- Email: [email protected]
Elasticity of alveolar bone near dental implant–bone interfaces after one month's healing
ARTICLE IN PRESS
Journal of Biomechanics 36 (2003) 1209–1214
Short communication
Elasticity of alveolar bone near dental implant–bone interfaces after one month’s healing M.C. Changa,b, C.C. Koa,*, C.C. Liua, W.H. Douglasa, R. DeLonga, W.-J. Seonga, J. Hodgesc, K.-N. And a
Department of Oral Sciences, Minnesota Dental Research Center for Biomaterials and Biomechanics, University of Minnesota, 16-212 Moos Tower 515 Delaware Street SE, Minneapolis, MN 55455, USA b Department of Materials Sciences and Chemical Engineering, Kunsan National University, South Korea c Division of Biostatistics and Oral Health Clinical Research Center, Department of Preventive Sciences, University of Minnesota, Minneapolis, MN 55455, USA d Orthopedic Biomechanics Laboratory, Mayo Clinic, Rochester, MN 55905, USA Accepted 12 March 2003
Abstract Information is scarce about Young’s modulus of healing bone surrounding an implant. The purpose of this preliminary study is to quantify elastic properties of pig alveolar bone that has healed for 1 month around titanium threaded dental implants, using the nanoindentation method. Two 2-year-old Sinclair miniswine were used for the study. Nanoindentation tests perpendicular to the bucco-lingual cross section were performed on harvested implant–bone blocks using the Hysitron TriboScope III. Nomarski differential interference contrast microscopy was used to identify pyramidal indentation measurements that were from bone. Reduced moduli, averaged for all anatomical regions, were found to start low (6.17 GPa) at the interface and gradually increase (slope=0.014) to a distance of 150 mm (7.89 GPa) from the implant surface, and then flatten to a slope of 0.001 from 150 to 1500 mm (10.13 GPa). Mean reduced modulus and its relationship to distance did not differ significantly by anatomic location (e.g., coronal, middle, and apical third; PX0:28 for all relevant tests) at 1 month after implantation. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Nanoindentation; Elasticity; Healing bone; Dental implant; Interface
1. Introduction Early loading on oral implants to promote osseointegration has not been consistently successful (SzmuklerMoncler et al., 1998), partly because the biomechanics of the interfacial bone are ill-understood. At early healing stages prior to maturation, microproperties of healing bone may depend on distance from the implant interface and on anatomic location. The physical properties (e.g., ultrasound propagation and microhardness) of such tissues are, in fact, microscopically heterogeneous across the interface (Zimmerman et al., 1989; Huja et al., 1998). Young’s modulus—which differs from hardness, determining stress and strain distributions around the implant and is thus more *Corresponding author. Tel.: +1-612-625-4430; fax: +1-612-6261484. E-mail address: [email protected] (C.C. Ko).
important in studying osseointegration—has not been measured near the implant–bone interface (Brunski, 1999). The present study used the nanoindentation method (Ko et al., 1995; Rho et al., 1997, 1999; Turner et al., 1999; Zysset et al., 1999) to measure interfacial elasticity of pig alveolar bone that has healed for 1 month around threaded titanium dental implants. Young’s moduli were measured at mm scale for multiple distances from the interface. Confirmation of data from tissue indents was obtained using Nomarski differential interference contrast (DIC) light microscopy.
2. Method The 4th premolar of two 2-year-old Sinclair miniswine (weight 58 kg, Sinclair Research Center Inc., Columbia,
0021-9290/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0021-9290(03)00113-1
ARTICLE IN PRESS M.C. Chang et al. / Journal of Biomechanics 36 (2003) 1209–1214
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MO) was surgically removed unilaterally (Animal Protocol #9910A22661). A smooth titanium threaded dental implant (3.75 mm diameter and 13 mm length, Walter Lorenz Co., Jacksonville, FL) was inserted in the alveolar ridge after the extraction wound had healed for 7 months. The implant was protected from bite forces for 1 month, then the animal was sacrificed. Implant–bone blocks were harvested and sectioned through the mid-plane of the implant along the buccolingual direction. The mesial section was divided into three specimens: the coronal third containing mostly cortical bone; and the middle and apical thirds containing trabecular bone (Fig. 1). A low exothermal liquid resin (PL-1, Measurements Group Inc., Raleigh, NC) was used to embed the sectioned tissue. The mid-plane was polished with carbimet abrasive discs and diamond paste followed by a 0.05-mm alumina suspension; each step was followed by 10 min of ultrasound cleaning. These procedures are similar to those of Rho et al. (1997) and Zysset et al. (1999), and do not seem to affect the samples’ physical properties. Specimens with final thickness of 2 mm were glued to metal disks of 1 cm diameter and 2 mm thickness using super glue, and stored at 10 C for approximately 3 months before testing. Nanoindentation tests were performed on polished specimen surfaces using the TriboScope (Hysitron Inc, Minneapolis, MN), a nanomechanical testing device operated through an atomic force microscopy (AFM)
stage (Digital Instrument, Santa Barbara, CA). The device, containing an indenter and a capacitance transducer, detects force and displacement at 10 nN and 0.2 nm resolution, respectively. AFM magnetically holds the sample and controls its position. A trapezoidal force profile (load rising from 0 to 6000 mN over 5 s; holding for 1 s; un-loading over 5 s) was used for the measurement. The un-loading force–displacement curve was used to calculate reduced modulus using the equations of Oliver and Pharr (1992). A new tip area function based on the PL-1 resin (a polymer material used in photoelastic analyses) was developed to convert the depth data (300–1300 nm) to contact areas; the depth is out of range for the fused silica area tip function using the TriboScope. The device can only execute a maximum force of 10 mN producing a depth of 250 nm on fused silica. This PL-1 area function yields a more reasonable elastic modulus for hard tissues than the fused silica area function (Table 1). Poisson’s ratio of healing bone is assumed to be 0.3, which yields errors associated with Young’s modulus, approximately, between 8.2% and +9.9% (Zysset et al., 1999). Table 1 Comparison of Young’s modulus (GPa) obtained using different area tip functions. Data from the literature are shown for comparison. The fused silica area function overestimates Young’s modulus for both PL1 resin and human dentina, by 77% and 31%, respectively, while the PL-1 area function overestimates fused silica’s Young’s modulus by 7% and underestimates dentin’s by 8% (n ¼ 20) Methods
Top of Implant Alveolar Crest 1 Coronal Third
2 3
Middle Third
4 Bone
5 6
Apical Third
7 8 9
Bottom of Alveolar Bone Fig. 1. Implant–bone specimen obtained from the lingual section of the mandibular block. Nanoindentations were performed along the nine dashed lines to quantify Young’s modulus of the healing bone. Three anatomic locations (coronal, middle, and apical third) were investigated.
Materials PL-1
PL-1 area function Fused silica Area function Tensile tests/literature
Dentin a
Fused silica a
3.570.1 4.670.2b
15.372.1 22.372.8b
77.276.4a 72.472.0b
3.570.6c (3.0d)
18.3e
72
a Young’s modulus was calculated from the derivation of Oliver and Pharr (1992) with Poisson’s ratio of 0.36, 0.3, and 0.17 for PL-1, Dentin, and Fused Silica, respectively. The Poisson ratio 0.36 for PL-1 was given by the manufacturer. b The high Young’s moduli of dentin and PL-1 may be attributed to the underestimates of the contact areas by the fuse silica area tip function. The TriboScope can only execute a maximum force of 10 mN, which produces a depth of 250 nm on fused silica. The peak indentation depths for dentin and PL-1 were out of range for the conventional area tip function calibrated from fused silica using the Hysitron TriboScope III. c Average Young’s modulus measured in our laboratory using dumbbell samples. Ten specimens were fabricated at room temperature (24 C) following manufacture’s recommendation. Each sample was made in separate processes, and sat in a room for 7 days prior to the test. The samples were tested using an Instron 4204 at a cross speed 0.1 mm/min. The deformation of the samples was recorded using an extensometer under a tensile load. The shapes of the samples was based on ASTM (D638-84) ‘‘standard test method for tensile properties of plastics’’. d Young’s modulus provided by Measurements Group Inc., Raleigh, NC. e Craig and Peyton (1958).
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moved along the line in 100 mm steps (Fig. 2) by a screw adjustment in the transducer holder. For each placement of the indenter, the indenting tip was moved in 15 mm steps along the diagonal of the 100 mm 100 mm square defined by the AFM software. Only points on this diagonal line were indented; the rest of the square was not scanned. At successive placements of the indenter, the scanned diagonal was alternated between the two diagonals of the square to create a saw-tooth pattern of indentations. The indents were observed using polarized light and Nomarski DIC illumination (Nikon Optiphot-Pol, Nikon, Melville, NY) within 12 h after indentation, to exclude data obtained from embedding resins and bone defects, i.e., lacunae, Haversian canals and marrow space. The Nomarski images required no additional sample preparation. Reduced moduli were compared according to anatomic locations and perpendicular distances to the implant surface, which were grouped into four distance groups: A: o 150 mm, B: 150–500 mm, C: 500–800 mm, and D: >800 mm. If the distance of the indents from the implant surface was less than 7 mm, the data were excluded to avoid an edge effect. Statistical analyses used analysis of variance (ANOVA) and multiple linear regression. Standard errors were derived from the ANOVA, to increase power.
3. Results
Fig. 2. Pooled raw data (864 points) shows (A) the distribution of reduced Young’s modulus around the line profile and (B) the relationship between reduced modulus and hardness. Large variations were present at all distances from the interface. A third-order B-spline fitted to the mean at each distance interval (every 15 mm) indicates the changes in elasticity across the interface. The numbers in mm indicate the distance away from the implant interface; the distance 0 represents the implant surface. Linear regression of the data within the first 150 mm showed a positive slope 0.014; Po0:001: Otherwise, the apparent trend showed a small slope 0.001; Po0:001: Simple correlation (ignoring pigs, lines, etc.) between the reduced modulus and hardness is 0.8. The distribution of hardness along the line profile is similar to that of reduced modulus (not shown).
Nine series of indentations were made (Fig. 1); each started adjacent to the implant–bone contact region and moved away from the interface in 15 mm intervals. Each series (one line profile) required approximately 1.5-h 100 indentations. The sample was rehydrated for 30 min before beginning each new series. The indenter tip was
A scatterplot smoother found that reduced moduli averaged 6.17 GPa at the interface, gradually increased until about 150 mm from the implant, then flattened out (Fig. 3A). The overall means of reduced modulus for the two animals did not differ (animal main effect P ¼ 0:48) (Table 2). Analyzing according to the distance groups, elastic modulus was lower within 150 mm of the interface, but did not differ among the three most distant groupings (distance main effect Po0:0001). Linear regression using only measurements within 150 mm of the interface showed that the moduli had positive slope, 0.014 GPa/ mm (Po0:001), which did not differ significantly between animals (P ¼ 0:31) or anatomical regions (P ¼ 0:49). The anatomical areas did not differ overall (anatomy main effect P ¼ 0:73) (Table 3). The trend of bone elasticity perpendicular to the interface was similar in the anatomical areas (distance group-by-anatomic region interaction P ¼ 0:28).
4. Discussion A small but significant gradient in elastic modulus was found out to be 1500 mm. A distinct change in
13
7 6 5
4 3
15 µm interval
2
1
Embedding Resin
Implant
Fig. 3. Nomarski images show stereo-impressions of nanoindentations with pyramidal shape labeled with numerals, and colored tissue microstructures, for the first 230 mm from the implant surface in one of the scanned line profiles. The saw-tooth pattern provides easy identification of the indentation data and its location. The size of each indentation is approximately 3 mm and is smaller than that of lacunae (arrows). The indentations located in defects (e.g., measurements 12 and 15 in lacunae) were excluded from the data pool. Note that the sample was not stained or coated. Colors reflect optical path differences due to refractive index variations in tissue composition. Different colors between images are due to optical adjustment that provides optimal indentation contrast within individual views.
Resin in Haversian Canal
16
15
14
12
11
8
Bone
1212
10
9
100 µm Movement
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ARTICLE IN PRESS M.C. Chang et al. / Journal of Biomechanics 36 (2003) 1209–1214 Table 2 (A) Adjusted mean reduced modulus, mean7SE (GPa), and (B) hardness, mean7SE (GPa), for pooled data and the two animals’ data are tabulated in relation to four predefined regions. Statistically, no differences between two animals were found with regard to the distribution patterns (animal-by-distance group interaction P ¼ 0:46) Distance Measurements group (A) A B C D
Reduced Reduced Reduced Reduced
(B) A B C D
Hardness Hardness Hardness Hardness
modulus modulus modulus modulus
Pooled
Pig ID#68
Pig ID#66
7.7870.47 8.6170.45 9.1970.48 9.0170.45
7.5370.66 8.0970.65 9.0070.69 8.7370.63
8.0370.65 9.1370.63 9.3770.66 9.3070.64
0.18970.015 0.20970.014 0.21570.015 0.21570.014
0.18070.021 0.19970.021 0.21570.022 0.22470.020
0.19870.021 0.22070.020 0.21670.021 0.20670.020
Table 3 (A) Adjusted mean values of reduced modulus, mean7SE (GPa), and (B) hardness, mean7SE (GPa), for coronal, middle and apical bone areas in four predefined regions. A: p150 mm; B: 151–500 mm; C: 501– 800 mm; D: >800 mm. Region A had a significantly lower modulus than other three regions Distance Measurements group (A) A B C D
Reduced Reduced Reduced Reduced
(B) A B C D
Hardness Hardness Hardness Hardness
modulus modulus modulus modulus
Coronal
Middle
Apical
8.3970.78 9.0170.75 9.1670.76 9.4970.76
7.1770.78 7.8670.80 8.9570.77 8.8070.77
7.7870.85 8.9770.79 9.4670.93 8.7570.81
0.20870.025 0.22070.024 0.22270.024 0.23070.024
0.18870.025 0.19970.026 0.21070.024 0.21270.024
0.17170.027 0.20870.025 0.21470.031 0.20370.026
elasticity was identified roughly 150 mm from the interface, as suggested by Fig. 3. However, our data do not support a preference for a threshold of 150 mm over nearby values, e.g. 135 or 165 mm. It is unlikely that any sharp biological threshold exists; 150 mm is a convenient round number. The wide data variation associated with tissue microstructures indicates that micromechanical analyses accounting for changes of local tissue properties may be important for interfacial biomechanics. Nomarski DIC microscopy showed nanoindents (sized 3–10 mm) in unstained and uncoated specimens, similar to topological studies in cells and chromosomes (Takayama et al., 1981; Baldwin and Bankston, 1988). The pyramidal indents were better visualized by DIC microscopy than by SEM as previously shown (Rho et al., 1999). Another advantage of this method is the ability to retrieve samples for additional tests after
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imaging, because it leaves samples virtually unaltered. Sample preparation for SEM (e.g., drying and coating) may affect the indents. The increasing trend in elastic modulus in the present study is much smaller than that of microhardness described by Huja et al. (1998) who found microhardness increasing exponentially from 200 to 600 mm from the implant surface. Cheng and Douglas (2001, 2002) showed that microhardness exponentially declined at the free end of a homogenous sample. Microhardness is extremely sensitive to edge effects (i.e., the area closest to the implant surface). The nanoindentation data, however, does not show such an edge effect as measured in our pilot study making the nanoindentation path parallel to the implant 2 mm away from the interface (data not shown). The small force and embedding resin probably reduce the edge effect, especially for edges without supporting tissues. The small increasing trend of nanoindentation hardness perpendicular to the interface (Tables 2 and 3) resembles the trend in reduced moduli. Hardness was linearly related to reduced modulus (Fig. 3B), and was close to the range (0.234–0.760 GPa) reported in the literature for bony tissues (Rho et al., 1999; Zysset et al., 1999). Our hardness and reduced modulus may be higher than their actual values because tissue surface moisture may change during the study. Our data showed low reduced moduli and hardness, compared to past nanoindentation studies. This may be attributed to differences in bone maturation, species, and area tip function. Bone healed for 1 month contains approximately half the calcified contents of mature bone. Mature pig bone is about 14% less stiff than human bone (Fung, 1981). The polymer area tip function also yielded low Young’s moduli for dentin and bone compared to the fused silica area function. We assume that the deformation of hard tissues, especially healing bone, is more comparable to PL-1 resin. Table 1 shows that using the PL-1 area function, dentin with mineral content similar to bone had moduli reasonably comparable to those measured by standard stress–strain apparatus. Whether time dependency of the polymer and its polymerization affect accuracy of the calibration function remains undetermined. Further investigation comparing area functions between calibration and testing materials will advance this area of research.
Acknowledgements This study was supported in part by the Whitaker Foundation (RG97-455), Minnesota Dental Research Center for Biomaterials and Biomechanics, the Graduate School of University of Minnesota, and NIDCR grant DE 09737. Thanks to Mr. Manuel Chan for his assistance in analyzing data.
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References Baldwin, W.W., Bankston, P.W., 1988. Measurement of live bacteria by Nomarski interference microscopy and stereologic methods as tested with macroscopic rod-shaped models. Applied and Environmental Microbiology 54 (1), 105–109. Brunski, J.B., 1999. In vivo bone response to biomechanical loading at the bone/dental implant interface. Advances in Dental Research 13, 99–119. Cheng, Y.-S., Douglas, W.H., 2001. Boundary effect of microhardness. Journal of Dental Research 80 (Special Issue), 203. Cheng, Y.-S., Douglas, W.H., 2002. Comprehensive boundary effect of microhardness. Journal of Dental Research 81 (Spec. Issue), A471. Craig, R.G., Peyton, F.A., 1958. Elastic and mechanical properties of human dentin. Journal of Dental Research 37 (4), 710–718. Fung, Y.C., 1981. A First Course in Continuum Mechanics, 2nd Edition. Prentice-Hall, Englewood Cliffs, NJ. Huja, S.S., Katona, T.R., Moore, B.K., Roberts, W.E., 1998. Microhardness and anisotropy of the vital osseous interface and endosseous implant supporting bone. Journal of Orthopaedic Research 16, 54–60. Ko, C.C., Douglas, W.H., Cheng, Y.S., 1995. Intrinsic mechanical competence of cortical and trabecular bone measured by nanoindentation and microindentation probes. ASME Bioengineering Conference, AMSE-BED-Vol. 29, pp. 415–416. Oliver, W.C., Pharr, G.M., 1992. An improved technique for determining hardness and elastic modulus using loading and displacement sensing indentation experiments. Journal of Materials Research 7, 1564–1583.
Rho, J.Y., Tsui, T.Y., Parr, G.M., 1997. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials 18, 1325–1330. Rho, J.Y., Zioupos, P., Currey, J.D., Pharr, G.M., 1999. Variations in the individual thick lamellar properties within osteons by nanoindentation. Bone 25 (3), 295–300. Szmukler-Moncler, S., Salama, H., Reingewirtz, Y., Dubruille, J.H., 1998. Timing of loading and effect of micromotion on bone-dental implant interface: review of experimental literature. Journal of Biomedical Materials Research (Applied Biomaterials) 43, 192–203. Takayama, S., Utsumi, K.R., Sasaki, Y., 1981. Topographic examination of sister chromatid differential staining by Nomarski interference microscopy and scanning electron microscopy. Chromosoma (Berl.) 82, 113–119. Turner, C.H., Rho, J., Takano, Y., Tsui, T.Y., Pharr, G.M., 1999. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. Journal of Biomechanics 32, 437–441. Zimmerman, M.C., Meunier, A., Katz, J.L., Christel, P., Sedel, L., 1989. The evaluation of bone remodeling about orthopaedic implants with ultrasound. Journal of Orthopaedic Research 7, 607–611. Zysset, P.K., Guo, X.E., Hoffler, C.E., Moore, K.E., Goldstein, S.A., 1999. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. Journal of Biomechanics 32, 1005–1012.
Journal of Biomechanics 36 (2003) 1209–1214
Short communication
Elasticity of alveolar bone near dental implant–bone interfaces after one month’s healing M.C. Changa,b, C.C. Koa,*, C.C. Liua, W.H. Douglasa, R. DeLonga, W.-J. Seonga, J. Hodgesc, K.-N. And a
Department of Oral Sciences, Minnesota Dental Research Center for Biomaterials and Biomechanics, University of Minnesota, 16-212 Moos Tower 515 Delaware Street SE, Minneapolis, MN 55455, USA b Department of Materials Sciences and Chemical Engineering, Kunsan National University, South Korea c Division of Biostatistics and Oral Health Clinical Research Center, Department of Preventive Sciences, University of Minnesota, Minneapolis, MN 55455, USA d Orthopedic Biomechanics Laboratory, Mayo Clinic, Rochester, MN 55905, USA Accepted 12 March 2003
Abstract Information is scarce about Young’s modulus of healing bone surrounding an implant. The purpose of this preliminary study is to quantify elastic properties of pig alveolar bone that has healed for 1 month around titanium threaded dental implants, using the nanoindentation method. Two 2-year-old Sinclair miniswine were used for the study. Nanoindentation tests perpendicular to the bucco-lingual cross section were performed on harvested implant–bone blocks using the Hysitron TriboScope III. Nomarski differential interference contrast microscopy was used to identify pyramidal indentation measurements that were from bone. Reduced moduli, averaged for all anatomical regions, were found to start low (6.17 GPa) at the interface and gradually increase (slope=0.014) to a distance of 150 mm (7.89 GPa) from the implant surface, and then flatten to a slope of 0.001 from 150 to 1500 mm (10.13 GPa). Mean reduced modulus and its relationship to distance did not differ significantly by anatomic location (e.g., coronal, middle, and apical third; PX0:28 for all relevant tests) at 1 month after implantation. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Nanoindentation; Elasticity; Healing bone; Dental implant; Interface
1. Introduction Early loading on oral implants to promote osseointegration has not been consistently successful (SzmuklerMoncler et al., 1998), partly because the biomechanics of the interfacial bone are ill-understood. At early healing stages prior to maturation, microproperties of healing bone may depend on distance from the implant interface and on anatomic location. The physical properties (e.g., ultrasound propagation and microhardness) of such tissues are, in fact, microscopically heterogeneous across the interface (Zimmerman et al., 1989; Huja et al., 1998). Young’s modulus—which differs from hardness, determining stress and strain distributions around the implant and is thus more *Corresponding author. Tel.: +1-612-625-4430; fax: +1-612-6261484. E-mail address: [email protected] (C.C. Ko).
important in studying osseointegration—has not been measured near the implant–bone interface (Brunski, 1999). The present study used the nanoindentation method (Ko et al., 1995; Rho et al., 1997, 1999; Turner et al., 1999; Zysset et al., 1999) to measure interfacial elasticity of pig alveolar bone that has healed for 1 month around threaded titanium dental implants. Young’s moduli were measured at mm scale for multiple distances from the interface. Confirmation of data from tissue indents was obtained using Nomarski differential interference contrast (DIC) light microscopy.
2. Method The 4th premolar of two 2-year-old Sinclair miniswine (weight 58 kg, Sinclair Research Center Inc., Columbia,
0021-9290/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0021-9290(03)00113-1
ARTICLE IN PRESS M.C. Chang et al. / Journal of Biomechanics 36 (2003) 1209–1214
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MO) was surgically removed unilaterally (Animal Protocol #9910A22661). A smooth titanium threaded dental implant (3.75 mm diameter and 13 mm length, Walter Lorenz Co., Jacksonville, FL) was inserted in the alveolar ridge after the extraction wound had healed for 7 months. The implant was protected from bite forces for 1 month, then the animal was sacrificed. Implant–bone blocks were harvested and sectioned through the mid-plane of the implant along the buccolingual direction. The mesial section was divided into three specimens: the coronal third containing mostly cortical bone; and the middle and apical thirds containing trabecular bone (Fig. 1). A low exothermal liquid resin (PL-1, Measurements Group Inc., Raleigh, NC) was used to embed the sectioned tissue. The mid-plane was polished with carbimet abrasive discs and diamond paste followed by a 0.05-mm alumina suspension; each step was followed by 10 min of ultrasound cleaning. These procedures are similar to those of Rho et al. (1997) and Zysset et al. (1999), and do not seem to affect the samples’ physical properties. Specimens with final thickness of 2 mm were glued to metal disks of 1 cm diameter and 2 mm thickness using super glue, and stored at 10 C for approximately 3 months before testing. Nanoindentation tests were performed on polished specimen surfaces using the TriboScope (Hysitron Inc, Minneapolis, MN), a nanomechanical testing device operated through an atomic force microscopy (AFM)
stage (Digital Instrument, Santa Barbara, CA). The device, containing an indenter and a capacitance transducer, detects force and displacement at 10 nN and 0.2 nm resolution, respectively. AFM magnetically holds the sample and controls its position. A trapezoidal force profile (load rising from 0 to 6000 mN over 5 s; holding for 1 s; un-loading over 5 s) was used for the measurement. The un-loading force–displacement curve was used to calculate reduced modulus using the equations of Oliver and Pharr (1992). A new tip area function based on the PL-1 resin (a polymer material used in photoelastic analyses) was developed to convert the depth data (300–1300 nm) to contact areas; the depth is out of range for the fused silica area tip function using the TriboScope. The device can only execute a maximum force of 10 mN producing a depth of 250 nm on fused silica. This PL-1 area function yields a more reasonable elastic modulus for hard tissues than the fused silica area function (Table 1). Poisson’s ratio of healing bone is assumed to be 0.3, which yields errors associated with Young’s modulus, approximately, between 8.2% and +9.9% (Zysset et al., 1999). Table 1 Comparison of Young’s modulus (GPa) obtained using different area tip functions. Data from the literature are shown for comparison. The fused silica area function overestimates Young’s modulus for both PL1 resin and human dentina, by 77% and 31%, respectively, while the PL-1 area function overestimates fused silica’s Young’s modulus by 7% and underestimates dentin’s by 8% (n ¼ 20) Methods
Top of Implant Alveolar Crest 1 Coronal Third
2 3
Middle Third
4 Bone
5 6
Apical Third
7 8 9
Bottom of Alveolar Bone Fig. 1. Implant–bone specimen obtained from the lingual section of the mandibular block. Nanoindentations were performed along the nine dashed lines to quantify Young’s modulus of the healing bone. Three anatomic locations (coronal, middle, and apical third) were investigated.
Materials PL-1
PL-1 area function Fused silica Area function Tensile tests/literature
Dentin a
Fused silica a
3.570.1 4.670.2b
15.372.1 22.372.8b
77.276.4a 72.472.0b
3.570.6c (3.0d)
18.3e
72
a Young’s modulus was calculated from the derivation of Oliver and Pharr (1992) with Poisson’s ratio of 0.36, 0.3, and 0.17 for PL-1, Dentin, and Fused Silica, respectively. The Poisson ratio 0.36 for PL-1 was given by the manufacturer. b The high Young’s moduli of dentin and PL-1 may be attributed to the underestimates of the contact areas by the fuse silica area tip function. The TriboScope can only execute a maximum force of 10 mN, which produces a depth of 250 nm on fused silica. The peak indentation depths for dentin and PL-1 were out of range for the conventional area tip function calibrated from fused silica using the Hysitron TriboScope III. c Average Young’s modulus measured in our laboratory using dumbbell samples. Ten specimens were fabricated at room temperature (24 C) following manufacture’s recommendation. Each sample was made in separate processes, and sat in a room for 7 days prior to the test. The samples were tested using an Instron 4204 at a cross speed 0.1 mm/min. The deformation of the samples was recorded using an extensometer under a tensile load. The shapes of the samples was based on ASTM (D638-84) ‘‘standard test method for tensile properties of plastics’’. d Young’s modulus provided by Measurements Group Inc., Raleigh, NC. e Craig and Peyton (1958).
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moved along the line in 100 mm steps (Fig. 2) by a screw adjustment in the transducer holder. For each placement of the indenter, the indenting tip was moved in 15 mm steps along the diagonal of the 100 mm 100 mm square defined by the AFM software. Only points on this diagonal line were indented; the rest of the square was not scanned. At successive placements of the indenter, the scanned diagonal was alternated between the two diagonals of the square to create a saw-tooth pattern of indentations. The indents were observed using polarized light and Nomarski DIC illumination (Nikon Optiphot-Pol, Nikon, Melville, NY) within 12 h after indentation, to exclude data obtained from embedding resins and bone defects, i.e., lacunae, Haversian canals and marrow space. The Nomarski images required no additional sample preparation. Reduced moduli were compared according to anatomic locations and perpendicular distances to the implant surface, which were grouped into four distance groups: A: o 150 mm, B: 150–500 mm, C: 500–800 mm, and D: >800 mm. If the distance of the indents from the implant surface was less than 7 mm, the data were excluded to avoid an edge effect. Statistical analyses used analysis of variance (ANOVA) and multiple linear regression. Standard errors were derived from the ANOVA, to increase power.
3. Results
Fig. 2. Pooled raw data (864 points) shows (A) the distribution of reduced Young’s modulus around the line profile and (B) the relationship between reduced modulus and hardness. Large variations were present at all distances from the interface. A third-order B-spline fitted to the mean at each distance interval (every 15 mm) indicates the changes in elasticity across the interface. The numbers in mm indicate the distance away from the implant interface; the distance 0 represents the implant surface. Linear regression of the data within the first 150 mm showed a positive slope 0.014; Po0:001: Otherwise, the apparent trend showed a small slope 0.001; Po0:001: Simple correlation (ignoring pigs, lines, etc.) between the reduced modulus and hardness is 0.8. The distribution of hardness along the line profile is similar to that of reduced modulus (not shown).
Nine series of indentations were made (Fig. 1); each started adjacent to the implant–bone contact region and moved away from the interface in 15 mm intervals. Each series (one line profile) required approximately 1.5-h 100 indentations. The sample was rehydrated for 30 min before beginning each new series. The indenter tip was
A scatterplot smoother found that reduced moduli averaged 6.17 GPa at the interface, gradually increased until about 150 mm from the implant, then flattened out (Fig. 3A). The overall means of reduced modulus for the two animals did not differ (animal main effect P ¼ 0:48) (Table 2). Analyzing according to the distance groups, elastic modulus was lower within 150 mm of the interface, but did not differ among the three most distant groupings (distance main effect Po0:0001). Linear regression using only measurements within 150 mm of the interface showed that the moduli had positive slope, 0.014 GPa/ mm (Po0:001), which did not differ significantly between animals (P ¼ 0:31) or anatomical regions (P ¼ 0:49). The anatomical areas did not differ overall (anatomy main effect P ¼ 0:73) (Table 3). The trend of bone elasticity perpendicular to the interface was similar in the anatomical areas (distance group-by-anatomic region interaction P ¼ 0:28).
4. Discussion A small but significant gradient in elastic modulus was found out to be 1500 mm. A distinct change in
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7 6 5
4 3
15 µm interval
2
1
Embedding Resin
Implant
Fig. 3. Nomarski images show stereo-impressions of nanoindentations with pyramidal shape labeled with numerals, and colored tissue microstructures, for the first 230 mm from the implant surface in one of the scanned line profiles. The saw-tooth pattern provides easy identification of the indentation data and its location. The size of each indentation is approximately 3 mm and is smaller than that of lacunae (arrows). The indentations located in defects (e.g., measurements 12 and 15 in lacunae) were excluded from the data pool. Note that the sample was not stained or coated. Colors reflect optical path differences due to refractive index variations in tissue composition. Different colors between images are due to optical adjustment that provides optimal indentation contrast within individual views.
Resin in Haversian Canal
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15
14
12
11
8
Bone
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10
9
100 µm Movement
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ARTICLE IN PRESS M.C. Chang et al. / Journal of Biomechanics 36 (2003) 1209–1214 Table 2 (A) Adjusted mean reduced modulus, mean7SE (GPa), and (B) hardness, mean7SE (GPa), for pooled data and the two animals’ data are tabulated in relation to four predefined regions. Statistically, no differences between two animals were found with regard to the distribution patterns (animal-by-distance group interaction P ¼ 0:46) Distance Measurements group (A) A B C D
Reduced Reduced Reduced Reduced
(B) A B C D
Hardness Hardness Hardness Hardness
modulus modulus modulus modulus
Pooled
Pig ID#68
Pig ID#66
7.7870.47 8.6170.45 9.1970.48 9.0170.45
7.5370.66 8.0970.65 9.0070.69 8.7370.63
8.0370.65 9.1370.63 9.3770.66 9.3070.64
0.18970.015 0.20970.014 0.21570.015 0.21570.014
0.18070.021 0.19970.021 0.21570.022 0.22470.020
0.19870.021 0.22070.020 0.21670.021 0.20670.020
Table 3 (A) Adjusted mean values of reduced modulus, mean7SE (GPa), and (B) hardness, mean7SE (GPa), for coronal, middle and apical bone areas in four predefined regions. A: p150 mm; B: 151–500 mm; C: 501– 800 mm; D: >800 mm. Region A had a significantly lower modulus than other three regions Distance Measurements group (A) A B C D
Reduced Reduced Reduced Reduced
(B) A B C D
Hardness Hardness Hardness Hardness
modulus modulus modulus modulus
Coronal
Middle
Apical
8.3970.78 9.0170.75 9.1670.76 9.4970.76
7.1770.78 7.8670.80 8.9570.77 8.8070.77
7.7870.85 8.9770.79 9.4670.93 8.7570.81
0.20870.025 0.22070.024 0.22270.024 0.23070.024
0.18870.025 0.19970.026 0.21070.024 0.21270.024
0.17170.027 0.20870.025 0.21470.031 0.20370.026
elasticity was identified roughly 150 mm from the interface, as suggested by Fig. 3. However, our data do not support a preference for a threshold of 150 mm over nearby values, e.g. 135 or 165 mm. It is unlikely that any sharp biological threshold exists; 150 mm is a convenient round number. The wide data variation associated with tissue microstructures indicates that micromechanical analyses accounting for changes of local tissue properties may be important for interfacial biomechanics. Nomarski DIC microscopy showed nanoindents (sized 3–10 mm) in unstained and uncoated specimens, similar to topological studies in cells and chromosomes (Takayama et al., 1981; Baldwin and Bankston, 1988). The pyramidal indents were better visualized by DIC microscopy than by SEM as previously shown (Rho et al., 1999). Another advantage of this method is the ability to retrieve samples for additional tests after
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imaging, because it leaves samples virtually unaltered. Sample preparation for SEM (e.g., drying and coating) may affect the indents. The increasing trend in elastic modulus in the present study is much smaller than that of microhardness described by Huja et al. (1998) who found microhardness increasing exponentially from 200 to 600 mm from the implant surface. Cheng and Douglas (2001, 2002) showed that microhardness exponentially declined at the free end of a homogenous sample. Microhardness is extremely sensitive to edge effects (i.e., the area closest to the implant surface). The nanoindentation data, however, does not show such an edge effect as measured in our pilot study making the nanoindentation path parallel to the implant 2 mm away from the interface (data not shown). The small force and embedding resin probably reduce the edge effect, especially for edges without supporting tissues. The small increasing trend of nanoindentation hardness perpendicular to the interface (Tables 2 and 3) resembles the trend in reduced moduli. Hardness was linearly related to reduced modulus (Fig. 3B), and was close to the range (0.234–0.760 GPa) reported in the literature for bony tissues (Rho et al., 1999; Zysset et al., 1999). Our hardness and reduced modulus may be higher than their actual values because tissue surface moisture may change during the study. Our data showed low reduced moduli and hardness, compared to past nanoindentation studies. This may be attributed to differences in bone maturation, species, and area tip function. Bone healed for 1 month contains approximately half the calcified contents of mature bone. Mature pig bone is about 14% less stiff than human bone (Fung, 1981). The polymer area tip function also yielded low Young’s moduli for dentin and bone compared to the fused silica area function. We assume that the deformation of hard tissues, especially healing bone, is more comparable to PL-1 resin. Table 1 shows that using the PL-1 area function, dentin with mineral content similar to bone had moduli reasonably comparable to those measured by standard stress–strain apparatus. Whether time dependency of the polymer and its polymerization affect accuracy of the calibration function remains undetermined. Further investigation comparing area functions between calibration and testing materials will advance this area of research.
Acknowledgements This study was supported in part by the Whitaker Foundation (RG97-455), Minnesota Dental Research Center for Biomaterials and Biomechanics, the Graduate School of University of Minnesota, and NIDCR grant DE 09737. Thanks to Mr. Manuel Chan for his assistance in analyzing data.
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