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Age-related and regional differences in the stress–strain and stress–relaxation behaviours of the rat incisor periodontal ligament
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Journal of Biomechanics 37 (2004) 1097–1106
Age-related and regional differences in the stress–strain and stress–relaxation behaviours of the rat incisor periodontal ligament K. Komatsua,*, T. Shibataa, A. Shimadaa, A. Viidikb,c, M. Chibaa a
Department of Pharmacology, School of Dental Medicine, Tsurumi University, 2-1-3 Tsurumi, Tsurumi-ku, Yokohama 230-8501, Japan b Department of Connective Tissue Biology, Institute of Anatomy, University of Aarhus, Aarhus C DK-8000, Denmark c Sozialmedizinisches Zentrum Sophienspital, Apollogasse 19, Wien A-1070, Austria Accepted 19 November 2003
Abstract Groups of rats were killed at 2, 6, 12, and 24 months of age. From dissected left and right mandibles in each rat, three pairs of transverse sections were cut at the incisal, middle, and basal regions of the incisor. One section in each pair was loaded until failure and a stress–strain curve for the periodontal ligament (PDL) was obtained. The other section was loaded to up to 50% of the maximum shear stress as determined from the contralateral section and then kept at a constant strain for 10 min, to obtain the stress–relaxation curve at the same region of the PDL. The maximum shear stress and toughness increased with age at the incisal region and the maximum shear strain increased with age at the incisal and middle regions. The tangent modulus decreased with advancing age at the middle region. The stress–relaxation during 10 min decreased with advancing age at the incisal and basal regions, but not at the middle region. The relaxation process was well described by a sum of three exponential decay functions, reflecting the short-, medium-, and long-term relaxation components. The age-related decrease in the relaxation was mainly attributable to increases in the ratio and relaxation time of the long-term relaxation component. These results suggest that with advancing age the mechanical strength and toughness of the PDL are enhanced mostly at the incisal region and that the viscous fraction is relatively decreased at the incisal and basal regions along the long axis of the rat incisor. r 2003 Elsevier Ltd. All rights reserved. Keywords: Periodontal ligament; Stress–strain; Stress–relaxation; Ageing; Regional difference
1. Introduction Age-related changes in the stress–strain curves of the periodontal ligament (PDL) have not been demonstrated at the middle region of continuously erupting incisors of growing young rats from 3 weeks to 24 months of age (Yamane, 1990; Yamane et al., 1990). However, regional differences in the mechanical properties of the PDL have clearly been shown in continuously erupting incisors of mice, rats, hamsters, and rabbits (Chiba et al., 1990; Komatsu et al., 1998). However, it is unclear whether age-related changes in the stress–strain properties occur within specific regions of the PDL of continuously erupting incisors. The supportive function of the PDL has been argued to be intimately related not only to the stress–strain
properties but also to the viscoelastic properties of the tissue (e.g. Moxham and Berkovitz, 1995). The viscoelasticity could be examined in creep (Wills et al., 1972; Moxham and Berkovitz, 1995) and stress–relaxation (Komatsu et al., 2002a; Toms et al., 2002) tests. However, there seems to be few studies, which examined the viscoelastic properties of the PDL in relation to age of animals and to regions of a tooth. The aims of the present study were to examine the stress–strain and stress–relaxation behaviours of the PDL at three different regions along the long axis of the mandibular incisor in rats of various ages and to evaluate age-related and regional differences in such properties of the PDL.
2. Materials and methods *Corresponding author. Tel.: +81-45-580-8452; fax: +81-45-5739599. E-mail address: [email protected] (K. Komatsu). 0021-9290/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2003.11.013
Forty male Wistar rats, 4 weeks of age, were initially divided into four equal groups. They were fed a
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powdered diet (CE-2, Nippon Clea, Tokyo, Japan) and given water ad libitum. Groups of rats were killed by an overdose of ether at 2, 6, 12, or 24 months of age. Since all but two of the rats in the 24-month-old group survived and reached the expected ages, we used eight rats in this group. The mean body weights were 27079 (SD), 468739, 531729, and 591751 g in the 2-, 6-, 12-, and 24-month-old groups, respectively, at the time of killing. The experiment was approved by the Institutional Animal Care Committee of Tsurumi University School of Dental Medicine. 2.1. Preparation of mechanical specimens Immediately after the rats were killed, the left and right mandibles in each rat were dissected free and the adherent soft tissues were removed. From each mandible, three transverse sections (about 0.65 mm in thickness) of the incisor with its surrounding PDL and alveolar bone were cut at the incisal (near the labial alveolar crest), middle (near the mesial side of the first molar), and basal (near the mesial root of the second molar) regions (Fig. 1; Komatsu et al., 1998) with a bone saw (Buhler, USA). Thus, three pairs of sections from three different regions were obtained in each animal. 2.2. Radiographic analysis Radiographs of the transverse sections were taken in a soft X-ray apparatus and were processed in an image analyzer (Luzex 3U, Nikon, Japan). We measured the perimeters of the cementum and socket wall of the incisor and the sectional area of the PDL, and we calculated the area of the PDL facing the cementum and the average width of the PDL according to methods described previously (Mandel et al., 1986; Chiba and Komatsu, 1993). 2.3. Biomechanical testing
detail (Chiba and Komatsu, 1993). In brief, the bony part of a transverse section was clamped between two plates of a sample holder, and the holder was placed in a chamber mounted on the testing machine. The chamber was filled with phosphate-buffered saline (pH 7.2). The tooth part in one of the paired sections was loaded until failure of the PDL, and the load–deformation curve for the PDL was obtained (Fig. 2a). The contralateral section was initially loaded to up to 50% of the maximum load as determined from the load– deformation curve, and the movement of the machine was then stopped and the deformation was kept constant for 10 min (Komatsu et al., 2002a) to obtain the load–relaxation curve (Fig. 2b). The direction of loading was extrusive and the velocity of loading was 1 mm/min in both experiments. The time between killing the rats and performing the mechanical testing ranged from 67 to 103 min. The experiments were performed at room temperature of 22– 26 C. When the bony part was broken during mechanical testing, the data from such specimens were excluded. 2.4. Analysis of the biomechanical behaviours Shear stress was calculated by dividing the load by the area of the PDL. Shear strain was calculated by dividing the deformation by the average width of the PDL (Mandel et al., 1986; Chiba et al., 1990). (1) Stress–strain data: Each load–deformation curve was transformed into a shear stress–strain curve. From each stress–strain curve, the biomechanical measures of maximum shear stress, maximum shear strain, tangent modulus, and failure strain energy density were estimated (Mandel et al., 1986; Chiba and Komatsu, 1993). (2) Stress–relaxation data: The resulting stress PðtÞ was divided by the strain eðtÞ to give a relaxation shear modulus GðtÞ as a function of time tðsÞ (Wineman
The characteristics of the testing machine and the method of loading have previously been described in
Fig. 1. Diagrammatic representation of a hemi-mandible of the rat. Three pairs of transverse sections (about 0.65 mm in thickness) were cut from the incisal, middle, and basal regions of the left and right incisors in each animal. One of the sections in each pair was used for stress–strain experiments, and the other was used for stress–relaxation experiments. I, incisor.
Fig. 2. Examples of a load–deformation curve (a) and a load– relaxation curve (b). One of the paired sections was loaded until failure of the periodontal ligament and the maximum load (Mx ) was determined (a). The contralateral section was initially loaded to up to 50% of the maximum load (Mx =2), and thereafter the deformation was kept constant for 10 min (b).
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2.6. Statistics
and Rajagopal, 2000). Then, GðtÞ ¼ PðtÞ=eðtÞ
ð1Þ
GðtÞ was then normalized with respect to the value Gð0Þ as ð2Þ Gr ðtÞ ¼ GðtÞ=Gð0Þ;
We used a one-way analysis of variance (ANOVA) to examine the differences among the four age groups. The
where Gr ðtÞ is normalized relaxation shear modulus. Models can be constructed by combining several Maxwell elements in parallel (Wineman and Rajagopal, 2000). The relaxation process may be represented as Gr ðtÞ ¼ SAi expðt=ti Þ; ð3Þ where Ai and ti are the ratio and relaxation time (s) of each exponential function, respectively. The relaxation measures Ai and ti were determined using the method of exponential curve fitting.
2.5. Morphological examination In a separate experiment, we examined the morphological changes of the periodontal cells and collagen fibres in the mechanical specimens during the stress– relaxation process. Eight male Wistar rats, 2 months of age, were used in this analysis. A pair of mechanical specimens was prepared from the middle region of the left and right incisors in each rat (Fig. 1). Each specimen was placed in a clamping apparatus designed to maintain the periodontal ligament in a deformed state after unloading and during the fixation and decalcification procedures (Komatsu and Viidik, 1996). The specimen was loaded to up to 50% of the maximum load as determined from the contralateral section. The specimen maintained in a deformed state was fixed with 4% phosphate-buffered formaldehyde solution for 1 h at room temperature, was further kept in the same fixative solution for a few days at 4 C, and was then decalcified in 5% EDTA solution for 2 weeks at 4 C. Frozen sections were cut longitudinally with a microtome setting at 20 mm, stained with toluidine blue, and observed under a polarized light microscope (Laborlux 12 Pol S, Leitz, Germany) with and without crossed polars.
Table 1 Average widths (mm) of the periodontal ligament at three different regions of the incisor in four age groups Age (months)
Incisal
Middle
Basal
n
2 6 12 24
175717 188719 163717 144714
159720 184710 163716 140725
184714 257715 225718 190734
10 10 10 8
n; number of rats.
Fig. 3. Stress–strain curves for the periodontal ligament obtained at three different regions of the mandibular incisor in four age groups. Each point represents the mean values for the shear stress and shear strain of 7–10 animals. Vertical and horizontal bars at the end of each curve represent the mean 71 SD for the maximum shear stress and the maximum shear strain, respectively.
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Fig. 4. Biomechanical measures estimated from the stress–strain curves for the periodontal ligament at three different regions of the mandibular incisor in four age groups. Each column and vertical bar represent the mean +1 SD of 7–10 animals. Significant differences among the values in the four age groups (ANOVA): po0:05; po0:01; po0:001:
differences in the mean values between the groups and regions were examined by Scheffe’s method.
3. Results 3.1. Radiographic measurements Table 1 shows the average widths of the PDL for the three regions in the four age groups. The mean values increased from 2 to 6 months of age; the differences were significant at the middle (po0:05) and basal (po0:001) regions, but not at the incisal region. Thereafter, the mean values decreased from 6 to 24 months of age at all three regions (po0:001). The average widths of the ligament were greatest at 6 months of age at all three regions, and at the basal region in all four age groups. 3.2. Biomechanical measurements Stress–strain behaviour: Fig. 3 shows the mean stress– strain curves at the three different regions in the four age groups. At the incisal region, the slopes of the linear parts of the four curves were similar, but the maximum points tended to be greater in the older age groups. At the middle region, the slopes of the curves decreased, the
maximum stresses decreased slightly, and the maximum strains increased in the older age groups. At the basal region, the slopes and the maximum points appeared to be similar among the four age groups. Fig. 4 shows the stress–strain measures estimated from the stress–strain curves (Fig. 3). At the incisal region, the age-related increases from 2 to 24 months of age were significant for the maximum shear stress, maximum shear strain, and failure strain energy density (ANOVA, po0:01 or 0.001). However, the tangent modulus did not show significant changes with age. At the middle region, the maximum shear strain increased (ANOVA, po0:001) and the tangent modulus decreased (ANOVA, po0:01) with age, while the maximum shear stress and failure strain energy density showed no significant change with age. At the basal region, none of these four measures changed with age. Stress–relaxation behaviour: Fig. 5 shows the mean curves of the normalized relaxation shear modulus, Gr ðtÞ; at the three different regions in the four age groups for 10 min. Each curve exhibited an initial rapid decrease followed by a more gradual decrease. The PDL at the incisal and basal regions relaxed more rapidly in the 2-month-old group than in the older groups. The curves of Gr ðtÞ at the middle region showed no marked differences among the four age groups. Fig. 6 shows the
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Fig. 6. The percentages of relaxation for a period of 10 min at three different regions in four age groups. Significant differences among the four age groups (ANOVA): po0:001:
Fig. 5. The mean curves of the normalized relaxation shear modulus, Gr ðtÞ; of the periodontal ligament at three different regions of the mandibular incisor in four age groups for 10 min. Each point represents the mean of 7–10 animals at intervals of 20 s; t; time ðsÞ:
percentages of relaxation for a period of 10 min at the three different regions in the four age groups. The relaxations at the incisal and basal regions decreased significantly with age (ANOVA, po0:001), but those at the middle region did not differ among the four age groups. The mean relaxations ranged from 80.672.2% (SD) to 65.372.9% at the incisal region, from 75.8% to 80.8% at the middle region, and from 85.173.6% to 75.173.5% at the basal region. Fig. 7 shows a typical example of the exponential curve fitting. The points of the Gr ðtÞ values obtained from a 2-month-old rat fitted well with the curve showing a sum of three exponential decay functions. The formula is represented as Gr ðtÞ ¼ A1 expðt=t1 Þ þ A2 expðt=t2 Þ þ A3 expðt=t3 Þ:
ð4Þ
The other data obtained in the present study were well expressed by the equation. Fig. 8 shows the changes in the ratios of the first ðA1 Þ; second ðA2 Þ; and third ðA3 Þ functions at three different regions with age. The ratios of the first function ðA1 Þ at the incisal and middle regions, and of the second function ðA2 Þ at the incisal and basal regions decreased significantly with advancing age (ANOVA, po0:01 or 0.001). By contrast, the ratios of the third function ðA3 Þ increased significantly with advancing age (ANOVA, po0:05 or 0.001). Fig. 9 shows the changes in the relaxation times of the first ðt1 Þ; second ðt2 Þ; and third ðt3 Þ functions at three different regions with age. The relaxation times of the first function ðt1 Þ at the incisal region and of the second function ðt2 Þ at all three regions decreased significantly with advancing age (ANOVA, po0:01 0:001). By contrast, the relaxation times of the third function ðt3 Þ at the incisal and basal regions increased significantly with advancing age (ANOVA, po0:001). The relaxation times of t1 ; t2 ; and t3 ranged from 4 to 6, 80 to 100, and 500 to 1000 s, respectively. 3.3. Morphological observation Fig. 10 shows the light (Figs. 10a and c) and polarized light (Figs. 10b and d) micrographs of the PDL from a control specimen (Figs. 10a and b) and an experimental specimen during the stress–relaxation process just after the application of the initial load (Figs. 10c and d). In the control specimen, the ordinary light micrograph (Fig. 10a) showed that the periodontal cell nuclei appeared to be oval in shape. The polarized light micrograph (Fig. 10b) showed that the birefringent fibre bundles extended out from the bone surface and ran across the ligament obliquely upwards to the cementum surface. In the specimen during the stress–relaxation process just after the load application, the ordinary light
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Fig. 7. A typical example of exponential curve fitting. Open circles represent the data obtained from a 2-month-old rat. The solid line represents the curve showing a sum of three exponential decay functions. In each function, ‘‘A’’ and ‘‘t’’ are the ratio and relaxation time (s), respectively.
micrograph (Fig. 10c) showed that the periodontal cell nuclei appeared to exhibit indistinct contours. The cells in the bone-related region of the ligament tended to align towards the direction of loading. The polarized light micrograph (Fig. 10d) showed that the birefringent fibre bundles were stretched and aligned towards the direction of the extrusive loading. Similar results were obtained in specimens during the stress–relaxation process at 1, 5 and 10 min after load application (pictures not shown).
4. Discussion The present study demonstrated that the PDL at the incisal region showed age-related increases in the mechanical strength, extensibility, and toughness from 2 to 24 months of age in the rat mandibular incisor (Fig. 4). The ligament at the middle region showed an increase in the extensibility (Fig. 4), which caused an age-related decrease in the slopes of the stress–strain curves (stiffness) as the maximum shear stresses did not change much. The ligament at the basal region showed no significant changes in the mechanical measures with age. These results suggest that the developmental stages and mechanical properties of the PDL differ markedly according to the regions of the tooth (Chiba et al., 1990; Komatsu et al., 1998) and according to age. We assume that the PDL is immature at the basal region, transitional at the middle region, and well-developed and maximally functional at the incisal region. These features seem to be specific to the rat mandibular incisor as compared with other soft connective tissues, such as tail tendon (Danielsen and Andreassen, 1988) and limb muscle tendons (Nielsen et al., 1998) in rats.
In a parallel study (Komatsu et al., 2002b), we found increases in birefringent retardation of the periodontal collagen at the incisal region, but not at the middle and basal regions, of the mandibular incisor from 2 to 24 months of age. A significant correlation was found (r ¼ 0:868; po0:001) between the maximum shear stress (Fig. 4) and the retardation value (Komatsu et al., 2002b) for the PDL at the incisal region in the four age groups. It is recognized that the increases in the organization of the collagen molecules and fibers that occur during the maturation process change the optical properties of the collagen, thus increasing the retardation of the polarized light (Mello et al., 1979; Whittaker et al., 1988). Therefore, the increase in the mechanical strength of the PDL could mainly be due to increases in the molecular aggregation of collagens and/or in the organization of collagen fibres at the incisal region with advancing age. Other important features of the ageing of connective tissues appear to involve changes in the diameters of the collagen fibrils and other changes in the interfibrillar substances (Parry, 1988; Scott, 1995). However, no agerelated differences in the diameters of the collagen fibrils have been found in the PDLs of rats (Moxham and Evans, 1995) and humans (Luder et al., 1988). We have found no data to correlate collagen fibril diameters and/ or interfibrillar substances with age-related and regional differences in the mechanical properties of the PDL in the rat incisor. The mechanical strength of the PDL increased from 1 to 1.6 MPa from 2 to 24 months of age at the incisal region, and from 0.4 to 1.6 MPa at 24 months of age from the basal towards the incisal regions (Fig. 4). The mechanical strength of the PDL has been reported to vary between 1.3 and 3 MPa in humans (Mandel et al.,
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Fig. 8. Changes in the ratios of the first ðA1 Þ; second ðA2 Þ; and third ðA3 Þ exponential decay functions for the periodontal ligament at three different regions in four age groups. Each column and vertical bar represent the mean +1 SD of 7–10 animals. Significant differences among the four age groups (ANOVA): po0:05; po0:01; po0:001:
1986; Toms et al., 2002), monkeys (Mandel and Viidik, 1989), and bovine (Pini et al., 2002). The tensile maximum stress has also been reported to increase from 6 to 12 MPa in skin, and from 30 to 80 MPa in the tail tendons of rats between 2 and 24 months of age (Vogel, 1978). Biochemical studies have shown that the PDL of the bovine incisor contains only small amounts of mature cross-links in type I collagen (Yamauchi et al.,
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Fig. 9. Changes in the relaxation times of the first ðt1 Þ; second ðt2 Þ; and third ðt3 Þ exponential decay functions for the periodontal ligament at three different regions in four age groups. Each column and vertical bar represent the mean +1 SD of 7–10 animals. Significant differences among the four age groups (ANOVA): po0:05; po0:01; po0:001:
1986). By contrast, other connective tissues exhibit agerelated increases in insoluble collagens in skin and tendons (Vogel, 1978; Haut et al., 1992) and in mature cross-links in equine digital flexor tendons (Gills et al., 1997) and bovine articular cartilage (Wong et al., 2000). It has been suggested that aged collagen becomes more cross-linked and, therefore, more insoluble, which correlates with the age-related increases in the mechanical strength and stiffness (Haut et al., 1992; Gills et al.,
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Fig. 10. Mid-sagittal sections of the lingual periodontal ligament during the stress–relaxation process (see Materials and Methods). Pictures from the control (a and b) and experimental specimens (c and d) from 2-month-old rats are shown. Sections were stained with toluidine blue and observed under ordinary light (a and c) and polarized light (b and d) microscopes. Arrows indicate the direction of loading: B, bone; L, periodontal ligament; D, dentine.
1997; Bailey, 2001). Therefore, we assume that the relative amount of mature insoluble collagen in the PDL is less than that in other connective tissues, resulting in less mechanical strength and less age-related change in the strength of the PDL. In the present study, we also observed changes in the viscoelastic properties of the PDL at three different regions with advancing age. The mean relaxations
decreased from 81% to 65% at the incisal region and from 85% to 75% at the basal region with advancing age (Fig. 6). It has been shown that the relaxations decreased from 60% at 3 months to 30% at 12 months of age in the rabbit medial collateral ligament (Lam et al., 1993) and from 25% at 54 days to 8% at 900 days of age in the rat tail tendon (Reihsner and Menzel, 1994). These findings suggest that the relaxations of the
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rat incisor PDL are much greater than those of other soft connective tissues and that a large energy dissipation mechanism exists in the PDL. We initially applied 50% of the maximum load in the stress–relaxation experiments (Fig. 2), since the functional stress level is considered to not exceed 50% of the maximum stress for the PDL (Komatsu and Viidik, 1996; Komatsu et al., 1998; Komatsu and Chiba, 2001). At this load level, most of the periodontal collagen fibre bundles had been stretched, and the periodontal cells had been aligned towards the direction of loading before the stress–relaxation started to occur (Fig. 10). Therefore, it is reasonable to suppose that the stress– relaxation curves in the present study reflect changes in stretched collagen fibres and aligned cells. It has been reported that the creep behaviour of the monkey periodontium can be represented by a serial combination of three Voigt elements (Wills et al., 1972). The normalized relaxation modulus of bovine bone has been shown to be expressed by the combination of the simple exponential type relaxation function and the Kohlrausch–Williams–Watts function (Sasaki et al., 1993). In the present study, the stress relaxation process was satisfactorily expressed as a sum of three exponential decay functions with different relaxation times, as in the human PDL (Toms et al., 2002). This would imply the presence of short-, medium-, and long-term relaxation components in the whole relaxation process of the PDL. Our analysis showed that the age-related decreases in relaxation were mainly due to increases in the ratio (Fig. 8) and relaxation time (Fig. 9) of the long-term relaxation component (formula (4), third function). It has been suggested that the decreases in the stress– relaxation in older animals reflect increases in the density and/or organization of collagen fibres in the rabbit medial collateral ligament (Lam et al., 1993) and bovine temporomandibular articular disc (Tanaka et al., 2001). Our parallel study (Komatsu et al., 2002b) has shown that the molecular aggregation of the incisal periodontal collagen fibres might increase with age. It is suggested that age-related changes in the long-term relaxation component in the rat incisor PDL are notable and closely related to those in the collagen fibre structures. It has also been reported that higher water contents caused greater stress–relaxation of the rabbit medial collateral ligament (Chimich et al., 1992) and human patellar tendon (Haut and Haut, 1997). It has been suggested that water molecules decrease the intermolecular force acting between the collagen fibres, thereby increasing their freedom of movement and increasing stress relaxation (Lam et al., 1993). Therefore, we assume that the decreases in the stress–relaxation of the incisor PDL in older rats are partly associated with loss of tissue water with advancing age.
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We could not detect morphological changes in the stretched collagen fibres and aligned cells under the light microscope during the stress–relaxation process. Purslow et al. (1998) also found no changes in the Dperiodicity and angular orientation of collagen during stress relaxation in rat skin and bovine perimysium. On the other hand, it has been shown that exudation of glycosaminoglycans and fluids to the external bath occurred and that the diameter of a fibre bundle decreased during stress relaxations in the rat tail tendon (Lanir et al., 1988) and canine flexor tendon (Hannafin and Arnoczky, 1994). Further analysis would be needed to clarify the structural changes during the stress– relaxation process.
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Purslow, P.P., Wess, T.J., Hukins, D.W.L., 1998. Collagen orientation and molecular spacing during creep and stress-relaxation in soft connective tissues. Journal of Experimental Biology 201, 135–142. Reihsner, R., Menzel, E.J., 1994. Mechanical changes in rat tail tendons induced by dibasic amino acids as a function of age. Biorheology 31, 37–55. Sasaki, N., Nakayama, Y., Yoshikawa, M., Enyo, A., 1993. Stress relaxation function of bone and bone collagen. Journal of Biomechanics 26, 1369–1376. Scott, J.E., 1995. Extracellular matrix, supramolecular organisation and shape. Journal of Anatomy 187, 259–269. Tanaka, E., Tanaka, M., Hattori, Y., Aoyama, J., Watanabe, M., Sasaki, A., Sugiyama, M., Tanne, K., 2001. Biomechanical behaviour of bovine temporomandibular articular discs with age. Archives of Oral Biology 46, 997–1003. Toms, S.R., Dakin, G.J., Lemons, J.E., Eberhardt, A.W., 2002. Quasilinear viscoelastic behavior of the human periodontal ligament. Journal of Biomechanics 35, 1411–1415. Vogel, H.G., 1978. Influence of maturation and age on mechanical and biochemical parameters of connective tissue of various organs in the rat. Connective Tissue Research 6, 161–166. Whittaker, P., Schwab, M.E., Canham, P.B., 1988. The molecular organization of collagen in saccular aneurysms assessed by polarized light microscopy. Connective Tissue Research 17, 43–54. Wills, D.J., Picton, D.C.A., Davies, W.I.R., 1972. An investigation of the viscoelastic properties of the periodontium in monkeys. Journal of Periodontal Research 7, 42–51. Wineman, A.S., Rajagopal, K.R., 2000. Mechanical Response of Polymers. An Introduction. Cambridge University Press, Cambridge, pp. 28–53. Wong, M., Ponticiello, M., Kovanen, V., Jurvelin, J.S., 2000. Volumetric changes of articular cartilage during stress relaxation in unconfined compression. Journal of Biomechanics 33, 1049–1054. Yamane, A., 1990. The effect of age on the mechanical properties of the periodontal ligament in the incisor teeth of growing young rats. Gerodontology 9, 9–16. Yamane, A., Ohshima, S., Komatsu, K., Chiba, M., 1990. Mechanical properties of the periodontal ligament in the incisor teeth of rats from 6 to 24 months of age. Gerodontology 9, 17–23. Yamauchi, M., Katz, E.P., Mechanic, G.L., 1986. Intermolecular cross-linking and stereospecific molecular packing in type I collagen fibrils of the periodontal ligament. Biochemistry 25, 4907–4913.
Journal of Biomechanics 37 (2004) 1097–1106
Age-related and regional differences in the stress–strain and stress–relaxation behaviours of the rat incisor periodontal ligament K. Komatsua,*, T. Shibataa, A. Shimadaa, A. Viidikb,c, M. Chibaa a
Department of Pharmacology, School of Dental Medicine, Tsurumi University, 2-1-3 Tsurumi, Tsurumi-ku, Yokohama 230-8501, Japan b Department of Connective Tissue Biology, Institute of Anatomy, University of Aarhus, Aarhus C DK-8000, Denmark c Sozialmedizinisches Zentrum Sophienspital, Apollogasse 19, Wien A-1070, Austria Accepted 19 November 2003
Abstract Groups of rats were killed at 2, 6, 12, and 24 months of age. From dissected left and right mandibles in each rat, three pairs of transverse sections were cut at the incisal, middle, and basal regions of the incisor. One section in each pair was loaded until failure and a stress–strain curve for the periodontal ligament (PDL) was obtained. The other section was loaded to up to 50% of the maximum shear stress as determined from the contralateral section and then kept at a constant strain for 10 min, to obtain the stress–relaxation curve at the same region of the PDL. The maximum shear stress and toughness increased with age at the incisal region and the maximum shear strain increased with age at the incisal and middle regions. The tangent modulus decreased with advancing age at the middle region. The stress–relaxation during 10 min decreased with advancing age at the incisal and basal regions, but not at the middle region. The relaxation process was well described by a sum of three exponential decay functions, reflecting the short-, medium-, and long-term relaxation components. The age-related decrease in the relaxation was mainly attributable to increases in the ratio and relaxation time of the long-term relaxation component. These results suggest that with advancing age the mechanical strength and toughness of the PDL are enhanced mostly at the incisal region and that the viscous fraction is relatively decreased at the incisal and basal regions along the long axis of the rat incisor. r 2003 Elsevier Ltd. All rights reserved. Keywords: Periodontal ligament; Stress–strain; Stress–relaxation; Ageing; Regional difference
1. Introduction Age-related changes in the stress–strain curves of the periodontal ligament (PDL) have not been demonstrated at the middle region of continuously erupting incisors of growing young rats from 3 weeks to 24 months of age (Yamane, 1990; Yamane et al., 1990). However, regional differences in the mechanical properties of the PDL have clearly been shown in continuously erupting incisors of mice, rats, hamsters, and rabbits (Chiba et al., 1990; Komatsu et al., 1998). However, it is unclear whether age-related changes in the stress–strain properties occur within specific regions of the PDL of continuously erupting incisors. The supportive function of the PDL has been argued to be intimately related not only to the stress–strain
properties but also to the viscoelastic properties of the tissue (e.g. Moxham and Berkovitz, 1995). The viscoelasticity could be examined in creep (Wills et al., 1972; Moxham and Berkovitz, 1995) and stress–relaxation (Komatsu et al., 2002a; Toms et al., 2002) tests. However, there seems to be few studies, which examined the viscoelastic properties of the PDL in relation to age of animals and to regions of a tooth. The aims of the present study were to examine the stress–strain and stress–relaxation behaviours of the PDL at three different regions along the long axis of the mandibular incisor in rats of various ages and to evaluate age-related and regional differences in such properties of the PDL.
2. Materials and methods *Corresponding author. Tel.: +81-45-580-8452; fax: +81-45-5739599. E-mail address: [email protected] (K. Komatsu). 0021-9290/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2003.11.013
Forty male Wistar rats, 4 weeks of age, were initially divided into four equal groups. They were fed a
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powdered diet (CE-2, Nippon Clea, Tokyo, Japan) and given water ad libitum. Groups of rats were killed by an overdose of ether at 2, 6, 12, or 24 months of age. Since all but two of the rats in the 24-month-old group survived and reached the expected ages, we used eight rats in this group. The mean body weights were 27079 (SD), 468739, 531729, and 591751 g in the 2-, 6-, 12-, and 24-month-old groups, respectively, at the time of killing. The experiment was approved by the Institutional Animal Care Committee of Tsurumi University School of Dental Medicine. 2.1. Preparation of mechanical specimens Immediately after the rats were killed, the left and right mandibles in each rat were dissected free and the adherent soft tissues were removed. From each mandible, three transverse sections (about 0.65 mm in thickness) of the incisor with its surrounding PDL and alveolar bone were cut at the incisal (near the labial alveolar crest), middle (near the mesial side of the first molar), and basal (near the mesial root of the second molar) regions (Fig. 1; Komatsu et al., 1998) with a bone saw (Buhler, USA). Thus, three pairs of sections from three different regions were obtained in each animal. 2.2. Radiographic analysis Radiographs of the transverse sections were taken in a soft X-ray apparatus and were processed in an image analyzer (Luzex 3U, Nikon, Japan). We measured the perimeters of the cementum and socket wall of the incisor and the sectional area of the PDL, and we calculated the area of the PDL facing the cementum and the average width of the PDL according to methods described previously (Mandel et al., 1986; Chiba and Komatsu, 1993). 2.3. Biomechanical testing
detail (Chiba and Komatsu, 1993). In brief, the bony part of a transverse section was clamped between two plates of a sample holder, and the holder was placed in a chamber mounted on the testing machine. The chamber was filled with phosphate-buffered saline (pH 7.2). The tooth part in one of the paired sections was loaded until failure of the PDL, and the load–deformation curve for the PDL was obtained (Fig. 2a). The contralateral section was initially loaded to up to 50% of the maximum load as determined from the load– deformation curve, and the movement of the machine was then stopped and the deformation was kept constant for 10 min (Komatsu et al., 2002a) to obtain the load–relaxation curve (Fig. 2b). The direction of loading was extrusive and the velocity of loading was 1 mm/min in both experiments. The time between killing the rats and performing the mechanical testing ranged from 67 to 103 min. The experiments were performed at room temperature of 22– 26 C. When the bony part was broken during mechanical testing, the data from such specimens were excluded. 2.4. Analysis of the biomechanical behaviours Shear stress was calculated by dividing the load by the area of the PDL. Shear strain was calculated by dividing the deformation by the average width of the PDL (Mandel et al., 1986; Chiba et al., 1990). (1) Stress–strain data: Each load–deformation curve was transformed into a shear stress–strain curve. From each stress–strain curve, the biomechanical measures of maximum shear stress, maximum shear strain, tangent modulus, and failure strain energy density were estimated (Mandel et al., 1986; Chiba and Komatsu, 1993). (2) Stress–relaxation data: The resulting stress PðtÞ was divided by the strain eðtÞ to give a relaxation shear modulus GðtÞ as a function of time tðsÞ (Wineman
The characteristics of the testing machine and the method of loading have previously been described in
Fig. 1. Diagrammatic representation of a hemi-mandible of the rat. Three pairs of transverse sections (about 0.65 mm in thickness) were cut from the incisal, middle, and basal regions of the left and right incisors in each animal. One of the sections in each pair was used for stress–strain experiments, and the other was used for stress–relaxation experiments. I, incisor.
Fig. 2. Examples of a load–deformation curve (a) and a load– relaxation curve (b). One of the paired sections was loaded until failure of the periodontal ligament and the maximum load (Mx ) was determined (a). The contralateral section was initially loaded to up to 50% of the maximum load (Mx =2), and thereafter the deformation was kept constant for 10 min (b).
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2.6. Statistics
and Rajagopal, 2000). Then, GðtÞ ¼ PðtÞ=eðtÞ
ð1Þ
GðtÞ was then normalized with respect to the value Gð0Þ as ð2Þ Gr ðtÞ ¼ GðtÞ=Gð0Þ;
We used a one-way analysis of variance (ANOVA) to examine the differences among the four age groups. The
where Gr ðtÞ is normalized relaxation shear modulus. Models can be constructed by combining several Maxwell elements in parallel (Wineman and Rajagopal, 2000). The relaxation process may be represented as Gr ðtÞ ¼ SAi expðt=ti Þ; ð3Þ where Ai and ti are the ratio and relaxation time (s) of each exponential function, respectively. The relaxation measures Ai and ti were determined using the method of exponential curve fitting.
2.5. Morphological examination In a separate experiment, we examined the morphological changes of the periodontal cells and collagen fibres in the mechanical specimens during the stress– relaxation process. Eight male Wistar rats, 2 months of age, were used in this analysis. A pair of mechanical specimens was prepared from the middle region of the left and right incisors in each rat (Fig. 1). Each specimen was placed in a clamping apparatus designed to maintain the periodontal ligament in a deformed state after unloading and during the fixation and decalcification procedures (Komatsu and Viidik, 1996). The specimen was loaded to up to 50% of the maximum load as determined from the contralateral section. The specimen maintained in a deformed state was fixed with 4% phosphate-buffered formaldehyde solution for 1 h at room temperature, was further kept in the same fixative solution for a few days at 4 C, and was then decalcified in 5% EDTA solution for 2 weeks at 4 C. Frozen sections were cut longitudinally with a microtome setting at 20 mm, stained with toluidine blue, and observed under a polarized light microscope (Laborlux 12 Pol S, Leitz, Germany) with and without crossed polars.
Table 1 Average widths (mm) of the periodontal ligament at three different regions of the incisor in four age groups Age (months)
Incisal
Middle
Basal
n
2 6 12 24
175717 188719 163717 144714
159720 184710 163716 140725
184714 257715 225718 190734
10 10 10 8
n; number of rats.
Fig. 3. Stress–strain curves for the periodontal ligament obtained at three different regions of the mandibular incisor in four age groups. Each point represents the mean values for the shear stress and shear strain of 7–10 animals. Vertical and horizontal bars at the end of each curve represent the mean 71 SD for the maximum shear stress and the maximum shear strain, respectively.
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Fig. 4. Biomechanical measures estimated from the stress–strain curves for the periodontal ligament at three different regions of the mandibular incisor in four age groups. Each column and vertical bar represent the mean +1 SD of 7–10 animals. Significant differences among the values in the four age groups (ANOVA): po0:05; po0:01; po0:001:
differences in the mean values between the groups and regions were examined by Scheffe’s method.
3. Results 3.1. Radiographic measurements Table 1 shows the average widths of the PDL for the three regions in the four age groups. The mean values increased from 2 to 6 months of age; the differences were significant at the middle (po0:05) and basal (po0:001) regions, but not at the incisal region. Thereafter, the mean values decreased from 6 to 24 months of age at all three regions (po0:001). The average widths of the ligament were greatest at 6 months of age at all three regions, and at the basal region in all four age groups. 3.2. Biomechanical measurements Stress–strain behaviour: Fig. 3 shows the mean stress– strain curves at the three different regions in the four age groups. At the incisal region, the slopes of the linear parts of the four curves were similar, but the maximum points tended to be greater in the older age groups. At the middle region, the slopes of the curves decreased, the
maximum stresses decreased slightly, and the maximum strains increased in the older age groups. At the basal region, the slopes and the maximum points appeared to be similar among the four age groups. Fig. 4 shows the stress–strain measures estimated from the stress–strain curves (Fig. 3). At the incisal region, the age-related increases from 2 to 24 months of age were significant for the maximum shear stress, maximum shear strain, and failure strain energy density (ANOVA, po0:01 or 0.001). However, the tangent modulus did not show significant changes with age. At the middle region, the maximum shear strain increased (ANOVA, po0:001) and the tangent modulus decreased (ANOVA, po0:01) with age, while the maximum shear stress and failure strain energy density showed no significant change with age. At the basal region, none of these four measures changed with age. Stress–relaxation behaviour: Fig. 5 shows the mean curves of the normalized relaxation shear modulus, Gr ðtÞ; at the three different regions in the four age groups for 10 min. Each curve exhibited an initial rapid decrease followed by a more gradual decrease. The PDL at the incisal and basal regions relaxed more rapidly in the 2-month-old group than in the older groups. The curves of Gr ðtÞ at the middle region showed no marked differences among the four age groups. Fig. 6 shows the
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Fig. 6. The percentages of relaxation for a period of 10 min at three different regions in four age groups. Significant differences among the four age groups (ANOVA): po0:001:
Fig. 5. The mean curves of the normalized relaxation shear modulus, Gr ðtÞ; of the periodontal ligament at three different regions of the mandibular incisor in four age groups for 10 min. Each point represents the mean of 7–10 animals at intervals of 20 s; t; time ðsÞ:
percentages of relaxation for a period of 10 min at the three different regions in the four age groups. The relaxations at the incisal and basal regions decreased significantly with age (ANOVA, po0:001), but those at the middle region did not differ among the four age groups. The mean relaxations ranged from 80.672.2% (SD) to 65.372.9% at the incisal region, from 75.8% to 80.8% at the middle region, and from 85.173.6% to 75.173.5% at the basal region. Fig. 7 shows a typical example of the exponential curve fitting. The points of the Gr ðtÞ values obtained from a 2-month-old rat fitted well with the curve showing a sum of three exponential decay functions. The formula is represented as Gr ðtÞ ¼ A1 expðt=t1 Þ þ A2 expðt=t2 Þ þ A3 expðt=t3 Þ:
ð4Þ
The other data obtained in the present study were well expressed by the equation. Fig. 8 shows the changes in the ratios of the first ðA1 Þ; second ðA2 Þ; and third ðA3 Þ functions at three different regions with age. The ratios of the first function ðA1 Þ at the incisal and middle regions, and of the second function ðA2 Þ at the incisal and basal regions decreased significantly with advancing age (ANOVA, po0:01 or 0.001). By contrast, the ratios of the third function ðA3 Þ increased significantly with advancing age (ANOVA, po0:05 or 0.001). Fig. 9 shows the changes in the relaxation times of the first ðt1 Þ; second ðt2 Þ; and third ðt3 Þ functions at three different regions with age. The relaxation times of the first function ðt1 Þ at the incisal region and of the second function ðt2 Þ at all three regions decreased significantly with advancing age (ANOVA, po0:01 0:001). By contrast, the relaxation times of the third function ðt3 Þ at the incisal and basal regions increased significantly with advancing age (ANOVA, po0:001). The relaxation times of t1 ; t2 ; and t3 ranged from 4 to 6, 80 to 100, and 500 to 1000 s, respectively. 3.3. Morphological observation Fig. 10 shows the light (Figs. 10a and c) and polarized light (Figs. 10b and d) micrographs of the PDL from a control specimen (Figs. 10a and b) and an experimental specimen during the stress–relaxation process just after the application of the initial load (Figs. 10c and d). In the control specimen, the ordinary light micrograph (Fig. 10a) showed that the periodontal cell nuclei appeared to be oval in shape. The polarized light micrograph (Fig. 10b) showed that the birefringent fibre bundles extended out from the bone surface and ran across the ligament obliquely upwards to the cementum surface. In the specimen during the stress–relaxation process just after the load application, the ordinary light
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Fig. 7. A typical example of exponential curve fitting. Open circles represent the data obtained from a 2-month-old rat. The solid line represents the curve showing a sum of three exponential decay functions. In each function, ‘‘A’’ and ‘‘t’’ are the ratio and relaxation time (s), respectively.
micrograph (Fig. 10c) showed that the periodontal cell nuclei appeared to exhibit indistinct contours. The cells in the bone-related region of the ligament tended to align towards the direction of loading. The polarized light micrograph (Fig. 10d) showed that the birefringent fibre bundles were stretched and aligned towards the direction of the extrusive loading. Similar results were obtained in specimens during the stress–relaxation process at 1, 5 and 10 min after load application (pictures not shown).
4. Discussion The present study demonstrated that the PDL at the incisal region showed age-related increases in the mechanical strength, extensibility, and toughness from 2 to 24 months of age in the rat mandibular incisor (Fig. 4). The ligament at the middle region showed an increase in the extensibility (Fig. 4), which caused an age-related decrease in the slopes of the stress–strain curves (stiffness) as the maximum shear stresses did not change much. The ligament at the basal region showed no significant changes in the mechanical measures with age. These results suggest that the developmental stages and mechanical properties of the PDL differ markedly according to the regions of the tooth (Chiba et al., 1990; Komatsu et al., 1998) and according to age. We assume that the PDL is immature at the basal region, transitional at the middle region, and well-developed and maximally functional at the incisal region. These features seem to be specific to the rat mandibular incisor as compared with other soft connective tissues, such as tail tendon (Danielsen and Andreassen, 1988) and limb muscle tendons (Nielsen et al., 1998) in rats.
In a parallel study (Komatsu et al., 2002b), we found increases in birefringent retardation of the periodontal collagen at the incisal region, but not at the middle and basal regions, of the mandibular incisor from 2 to 24 months of age. A significant correlation was found (r ¼ 0:868; po0:001) between the maximum shear stress (Fig. 4) and the retardation value (Komatsu et al., 2002b) for the PDL at the incisal region in the four age groups. It is recognized that the increases in the organization of the collagen molecules and fibers that occur during the maturation process change the optical properties of the collagen, thus increasing the retardation of the polarized light (Mello et al., 1979; Whittaker et al., 1988). Therefore, the increase in the mechanical strength of the PDL could mainly be due to increases in the molecular aggregation of collagens and/or in the organization of collagen fibres at the incisal region with advancing age. Other important features of the ageing of connective tissues appear to involve changes in the diameters of the collagen fibrils and other changes in the interfibrillar substances (Parry, 1988; Scott, 1995). However, no agerelated differences in the diameters of the collagen fibrils have been found in the PDLs of rats (Moxham and Evans, 1995) and humans (Luder et al., 1988). We have found no data to correlate collagen fibril diameters and/ or interfibrillar substances with age-related and regional differences in the mechanical properties of the PDL in the rat incisor. The mechanical strength of the PDL increased from 1 to 1.6 MPa from 2 to 24 months of age at the incisal region, and from 0.4 to 1.6 MPa at 24 months of age from the basal towards the incisal regions (Fig. 4). The mechanical strength of the PDL has been reported to vary between 1.3 and 3 MPa in humans (Mandel et al.,
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Fig. 8. Changes in the ratios of the first ðA1 Þ; second ðA2 Þ; and third ðA3 Þ exponential decay functions for the periodontal ligament at three different regions in four age groups. Each column and vertical bar represent the mean +1 SD of 7–10 animals. Significant differences among the four age groups (ANOVA): po0:05; po0:01; po0:001:
1986; Toms et al., 2002), monkeys (Mandel and Viidik, 1989), and bovine (Pini et al., 2002). The tensile maximum stress has also been reported to increase from 6 to 12 MPa in skin, and from 30 to 80 MPa in the tail tendons of rats between 2 and 24 months of age (Vogel, 1978). Biochemical studies have shown that the PDL of the bovine incisor contains only small amounts of mature cross-links in type I collagen (Yamauchi et al.,
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Fig. 9. Changes in the relaxation times of the first ðt1 Þ; second ðt2 Þ; and third ðt3 Þ exponential decay functions for the periodontal ligament at three different regions in four age groups. Each column and vertical bar represent the mean +1 SD of 7–10 animals. Significant differences among the four age groups (ANOVA): po0:05; po0:01; po0:001:
1986). By contrast, other connective tissues exhibit agerelated increases in insoluble collagens in skin and tendons (Vogel, 1978; Haut et al., 1992) and in mature cross-links in equine digital flexor tendons (Gills et al., 1997) and bovine articular cartilage (Wong et al., 2000). It has been suggested that aged collagen becomes more cross-linked and, therefore, more insoluble, which correlates with the age-related increases in the mechanical strength and stiffness (Haut et al., 1992; Gills et al.,
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Fig. 10. Mid-sagittal sections of the lingual periodontal ligament during the stress–relaxation process (see Materials and Methods). Pictures from the control (a and b) and experimental specimens (c and d) from 2-month-old rats are shown. Sections were stained with toluidine blue and observed under ordinary light (a and c) and polarized light (b and d) microscopes. Arrows indicate the direction of loading: B, bone; L, periodontal ligament; D, dentine.
1997; Bailey, 2001). Therefore, we assume that the relative amount of mature insoluble collagen in the PDL is less than that in other connective tissues, resulting in less mechanical strength and less age-related change in the strength of the PDL. In the present study, we also observed changes in the viscoelastic properties of the PDL at three different regions with advancing age. The mean relaxations
decreased from 81% to 65% at the incisal region and from 85% to 75% at the basal region with advancing age (Fig. 6). It has been shown that the relaxations decreased from 60% at 3 months to 30% at 12 months of age in the rabbit medial collateral ligament (Lam et al., 1993) and from 25% at 54 days to 8% at 900 days of age in the rat tail tendon (Reihsner and Menzel, 1994). These findings suggest that the relaxations of the
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rat incisor PDL are much greater than those of other soft connective tissues and that a large energy dissipation mechanism exists in the PDL. We initially applied 50% of the maximum load in the stress–relaxation experiments (Fig. 2), since the functional stress level is considered to not exceed 50% of the maximum stress for the PDL (Komatsu and Viidik, 1996; Komatsu et al., 1998; Komatsu and Chiba, 2001). At this load level, most of the periodontal collagen fibre bundles had been stretched, and the periodontal cells had been aligned towards the direction of loading before the stress–relaxation started to occur (Fig. 10). Therefore, it is reasonable to suppose that the stress– relaxation curves in the present study reflect changes in stretched collagen fibres and aligned cells. It has been reported that the creep behaviour of the monkey periodontium can be represented by a serial combination of three Voigt elements (Wills et al., 1972). The normalized relaxation modulus of bovine bone has been shown to be expressed by the combination of the simple exponential type relaxation function and the Kohlrausch–Williams–Watts function (Sasaki et al., 1993). In the present study, the stress relaxation process was satisfactorily expressed as a sum of three exponential decay functions with different relaxation times, as in the human PDL (Toms et al., 2002). This would imply the presence of short-, medium-, and long-term relaxation components in the whole relaxation process of the PDL. Our analysis showed that the age-related decreases in relaxation were mainly due to increases in the ratio (Fig. 8) and relaxation time (Fig. 9) of the long-term relaxation component (formula (4), third function). It has been suggested that the decreases in the stress– relaxation in older animals reflect increases in the density and/or organization of collagen fibres in the rabbit medial collateral ligament (Lam et al., 1993) and bovine temporomandibular articular disc (Tanaka et al., 2001). Our parallel study (Komatsu et al., 2002b) has shown that the molecular aggregation of the incisal periodontal collagen fibres might increase with age. It is suggested that age-related changes in the long-term relaxation component in the rat incisor PDL are notable and closely related to those in the collagen fibre structures. It has also been reported that higher water contents caused greater stress–relaxation of the rabbit medial collateral ligament (Chimich et al., 1992) and human patellar tendon (Haut and Haut, 1997). It has been suggested that water molecules decrease the intermolecular force acting between the collagen fibres, thereby increasing their freedom of movement and increasing stress relaxation (Lam et al., 1993). Therefore, we assume that the decreases in the stress–relaxation of the incisor PDL in older rats are partly associated with loss of tissue water with advancing age.
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We could not detect morphological changes in the stretched collagen fibres and aligned cells under the light microscope during the stress–relaxation process. Purslow et al. (1998) also found no changes in the Dperiodicity and angular orientation of collagen during stress relaxation in rat skin and bovine perimysium. On the other hand, it has been shown that exudation of glycosaminoglycans and fluids to the external bath occurred and that the diameter of a fibre bundle decreased during stress relaxations in the rat tail tendon (Lanir et al., 1988) and canine flexor tendon (Hannafin and Arnoczky, 1994). Further analysis would be needed to clarify the structural changes during the stress– relaxation process.
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