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SPINAL LEVEL EFFECTS ON VISCOELASTIC PROPERTIES OF LIGAMENTS UNDER FAST STRAIN RATE DEFORMATIONS
Injury 4 – Bone and Ligament Injury. 16:45, Room 102,
Presentation SI03
S173
SPINAL LEVEL EFFECTS ON VISCOELASTIC PROPERTIES OF LIGAMENTS UNDER FAST STRAIN RATE DEFORMATIONS S.R. Lucas1, C.R. Bass1, R.S. Salzar1, B.S. Shender2, and G. Paskoff2 University of Virginia – Center for Applied Biomechanics, Charlottesville, VA, USA 2 NAVAIR, Patuxent River, MD, USA; email: [email protected], web: www.centerforappliedbiomechanics.org 1
METHODS The thoracic and lumbar spines were excised from four male and four female human cadavers. From each spine, the T6T7, T10-T11, T12-L1, L2-L3, and L4-L5 functional spinal units were isolated and further segmented into anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), and ligamentum flavum (LF) bone-ligament-bone complexes. The potted bone-ligament-bone complexes were mounted in a universal test machine (Instron, Inc. # 8874 Canton, MA) for uniaxial tensile tests. The fixture was enclosed in an environmental chamber to maintain physiological temperature (37.2 ± 0.6 ˚C) and hydration (relative humidity >90%) [1-3]. Each ligament was preconditioned with a 10% engineering strain (HE) sinusoidal input at 2 Hz for 120 cycles (P10). Then, each ligament was subjected to tensile ramp-hold inputs to 25% HE (R25) and 50% HE (R50), an oscillatory sinusoid input to 50% engineering strain (V50). The V50 test was conducted at 20 Hz for 20 cycles immediately followed by a sinusoid at 2 Hz for 20 cycles. The ramp onset was approximately 10 ms for each relaxation test and each ramp was held for one minute with 10 minutes of recovery between each test. The uniaxial force, displacement, and acceleration were recorded for each test. Force and displacement were then converted to true stress and true strain. From the R50 tests, the true stress response was characterized using Boltzmann superposition: t dV e dH (1) V (H , t ) ³ Gred (t t c) dt c . dH d t c 0 Gred is the reduced relaxation function and a series of summed exponentials: t t Gred (t ) G1e 100 ms G2 e 1s Gf ; G1 G2 Gf 1. (2)
V
e
is the instantaneous elastic stress and is linearly approximated as: (3) V e (H ) DH where D is the instantaneous elastic parameter. The viscoelastic parameters from the existing cervical model [1] and the new thoracic and lumbar models were combined in a statistical analysis to quantify any spinal level effects. A general linear model (ANOVA) was used and subsequent multiple comparisons were performed using Tukey tests.
XXI ISB Congress, Podium Sessions, Monday 2 July 2007
RESULTS AND DISCUSSION For the cervical, thoracic and lumbar regions combined, the average (one stdev) of G1, G2, G, and D are shown in Table 1. There is a large standard deviation in the parameters, which may be attributed to spinal level effects. For the ALL, the reduced relaxation functions separated by spinal region are shown in Figure 1. The thoracic and lumbar regions exhibit similar relaxation behavior; however, relative to the thoracic and lumbar regions, the cervical region exhibits more relaxation. The PLL and LF also show these trends. Table 1: Viscoelastic model parameters: avg (one stdev) G1 G2 G D 0.185 (0.178) 0.155 (0.166) 0.241 (0.172)
ALL PLL LF Reduced Relaxation Function, G(t)
INTRODUCTION Spinal ligaments are important for stabilization and motion during normal spine function. Because of the morbidity associated with spine ligament injury, it is important to ascertain the material properties of spinal ligaments. The Center for Applied Biomechanics has performed extensive mechanical testing on spinal soft tissues [1-3]. The objective of this study is to investigate spinal leveldependency on spine ligament viscoelasticity.
0.422 (0.233) 0.425 (0.330) 0.432 (0.331)
0.393 (0.201) 0.419 (0.241) 0.327 (0.276)
1
46.8 (28.4) 259 (177) 7.09 (10.7)
Cervical Thoracic Lumbar
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.0001
0.001
0.01 Time, sec
0.1
1
Figure 1: Comparison of reduced relaxation function by spinal region for the ALL. From the general linear model based on spinal level, there is a significant difference in G1, G2, G, and D (p < 0.05). Apparent from the Tukey tests, the cervical spinal region exhibits significantly different relaxation and instantaneous elastic behavior than the thoracic and lumbar spinal regions. CONCLUSIONS This study reported a significant difference in cervical relaxation and instantaneous elastic parameters, relative to thoracic and lumbar parameters. This implies that the relaxation function and instantaneous elastic function may not be averaged over the spinal regions. REFERENCES 1. Lucas SR, et al. Submitted for publication (Acta Biomaterialia), 2007. 2. Lucas SR, et al. Proc. from ASB meeting, Blacksburg, VA, 2006. 3. Bass CR, et al. Spine 32 (1), E7-E13, 2007. ACKNOWLEDGEMENTS This study was supported by the Naval Air Systems Command, Patuxent River, MD, USA and the University of Virginia School of Engineering and Applied Science. Journal of Biomechanics 40(S2)
Presentation SI03
S173
SPINAL LEVEL EFFECTS ON VISCOELASTIC PROPERTIES OF LIGAMENTS UNDER FAST STRAIN RATE DEFORMATIONS S.R. Lucas1, C.R. Bass1, R.S. Salzar1, B.S. Shender2, and G. Paskoff2 University of Virginia – Center for Applied Biomechanics, Charlottesville, VA, USA 2 NAVAIR, Patuxent River, MD, USA; email: [email protected], web: www.centerforappliedbiomechanics.org 1
METHODS The thoracic and lumbar spines were excised from four male and four female human cadavers. From each spine, the T6T7, T10-T11, T12-L1, L2-L3, and L4-L5 functional spinal units were isolated and further segmented into anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), and ligamentum flavum (LF) bone-ligament-bone complexes. The potted bone-ligament-bone complexes were mounted in a universal test machine (Instron, Inc. # 8874 Canton, MA) for uniaxial tensile tests. The fixture was enclosed in an environmental chamber to maintain physiological temperature (37.2 ± 0.6 ˚C) and hydration (relative humidity >90%) [1-3]. Each ligament was preconditioned with a 10% engineering strain (HE) sinusoidal input at 2 Hz for 120 cycles (P10). Then, each ligament was subjected to tensile ramp-hold inputs to 25% HE (R25) and 50% HE (R50), an oscillatory sinusoid input to 50% engineering strain (V50). The V50 test was conducted at 20 Hz for 20 cycles immediately followed by a sinusoid at 2 Hz for 20 cycles. The ramp onset was approximately 10 ms for each relaxation test and each ramp was held for one minute with 10 minutes of recovery between each test. The uniaxial force, displacement, and acceleration were recorded for each test. Force and displacement were then converted to true stress and true strain. From the R50 tests, the true stress response was characterized using Boltzmann superposition: t dV e dH (1) V (H , t ) ³ Gred (t t c) dt c . dH d t c 0 Gred is the reduced relaxation function and a series of summed exponentials: t t Gred (t ) G1e 100 ms G2 e 1s Gf ; G1 G2 Gf 1. (2)
V
e
is the instantaneous elastic stress and is linearly approximated as: (3) V e (H ) DH where D is the instantaneous elastic parameter. The viscoelastic parameters from the existing cervical model [1] and the new thoracic and lumbar models were combined in a statistical analysis to quantify any spinal level effects. A general linear model (ANOVA) was used and subsequent multiple comparisons were performed using Tukey tests.
XXI ISB Congress, Podium Sessions, Monday 2 July 2007
RESULTS AND DISCUSSION For the cervical, thoracic and lumbar regions combined, the average (one stdev) of G1, G2, G, and D are shown in Table 1. There is a large standard deviation in the parameters, which may be attributed to spinal level effects. For the ALL, the reduced relaxation functions separated by spinal region are shown in Figure 1. The thoracic and lumbar regions exhibit similar relaxation behavior; however, relative to the thoracic and lumbar regions, the cervical region exhibits more relaxation. The PLL and LF also show these trends. Table 1: Viscoelastic model parameters: avg (one stdev) G1 G2 G D 0.185 (0.178) 0.155 (0.166) 0.241 (0.172)
ALL PLL LF Reduced Relaxation Function, G(t)
INTRODUCTION Spinal ligaments are important for stabilization and motion during normal spine function. Because of the morbidity associated with spine ligament injury, it is important to ascertain the material properties of spinal ligaments. The Center for Applied Biomechanics has performed extensive mechanical testing on spinal soft tissues [1-3]. The objective of this study is to investigate spinal leveldependency on spine ligament viscoelasticity.
0.422 (0.233) 0.425 (0.330) 0.432 (0.331)
0.393 (0.201) 0.419 (0.241) 0.327 (0.276)
1
46.8 (28.4) 259 (177) 7.09 (10.7)
Cervical Thoracic Lumbar
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.0001
0.001
0.01 Time, sec
0.1
1
Figure 1: Comparison of reduced relaxation function by spinal region for the ALL. From the general linear model based on spinal level, there is a significant difference in G1, G2, G, and D (p < 0.05). Apparent from the Tukey tests, the cervical spinal region exhibits significantly different relaxation and instantaneous elastic behavior than the thoracic and lumbar spinal regions. CONCLUSIONS This study reported a significant difference in cervical relaxation and instantaneous elastic parameters, relative to thoracic and lumbar parameters. This implies that the relaxation function and instantaneous elastic function may not be averaged over the spinal regions. REFERENCES 1. Lucas SR, et al. Submitted for publication (Acta Biomaterialia), 2007. 2. Lucas SR, et al. Proc. from ASB meeting, Blacksburg, VA, 2006. 3. Bass CR, et al. Spine 32 (1), E7-E13, 2007. ACKNOWLEDGEMENTS This study was supported by the Naval Air Systems Command, Patuxent River, MD, USA and the University of Virginia School of Engineering and Applied Science. Journal of Biomechanics 40(S2)