TENSILE AND COMPRESSIVE PROPERTIES CANCELLOUS BONE
OF
L~SBETH ROHL, EJNAR LARSEN, FRANK LINDE, ANDERS ODGAARD and JDRGEN JORGENSEN*
Biomechanics Laboratory, The Orthopaedic Hospital. University of Aarhus, Aarhus, Denmark and *Department of Diagnostic Radiology, Aarhus Kommunehospital. Aarhus, Denmark Abstract-The
relationship between the mechanical properties of trabecular bone in tension and compression was investigated by non-destructive testing of the same specimens in tension and compression, followed by random allocation to a destructive test in either tension or compression. There was no difference between Young’s modulus in tensionand compression, and therewasa strongpositivecorrelationbetween the values(R =0.97). Strength.ultimate strainand work to failure was significantly higher in tensile testing than in compressive testing.
INTRODUCllON
Previous studies addressing the relationship between mechanical properties of cancellous bone in tension and compression have reached ditTerent conclusions. Sonoda (1962). Stone et al. (1983) and Kaplan et 01. (1985) all found that strength was significantly higher in compression than tension. Others found no significant difference in values of strength (Carter et al.. 1980; Hcnsusan et ul.. 1983; Neil et uf., 1983). and this view has been supported by Rice et 01. (1988) in a review article ba.scdon previous experiments. Neither Carter or (11.(1980). Bensusan et (11.(1983) or Ashman et ul. (19119)found dilferences in the elastic modulus detcrmined in compression and tension. whereas the results of Neil et (11.(1983) were inconclusive in this regard. Ashman et 01. (1989) performed a non-destructive study of the same IO specimens in tension and compression, and Neil made a test on paired symmetrically taken specimens from the same vertebral body. The other investigators performed their studies in non-paired designs. This means that the tests are very sensitive to the large regional variations in strength and modulus of elasticity, and the number of specimens must thus be high to discover any ditTerences. The purpose ofthe present study was to investigate tensile and compressive Young’s modulus of trabecular bone by testing the same specimens non-destructively in compression and tension. Ultimate properties were determined after random allocation to a destructive test in either tension or compression.
ining. The donors had been normally mobile until 2 weeks before death, and there was no history of musculoskeletal disorders. Four donors were males and three were females. The age range was 42-76 yr. From each proximal tibia a 20 mm thick bone slice, parallel to the subchondral bone plate. was cut using an EXAKT cutting-grinding machine (EXAKT Cutting-Grinding System, EXAKT Apparaterbau, Norderstedt. Germany). The tibiae were fixed to a carriage equipped with parallel control to provide parallel cuts. The first cut was made 2 mm below the subchondral bone plate and parallel to this. The second cut was made 20 mm distal to the first, providing a 20 mm thick bone slice. This bone slice was blown Treeof marrow in about 2 mm depth with an air jet, and embedded between two 2 cm thick layers of epoxy-resin, penetrating about 2 mm into the bone. The resin was fast hardening, and to avoid air bubbles we let it harden at -20°C. which delayed the hardening process. From the composed trilayer block square columns were cut, with transverse dimensions 9 x 9 mm (Fig I). The precise dimensions of each specimen were measured using a caliper. Density
measurements
The density of the specimens was quantified by CTscanning prior to mechanical testing. The relationship between apparent density and CT-values is linear (v(g/ccm) = 0.00130 x CT-value + 0.103 (R =0.935), Hvid et al., 1989). The specimens were kept in an airtight plastic container with physiologic saline. Specimens and container were vacuumed and then scanned. The specimen axis was held orthogonal to and in MATERIALS AND METHODS the centre of the gantry. Using an EMI 7070 scanner, Mareriuls the scan parameters were 140 kV. 40 mA, 3 s scan time Eleven proximal tibiae were taken from seven and a smooth reconstruction filter was used. Succeshuman cadavers and stored at -20°C until mach- sive 2 mm scans were recorded from the top to the bottom of the specimen. From the slices recorded, we determined the two epoxy ends characterized by high Received injnalfirm 19 March 1991. density. In the mid-trabecular bone slice, mean CTAddress for correspondence: LisbethRehl. Biomechanics values were calculated within a circular region of Laboratory, Orthopaedic Hospital, Randersvej 1. DK-g2OO interest. Since negative CT-values were obtained in Aarhus N. BM
24:12-E
1143
114-t
L.
ROHL et ul.
structural end-phenomenon (Linde and Hvid, 1989; Odgaard and Linde. 1991). it is expected that a much smaller specimen strain should be used in embedded specimens in order to obtain a similar bone strain centrally in the specimen as in embedded specimens. During a pilot study several specimens failed before 0.6% strain. A 0.2% upper strain limit was experi20 mentally found to be more appropriate. Between each of the four sequences in the nonband .destructive test procedure the machine was set for compressive or tensile testing by moving two lever arms. By this manoeuvre the crosshead moved a little. Care was taken to avoid increase in load above the load obtained during testing by simultaneously moving the crosshead in the opposite direction. Specimens, in which load during the adjustment exceeded the I r/( values of the prior sequence,were excluded. Of the 102 9 mm specimens tested non-destructively 42 were rejected Fig. I. The extensometerfixedby two rubberbandsdirectly either because of excessiveloading during adjustment, on the trabecularbonewhichisembeddedin an epoxy-resin. or because the specimens failed during testing. The latter occurred mainly in tensile testing. very porous specimens (density of fat is less than the density of water). these were converted to a relative linear attenuation coefficient r0 (rO= I +O.OOl X CTvalue) to obtain only positive values, as described by Bcntzcn rr cl/. (1987). This mndc it possible to make a power fit analysis between density and mechanical propcrtics. Mrchunicul
WI up
The specimen were kept frozen at -20°C until testing, and during testing they were kept moist with saline at room temperature. Mechanical testing was performed in an INSTRON universal screw-driven machine, using a IO kN load cell and a dynamic strain gauge cxtensometer. The specimens were fixed between two wedge grips. The extensometer was fixed by two rubber bands directly on the trabecular bone with a distance of approximately 9 mm between the extensometer pins (Fig. I). The precise distance was measured from a reference length of the extensometer. Non-&srrucdor testing The non-destructive mechanical test procedure was composed of four successive sequences: one compressive, one tensile, one compressive and one tensile sequence. Each sequence was composed of a number of conditioning cycles between zero deformation detined at preload 2 N and a 0.2% strain limit, until zero deformation was reproduced within +2 pm in three consecutive cycles.The number of conditioning cycles necessaryfor reaching a steady state was usually < 5. Strain rate was O.OOSs-t. After conditioning, a single non-destructive test was made between the same limits. An upper strain limit -0.6% strain has been suggested for non-destructive uniaxial compression testing (Linde er al., 1988. 1989). This figure was based on testing of specimens with uncmbedded ends. Due to
Testing
to failure
The remaining 60 specimens were allocated randomly to either a dcstructivc tensile test or a dcstructive compressive test. and of thcsc the testing of I5 specimens in each group succccdcd.The remaining 30 specimens had been rejected, cithcr because of hilurc during the test procedure, or because they broke outside the extcnsometcr attachment. This occurred mainly in destructive tensile testing. and it was the impression that it happened most often for highdensity specimens. To reduce the effect of a possible selection of low-density specimens,strength and work to failure were adjusted to a mean r0 = 1.03. based on a power law relationship between r,, and the pooled data of the 30 specimens tested to failure. As ultimate strain did not show any significant correlation to re, these data were not adjusted.
Duta sampling
All deformation/load data were sampled by a PC with a sampling frequency of 48 Hz. A non-destructive cycle consisted of * 100-200 recordings. Deformation data were converted to strain data using the distance between the extensometer pins; and the load data to stress data based on the cross-sectional area of the specimens. A tifth-degree polynomial was fitted to the. stress-strain data, as this polynomial made a good fit of both destructive and non-destructive curves. Young’s moduli in tension (Et) and compression (EC) were determined from the slope of the fitted loading curve at 0.18% strain [Fig. 2 (a, b)]. Strength u, and ultimate strain E, were detined by the first load peak of the destructive test-curve [Fig. 3(a. b)]. Work to failure EA, was determined as the integral of the load-compression curve, stopping at the first load peak.
Properties
of canallous
bone
r
2.0 ,
0.00
0.03
0.10
Strain
(a)
0.15
0.20
(X)
(b)
Strain
(%)
Fig. 2. Stress-strain curve from a non-destructive test of the same specimen in compression (a) and tension (b). Closed circles represent loading and open circles unloading. The solid line is a fifth-grade polynomial fitted to the data in loading. Young’s modulus is found as the slope of this curve in 0.18% strain.
.. *-. *.
.
(a)
t
2
Strain Fig. 3. Stress-strain
J
4
(b)
5
(%)
1
2 Strain
3
.. *.
4
5
(X)
curve from a destructive testing in compression (a) and in tension (b). One out of every IO samplings is seen on the curves.
RFSULTS
Shupe oJ the testbly
curur
The stress-strain curves obtained in non-destructive tensile and compressive testing showed no difference, and were almost linear without a non-linear foot part. There was only a small hysteresis, indicating a small energy loss [Fig. 2(a. b)]. The stress-strain curves obtained in destructive compression and tension consisted both ol an initial linear region followed by a non-linear region until maximal stress was achieved [Fig. 3(a. b)]. After this the curve declined gradually, but sometimes more abrupt in tensile testing when the cancellous bone was divided physically.
The mean values of Young’s modulus in compression were 485 M Pa. and in tension 483 MPa (S.E.D. = 1I MPa). There was no significant difference between these values. There was a strong linear correlation between Young’s modulus in compression and tension (Fig. 4): Et = 27.4 Mpa+0.94Ec, R 10.97, p
OF
L~SBETH ROHL, EJNAR LARSEN, FRANK LINDE, ANDERS ODGAARD and JDRGEN JORGENSEN*
Biomechanics Laboratory, The Orthopaedic Hospital. University of Aarhus, Aarhus, Denmark and *Department of Diagnostic Radiology, Aarhus Kommunehospital. Aarhus, Denmark Abstract-The
relationship between the mechanical properties of trabecular bone in tension and compression was investigated by non-destructive testing of the same specimens in tension and compression, followed by random allocation to a destructive test in either tension or compression. There was no difference between Young’s modulus in tensionand compression, and therewasa strongpositivecorrelationbetween the values(R =0.97). Strength.ultimate strainand work to failure was significantly higher in tensile testing than in compressive testing.
INTRODUCllON
Previous studies addressing the relationship between mechanical properties of cancellous bone in tension and compression have reached ditTerent conclusions. Sonoda (1962). Stone et al. (1983) and Kaplan et 01. (1985) all found that strength was significantly higher in compression than tension. Others found no significant difference in values of strength (Carter et al.. 1980; Hcnsusan et ul.. 1983; Neil et uf., 1983). and this view has been supported by Rice et 01. (1988) in a review article ba.scdon previous experiments. Neither Carter or (11.(1980). Bensusan et (11.(1983) or Ashman et ul. (19119)found dilferences in the elastic modulus detcrmined in compression and tension. whereas the results of Neil et (11.(1983) were inconclusive in this regard. Ashman et 01. (1989) performed a non-destructive study of the same IO specimens in tension and compression, and Neil made a test on paired symmetrically taken specimens from the same vertebral body. The other investigators performed their studies in non-paired designs. This means that the tests are very sensitive to the large regional variations in strength and modulus of elasticity, and the number of specimens must thus be high to discover any ditTerences. The purpose ofthe present study was to investigate tensile and compressive Young’s modulus of trabecular bone by testing the same specimens non-destructively in compression and tension. Ultimate properties were determined after random allocation to a destructive test in either tension or compression.
ining. The donors had been normally mobile until 2 weeks before death, and there was no history of musculoskeletal disorders. Four donors were males and three were females. The age range was 42-76 yr. From each proximal tibia a 20 mm thick bone slice, parallel to the subchondral bone plate. was cut using an EXAKT cutting-grinding machine (EXAKT Cutting-Grinding System, EXAKT Apparaterbau, Norderstedt. Germany). The tibiae were fixed to a carriage equipped with parallel control to provide parallel cuts. The first cut was made 2 mm below the subchondral bone plate and parallel to this. The second cut was made 20 mm distal to the first, providing a 20 mm thick bone slice. This bone slice was blown Treeof marrow in about 2 mm depth with an air jet, and embedded between two 2 cm thick layers of epoxy-resin, penetrating about 2 mm into the bone. The resin was fast hardening, and to avoid air bubbles we let it harden at -20°C. which delayed the hardening process. From the composed trilayer block square columns were cut, with transverse dimensions 9 x 9 mm (Fig I). The precise dimensions of each specimen were measured using a caliper. Density
measurements
The density of the specimens was quantified by CTscanning prior to mechanical testing. The relationship between apparent density and CT-values is linear (v(g/ccm) = 0.00130 x CT-value + 0.103 (R =0.935), Hvid et al., 1989). The specimens were kept in an airtight plastic container with physiologic saline. Specimens and container were vacuumed and then scanned. The specimen axis was held orthogonal to and in MATERIALS AND METHODS the centre of the gantry. Using an EMI 7070 scanner, Mareriuls the scan parameters were 140 kV. 40 mA, 3 s scan time Eleven proximal tibiae were taken from seven and a smooth reconstruction filter was used. Succeshuman cadavers and stored at -20°C until mach- sive 2 mm scans were recorded from the top to the bottom of the specimen. From the slices recorded, we determined the two epoxy ends characterized by high Received injnalfirm 19 March 1991. density. In the mid-trabecular bone slice, mean CTAddress for correspondence: LisbethRehl. Biomechanics values were calculated within a circular region of Laboratory, Orthopaedic Hospital, Randersvej 1. DK-g2OO interest. Since negative CT-values were obtained in Aarhus N. BM
24:12-E
1143
114-t
L.
ROHL et ul.
structural end-phenomenon (Linde and Hvid, 1989; Odgaard and Linde. 1991). it is expected that a much smaller specimen strain should be used in embedded specimens in order to obtain a similar bone strain centrally in the specimen as in embedded specimens. During a pilot study several specimens failed before 0.6% strain. A 0.2% upper strain limit was experi20 mentally found to be more appropriate. Between each of the four sequences in the nonband .destructive test procedure the machine was set for compressive or tensile testing by moving two lever arms. By this manoeuvre the crosshead moved a little. Care was taken to avoid increase in load above the load obtained during testing by simultaneously moving the crosshead in the opposite direction. Specimens, in which load during the adjustment exceeded the I r/( values of the prior sequence,were excluded. Of the 102 9 mm specimens tested non-destructively 42 were rejected Fig. I. The extensometerfixedby two rubberbandsdirectly either because of excessiveloading during adjustment, on the trabecularbonewhichisembeddedin an epoxy-resin. or because the specimens failed during testing. The latter occurred mainly in tensile testing. very porous specimens (density of fat is less than the density of water). these were converted to a relative linear attenuation coefficient r0 (rO= I +O.OOl X CTvalue) to obtain only positive values, as described by Bcntzcn rr cl/. (1987). This mndc it possible to make a power fit analysis between density and mechanical propcrtics. Mrchunicul
WI up
The specimen were kept frozen at -20°C until testing, and during testing they were kept moist with saline at room temperature. Mechanical testing was performed in an INSTRON universal screw-driven machine, using a IO kN load cell and a dynamic strain gauge cxtensometer. The specimens were fixed between two wedge grips. The extensometer was fixed by two rubber bands directly on the trabecular bone with a distance of approximately 9 mm between the extensometer pins (Fig. I). The precise distance was measured from a reference length of the extensometer. Non-&srrucdor testing The non-destructive mechanical test procedure was composed of four successive sequences: one compressive, one tensile, one compressive and one tensile sequence. Each sequence was composed of a number of conditioning cycles between zero deformation detined at preload 2 N and a 0.2% strain limit, until zero deformation was reproduced within +2 pm in three consecutive cycles.The number of conditioning cycles necessaryfor reaching a steady state was usually < 5. Strain rate was O.OOSs-t. After conditioning, a single non-destructive test was made between the same limits. An upper strain limit -0.6% strain has been suggested for non-destructive uniaxial compression testing (Linde er al., 1988. 1989). This figure was based on testing of specimens with uncmbedded ends. Due to
Testing
to failure
The remaining 60 specimens were allocated randomly to either a dcstructivc tensile test or a dcstructive compressive test. and of thcsc the testing of I5 specimens in each group succccdcd.The remaining 30 specimens had been rejected, cithcr because of hilurc during the test procedure, or because they broke outside the extcnsometcr attachment. This occurred mainly in destructive tensile testing. and it was the impression that it happened most often for highdensity specimens. To reduce the effect of a possible selection of low-density specimens,strength and work to failure were adjusted to a mean r0 = 1.03. based on a power law relationship between r,, and the pooled data of the 30 specimens tested to failure. As ultimate strain did not show any significant correlation to re, these data were not adjusted.
Duta sampling
All deformation/load data were sampled by a PC with a sampling frequency of 48 Hz. A non-destructive cycle consisted of * 100-200 recordings. Deformation data were converted to strain data using the distance between the extensometer pins; and the load data to stress data based on the cross-sectional area of the specimens. A tifth-degree polynomial was fitted to the. stress-strain data, as this polynomial made a good fit of both destructive and non-destructive curves. Young’s moduli in tension (Et) and compression (EC) were determined from the slope of the fitted loading curve at 0.18% strain [Fig. 2 (a, b)]. Strength u, and ultimate strain E, were detined by the first load peak of the destructive test-curve [Fig. 3(a. b)]. Work to failure EA, was determined as the integral of the load-compression curve, stopping at the first load peak.
Properties
of canallous
bone
r
2.0 ,
0.00
0.03
0.10
Strain
(a)
0.15
0.20
(X)
(b)
Strain
(%)
Fig. 2. Stress-strain curve from a non-destructive test of the same specimen in compression (a) and tension (b). Closed circles represent loading and open circles unloading. The solid line is a fifth-grade polynomial fitted to the data in loading. Young’s modulus is found as the slope of this curve in 0.18% strain.
.. *-. *.
.
(a)
t
2
Strain Fig. 3. Stress-strain
J
4
(b)
5
(%)
1
2 Strain
3
.. *.
4
5
(X)
curve from a destructive testing in compression (a) and in tension (b). One out of every IO samplings is seen on the curves.
RFSULTS
Shupe oJ the testbly
curur
The stress-strain curves obtained in non-destructive tensile and compressive testing showed no difference, and were almost linear without a non-linear foot part. There was only a small hysteresis, indicating a small energy loss [Fig. 2(a. b)]. The stress-strain curves obtained in destructive compression and tension consisted both ol an initial linear region followed by a non-linear region until maximal stress was achieved [Fig. 3(a. b)]. After this the curve declined gradually, but sometimes more abrupt in tensile testing when the cancellous bone was divided physically.
The mean values of Young’s modulus in compression were 485 M Pa. and in tension 483 MPa (S.E.D. = 1I MPa). There was no significant difference between these values. There was a strong linear correlation between Young’s modulus in compression and tension (Fig. 4): Et = 27.4 Mpa+0.94Ec, R 10.97, p
