capability for recovery and the prediction of permanent deformation in the disc. The residual strain after 20 min of creep is less than 1%, which is almost similar among the central, lateral, and medial regions of the intermediate zone (Tanaka et al., 2002a). This implies that the disc has a great capability of recovery after sustained stress. The creep time of 20 min is long when compared with in vivo loading conditions, such as sustained clenching. However, sustained stress with high magnitude is considered to generate catabolic effects (Burger et al., 1992). Therefore, information on creep time may help to assess the possible effects of permanent changes of the disc as a result of prolonged stress.
(b) Dynamic behavior
The above-mentioned quasi-static experiments have provided valuable information on how the behavior of the disc changes over time. With quasi-static experimental set-ups, however, only the linear viscoelastic behavior of the disc can be studied. The disc should essentially be approached as a structure with non-linear behavior, and thus its dynamic viscoelastic properties need to be examined, although the mechanisms responsible for stress distribution, energy dissipation, and stress absorption are the same as those for quasi-static loading. Therefore, dynamic experiments have recently been performed (compression, Beek et al., 2001a; tension, Tanaka et al., 2002b). In general, the dynamic properties are determined in cyclic tests at a physiologic strain range (Fig. 9).
|
; Beek et al., 2001a). The phase shift between the strain and stress depends on the difference between the viscous and elastic properties of the disc. In subsequent cycles, the value of the maximum stress decreases asymptotically, and the stress shows an almost steady level after 7 to 10 cycles. Therefore, the hysteresis loop during loading and unloading at a constant rate after 7 to 10 cycles will remain essentially unchanged. The hysteresis loops show that energy is dissipated inside the disc. As a result, dynamic cycle tests enable us to comprehend the viscous and elastic properties of the disc, and its energy dissipation function. The dynamic properties of the disc are dependent on the frequency and strain of loading. For example, in dynamic compression tests on the human disc, the indentation amplitude (strain: 0.25, 0.30, and 0.35) and frequency (0.02, 0.05, and 0.1 Hz) had a proportional effect on the value of the maximal stress and the amount of energy dissipation (Beek et al., 2001a). Furthermore, the maximal stress and the energy dissipation are significantly larger in the intermediate zone than in the anterior and posterior bands (Beek et al., 2001a). In contrast, the anterior band of the bovine disc shows a greater compressive modulus than the intermediate zone in a quasi-static test (del Pozo et al., 2002). Cyclic testing of articular cartilage specimens at a constant strain amplitude and at moderate strain levels showed repeatable stress-strain relationships within 7 to 10 cycles of pre-conditioning (Fung, 1972). Furthermore, it is known that the curves showing the experimental peak and valley stresses in cyclic testing match well with those obtained by the theoretical load-relaxation curves according to the quasi-linear viscoelastic theory (Woo et al., 1988). Therefore, the dynamic properties are likely to exhibit smaller values than the static ones, and present some resemblance to the static modulus after load-relaxation rather than the elastic modulus.
Under dynamic tension, a storage modulus (E') of about 0.7 to 1.4 MPa and a loss modulus (E'') of about 0.1 to 0.2 MPa were found (Tanaka et al., 2002b). These values are very small but close to the relaxed moduli described in previous studies (Fontenot, 1985; Chin et al., 1996). This finding implies that, under cyclic conditions, the disc exhibits a dynamic equilibrium which is similar to that after stress-relaxation. The relaxed modulus of the intermediate zone is larger than that of the anterior band (del Pozo et al., 2002). This suggests that the intermediate zone shows a great capacity of energy dissipation, especially during dynamic loading such as mastication and chewing.
When one compares the results of tests with a relatively large strain (30%; Beek et al., 2001a) with those of tests with a small strain (0.5%; Tanaka et al., 2002b), all dynamic moduli become larger when a larger strain is applied. Presumably, this difference is due to differences in fluid flow. The small permeability of the collagen network (pore size of 10-60; Mow et al., 1984, 1993) impedes the fluid flow through the collagen network. Under small strains, the hydrostatic pressure in the interstitial fluid due to the hydrophilic character of the proteoglycans is in balance with the applied force (Tanaka et al., 2002b). Therefore, the load acting on the disc can be assumed to be carried by pressurization of fluid without much deformation of the collagen network (Soltz and Ateshian, 1998). This mechanism protects the collagen network against extreme local deformations during loading. Under relatively high strain, fluid flow through the collagen network is nonetheless possible, which may lead to a gradual transfer of the load from the fluid to the collagen network (Beek et al., 2001a). When loaded, the collagen network deforms. This enables the disc to adapt its shape continuously to fit the space between the opposing articular surfaces. However, the return of the fluid squeezed out of the disc under loading is relatively slow, as mentioned above. As a result, the disc cannot keep sufficient fluid in itself during cyclic loading, resulting in a higher stiffness than that under small strain.
The values of dynamic viscoelastic E-moduli (|E*|, E', and E'' also increase as the frequency increased from 0.1 to 100 Hz (Tanaka et al., 2002b). In dynamic tensile tests, the dynamic viscoelastic E-moduli are about 2 times larger at 100 Hz than those at 1 Hz (Tanaka et al., 2002b). This non-linear dependency on the frequency is due to fluid flow and squeezing within the matrix of the disc. At higher frequencies, the proteoglycans occupying the interfibrilar spaces interfere with smooth fluid flow, which leads to strain energy dissipation, resulting in a higher stiffness.
| (IV) Adaptive Changes of the Disc |
|---|
|
TopPreviousNext |
|---|
(A) AGE
Age-related changes in viscoelasticity have been extensively studied in connective tissues, such as skin and tendon (Walker et al., 1976; Vogel, 1980; Woo, 1986). The tensile modulus of the rat skin increases with maturation and decreases with senescence (Vogel, 1980). In canine tendon, an increased stiffness and reduced viscoelasticity were found during aging (Walker et al., 1976). Age-related changes have also been demonstrated in the disc. The calcium content of the human disc increases progressively with aging (Takano et al., 1999). The increase in calcification may be caused by an intrinsic aging process or by an altered mechanical stress (Jibiki et al., 1999). With respect to the GAG composition in the disc, the amounts of total and sulfated GAGs markedly increase from mature fetuses to mature adults (Nakano and Scott, 1996). An increase in the content of sulfated GAGs relative to the tissue fluid will elevate the osmotic swelling pressure and, hence, the compressive stiffness of the disc. Accordingly, the material properties of the disc can also be expected to be related to age. Lai et al. (1998) were the first who demonstrated that the shear modulus of the human disc increases with age and suggested that the increase of this modulus may be the result of a decrease of collagen-remodeling capacity. The elastic modulus of normal human discs has a constant value of about 45 MPa up to 50 years of age, but increases thereafter to about 65 MPa (Tanaka et al., 2001b). The elastic moduli of bovine discs increase slightly but significantly from those of the young adult (about 22 MPa) to those of the mature adult (about 25 MPa; Tanaka et al., 2001b). The ratio of collagen to water in the disc increases with age, while the water content remains constant (Nakano and Scott, 1996). Young discs contain relatively more fluid and are capable of releasing much more fluid out of the disc, resulting in a smaller elasticity. In contrast, mature discs consist of relatively abundant collagen fibers, and may exhibit less water loss after relaxation.
(B) TRAUMA AND PATHOLOGY
The biomechanical properties of the disc also change due to trauma and pathology of the TMJ. In the case of pathology or trauma, the quantity of damage exceeds the normal repair capacity of the articular tissues. It has been reported that the articular cartilage of the knee joint shows a reduction in tensile strength, prior to evidence of surface damage (McCormack and Mansour, 1998). This suggests that, under pathologic conditions, the biomechanical properties of the articular cartilage change with molecular composition. Similar observations have been reported for the disc. For example, human pathological discs with extensive degenerative alterations, such as hyalinization and cell-free areas, had significantly greater relaxed tensile moduli than normal discs (Tanaka et al., 2000). Proteoglycans and GAGs in the disc are also redistributed and newly synthesized after an oral splint is worn for two months (Sindelar et al., 2000).
Continuous sustained loading in the joint can also induce increase of joint friction, because only solid contact may exist between the articular surfaces after prolonged loading (Forster and Fisher, 1996, 1999). Continuous loading may lead to an increase of surface roughness of the articular cartilage and subsequently to surface wear (Forster and Fisher, 1999). The resulting increase of friction may induce increased shear stress in the disc. As mentioned above (Part 3), shear stress can be associated with fatigue and damage of the disc and can lead to changes in GAG composition and thus to changes in mechanical properties of the disc.
| (V) Concluding Remarks |
|---|
|
TopPreviousNext |
|---|
The finite element method has been proven to be a suitable tool for approximating the distribution of loads in the structures of the TMJ. Since 1990, several three-dimensional finite element models of the TMJ, including the disc, have been developed (Korioth et al., 1992; Chen and Xu, 1994; Tanaka et al., 1994; Chin et al., 1996; DeVocht et al., 1996; Nagahara et al., 1999; Beek et al., 2000). These models have shown, for example, that the predicted stress in the joint components and the sizes of the contact areas depend on the elastic modulus of the disc (DeVocht et al., 1996; Beek et al., 2000; Tanaka et al., 2001b). However, thus far, the material properties of the disc have been assumed to be linearly elastic in these models. It will be a challenge to develop future models into which the viscoelastic, anisotropic, and heterogeneous properties of the disc are incorporated. A first approximation could be the application of an adequate material model of the disc that includes both fluid and solid constituents. To assess the interaction of the solid matrix and the interstitial fluid, investigators have developed a biphasic theory (Mow et al., 1980), which shows that a large part of the load acting on cartilaginous structures is carried by interstitial fluid pressurization (Soltz and Ateshian, 1998). In contrast to the presently available models of the TMJ, such a biphasic or poro-elastic model would also account for the shock-absorbing properties of the disc.
Wear of the disc has been found primarily in its anterior band (Kopp, 1976) or intermediate region (Werner et al., 1991). The former is supported by the biomechanical and biochemical findings that the anterior band receives the largest loads (Tanaka et al., 1994), resulting in the concentration of chondroitin sulfate in this region (Nakano and Scott, 1989a; Mizoguchi et al., 1998). The latter is also in agreement with various studies predicting that the disc is predominantly loaded in its intermediate zone (DeVocht et al., 1996; Nagahara et al., 1999; Beek et al., 2000). Although the stress distribution in the disc is strongly affected by the direction of loading, the two regions probably play a role in stress absorption and stress distribution during clenching and mastication.
Translation of the condyle in the forward direction, to obtain a protrusive or open-jaw configuration, leads to a concentration of loading in the lateral part of the disc (Beek et al., 2001a; Tanaka et al., 2001c). This would suggest that, during open-close movements, the lateral part of the intermediate zone is primarily subjected to wear and friction. This is supported by Werner et al. (1991), who reported that wear leading to perforations of the disc was mainly located in the lateral part of its intermediate zone. Furthermore, Gallo et al. (2000) suggest that, during mastication, fatigue failure of the TMJ disc could result from shear stress produced by medio-lateral translation of stress location.
More information about the biomechanical properties of the disc is also required for the design of TMJ implants. Some of the available implant materials failed under functional conditions (Silastic—Dolwick and Aufdemorte, 1985; Eriksson and Westesson, 1986; Westesson et al., 1987; Sanders et al., 1990; Tucker and Watzke, 1991; Proplast—Heffez et al., 1987; Florine et al., 1988; Valentine et al., 1989; Wagner and Mosby, 1990). The major reason for these failures is that these biomaterials were not strong enough to withstand the functional loading applied to them.
| REFERENCES |
|---|
|
Top |
|---|
Beek M, Koolstra JH, van Ruijven LJ, van Eijden TMGJ (2000). Three-dimensional finite element analysis of the human temporomandibular joint disc. J Biomech 33:307–316.[Medline]
Beek M, Aarnts MP, Koolstra JH, Feilzer AJ, van Eijden TMGJ (2001a). Dynamic properties of the human temporomandibular joint disc. J Dent Res 80:876–880.
Beek M, Koolstra JH, van Ruijven LJ, van Eijden TMGJ (2001b). Three-dimensional finite element analysis of the cartilaginous structures in the human temporomandibular joint. J Dent Res 80:1913–1918.
Berg R (1978). Anatomía topográfica y aplicada de los animals domésticos. Madrid: AC Libros Científicos y Técnicos.
Berkovitz BKB (2000). Collagen crimping in the intra-articular disc and articular surfaces of the human temporomandibular joint. Arch Oral Biol 45:749–756.[Medline]
Bermejo FA, Puchades-Orts A, Sánchez del Campo F, Panchón-Ruiz A, Herrera-Lara M (1987). Morphology of the meniscotemporal part of the temporomandibular joint and its biomechanical implications. Acta Anat 129:220–226.[Medline]
Bermejo A, González O, González JM (1993). The pig as an animal model for experimentation on the temporomandibular articular complex. Oral Surg Oral Med Oral Pathol 75:18–23.[Medline]
Boyd RL, Gibbs CH, Mahan PE, Richmond AF, Laskin JL (1990). Temporomandibular joint forces measured at the condyle of Macaca arctoides. Am J Orthod Dentofac Orthop 97:472–479.[Medline]
Brehnan K, Boyd RL, Laskin J, Gibbs CH, Mahan P (1981). Direct measurement of loads at the temporomandibular joint in Macaca arctoides. J Dent Res 60:1820–1824.
Burger EH, Klein-Nulend J, Veldhuijzen JP (1992). Mechanical stress and osteogenes
, whereas Kelvin’s model is composed of a combination of two springs and a dashpot. A linear spring produces an instantaneous deformation proportional to the stress. A dashpot produces a velocity proportional to the stress at any instant.
, angular velocity) for a perfectly elastic solid (A, Hookean body), a viscoelastic material (B), and a perfectly viscous liquid (C, Newtonian body). In a viscoelastic material, the phase difference between stress and strain is somewhere between (
/2 > 
