Background
Methodology
Mechanical properties of vertebrae
Modulus of elasticity (MPa.) | Poisson’s ratio | |
---|---|---|
Cortical bone | Exx = 11,300 | vxy = 0.484 |
Eyy = 11,300 | ||
Ezz = 22,000 | vyz = 0.203 | |
Gxy = 3800 | ||
Gyz = 5400 | vxz = 0.203 | |
Gxz = 5400 | ||
Cancellous bone | Exx = 140 | vxy = 0.450 |
Eyy = 140 | ||
Ezz = 200 | vyz = 0.315 | |
Gxy = 48.3 | ||
Gyz = 48.3 | vxz = 0.250 | |
Gxz = 48.3 |
Tension | Compression | ||
---|---|---|---|
Mean (MPa.) | STD | Mean (MPa.) | STD |
Yield Stress – Cortical | |||
75 | 13.98 | 176 | 28.4 |
Yield Stress - Cancellous | |||
1.9 | 0.86 | 1.78 | 0.58 |
Mechanical properties of intervertebral discs
The Material Constants of Annulus Matrix and Nucleus Pulposus Using the Prony Series | |||
---|---|---|---|
Relaxation of | Shear Relaxation Modulus (MPa.) | Bulk Relaxation Modulus (MPa.) | Relaxation Time Constant (second) |
Annulus matrix, E = 8.0 (MPa.), ν = 0.45 | g1 = 0.399 | k1 = 0.399 | τ1 = 3.45 |
g2 = 0.000 | k2 = 0.300 | τ2 = 100 | |
g3 = 0.361 | k3 = 0.149 | τ3 = 1000 | |
g4 = 0.108 | k4 = 0.150 | τ4 = 5000 | |
Nucleus pulposus, E = 2.0 (MPa.), ν = 0.49 | g1 = 0.638 | k1 = 0.0 | τ1 = 0.141 |
g2 = 0.156 | k2 = 0.0 | τ2 = 2.21 | |
g3 = 0.120 | k3 = 0. 0 | τ3 = 39.9 | |
g4 = 0.0383 | k4 = 0.0 | τ4 = 266 | |
g5 = 0 | k4 = 0.0 | τ4 = 500 |
Tension | Compression | ||
Mean (MPa.) | STD | Mean (MPa.) | STD |
7.30 | 2.30 | 3.65 | 1.15 |
Yield Stress - Nucleus | |||
Tension | Compression | ||
Mean (MPa.) | STD | Mean (MPa.) | STD |
0.260 | 0.0819 | 0.260 | 0.0819 |
Structural analysis
Geometry modeling
Loads and supports
Validation
System reliability
Failure mechanics
Reliability analysis
Results
Normal | |||||
---|---|---|---|---|---|
Maximum Stress | |||||
Weight (KG) | Cortical | Cancellous | Annulus | Nucleus | |
30 | Tension | T2 | C7 | C7 | T6 |
Compression | C7 | C7 | C6 | C7 | |
40 | Tension | T2 | C7 | C7 | T6 |
Compression | C7 | L3-C7 | C6 | C7 | |
50 | Tension | T2 | C7 | C7 | T6 |
Compression | C7 | L3-C7 | C6 | C7 | |
60 | Tension | T2 | C7 | C7 | T6 |
Compression | C7 | L3-C7 | C6 | C7 | |
70 | Tension | T2 | C7 | C7 | T6 |
Compression | C7 | L3-C7 | C6 | C7 | |
80 | Tension | T2 | C7 | C7 | T6 |
Compression | C7 | L3-C7 | C6 | C7 |
Scoliosis | |||||
---|---|---|---|---|---|
Maximum Stress | |||||
Weight (KG) | Cortical | Cancellous | Annulus | Nucleus | |
30 | Tension | T1 | T7 | C7 | T7 |
Compression | T1 | T10 | C6 | T10 | |
40 | Tension | T1 | T7 | C7 | T7 |
Compression | C7 | T10 | C6 | T10 | |
50 | Tension | C7 | T7 | C7 | C7 |
Compression | C7 | T10 | C6 | C7 | |
60 | Tension | C7 | T7 | C7 | C6 |
Compression | C7 | T10 | C6 | C6 | |
70 | Tension | C7 | T8 | C7 | C6 |
Compression | C7 | T10 | C6 | C6 | |
80 | Tension | C7 | T8 | C7 | C6 |
Compression | C7 | T10 | C6 | C7 |
30 KG | 40 KG | 50 KG | 60 KG | 70 KG | 80 KG | ||
---|---|---|---|---|---|---|---|
Normal Spine | Pf | 2.05 × 10−5 | 2.57 × 10−5 | 3.75 × 10−5 | 4.93 × 10−5 | 6.59 × 10−5 | 8.82 × 10−5 |
Normal Spine | β | 4.10 | 4.05 | 3.96 | 3.89 | 3.82 | 3.75 |
Scoliosis Spine | Pf | 2. 77 × 10−4 | 1.14 × 10−3 | 1.82 × 10−3 | 2.22 × 10−3 | 2.45 × 10−3 | 3.18 ×10−3 |
Scoliosis Spine | β | 3.45 | 3.05 | 2.91 | 2.85 | 2.81 | 2.73 |