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An in vitro comparison of bone deformation measured with surface and staple mounted strain gauges
Journal of Biomechanics 32 (1999) 1359}1363
Technical note
An in vitro comparison of bone deformation measured with surface and staple mounted strain gauges A. Arndt *, P. Westblad , I. Ekenman , K. Halvorsen, A. Lundberg Department of Orthopaedic Surgery, Huddinge University Hospital, Huddinge, Sweden The Systems and Control Group, Uppsala University, Uppsala, Sweden Accepted 14 June 1999
Abstract Chicken tibiae were chosen as a model for human second metatarsals. Local surface bone deformation in a 4-point bending con"guration was measured in vitro by both strain gauge instrumented staples and strain gauges bonded to the bone's cortical surface. A series of staple bridge dimensions (0.5, 0.6, 0.8 and 1.0 mm) was compared to test for staple in#uence on bone characteristics and greatest measurement validity and reliability. Thicker staple inhibition of bone deformation was the greatest but di!erences to thinner staples were not statistically signi"cant (p'0.05). All staples except 0.5 mm had maximum deviations from linearity less than 1%. The 1.0 mm staple had an R value of 0.992$0.006 plotted against the 4-point bending input force and 0.994$0.002 plotted against the surface strain gauge signal. The mean intraclass correlation coe$cients (ICC) calculated with four input forces (30, 60, 90 and 120 N) and for loading and unloading conditions for the 0.5, 0.6, 0.8 and 1.0 mm staples were 0.75, 0.83, 0.87 and 0.92, respectively. Finally, the di!erences in slope of the staple strain gauge signal plotted against surface strain gauge signal between input force loading and unloading conditions (0.32), and between input compression and tension conditions (0.79) was least for the 1.0 mm staple which also resulted in the lowest standard deviations. These results suggested the appropriateness of the 1.0 mm staple for in vivo application. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Strain gauge; Local bone deformation
1. Introduction Human second metatarsals are a common site for stress fractures in military recruits (Milgrom et al., 1985; Finestone et al., 1992). Local bone deformation is regarded as an indicator of stress fracture risk and this in vitro study presents the development of a methodology suitable for future in vivo application in ascertaining local bone deformation of human second metatarsals. There are disadvantages involved in the in vivo application of strain gauges directly onto bone surfaces. Direct adhesion is quite invasive as the periosteum must be removed and the bone prepared to obtain an optimal bonding surface. The insertion of instrumented staples involves less traumatic surgery and is thus more appro* Corresponding author. Tel.: #46-8-5858-7154; fax: #46-8-7114292. E-mail address: [email protected] (A. Arndt)
priate for human in vivo application. Strain on the human tibia has previously been measured in vivo with rosette strain gauges (Lanyon et al., 1975; Burr et al., 1996), transcutaneous extensometers (Fyhrie et al., 1998) and inserted staples (Ekenman et al., 1998a). No such investigation has, however, been performed on metatarsals or bones of corresponding size and previous values for human metatarsal loading have been provided by theoretical biomechanical models (Stokes et al., 1979; Gross and Bunch, 1989) or investigations of human cadaver specimens (Lease and Evans, 1959; Sharkey et al., 1995; Courtney et al., 1997). This study tested the viability of the staple technique (Ekenman et al., 1998b) when applied to bones representing the human second metatarsal. Chicken tibiae were chosen as a metatarsal model because of ethical di$culties in obtaining human bone specimens. The aim was to assess the in vitro validity and reliability of this methodology and to determine the interactive e!ects between staple and bone during induced bending deformation.
0021-9290/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 9 ) 0 0 1 2 9 - 3
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A. Arndt et al. / Journal of Biomechanics 32 (1999) 1359}1363
2. Methods After the removal of soft tissue the "bular aspects of the chicken tibiae were degreased (CSM-1A Degreaser, Measurements Group Inc. Raleigh, NC, USA), wetted (M-Prep Conditioner A, Measurements Group Inc.), abraded and neutralised (M-Prep Neutralizer 5A, Measurements Group Inc.). The bone surface was dried for 10 min at 503C and the surface preparation process subsequently repeated. Two strain gauges (Types EA06-031DE-350 and EA-06-031EC-350, Measurements Group Inc.) were mounted perpendicular to each other on the underneath bridge surface of a 16 mm;15 mm orthopaedic titanium staple (3M, St. Paul, MN, USA). The staple was inserted in pre-drilled holes over the midpoint of the "bular aspect of each bone. An insertion tool and staple guide provided a pretensile staple leg distension of 0.4 mm, as described by Ekenman et al. (1998b). Staples were inserted to a depth of 4 mm ensuring the legs passed completely through the cortex (thickness: 1.9$0.3 mm). A further strain gauge was bonded to the prepared surface with cyanoacrylate polymer (MBond 200, Measurements Group Inc.). This was located centrally underneath the staple with the strain gauge measurement axes aligned (Fig. 1). A series of staple dimensions (0.5, 0.6, 0.8 and 1.0 mm bridge thickness) was tested and two bones were instrumented with each staple size. The strain was measured uniaxially in the longitudinal direction of the bone. Force input was provided by depressing the upper segment of the four-point con"guration of a material testing machine (MTS, MN, USA, electronic component model 8500#, Instron, Canton, MA, USA) (Fig. 1). An input force of 160 N was chosen to sub-maximally load the bones. This corresponded to a maximum surface strain of approximately 2000 le. A pretension force of
10 N was applied followed by loading to 150 N at a rate of 30 N/s. Each loading trial was followed by a corresponding unloading trial to the pretension state. Two experimental con"gurations were designed, producing both tensile and compressive strain on the instrumented aspect of the bone. Strain gauge signals were ampli"ed (2120A, Measurements Group Inc., USA) and recorded with standard PC analog data collection software (Bioware, Kistler Inc., Switzerland). The synchronised input force of the material testing machine was also recorded. All data were sampled at 100 Hz. Each bone was loaded and unloaded twice under both tension and compression conditions providing a total of 64 trials. 2.1. Analysis Variations in surface deformation relative to input force, with staple thickness as independent variable, were regarded as an indication of staple in#uence on bone behaviour. The thinnest staple (0.5 mm bridge) was assumed to have the least in#uence and any statistically signi"cant di!erences (p)0.05) to this would be due to an unacceptable staple in#uence. The linearity of the staple strain gauge signal relative to both the surface deformation and input force was regarded as a descriptor of the validity of the staple methodology. The slope k of the linear regression (y"kx#b) was used to describe the relation between the surface and staple deformation. Intraclass correlation coe$cients (ICC [1,1]; Shrout and Fleiss, 1979) were calculated as primary indicators of measurement reliability. Input data for each ICC class was a 4;4 array of the recorded strain at 30, 60, 90 and 120 N input force for the two bones instrumented with each staple thickness and loading and unloading conditions for that staple. Tension and compression conditions were separated. 3. Results 3.1. Staple inyuence on bone deformation
Fig. 1. The four-point bending experimental setup; tension. Approximately actual size. Tensile force was developed on the upper aspect of the bone by depressing the upper segment of the material loading machine. The distance between the contact points of the upper segment was 41 mm and between those of the lower; 18 and 80 mm in tension and compression, respectively.
Under the assumption that the input force was linear, k for surface deformation vs. input force was determined to assess the e!ect of di!erent staples (independent variable) on surface deformation (dependent) (Fig. 2A). A one-way analysis of variance (ANOVA) showed no statistical signi"cance (p'0.05) between the di!erences. Fig. 2B illustrates the decrease in k for all conditions combined from thinner to thicker staples (range: 16.48$1.15}8.96$0.63). 3.2. Staple reliability The ICC was the primary indication of staple reliability (Table 1).
A. Arndt et al. / Journal of Biomechanics 32 (1999) 1359}1363
1361
Fig. 2. (A) Staple in#uence on surface deformation; k value (input force plotted against strain recorded by surface strain gauge): tld: tension/load, tuld: tension/unload, cld: compression/load, culd: compression/unload. (B) Mean k (staple strain gauge plotted against surface strain gauge signals) for di!erent staple dimensions. Signi"cant di!erences (p)0.05) were seen between k(0.5 mm) and all other staples, and k(0.6 mm) to k(1.0 mm). (C) Mean k (staple against surface) comparison between tension and compression. Actual di!erences for 0.5, 0.6, 0.8 and 1.0 mm staples, respectively, were: 0.59, 1.20, 1.46 and 0.79. (D) Mean k (staple against surface) comparison between loading and unloading. Actual di!erences: 0.72, 1.41, 0.52 and 0.32.
Table 1 Intraclass correlation coe$cient (ICC). Staple bridge size (mm)
Compression/surface
Compression/staple
Tension/surface
Tension/staple
Mean
0.5 0.6 0.8 1.0
0.97 0.78 0.86 0.89
0.37 0.93 0.89 0.85
0.85 0.69 0.90 0.98
0.81 0.91 0.82 0.96
0.75 0.83 0.87 0.92
From left to right: surface strain measured during the compression condition, staple strain during compression, surface strain during tension and staple strain during tension.
A further indicator of staple reliability was the similarity of staple output relative to the surface deformation under di!erent conditions (i.e., tension/compression and load/unload, Fig. 2C and D). The most similar response for tension and compression of the 1.0 mm staple in-
dicated the greatest robustness to variations in bone loading. Loss of hysteresis energy was indicated by variations in k dependent upon loading and unloading of the bone. This loss successively decreased with thicker staples and was also least for the 1.0 mm staple.
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A. Arndt et al. / Journal of Biomechanics 32 (1999) 1359}1363
3.3. Staple validity Thicker staples demonstrated greater linearity relative to both input force and surface deformation (Table 2). Furthermore, the standard deviations were less for thicker staples indicating more consistent measuring performance. The response of the 1.0 mm staple varied by an average of 0.6% compared to the measured surface deformation whereas the 0.5 mm staple di!ered by 4.2%.
4. Discussion Di!erent staple dimensions were compared for two reasons: (a) It was feasible that the stress}strain behavior and therefore, the elastic modulus of the bone would be in#uenced by the inserted staple and that this in#uence would be greater for sti!er staples. (b) Although strain has been successfully measured with 1.0 mm staple bridges on human tibiae (Ekenman et al., 1998a), it was uncertain whether such thick staples would be sensitive to local deformation in bones of comparatively small proportions. The results showed no signi"cant di!erence in the in#uence of di!erent staple dimensions on the bone bending behaviour and similar strain ranges for the 1.0 mm staple as reported by Ekenman et al. (1998a). In model calculations Gross and Bunch (1989) predicted human second metatarsal strain of 6662 le during running with a corresponding bending moment of 7.71 N m. These values were considerably higher than those recorded in the present study (input bending moments of 1.84 and 3.12 N m in tensile and compressive conditions, respectively). Sharkey et al., (1995) measured in vitro the bone surface strains up to approximately 1000 le with an induced external ground reaction force of 750 N. This indicated that the approximate maximum of 2000 le in this study covered the expected range of in vivo human second metatarsal loading. The maximum load also corresponded well to the peak strain of 1870 le measured on chicken tibiae during strenuous activity by Biewener (1993). Butterman et al. (1994) reported a 3% deviation in linearity between staple and surface measurements. In this study, a similar deviation was found for the 0.5 mm staple (4.2%), whereas all thicker staples proved more linear with deviations less than 1%. The ICC value for the 0.5 mm staple under compression demonstrated very poor reliability (0.37). The highest ICC value was calculated for the 1.0 mm staple (0.96 in tension). An overview of all validity and reliability calculations conducted in this study indicated the greatest potential for accurate determination of local bone deformation of the 1.0 mm staple. This study demonstrated that a strain gauge instrumented staple is valid for studying human metatarsal
Table 2 Linearity of strain measurements. Staple bridge size (mm)
Surface
Staple
Staple to surface
0.5 0.6 0.8 1.0
0.995$0.005 0.996$0.003 0.996$0.002 0.995$0.004
0.963$0.037 0.990$0.009 0.991$0.007 0.992$0.006
0.958$0.046 0.993$0.005 0.991$0.004 0.994$0.002
Total
0.995$0.004
0.984$0.023
0.984$0.028
Values show mean R$S.D. Columns 1 and 2 show R values for the surface and staple strain gauge recordings plotted against the input deforming force. The last column represents R values for the two strain gauge signals plotted against each other. All values were statistically signi"cant (p)0.001).
strain in vivo and that reducing the staple bridge dimensions to increase output may decrease measurement accuracy.
References Biewener, A.A., 1993. Safety factors in bone strength. Calci"ed Tissue International 53 (Suppl. 1), S68}S74. Burr, D.B., Milgrom, C., Fyhrie, D., Forwood, M., Nyska, M., Finestone, A., Hoshaw, S., Saiag, E., Simkin, A., 1996. In vivo measurement of human tibial strains during vigorous activity. Bone 18 (5), 405}410. Butterman, G.R., Janevic, J.T., Lewis, J.L., Lindquist, C.M., Wood, K.B., Schendel, M.J., 1994. Description and application of instrumented staples for measuring in vivo bone strain. Journal of Biomechanics 27, 1087}1094. Courtney, A.C., Davis, B.L., Manning, T., Kambic, H.E., 1997. E!ects of age, density, and geometry on the bending strength of human metatarsals. Foot and Ankle International 18 (4), 216}221. Ekenman, I., Halvorsen, K., Westblad, P., FellaK nder-Tsai, L., Rolf, C., 1998a. Local bone deformation at two predominant sites for stress fracture of the tibia * an in vivo study. Foot and Ankle International 19 (7), 479}484. Ekenman, I., Halvorsen, K., Westblad, P., FellaK nder-Tsai, L., Rolf, C., 1998b. The reliability and validity of an instrumented staple system for in vivo measurement of local bone deformation * an in vitro study. Scandinavian Journal of Medicine Science and Sports 8 (3), 172}176. Finestone, A., Shlamkovitch, N., Eldad, A., 1992. A prospective study on the e!ect of the appropriateness of foot}shoe "t and the training shoe type on the incidence of overuse injuries among infantry recruits. Military Medicine 157 (9), 489}490. Fyhrie, D.P., Milgrom, C., Hoshaw, S.J., Simkin, A., Dar, S., Drumb, D., Burr, D.B., 1998. E!ect of fatiguing exercise on longitudinal bone strain as related to stress fractures in humans. Annual Biomedical Engineering 26, 660}665. Gross, T.S., Bunch, R.P., 1989. A mechanical model of metatarsal stress fracture During distance running. American Journal of Sports Medicine 17 (5), 669}674. Lanyon, L.E., Hampson, W.G.J., Goodship, A.E., Shah, J.S., 1975. Bone deformation recorded in vivo from strain gauges attached to the human tibial shaft. Acta Orthopaedics Scandinavia 46, 256}268.
A. Arndt et al. / Journal of Biomechanics 32 (1999) 1359}1363 Lease, G.O'D., Evans, F.G., 1959. Strength of human metatarsal bones under repetitive loading. Journal of Applied Physiology 14, 49}51. Milgrom, C., Giladi, M., Stein, M., Kashtan, H., Marguiles, Y., Chisin, R., Steinberg, R., Ahronson, Z., 1985. Stress fractures in military recruits. A prospective study showing an unusually high incidence. Journal of Bone and Joint Surgery 67B (5), 732}735.
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Sharkey, N.A., Ferris, L., Smith, T.S., Matthews, D.K., 1995. Strain and loading of the second metatarsal during heel lift. Journal of Bone and Joint Surgery 77A (5), 1050}1057. Shrout, P.E., Fleiss, J.L., 1979. Intraclass correlations: uses in assessing rater reliability. Psychology Bulletin 86, 420}428. Stokes, I.A.F., Hutton, W.C., Stott, J.R.R., 1979. Forces acting on the metatarsals during normal walking. Journal of Anatomy 129 (3), 579}590.
Technical note
An in vitro comparison of bone deformation measured with surface and staple mounted strain gauges A. Arndt *, P. Westblad , I. Ekenman , K. Halvorsen, A. Lundberg Department of Orthopaedic Surgery, Huddinge University Hospital, Huddinge, Sweden The Systems and Control Group, Uppsala University, Uppsala, Sweden Accepted 14 June 1999
Abstract Chicken tibiae were chosen as a model for human second metatarsals. Local surface bone deformation in a 4-point bending con"guration was measured in vitro by both strain gauge instrumented staples and strain gauges bonded to the bone's cortical surface. A series of staple bridge dimensions (0.5, 0.6, 0.8 and 1.0 mm) was compared to test for staple in#uence on bone characteristics and greatest measurement validity and reliability. Thicker staple inhibition of bone deformation was the greatest but di!erences to thinner staples were not statistically signi"cant (p'0.05). All staples except 0.5 mm had maximum deviations from linearity less than 1%. The 1.0 mm staple had an R value of 0.992$0.006 plotted against the 4-point bending input force and 0.994$0.002 plotted against the surface strain gauge signal. The mean intraclass correlation coe$cients (ICC) calculated with four input forces (30, 60, 90 and 120 N) and for loading and unloading conditions for the 0.5, 0.6, 0.8 and 1.0 mm staples were 0.75, 0.83, 0.87 and 0.92, respectively. Finally, the di!erences in slope of the staple strain gauge signal plotted against surface strain gauge signal between input force loading and unloading conditions (0.32), and between input compression and tension conditions (0.79) was least for the 1.0 mm staple which also resulted in the lowest standard deviations. These results suggested the appropriateness of the 1.0 mm staple for in vivo application. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Strain gauge; Local bone deformation
1. Introduction Human second metatarsals are a common site for stress fractures in military recruits (Milgrom et al., 1985; Finestone et al., 1992). Local bone deformation is regarded as an indicator of stress fracture risk and this in vitro study presents the development of a methodology suitable for future in vivo application in ascertaining local bone deformation of human second metatarsals. There are disadvantages involved in the in vivo application of strain gauges directly onto bone surfaces. Direct adhesion is quite invasive as the periosteum must be removed and the bone prepared to obtain an optimal bonding surface. The insertion of instrumented staples involves less traumatic surgery and is thus more appro* Corresponding author. Tel.: #46-8-5858-7154; fax: #46-8-7114292. E-mail address: [email protected] (A. Arndt)
priate for human in vivo application. Strain on the human tibia has previously been measured in vivo with rosette strain gauges (Lanyon et al., 1975; Burr et al., 1996), transcutaneous extensometers (Fyhrie et al., 1998) and inserted staples (Ekenman et al., 1998a). No such investigation has, however, been performed on metatarsals or bones of corresponding size and previous values for human metatarsal loading have been provided by theoretical biomechanical models (Stokes et al., 1979; Gross and Bunch, 1989) or investigations of human cadaver specimens (Lease and Evans, 1959; Sharkey et al., 1995; Courtney et al., 1997). This study tested the viability of the staple technique (Ekenman et al., 1998b) when applied to bones representing the human second metatarsal. Chicken tibiae were chosen as a metatarsal model because of ethical di$culties in obtaining human bone specimens. The aim was to assess the in vitro validity and reliability of this methodology and to determine the interactive e!ects between staple and bone during induced bending deformation.
0021-9290/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 9 ) 0 0 1 2 9 - 3
1360
A. Arndt et al. / Journal of Biomechanics 32 (1999) 1359}1363
2. Methods After the removal of soft tissue the "bular aspects of the chicken tibiae were degreased (CSM-1A Degreaser, Measurements Group Inc. Raleigh, NC, USA), wetted (M-Prep Conditioner A, Measurements Group Inc.), abraded and neutralised (M-Prep Neutralizer 5A, Measurements Group Inc.). The bone surface was dried for 10 min at 503C and the surface preparation process subsequently repeated. Two strain gauges (Types EA06-031DE-350 and EA-06-031EC-350, Measurements Group Inc.) were mounted perpendicular to each other on the underneath bridge surface of a 16 mm;15 mm orthopaedic titanium staple (3M, St. Paul, MN, USA). The staple was inserted in pre-drilled holes over the midpoint of the "bular aspect of each bone. An insertion tool and staple guide provided a pretensile staple leg distension of 0.4 mm, as described by Ekenman et al. (1998b). Staples were inserted to a depth of 4 mm ensuring the legs passed completely through the cortex (thickness: 1.9$0.3 mm). A further strain gauge was bonded to the prepared surface with cyanoacrylate polymer (MBond 200, Measurements Group Inc.). This was located centrally underneath the staple with the strain gauge measurement axes aligned (Fig. 1). A series of staple dimensions (0.5, 0.6, 0.8 and 1.0 mm bridge thickness) was tested and two bones were instrumented with each staple size. The strain was measured uniaxially in the longitudinal direction of the bone. Force input was provided by depressing the upper segment of the four-point con"guration of a material testing machine (MTS, MN, USA, electronic component model 8500#, Instron, Canton, MA, USA) (Fig. 1). An input force of 160 N was chosen to sub-maximally load the bones. This corresponded to a maximum surface strain of approximately 2000 le. A pretension force of
10 N was applied followed by loading to 150 N at a rate of 30 N/s. Each loading trial was followed by a corresponding unloading trial to the pretension state. Two experimental con"gurations were designed, producing both tensile and compressive strain on the instrumented aspect of the bone. Strain gauge signals were ampli"ed (2120A, Measurements Group Inc., USA) and recorded with standard PC analog data collection software (Bioware, Kistler Inc., Switzerland). The synchronised input force of the material testing machine was also recorded. All data were sampled at 100 Hz. Each bone was loaded and unloaded twice under both tension and compression conditions providing a total of 64 trials. 2.1. Analysis Variations in surface deformation relative to input force, with staple thickness as independent variable, were regarded as an indication of staple in#uence on bone behaviour. The thinnest staple (0.5 mm bridge) was assumed to have the least in#uence and any statistically signi"cant di!erences (p)0.05) to this would be due to an unacceptable staple in#uence. The linearity of the staple strain gauge signal relative to both the surface deformation and input force was regarded as a descriptor of the validity of the staple methodology. The slope k of the linear regression (y"kx#b) was used to describe the relation between the surface and staple deformation. Intraclass correlation coe$cients (ICC [1,1]; Shrout and Fleiss, 1979) were calculated as primary indicators of measurement reliability. Input data for each ICC class was a 4;4 array of the recorded strain at 30, 60, 90 and 120 N input force for the two bones instrumented with each staple thickness and loading and unloading conditions for that staple. Tension and compression conditions were separated. 3. Results 3.1. Staple inyuence on bone deformation
Fig. 1. The four-point bending experimental setup; tension. Approximately actual size. Tensile force was developed on the upper aspect of the bone by depressing the upper segment of the material loading machine. The distance between the contact points of the upper segment was 41 mm and between those of the lower; 18 and 80 mm in tension and compression, respectively.
Under the assumption that the input force was linear, k for surface deformation vs. input force was determined to assess the e!ect of di!erent staples (independent variable) on surface deformation (dependent) (Fig. 2A). A one-way analysis of variance (ANOVA) showed no statistical signi"cance (p'0.05) between the di!erences. Fig. 2B illustrates the decrease in k for all conditions combined from thinner to thicker staples (range: 16.48$1.15}8.96$0.63). 3.2. Staple reliability The ICC was the primary indication of staple reliability (Table 1).
A. Arndt et al. / Journal of Biomechanics 32 (1999) 1359}1363
1361
Fig. 2. (A) Staple in#uence on surface deformation; k value (input force plotted against strain recorded by surface strain gauge): tld: tension/load, tuld: tension/unload, cld: compression/load, culd: compression/unload. (B) Mean k (staple strain gauge plotted against surface strain gauge signals) for di!erent staple dimensions. Signi"cant di!erences (p)0.05) were seen between k(0.5 mm) and all other staples, and k(0.6 mm) to k(1.0 mm). (C) Mean k (staple against surface) comparison between tension and compression. Actual di!erences for 0.5, 0.6, 0.8 and 1.0 mm staples, respectively, were: 0.59, 1.20, 1.46 and 0.79. (D) Mean k (staple against surface) comparison between loading and unloading. Actual di!erences: 0.72, 1.41, 0.52 and 0.32.
Table 1 Intraclass correlation coe$cient (ICC). Staple bridge size (mm)
Compression/surface
Compression/staple
Tension/surface
Tension/staple
Mean
0.5 0.6 0.8 1.0
0.97 0.78 0.86 0.89
0.37 0.93 0.89 0.85
0.85 0.69 0.90 0.98
0.81 0.91 0.82 0.96
0.75 0.83 0.87 0.92
From left to right: surface strain measured during the compression condition, staple strain during compression, surface strain during tension and staple strain during tension.
A further indicator of staple reliability was the similarity of staple output relative to the surface deformation under di!erent conditions (i.e., tension/compression and load/unload, Fig. 2C and D). The most similar response for tension and compression of the 1.0 mm staple in-
dicated the greatest robustness to variations in bone loading. Loss of hysteresis energy was indicated by variations in k dependent upon loading and unloading of the bone. This loss successively decreased with thicker staples and was also least for the 1.0 mm staple.
1362
A. Arndt et al. / Journal of Biomechanics 32 (1999) 1359}1363
3.3. Staple validity Thicker staples demonstrated greater linearity relative to both input force and surface deformation (Table 2). Furthermore, the standard deviations were less for thicker staples indicating more consistent measuring performance. The response of the 1.0 mm staple varied by an average of 0.6% compared to the measured surface deformation whereas the 0.5 mm staple di!ered by 4.2%.
4. Discussion Di!erent staple dimensions were compared for two reasons: (a) It was feasible that the stress}strain behavior and therefore, the elastic modulus of the bone would be in#uenced by the inserted staple and that this in#uence would be greater for sti!er staples. (b) Although strain has been successfully measured with 1.0 mm staple bridges on human tibiae (Ekenman et al., 1998a), it was uncertain whether such thick staples would be sensitive to local deformation in bones of comparatively small proportions. The results showed no signi"cant di!erence in the in#uence of di!erent staple dimensions on the bone bending behaviour and similar strain ranges for the 1.0 mm staple as reported by Ekenman et al. (1998a). In model calculations Gross and Bunch (1989) predicted human second metatarsal strain of 6662 le during running with a corresponding bending moment of 7.71 N m. These values were considerably higher than those recorded in the present study (input bending moments of 1.84 and 3.12 N m in tensile and compressive conditions, respectively). Sharkey et al., (1995) measured in vitro the bone surface strains up to approximately 1000 le with an induced external ground reaction force of 750 N. This indicated that the approximate maximum of 2000 le in this study covered the expected range of in vivo human second metatarsal loading. The maximum load also corresponded well to the peak strain of 1870 le measured on chicken tibiae during strenuous activity by Biewener (1993). Butterman et al. (1994) reported a 3% deviation in linearity between staple and surface measurements. In this study, a similar deviation was found for the 0.5 mm staple (4.2%), whereas all thicker staples proved more linear with deviations less than 1%. The ICC value for the 0.5 mm staple under compression demonstrated very poor reliability (0.37). The highest ICC value was calculated for the 1.0 mm staple (0.96 in tension). An overview of all validity and reliability calculations conducted in this study indicated the greatest potential for accurate determination of local bone deformation of the 1.0 mm staple. This study demonstrated that a strain gauge instrumented staple is valid for studying human metatarsal
Table 2 Linearity of strain measurements. Staple bridge size (mm)
Surface
Staple
Staple to surface
0.5 0.6 0.8 1.0
0.995$0.005 0.996$0.003 0.996$0.002 0.995$0.004
0.963$0.037 0.990$0.009 0.991$0.007 0.992$0.006
0.958$0.046 0.993$0.005 0.991$0.004 0.994$0.002
Total
0.995$0.004
0.984$0.023
0.984$0.028
Values show mean R$S.D. Columns 1 and 2 show R values for the surface and staple strain gauge recordings plotted against the input deforming force. The last column represents R values for the two strain gauge signals plotted against each other. All values were statistically signi"cant (p)0.001).
strain in vivo and that reducing the staple bridge dimensions to increase output may decrease measurement accuracy.
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