the periodontal ligament ( pdl ) is a fibrous connective tissue that firmly binds the tooth to its surrounding bony socket .
its principal function is the mechanical support of the tooth during mastication [ 14 ] .
( 2003 ) , and chiba ( 2004 )   have described the mechanical strength and viscoelasticity of this tissue structure .
the extracellular compartment of the pdl tissue consists mostly of collagen fibre bundles with just a few oxytalan fibres , the latter running at approximately right angles to the collagen fibre bundles .
these fibres are embedded in ground substances together with cells , blood vessels , and nerves .
this review article describes the mechanical properties of the pdl with emphasis on the relations between its mechanical function and structural components .
our intention is to explore these relations to improve our understanding of the mechanisms behind the tooth support function of the pdl .
a pioneering study by yamada 's group was the first to measure the mechanical strength of the pdl .
they reported the force required to extract a tooth from its socket using specimens from human unembalmed cadavers ( table 1 ) . using a similar technique ( figure 1 ) , chiba and his colleagues measured the force required to extract teeth on the normal ( table 1 ) and
experimentally altered pdl in experimental animals [ 6 , 9 ] . since these raw values showed a rather simple association with tooth size ,
standardised values for mechanical strengths ( n / mm ) of the pdl per area facing the roots were then calculated   ( table 2 ) . thus , the mechanical strengths for human and mouse pdls show similar values ranging between 1.2 and 1.7 , and 1.8 and 3.0  n / mm , respectively .
therefore , the application of standardisation principles eliminated this variation due to size differences among species .
however , it was pointed out [ 11 , 14 ] that tooth extraction procedure may introduce an artifact , since the fibres would tend to rupture unevenly due to the root curvature and the different vertical alignment of the fibres : the apical fibres in the vertical direction would rupture first , followed by the horizontal fibres .
further , it is difficult to measure the surface area of the pdl facing the tooth roots . to control these artifacts ,
atkinson and ralph ( 1977 ) used a tooth - pdl - bone complex for tensional loading of the pdl .
further , ralph ( 1982 ) developed a preparation of a transverse section of a tooth with its surrounding pdl and alveolar bone and a technique for loading the pdl in shear .
1986 ) have devised an elaborate technique for shear loading of the human pdl using a similar specimen .  
thus , the artifact due to root curvature can be eliminated and it is now possible to obtain a standardised stress - strain curve of the pdl in shear [ 1222 ] or tension [ 11 , 2325 ] , allowing for comparisons between different species and between different sizes of teeth . 

the mechanical strengths of the pdl are of the same order in different sizes of teeth of different species . when compared to other connective tissues [ 2830 ] , the mechanical strength of the pdl was found to be most similar to that of skin , which comprises a three - dimensional mesh of collagen fibres .
interestingly , the mechanical strength of the rat tail tendon , which is composed of parallel - fibred collagen , is about 10 times those of the pdl . as cortical bone and tooth dentine containing large amounts of collagens
are mineralised , their mechanical strengths are 10- to 40-fold greater than that of the pdl .
artificial materials such as glass fibre and steel show strengths 200- to 600-fold greater   than those of the pdl . mechanical strength is measured as the load needed to fracture a specimen , which causes breaks in the covalent linkages of the collagen molecular chains and slippages between the unit molecular chains . from the functional point of view
, the ratio of the breaking stress to the stress experienced during function may be used to determine the safety margin ( safety factor ) of each tissue , as pointed out by alexander ( 1981 ) .
engineers design structural elements to have safety margins between 5 and 10 [ 32 , 33 ] .
komatsu et al . ( 1998 ) noted that the safety margin for the pdl ranges between 2 and 5 .
tendons and bones have similar safety margins between 1 and 6 [ 29 , 31 ] .
biological tissues or structures with this range of safety margins are considered strong enough to successfully fulfill their support function specific to their locations . in order to elucidate the tooth support mechanisms ,
chiba 's group systematically investigated the effects , on the mechanical properties of the pdl , of various experimental factors   such as periodontal disease [ 10 , 22 ] , hypofunction [ 18 , 35 , 36 ] , orthodontic forces [ 3739 ] , treatment with inhibitors ( lathyrogens ) of collagen cross - linking and an inhibitor ( hydrocortisone ) of collagen degradation or turnover [ 8 , 4043 ] , age [ 7 , 17 , 20 , 44 , 45 ] , and root levels [ 19 , 21 ] .
they found that the mechanical properties were sensitive to both experimental alterations and to differences in the content , direction , and organisation of the collagen fibre components of the pdl .
more specific investigations were done by in vitro treatment of mechanical specimens with specific enzymes .
the enzyme clostridium histolyticum collagenase cleaves the peptide bonds in collagen with specificity for the pro - x - gly - pro - y region and particularly between x and gly .
immunofluorescent analysis reveals that this enzyme digests types i and iii collagens ( figure 3 ) , which are the dominant types of collagen in the pdl .
kawada and komatsu ( 2000 ) have investigated the role of collagen fibres in the mechanical support of the pdl using collagenase . in vitro treatment of pdl specimens with
collagenase caused concentration - dependent removals of collagens ( figures 4 and 5 ) and reductions in mechanical strength of the pdl ( figure 6 ) .
image analyses were done after collagenase treatment of specimens : the area occupied by birefringent fibres within each square ( 30  30  m ) on each section ( figure 4 ) was analysed . in control specimens treated with pbs ( figure 5(a ) ) ,
large regional differences in the area occupied by birefringent fibres were seen across the pdl : birefringent collagen fibres occupy 61%78% of the squares in the pdl near the cementum surface . because the region of the pdl near the bone is highly vascular and innervated ,
. figures 5(b)5(d ) shows concentration - dependent digestions in the collagen fibres in the pdl specimens .
the total areas occupied by birefringent collagen fibres in the regions 0120  m from the cementum surface are smaller at the higher concentrations of collagenase . however , since the regions 120180  m distant contain blood vessels , nerve fibres , and bones , the reductions are relatively small .
treatments with 8 , 16 , and 24 units of collagenase reduced the fibre areas by 20%36% , 50%75% , and 3976% , respectively . from the analysis of the shear stress - strain curves ( figure 6 ) , treatments with 8 , 16 , and 24 units of collagenase were found to reduce the mechanical strengths by 55% , 88% , and 96% , respectively ( figure 6 ) .
these data show that the periodontal collagens are load - bearing , key structural components that provide structural and functional integrity to the ligament .
( 2007 ) have also recently investigated the effect of treatment of pdl specimens with elastase on the mechanical strength .
they found that in vitro treatment with elastase increased fragmentation of the oxytalan fibres ( figure 7 ) and reduced the mechanical strength of the pdl specimen ( figure 8) in a concentration - dependent manner .
this study suggests that the oxytalan fibres may play a role in the mechanical support of the pdl .
it has been reported that the interfibrillar ground substances occupies 65% ( volume ratio ) of the collagen fibre bundles or sheets in the rat pdl .
further studies have investigated the possible roles of interfibrillar ground substances in the mechanical support of the pdl .
after an in vitro treatment with -amylase , scanning electron microscopy ( sem ) and histochemistry observed removal of interfibrillar substances and remnant , exposed collagen fibre bundles .
the treated pdl specimens had concentration - dependent reduced mechanical strengths . however , as the authors did not quantify the fibre components in the specimens after the treatment , it is difficult to determine the relative contribution of interfibrillar substances to changes in strength .
other studies have used edta to remove the interfibrillar substances , and this has been confirmed in pdl specimens by immunohistochemistry with an antibody against chondroitin 6-sulfate and an antibody against chondroitin 4- and dermatan sulfate which are major proteoglycans of the interfibrillar substances in the pdl [ 50 , 51 ] , as well as via sem .
recent immunohistochemical and ultrastructural studies have shown that proteoglycan filaments run orthogonal and parallel to the collagen fibrils in human periodontal ligament and gingiva .
it is assumed that the treatment with -amylase or edta reduced the mechanical strength of the pdl not only by removing the interfibrillar substances but also by reducing the interactions between collagen fibrils and proteoglycans .
from the functional point of view , physiological stress levels are below the mechanical strength of the tissues and physiological responses exhibit time - dependence .
such functional mechanical responses may intimately be related to the viscoelastic time - dependent responses .
the viscoelastic responses of the pdl have been examined by hysterysis , creep , and stress - relaxation tests .
kurashima ( 1963 )   studied the viscoelastic behaviour of the pdl by measuring stress - relaxation responses in the human pdl and its applicability to the maxwell model .
wiils and picton ( 1972 , 1978 ) used a voigt model to describe the creep behaviour of the pdl [ 54 , 55 ] .
( 1990 ) used a linear viscoelastic model to simulate the behaviour of the pdl .
the studies by moxham and berkovitz are not only a description of the creep behaviour of the pdl of the rabbit incisor ( 1981 )   but also an investigation into a role of collagen crosslinks in the creep behaviour ( 1984 ) . by administration of an inhibitor of collagen cross - linking ( lathyrogens ) , reductions of collagen cross - linking in collagen fibres occur .
as expected , the instantaneous and gradual mobilities of the tooth were greater in the lathyritic than in the pair - fed animals , indicating a role of cross links of the collagen fibres in the viscoelastic response of the pdl .
the viscoelastic response of the pdl has also been demonstrated by varying the velocity of loading , in studies by chiba and komatsu ( 1993 ) , komatsu and chiba ( 1993 ) , and komatsu and chiba ( 1996 ) [ 16 , 60 , 61 ] .
these experiments investigated the shear stress - strain properties of the pdls in the rat incisor and molar teeth at a wide range of loading velocities using a custom - made testing apparatus .
the slowest velocity ( 1  mm/24  h ) imitates the eruption rate of the rat mandibular incisor ; the fastest one was 10  mm/24  h , equivalent to 7  mm / min .
they found that the linear parts of the stress - strain curves became steeper and the shear mechanical strength increased with increasing velocity , demonstrating typical characteristics of viscoelastic tissues .
the mechanisms responsible for decreased mechanical stress at slower strain rates have yet to be determined but may involve the increased time available for stress - relaxation of the tissues at lower velocities .
several methods of measurement and analysis of the stress - relaxation response of the pdl have recently been reported [ 13 , 17 , 20 , 26 , 6266 ] .
the distinctive property of the stress - relaxation of the pdl is that the amount of stress - relaxation during 10 minutes reaches about 50% of the initially applied stress , which is greater than those of other soft connective tissues .
these phenomena indicate that the pdl tissue dissipates the strain energy stored in the tissue , during excessive force application , through viscoelastic responses [ 26 , 27 , 62 ] .
this mechanism could reduce the risk of injury to the pdl in the case of prolonged static deformation . this sort of viscoelastic response may play an important physiological role in the tooth support mechanisms of the pdl .
in this chapter , i will introduce a typical method for measurement and analysis of stress - relaxation response of the pdl as described by sanctuary , komatsu , and botsis ( 2003 , 2007 ) [ 62 , 63 ] . from a rabbit hemimandible ,
a transverse section ( about 0.25  mm in thickness ) of the middle region of the incisor tooth with its surrounding pdl and bone is cut .
then , the original width ( wi ) of the pdl can be measured with a stereomicroscope as the distance ( about 0.45  mm ) between the bone and cementum surfaces at the central region on the lingual side of the tooth . both of the lateral parts of each section are trimmed , and then a final specimen is obtained .
the final rectangular specimen consists of tooth , pdl , and bone ( figures 9(a ) and 9(b ) ) .
the direction of most of the principal collagen fibre bundles in the pdl of the specimen is almost parallel to the direction of testing , as evident under polarised light microscopy ( figure 9(c ) ) .
the sectional area ( sa , mm ) of the pdl can be calculated as the breadth ( mm )  thickness ( mm ) of the specimen .
stress - relaxation tests require precise and quick movements of the actuator and preservation of the initially applied deformations during the relaxation process .
a novel uniaxial testing machine was designed by komatsu and chiba ( 2001 )   ( figure 10 ) . for stress - relaxation tests , this machine was improved ; the improvements   include , ( 1 ) a stepping motor with greater torque , ( 2 ) uniaxial movement of the actuator by more precise regulation via a pc - controlled stepping motor , ( 3 ) a new load cell with negligible compliance , and ( 4 ) improved slippage control of the specimen between clamps during repeated mechanical tests via the use of waterproof sandpaper affixed to the clamps . by using the improved testing machine ,
initial deformations were able to remain nearly constant during relaxation tests , with mean values for the deformations of 5756 , 7877 , and 9997  m over a 300-second period .
these changes are negligible compared with the overall deformation levels , indicating a satisfactory regulation during their stress - relaxation tests . a standard ( mean ) load - deformation curve
is computed from several specimens to estimate the nondestructive range of deformation for the pdl specimens for stress - relaxation tests .
it has been shown that non - destructive range of deformation does not exceed the middle portion of the linear segment of the stress - strain curve for a pdl specimen [ 68 , 69 ] .
therefore , the functional and non - destructive range of deformation may be determined to be below 100  m from the mean load - deformation curve . to ensure the reproducibility of results as pointed out previously [ 28 , 62 , 63 , 70 ] , each specimen
is subjected to three cycles of tensile and compressive loadings between + 35 and 35  m before stress - relaxation tests . the specimen
is then stretched to a deformation level of 35  m at the fastest speed ( 63  mm / min ) of the testing machine , the movement of the actuator is abruptly stopped , and the deformation is kept constant for 300 seconds to obtain a load - relaxation curve .
the specimen is then returned to its original width at the same speed . after a 300-second recovery period , the stress - relaxation tests are repeated sequentially at three different deformation levels ( 55 , 75 , and 95  m ) with a recovery period of 300 seconds between each test .
the load - relaxation response after the initial deformation is characterised by a sharp decrease in load , followed by a gradual decrease .
finally , the specimen is first loaded in compression and then in tension at 1  mm / min until rupture of the pdl .
the mechanical homogeneity of the specimen can be assessed by comparing its load - deformation curve with the standard load - deformation curve .
load f(t ) and deformation d(t ) at time ( t ) are transformed into stress (t ) and strain (t ) , respectively , using the formulae , f(t)/sa = (t ) , and d(t)/wi = (t ) .
the relaxation process of a biological specimen may be represented as a relaxation modulus g(t ) : 
										 ( 1)g(t)=(t)(t ) . 

g(t ) is then normalised with respect to the initial value g(0 ) to give a normalised relaxation modulus gr(t ) as 
										 ( 2)gr(t)=g(t)g(0 ) . 

figure 11(a ) shows mean stress - relaxation responses of the pdl at different deformation levels as represented by gr(t ) . in this instance , notice that the values for gr(t ) initially decreased rapidly and then did so gradually thereafter .
the amounts of the stress - relaxations during 300 seconds are less at greater deformations ( anova , p < .001 ) : the mean relaxations in this series were 63% , 53% , 48% , and 44% at 35 , 55 , 75 , and 95  m , respectively .
as the normalised relaxation curves gr(t ) at different strains do not coincide , the behaviour of the pdl can be considered as nonlinear [ 63 , 71 ] .
the nonlinearity of responses implies that several mechanisms are involved in tooth support [ 53 , 62 , 63 , 71 ] . a generalised model for viscoelastic materials
can be considered in which several maxwell elements are assembled in parallel . the relaxation process may be expressed as 
 ( 3)gr(t)=aiexp  ( ti ) , 
									 where ai and i are the ratio and relaxation time ( s ) of each exponential function , respectively . the stress - relaxation process of the pdl as represented by gr(t ) is well described by a function with three exponential decay terms and a constant ( figure 11(b ) ) as 
 ( 4)gr(t)=a1exp  ( t1)+a2exp  ( t2)+a3exp  ( t3)+c , 
									 where 1 < 2
< 3 , and c is constant , as in the pdls of rats [ 17 , 20 , 26 , 62 ] , humans , and cows . as 1 , 2 , and
3 are 0.20.4 seconds , 24 seconds , and 100400 seconds , respectively , the stress - relaxation process may consist of short- , medium- , and long - term relaxation components . a1
( anova , p < .02 ) , a2 ( anova , p > .05 ) , and a3 ( anova , p < .001 ) are less at greater deformations ( figure 12(a ) ) .
in contrast , c is greater at greater deformations ( anova , p < .001 ; figure 12(a ) ) .
the three relaxation times show decreasing tendencies at greater deformations ( figure 12(b ) ) .
the lower stress - relaxation values during 300 seconds at greater deformations ( figure 11(a ) ) could be attributable to decreases in the ratios of the short- and long - term relaxation components ( figure 12(a ) ) and , to a lesser extent , to the changes in the relaxation times ( figure 12(b ) ) . in other words
, the viscous components may contribute relatively less than do the elastic components at greater deformations .
it has been suggested that the decrease in the relaxation rate with increasing strain could reflect larger strains causing greater water loss , which causes the tissues to be more elastic ( less viscous ) than tissues subjected to lower strains .
although the viscoelastic response of any biological tissue is likely related to its structure , this relation has not been adequately investigated in the pdl .
komatsu and chiba   have shown by simultaneous recordings of the mechanical responses coupled with polarised - light video - microscopy that the area and brightness of the birefringent collagen fibre bundles in the pdl specimens are intimately related to its stress - strain behaviour .
quantitative polarised - light microscopy has shown to be useful for investigating the macromolecular orientation and organisation of collagen fibres in living connective tissues without the need for staining [ 73 , 74 ] .
komatsu , sanctuary , and botsis ( 2007a )   further applied the simultaneous recording system to observe the structural basis for the mechanisms of viscoelastic response of the pdl . before deformation application ( figure 13(a ) ) , most of the birefringent pdl collagen fibre bundles run parallel to the deformation direction . immediately after applying of a deformation of 95  m ( figure 13(b ) ) , the birefringent fibres are stretched towards the direction of uniaxial testing . during the load - relaxation for 300 seconds ( figures 13(b)13(f ) ,
the stretched bundles show indistinct changes in their arrangement , although there are gradual increases in the brightness of the birefringent fibres during the relaxation .
after the specimen is returned to its original width , it takes several seconds for the pdl fibres to recover their original waviness and birefringence ( figure 13(g ) ) . during stress - relaxation under each deformation , the area occupied by the birefringent fibres initially decreases rapidly and then gradually ( figure 14 ) . in this series ,
the amount of the decrease under 95  m of deformation was less than those under other deformations .
in contrast , during stress - relaxation under each deformation , the brightness of the birefringent fibres initially increases rapidly and then only gradually thereafter ( figure 14 ) . in this series , the mean values of the brightness at 55 , 75 , and 95 
this image analysis reveals the increasing tendency of the brightness of the birefringent stretched collagen fibres of the pdl during the stress - relaxation : the brightness correlates with progress of stress - relaxation under the four different deformations . the increased brightness may reflect that the collagen molecules and fibrils within the stretched collagen fibre bundles progressively align along the direction of the initial strain application during the relaxation .
such internal rearrangement of collagen could be driven by the strain energy imparted to the specimen on initial stretching , which gradually diminishes as the stress relaxes , as suggested by x - ray diffraction studies [ 75 , 76 ] .
2007b ) investigated into the effect of in vitro digestion of collagen with collagenase on the stress - relaxation process of pdl specimens .
the collagenase ( 8 units / ml)-treated specimens relaxed more rapidly than the control specimens over a 600-second period ( figure 15(a ) ) .
the amount of relaxation of the collagenase group was 37% greater than that of the pbs group ( p < .001 ) .
the stress - relaxation processes , as represented by gr(t ) , are well described by a function with three exponential decay terms .
the ratio ( a3 ) and relaxation time ( 3 ) of the third exponential term for the collagenase group ( figures 15(b ) and 15(c ) ) were significantly less than those for the pbs group .
these results show that the partial removal ( 20%36% , see section 2 ) of the collagen fibres from the pdl specimens mainly causes decreases of the ratio and relaxation time for the long - term relaxation component .
the decrease in the ratio may correspond to the decrease in the quantity of the collagen fibres , while the decrease in the relaxation time may be related to the decreased organisation of the collagen fibres .
therefore , it is likely that the viscoelastic properties of the collagen fibres may play an important role in the long - term relaxation component (  = 1900 seconds ) of the stress - relaxation process in the pdl . in the kww relaxation component (  = 1820 seconds ) of bone collagen prepared by demineralization of bone , the viscoelastic properties of the collagen fibres are also likely to play a role .
the viscoelastic responses of the pdl such as stress - relaxation to a load and creep to a strain , as mentioned in the previous chapters so far , are static properties . in contrast , the mechanical responses to oscillations are dynamic properties . with dynamic tests , the frequency dependent viscoelastic responses can be examined .
( 2005 ) have subjected bovine pdl specimens ( preparations similar to those in figure 9 ) to tension - compression harmonic oscillations under physiological conditions , that is , at strain amplitudes between 0.3 and + 0.5 with frequencies between 0.2 and 5  hz ( figure 16(a ) ) [ 26 , 63 ] .
the difference between the peak strain and the peak resulting stress is called phase lag and is expressed as an angle (  ) . for viscoelastic systems , 0 <  < 90. the tangent  is proportional to the ratio between the energy that is dissipated ( loss modulus g ) and the energy that is stored ( storage modulus g ) in the system . the phase lag ( tan   ) was found to be greater in compression than in tension , but independent of this range of frequency ( figure 16(b ) ) in line with other biological tissues .
these results suggest that the dissipated energy was higher in compression than in tension in the pdl tissue .
tanaka et al . ( 2006 )   have measured dynamic shear properties of the porcine incisor and molar pdls at an oscillation amplitude ( figure 17 ) of  = 1% with a wide range of frequencies ( 0.01100  hz ) .
they found that storage modulus g increased with frequency for both pdls while loss modulus g did so only for the incisor pdl ( figure 18(a ) ) .
tan   ( = g/g ) ranged between 0.1 and 0.2 , which was greater in the incisor than in the molar pdl with frequencies between 1 and 100  hz ( figure 18(b ) ) .
the incisor pdl may be considered to have better shock - absorbing characteristics for sudden loading .
shibata et al . ( 2006 )   have investigated the mechanical response of the bovine pdl at 35% of the pdl width with a frequency of 1  hz at different root levels and different locations around the roots .
it was found that the hysterisis and phase lag in compression were much higher than in tension , but independent of root levels ( figure 19 ) and locations around the root .
tanaka et al . ( 2007 )   have also investigated dynamic shear properties of the porcine molar pdl at an oscillation amplitudes of  =   0.5 , 1 , and 1.5% with a wide range of frequencies ( 0.01100  hz ) .
they found that at 2  hz the coronal pdl had a slight , but significantly , greater storage modulus g than the apical pdl while loss modulus g were similar between the two regions ( figure 20 ) .
the discrepancy between the former and latter results remains unknown but might be due to the different modes of loading ( tension - compression and shear ) and/or the different spices . in the bovine pdl as mentioned above [ 26 , 27 ] , the phase lag values in tension and compression ranged between 0 and 0.1 , and 0.2 and 0.4 , respectively .
the dynamic measurements for bovine and porcine pdls suggest that the pdl can absorb more energy in compression than in shear and tension .
recently , gene - targeted and mutant animals have been used as experimental models to explore the role of individual constituents in the biomechanical behaviour of connective tissues .
investigations into stress - relaxation and strain rate sensitivity of tendons from genetically engineered mice have shown greater and faster stress - relaxation among decorin knockout animals and the elastic parameter was less among those with reduced type i collagen .
histological findings in knockout mice suggest that decorin , fibromodulin , and lumican regulate the fibrillar and suprafibrillar organisation of collagen in the pdl [ 82 , 83 ]
. there may be further mechanisms of mechanical adaptation to functional stress including molecular adaptation to mechanical stress , which is now under investigation in the field of the biomechanics .
further , there have recently been an increasing number of reports on altered gene expression and protein changes in fibrillar and net - forming collagens triggered by the sensing and responding of connective tissue cells to mechanical loads .
future studies using such approaches should further elucidate the relations between viscoelastic behaviour and structure of the pdl .
 the mechanical strength of the periodontal ligament ( pdl ) was first measured as force required to extract a tooth from its socket using human specimens . 
 thereafter , tooth - pdl - bone preparations have extensively been used for measurement of the mechanical response of the pdl . in vitro treatments of such specimens with specific enzymes allowed one to investigate into the roles of the structural components in the mechanical support of the pdl . 
 the viscoelastic responses of the pdl may be examined by analysis of the stress - relaxation . 
 video polarised microscopy suggested that the collagen molecules and fibrils in the stretched fibre bundles progressively align along the deformation direction during the relaxation . 
 the stress - relaxation process of the pdl can be well expressed by a function with three exponential decay terms . 
 analysis after in vitro digestion of the collagen fibres by collagenase revealed that the collagen fibre components may play an important role in the long - term relaxation component of the stress - relaxation process of the pdl . 
 the dynamic measurements of the viscoelastic properties of the pdl have recently suggested that the pdl can absorb more energy in compression than in shear and tension . 
 these viscoelastic mechanisms of the pdl tissue could reduce the risk of injury to the pdl . 
1. Introduction
2. The Mechanical Strength of the PDL
3. The Viscoelastic Response of the PDL
4. Analysis of Stress-Relaxation Response of the PDL
5. Dynamic Measurements of Viscoelastic Responses of the PDL
6. Concluding Remarks