Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method
Abstract
:1. Introduction
2. Use of FEM for Modeling the Lumbar Intervertebral Disc
2.1. Biomechanics of the Intervertebral Disc
2.2. Spine Movement
2.3. Bulge
2.4. Experimental Behavior of the Intervertebral Disc
2.4.1. Compression
2.4.2. Flexion and Extension
2.4.3. Lateral Bending
2.4.4. Shear and Torsion
3. FE Model for Modeling the Intervertebral Disc Proposed
3.1. Configuration of the Finite Element Analysis and Mesh Size
3.2. Intervertebral Disc Dimensions
3.3. Boundary Conditions
4. Design of the Experiments and Design Matrix
4.1. Response Surface Method for Modeling and Optimizing Problems
4.2. Combining FEM and MRS to Optimize Mechanical Problems
5. Results and Discussion
5.1. FE Models’ Results
5.2. Analysis of Variance
5.3. Multiple Response Optimization
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
List of Symbols/Nomenclature
MAE | Mean Absolute Error | |
C10 | Mooney-Rivlin parameter for annulus ground substance | |
C0 | Mooney-Rivlin parameter for annulus ground substance | |
Annulus_E | Young’s modulus for the annulus ground substance | (MPa) |
Annulus_μ | Poisson’s modulus for the annulus ground substance | |
Fiber12 | Collagen fibers layer 1 | (mm2) |
Fiber34 | Collagen fibers layer 2 | (mm2) |
Fiber56 | Collagen fibers layer 3 | (mm2) |
Fiber78 | Collagen fibers layer 4 | (mm2) |
Fiber910 | Collagen fibers layer 5 | (mm2) |
Cartil_E | Young’s modulus for the endplate cartilage | (MPa) |
Cartil_μ | Poisson’s modulus for the endplate cartilage | - |
Comp_bulgeA | Bulge Anterior for the Compression Test | (mm) |
Comp_bulgeL | Bulge Lateral for the Compression Test | (mm) |
Comp_bulgeP | Bulge Posterior for the Compression Test | (mm) |
Comp_stiff | Stiffness for the Compression Test | (N/mm) |
Shear_stiff | Stiffness for the Shear Test | (N/mm) |
Exte_bulgeL | Bulge Lateral for the Extension Test | (mm) |
Exte_bulgeP | Bulge Posterior for the Extension Test | (mm) |
Exte_stiff | Stiffness for the Extension Test | (Nm/°) |
LBend_bulgeL | Bulge Lateral for the Lateral Bending Test | (mm) |
LBend_bulgeP | Bulge Posterior for the Lateral Bending Test | (mm) |
LBend_stiff | Stiffness for the Lateral Bending Test | (Nm/°) |
Flex_bulgeL | Bulge Lateral for the Flexion Test | (mm) |
Flex_bulgeP | Bulge Posterior for the Flexion Test | (mm) |
Flex_stiff | Stiffness for the Flexion Test | (Nm/°) |
Tors_stiff | Stiffness for the Torsion Test | (Nm/°) |
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Nucleus Pulposus | Cartilage Endplate | Annulus Ground | Annulus Fibers | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Authors | FE Parameters | FE Parameters | FE Parameters | FE Parameters | FE Parameters | |||||||||||
Mooney-Rivlin Max. | Isotropic | Isotropic | Mooney-Rivlin | Isotropic | F1 | F2 | F3 | F4 | F5 | |||||||
C10 | C0 | E | Μ | E | μ | C10 | C0 | E | μ | E | μ | |||||
Kim and Chun (2015) [36] | - | - | 1 | 0.4999 | 24 | 0.40 | - | - | 4.2 | 0.45 | 550–358 | 0.3 | ||||
Dicko et al. (2015) [37] | - | - | 1 | 0.4999 | 24 | 0.40 | 0.18 | 0.045 | - | 0.45 | Non-linear stress-strain curve | |||||
González et al. (2015) [42] | 0.12 | 0.03 | 0.5 < E < 1 | 0.4 < μ < 0.5 | 20 | 0.3 | - | - | 0.75–5 | 0.35–0.5 | - | - | ||||
Ibarz, Elena et al. (2014) [47] | 0.0343 | 0.1369 | - | - | - | - | - | - | 4.2 | 0.45 | 550 | 503 | 455 | 408 | 360 | 0.3 |
Tsouknidas et al (2012) [35] | - | - | 0.2 | 0.4999 | - | - | - | - | 4.2 | 0.45 | 550 | 485 | 440 | 420 | 360 | 0.45 |
Ayturk, U.M. (2010) [38] | - | - | 1 | 0.4999 | 23.8 | 0.8 | C10 = 0.0146; C20 = −0.0189; C30 = 0.041 | a3 = 0.03; b3 = 120 | ||||||||
Schmidt, Kettler (2007) [44] | 0.12 | 0.03 | - | 0.4999 | 23.8 | 0.8 | 0.10 | 0.05 | 0.45 | * Stress-strain curve by Shirazi: σ = 23,000 × ε1.9 | ||||||
Rohlmann et al. (2006) [46] | 0.10 | 0.09 | - | 0.4999 | 23.8 | 0.8 | 0.348 | 0.3 | 0.42 | 0.45 | * Stress-strain curve by Shirazi: σ = 23,000 × ε1.9 | |||||
Rohlmann, Zander (2006) [45] | 0.10 | 0.09 | - | 0.4999 | - | - | 0.348 | 0.3 | 0.42 | 0.45 | * Stress-strain curve by Shirazi: σ = 23,000 × ε1.9 | |||||
Grauer et al. (2006) [39] | - | - | 1 | 0.4999 | - | - | - | - | 4.2 | 0.45 | 175 | 175 | 175 | 175 | 175 | - |
Dietrich, M. et al. (2005) [51] | - | - | 0.012 | 0.4999 | - | - | - | - | 10 | 0.35 | - | - | - | - | - | - |
Denoziére, G. et al (2004) [2] | - | - | 0.1 | 0.4999 | 12 | 0.3 | - | - | 4.2 | 0.45 | 550 | 485 | 440 | 420 | 360 | 0.3 |
Baroud et al. (2003) [30] | 0.12 | 0.03 | - | - | - | - | - | - | 8 | 0.45 | 500 | 485 | 420 | 360 | - | - |
Pitzen et al. (2002) [33] | - | - | 0.1 | 0.4999 | - | - | - | - | 4.2 | 0.45 | 500 | 485 | 420 | 360 | - | - |
Dooris et al. (2001) [40] | - | - | 1 | 0.49 | - | - | - | - | - | - | - | - | - | - | - | - |
Eberlain et al. (2001) [52] | Incompress. Fluid | - | - | 23.8 | 0.4 | 0.348 | 0.3 | 4 | 0.4 | * Stress-strain curve by Shirazi:σ = 23,000 × ε1.9 | ||||||
Martínez et al. (1997) [49] | - | - | - | - | 20 | 0.3 | - | 0.3 | - | - | - | - | - | - | - | - |
Lu et al. (1996) [48] | - | - | - | - | 20 | 0.3 | - | - | 4.2 | 0.45 | - | - | - | - | - | - |
Smit et al. (1997) [41] | 0.12 | 0.09 | 0.5 < E < 1 | 0.4999 | - | - | - | - | - | - | - | - | - | - | - | - |
Sharma et al. (1995) [34] | 0.1 | 0.4999 | - | - | - | - | 4.2 | 0.5 | ||||||||
Lavaste et al. (1992) [43] | - | - | 1 < E < 4 | 0.5 | - | - | - | - | - | - | - | - | - | - | - | - |
Shirazi-Adl et al. (1984) [11] | Incompress. Fluid | - | - | - | - | - | - | 4.2 | 0.45 | σ = 23,000 × ε1.9 |
Compression Test | |||
Authors | Stiffness (N/mm) | Load (N) | Range of Load (N) |
Moroney et al. (1988) [68] | 500 | 74 | |
Brown et al. (2002) [69] | 400 | 200 | <400 |
Keller et al. (1987) [70] | 247 | 253 | |
Berkson et al. (1979) [8] | 800 | 400 | |
Nachemson et al. (1979) [67] | 571 | 500 | |
Rostedt et al. (1998) [5] | 810 | 500 | |
Stokes et al. (2002) [65] | 510 | 500 | 850–500 |
Panjabi et al. (1984) [66] | 750 | 600 | |
Gardner-Morse et al. (2004) [7] | 2420 | 850 | |
Hirsh and Nachemson (1954) [54] | 700 | 1000 | |
Schultz et al. (1973) [61] | 1500 | 1000 | |
González Gutierrez (2012) [3] | 833 | 1000 | |
González Gutierrez (2012) [3] | 933 | 1000 | |
González Gutierrez (2012) [3] | 1089 | 1000 | 5500–1000 |
Markolf (1970) [62] | 1800 | 1800 | |
Virgin (1951) [60] | 2500 | 4500 | |
Rolander and Blair (1975) [63] | 3000 | 5000 | |
Brown et al. (1957) [64] | 2300 | 5300 | |
Bulges Values | |||
Authors | Anterior/Post/Lateral (mm) | Load (N) | |
Reuber et al. (1982) [58] | -/0.24/0.66 | 400 | |
Schmidt, Kettler (2007) [44] | 0.7 to 0.9 | 500 | |
Shirazi-Adl et al. (1984) [11] | 0.5/0.75/0.35 | 500 | |
Shirazi-Adl et al. (1984) [11] | 0.7/1/0.4 | 720 | |
Reuber et al. (1982) [58] | -/0.34/0.8 | 800 | |
Brinckmann et al. (1991) [59] | 0.15 | 1000 | |
González Gutierrez (2012) [3] | 0.69 | 1000 | |
Shirazi-Adl et al. (1984) [11] | 0.8/1.5/0.6 | 1000 | |
Nachemson, A. (1960) [71] | - | 2000 | |
Denozière (2004) [2] | 0.5/0.7/0.4 | 2500 | |
Klein et al. (1983) [57] | 0.6 | - |
Flexion/Extension Test | ||
Authors | Stiffness Values (Nm/°) | Load (Nm) |
Guan et al. (2007) [75] | 0.82/1.53 | 4 |
Busscher et al. (2009) [76] | 0.8 | 4 |
Busscher et al. (2010) [77] | 0.8 | 5 |
González Gutierrez (2012) [3] | 1.18/1.38 | 5 |
Patwardhan et al. (2003) [78] | 1.33 | 8 |
White and Panjabi (1978) [79] | 0.8/2 | 10 |
Nachemson et al. (1979) [67] | 2.03/3.53 | 10 |
Gardner-Morse et al. (2004) [7] | 2.04 | 10 |
Schultz et al. (1979) [9] | 1.92/3.55 | 10.6 |
Adams et al. (1980) [74] | 1.34 | 10.7 |
Schultz et al. (1973) [61] | 4.5 | 20 |
Brown et al. (2002) [69] | 2 | 20 |
Miller et al. (1986) [72] | 5.51/7.60 | 70 |
Adams et al. (1996) [73] | 7.3 | 80 |
Bulges Values | ||
Authors | Anterior/Post/Lateral (mm) | Load (Nm) |
Denoziére, G. et al. (2004) [2] | 1.3/1.9/2.6 | 10 |
Reuber et al. (1982) [58] | -/0.73/0.07 | 3.9 |
Reuber et al. (1982) [58] | -/1.11/0.21 | 7.9 |
Lateral Bending Test | ||
Authors | Stiffness Values (Nm/°) | Load (Nm) |
Guan et al. (2007) [75] | 0.76 | 4 |
Busscher et al. (2009) [76] | 0.5 | 4 |
Busscher et al. (2010) [77] | 0.6 | 5 |
González Gutierrez (2012) [3] | 1.58 | 5 |
White and Panjabi (1978) [79] | 0.9 | 10 |
Nachemson et al. (1979) [67] | 1.1 | 10 |
Gardner-Morse et al. (2004) [7] | 1.29 | 10 |
Schultz et al. (1979) [9] | 2 | 10.6 |
Schultz et al. (1973) [61] | 2.8 | 20 |
Miller et al. (1986) [72] | 4.35 | 60 |
Bulges Values | ||
Authors | Anterior/Post/Lateral (mm) | Load (Nm) |
Reuber et al. (1982) [58] | -/0.49/0.83 | 3.9 |
Reuber et al. (1982) [58] | -/1.13/2.11 | 9.8 |
Shear Test | ||
Authors | Stiffness (N/mm) | Load (N) |
Moroney et al. (1988) [68] | 60 | 20 |
Markolf (1970) [62] | 260 | 150 |
Miller et al. (1986) [72] | 115 | 150 |
Liu et al. (1975) [6] | 300 | 450 |
Weisse et al. (2012) [80] | 830 | 950 |
Schultz et al. (1979) [9] | 1000 | 980 |
Schultz et al. (1973) [61] | 685 | 1000 |
Torsion Test | ||
Authors | Stiffness (Nm/°) | Load(Nm) |
Busscher et al. (2009) [76] | 2.5 | 4 |
Busscher et al. (2010) [77] | 1.6 | 5 |
González Gutierrez (2012) [3] | 4.4 | 5 |
Haughton et al. (1999) [83] | 7 | 6.6 |
Adams et al. (1981) [82] | 1.44 | 7.4 |
White and Panjabi (1978) [79] | 2.22 | 10 |
Nachemson et al. (1979) [67] | 8.48 | 10 |
Gardner-Morse et al. (2004) [7] | 2.1 | 10 |
Schultz et al. (1979) [9] | 7.07 | 10.6 |
Schultz et al. (1973) [61] | 4.5 | 30 |
Farfan et al. (1970) [81] | 2 | 31 |
Miller et al. (1986) [72] | 10.9 | 70 |
Test | Author | Load Used | Stiffness | ||
Compression | Rostedt et al. (1998) [5] | 500 N | 810 N/mm | ||
Flexion | González Gutierrez (2012) [3] | 5 Nm | 1.18 Nm/° | ||
Extension | Guan et al. (2007) [75] | 4 Nm | 1.53 Nm/° | ||
Lateral Bending Bending | Schultz et al. (1979) [9] | 10.6 Nm | 2.0 Nm/° | ||
Shear | Liu et al. (1975) [6] | 450 N | 300 N/mm | ||
Torsion | Gardner-Morse et al. (2004) [7] | 10 Nm | 2.1 Nm/° | ||
Test | Authors | Load Used | Bulge | Bulg | Bulge |
Anterior (mm) | Posterior (mm) | Lateral (mm) | |||
Compression | Shirazi-Adl et al. (1984) [11] | 500 N | 0.5 | 0.75 | 0.35 |
Flexion | Reuber et al. (1982) [58] | 3.9 Nm | - | 0.73 | 0.07 |
Extension | Reuber et al. (1982) [58] | 3.9 Nm | - | 0.24 | 0.1 |
Lateral Bending | Reuber et al. (1982) [58] | 9.8 Nm | - | 1.13 | 2.11 |
Tissue | FE Parameters | Tissue | FE Parameters | ||
---|---|---|---|---|---|
Min. | Max. | Min. | Max. | ||
Nucleus Pulposus | Annulus Fibrosus | ||||
C10 | 0.11 | 0.14 | Fiber12 | 515.0 | 550.0 |
C0 | 0.02 | 0.04 | Fiber34 | 503.0 | 515.0 |
Endplate | Fiber56 | 455.0 | 503.0 | ||
E | 23.0 | 55.0 | Fiber78 | 408.0 | 455.0 |
μ | 0.3 | 0.4 | Fiber910 | 360.0 | 408.0 |
- | - | - | E Annulus Fibrosus | 4.0 | 4.2 |
- | - | - | μ Annulus Fibrosus | 0.25 | 0.45 |
Summary of Anatomical Dimensions of L1–L5 | ||||||||
---|---|---|---|---|---|---|---|---|
Authors | Group Size (n) | Lumbar Level | Sex | Mean Age (From…to…) | Width (mm) | Depth (mm) | Height (mm) | Area (cm2) |
Rostedt et al. (1998) [5] | 4 | L3–L4 | - | 45 | - | - | 12 | - |
Schultz et al. (1979) [9] | 1 | L1–L5 | male | 35 | - | - | - | 1590 |
Schultz et al. (1979) [9] | 1 | L1–L5 | male | 40 | - | - | - | 1680 |
Schultz et al. (1979) [9] | 1 | L1–L5 | male | 53 | - | - | - | 1500 |
Zhou et al. (2000) [88] | 55 | L3–L5 | male | 50 (22–80) | 53 | 37.5 | 12.2 | 1492 ± 173.8 |
Zhou et al. (2000) [88] | 71 | L3–L5 | female | 49 (22–80) | 50.5 | 35.4 | 11.3 | 1492 ± 173.8 |
Panjabi (1992) [90] | 60 | L1–L5 | - | 46.3 (19–59) | 48.1 | 34.7 | - | - |
Eijkelkamp (2002) [91] | 60 | L1–L5 | - | (18–65) | - | - | 13.5 | - |
Nissan and Gilad (1986) [92] | 157 | L1–L5 | - | 26.8 (20–38) | - | 34.6 | 10.8 | - |
Tibrewal and Pearcy (1985) [93] | 11 | L1–L5 | - | 29.5 (25–36) | - | 33 | 9.8 | - |
Wolf et al. (2001) [94] | 55 | L1–L5 | - | (20–90) | 44.1 | 31.7 | - | - |
Amonoo-Kuofi (1991) [95] | 305 | L1–L5 | male | (10–64) | - | 42.8 | 13.5 | - |
Amonoo-Kuofi (1991) [95] | 310 | L1–L5 | female | (10–61) | - | 39.9 | 13 | - |
Schmidt et al. (2006) [24] | - | L4–L5 | - | - | 58.7 | 37.4 | - | - |
Kim and Chun (2015) [36] | 1 | L4–L5 | male | 46 | - | - | - | 1119 |
González et al. (2015) [42] | 5 | L2–L3 | male/female | (65–75) | - | - | 9.9 | 1739 |
González et al. (2015) [42] | 5 | L4–L5 | male/female | (65–75) | - | - | 10 | 1951 |
Shirazi-Adl et al. (1984) [11] | 1 | L2–L3 | female | 29 | 49.2 | 34 | 11 | 1371 |
Smit et al. (1997) [41] | - | L4 | - | - | 42 | 35 | - | - |
Ibarz, Elena et al. (2014) [47] | 25 | L5–S1 | 27.4 | |||||
Ayturk, U.M. (2010) [38] | - | L1–L5 | female | 49 | - | |||
Weisse et al. (2012) [80] | - | L4–L5 | male | 43 | 50.3 | 33.7 | 12.8 | - |
Denozière (2004) [2] | - | L3–L4 | - | - | 50 | 35 | 10 | 1440 |
Run | C10 | C0 | Fiber 12 | Fiber 34 | Fiber 56 | Fiber 78 | Fiber 910 | Annulus E | Annulus μ | Cartil E | Cartil μ |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.11 | 0.02 | 515 | 503 | 455 | 408 | 360 | 4 | 0.25 | 55 | 0.4 |
2 | 0.14 | 0.02 | 515 | 503 | 455 | 408 | 360 | 4.2 | 0.45 | 23 | 0.3 |
3 | 0.11 | 0.04 | 515 | 503 | 455 | 408 | 360 | 4.2 | 0.45 | 23 | 0.4 |
4 | 0.14 | 0.04 | 515 | 503 | 455 | 408 | 360 | 4 | 0.25 | 55 | 0.3 |
5 | 0.11 | 0.02 | 550 | 503 | 455 | 408 | 360 | 4.2 | 0.45 | 55 | 0.3 |
6 | 0.14 | 0.02 | 550 | 503 | 455 | 408 | 360 | 4 | 0.25 | 23 | 0.4 |
7 | 0.11 | 0.04 | 550 | 503 | 455 | 408 | 360 | 4 | 0.25 | 23 | 0.3 |
8 | 0.14 | 0.04 | 550 | 503 | 455 | 408 | 360 | 4.2 | 0.45 | 55 | 0.4 |
9 | 0.11 | 0.02 | 515 | 515 | 455 | 408 | 360 | 4.2 | 0.25 | 23 | 0.4 |
10 | 0.14 | 0.02 | 515 | 515 | 455 | 408 | 360 | 4 | 0.45 | 55 | 0.3 |
… | … | … | … | … | … | … | … | … | … | … | … |
120 | 0.14 | 0.04 | 550 | 503 | 503 | 455 | 408 | 4 | 0.45 | 23 | 0.4 |
121 | 0.11 | 0.02 | 515 | 515 | 503 | 455 | 408 | 4 | 0.25 | 55 | 0.4 |
122 | 0.14 | 0.02 | 515 | 515 | 503 | 455 | 408 | 4.2 | 0.45 | 23 | 0.3 |
123 | 0.11 | 0.04 | 515 | 515 | 503 | 455 | 408 | 4.2 | 0.45 | 23 | 0.4 |
124 | 0.14 | 0.04 | 515 | 515 | 503 | 455 | 408 | 4 | 0.25 | 55 | 0.3 |
125 | 0.11 | 0.02 | 550 | 515 | 503 | 455 | 408 | 4.2 | 0.45 | 55 | 0.3 |
126 | 0.14 | 0.02 | 550 | 515 | 503 | 455 | 408 | 4 | 0.25 | 23 | 0.4 |
127 | 0.11 | 0.04 | 550 | 515 | 503 | 455 | 408 | 4 | 0.25 | 23 | 0.3 |
128 | 0.14 | 0.04 | 550 | 515 | 503 | 455 | 408 | 4.2 | 0.45 | 55 | 0.4 |
Run | Comp BulgeA | Comp BulgeL | Comp BulgeP | Comp Stiff | Shear Stiff | Exte BulgeL | Exte BulgeP | Exte Stiff | LBend BulgeL | LBend BulgeP | LBend Stiff | Flex BulgeL | Flex BulgeP | Flex Stiff | Tors Stiff |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.265 | 0.089 | 0.593 | 984.510 | 305.752 | 0.095 | 0.574 | 1.744 | 0.773 | 1.085 | 1.998 | 0.076 | 0.351 | 1.635 | 3.593 |
2 | 0.337 | 0.133 | 0.730 | 1271.883 | 281.371 | 0.137 | 0.830 | 2.121 | 0.970 | 1.929 | 1.581 | 0.095 | 0.288 | 1.762 | 3.264 |
3 | 0.347 | 0.140 | 0.758 | 1253.827 | 275.927 | 0.139 | 0.861 | 2.094 | 1.386 | 2.136 | 1.320 | 0.093 | 0.301 | 1.646 | 3.150 |
4 | 0.256 | 0.085 | 0.553 | 1017.076 | 315.425 | 0.096 | 0.566 | 1.779 | 0.798 | 1.051 | 2.257 | 0.073 | 0.303 | 1.686 | 3.640 |
5 | 0.298 | 0.094 | 0.665 | 1500.886 | 306.597 | 0.096 | 0.696 | 2.406 | 0.617 | 1.254 | 3.268 | 0.080 | 0.321 | 2.227 | 3.618 |
6 | 0.290 | 0.111 | 0.694 | 897.694 | 284.611 | 0.135 | 0.667 | 1.627 | 1.520 | 1.805 | 1.160 | 0.076 | 0.331 | 1.348 | 3.191 |
7 | 0.286 | 0.108 | 0.683 | 891.309 | 285.801 | 0.135 | 0.644 | 1.619 | 1.349 | 1.653 | 1.322 | 0.082 | 0.334 | 1.394 | 3.271 |
8 | 0.295 | 0.092 | 0.634 | 1548.473 | 316.704 | 0.095 | 0.685 | 2.461 | 0.672 | 1.188 | 3.215 | 0.076 | 0.280 | 2.309 | 3.682 |
9 | 0.290 | 0.113 | 0.711 | 901.414 | 289.552 | 0.132 | 0.661 | 1.661 | 1.531 | 1.892 | 1.130 | 0.078 | 0.349 | 1.338 | 3.320 |
10 | 0.304 | 0.095 | 0.670 | 1474.443 | 300.617 | 0.099 | 0.728 | 2.351 | 0.625 | 1.237 | 3.229 | 0.081 | 0.301 | 2.192 | 3.447 |
… | … | … | … | … | … | … | … | … | … | … | … | … | … | … | … |
120 | 0.345 | 0.136 | 0.752 | 1256.486 | 278.278 | 0.139 | 0.875 | 2.063 | 1.322 | 2.070 | 1.382 | 0.090 | 0.284 | 1.673 | 3.016 |
121 | 0.260 | 0.088 | 0.596 | 989.416 | 313.213 | 0.094 | 0.574 | 1.749 | 0.778 | 1.086 | 1.990 | 0.076 | 0.352 | 1.635 | 3.665 |
122 | 0.333 | 0.131 | 0.731 | 1276.741 | 287.840 | 0.135 | 0.829 | 2.127 | 0.961 | 1.928 | 1.583 | 0.094 | 0.289 | 1.766 | 3.318 |
123 | 0.342 | 0.139 | 0.760 | 1258.926 | 282.358 | 0.137 | 0.860 | 2.100 | 1.374 | 2.137 | 1.325 | 0.092 | 0.302 | 1.652 | 3.201 |
124 | 0.252 | 0.085 | 0.555 | 1022.062 | 322.997 | 0.095 | 0.565 | 1.783 | 0.801 | 1.052 | 2.250 | 0.073 | 0.304 | 1.686 | 3.723 |
125 | 0.294 | 0.092 | 0.667 | 1507.286 | 314.067 | 0.094 | 0.693 | 2.414 | 0.614 | 1.251 | 3.262 | 0.079 | 0.322 | 2.230 | 3.670 |
126 | 0.286 | 0.110 | 0.697 | 901.330 | 291.307 | 0.133 | 0.667 | 1.630 | 1.524 | 1.809 | 1.160 | 0.076 | 0.332 | 1.350 | 3.255 |
127 | 0.282 | 0.107 | 0.685 | 894.800 | 292.534 | 0.134 | 0.644 | 1.621 | 1.351 | 1.654 | 1.321 | 0.082 | 0.335 | 1.395 | 3.333 |
128 | 0.291 | 0.091 | 0.635 | 1555.367 | 324.328 | 0.093 | 0.684 | 2.469 | 0.670 | 1.186 | 3.210 | 0.076 | 0.281 | 2.310 | 3.740 |
Compression Bulge Anterior BulgeL | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.00066 | 0.00066 | 35.8 | 2.41 × 10−8 | *** |
C0 | 1 | 0.00031 | 0.00031 | 16.7 | 8.01 × 10−5 | *** |
Fiber12 | 1 | 0.00008 | 0.00008 | 4.1 | 4.47 × 10−2 | * |
Fiber56 | 1 | 0.00006 | 0.00006 | 3.1 | 7.96 × 10−2 | . |
Fiber78 | 1 | 0.00004 | 0.00004 | 2.0 | 1.58 × 10−1 | |
Fiber910 | 1 | 0.00005 | 0.00005 | 2.6 | 1.09 × 10−1 | |
Annulus_E | 1 | 0.00149 | 0.00149 | 81.5 | 4.25 × 10−15 | *** |
Annulus_μ | 1 | 0.08796 | 0.08796 | 4805.3 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 0.04237 | 0.04237 | 2314.5 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 0.00054 | 0.00054 | 29.4 | 3.24 × 10−7 | *** |
Residuals | 117 | 0.00214 | 0.00002 |
Compression Bulge Lateral | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.00021 | 0.00021 | 8.3 | 4.73 × 10−3 | ** |
C0 | 1 | 0.00010 | 0.00010 | 3.9 | 5.12 × 10−2 | . |
Fiber12 | 1 | 0.00010 | 0.00010 | 4.0 | 4.89 × 10−2 | * |
Annulus_E | 1 | 0.00005 | 0.00005 | 2.0 | 1.60 × 10−1 | |
Annulus_μ | 1 | 0.00999 | 0.00999 | 398.4 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 0.03378 | 0.03378 | 1347.0 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 0.00031 | 0.00031 | 12.3 | 6.31 × 10−4 | *** |
Residuals | 1200 | 0.00301 | 0.00003 |
Compression Bulge Posterior | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.02444 | 0.02444 | 323.4 | <2.2 × 10−16 | *** |
C0 | 1 | 0.01072 | 0.01072 | 141.9 | <2.2 × 10−16 | *** |
Annulus_E | 1 | 0.01647 | 0.01647 | 217.9 | <2.2 × 10−16 | *** |
Annulus_μ | 1 | 0.25063 | 0.25063 | 3316.3 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 0.35753 | 0.35753 | 4730.9 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 0.00439 | 0.00439 | 58.2 | 6.11 × 10−12 | *** |
Residuals | 121 | 0.00914 | 0.00008 |
Compression Stiffness | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 19,462 | 19,462 | 14.7 | 2.00 × 10−4 | *** |
C0 | 1 | 8911 | 8911 | 6.7 | 1.06 × 10−2 | * |
Annulus_E | 1 | 41,500 | 41,500 | 31.4 | 1.34 × 10−7 | *** |
Annulus_μ | 1 | 5,389,427 | 5,389,427 | 4074.1 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 1,054,628 | 1,054,628 | 797.2 | <2.2 × 10−16 | *** |
Residuals | 122 | 161,387 | 1323 |
Shear Stiffness | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 1148.2 | 1148.2 | 438.8 | <2.2 × 10−16 | *** |
C0 | 1 | 510.6 | 510.6 | 195.1 | <2.2 × 10−16 | *** |
Fiber12 | 1 | 18.4 | 18.4 | 7.0 | 9.15 × 10−3 | ** |
Fiber34 | 1 | 14.0 | 14.0 | 5.4 | 2.24 × 10−2 | * |
Fiber56 | 1 | 73.8 | 73.8 | 28.2 | 5.34 × 10−7 | *** |
Fiber78 | 1 | 233.3 | 233.3 | 89.2 | 4.82 × 10−16 | *** |
Fiber910 | 1 | 144.4 | 144.4 | 55.2 | 2.02 × 10−11 | *** |
Annulus_E | 1 | 4328.4 | 4328.4 | 1654.0 | <2.2 × 10−16 | *** |
Annulus_μ | 1 | 6817.7 | 6817.7 | 2605.3 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 28,143.4 | 28,143.4 | 10,754.5 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 89.4 | 89.4 | 34.2 | 4.73 × 10−8 | *** |
Residuals | 116 | 303.6 | 2.6 |
Extension Bulge Lateral Stiffness | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
Fiber910 | 1 | 0.00189 | 0.00189 | 12.9 | 4.62 × 10−4 | *** |
Annulus_μ | 1 | 0.00101 | 0.00101 | 6.9 | 9.74 × 10−3 | ** |
Cartil_E | 1 | 0.04221 | 0.04221 | 288.7 | <2.2 × 10−16 | *** |
Residuals | 1244 | 0.01813 | 0.00015 |
Extension Bulge Posterior | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
Fiber910 | 1 | 0.29 | 0.29 | 17.9 | 4.54 × 10−5 | *** |
Annulus_μ | 1 | 0.74 | 0.74 | 45.6 | 4.90 × 10−10 | *** |
Cartil_E | 1 | 0.41 | 0.41 | 25.0 | 1.94 × 10−6 | *** |
Residuals | 124 | 2.02 | 0.02 |
Extension Stiffness | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
Fiber910 | 1 | 13.2 | 13.2 | 20.4 | 1.45 × 10−5 | *** |
Annulus_μ | 1 | 8.6 | 8.6 | 13.3 | 3.88 × 10−4 | *** |
Cartil_E | 1 | 2.3 | 2.3 | 3.5 | 6.42 × 10−2 | . |
Residuals | 124 | 80.4 | 0.6 |
Lateral Bending Bulge Lateral | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.03 | 0.03 | 3.2 | 7.57 × 10−2 | . |
Annulus_μ | 1 | 1.11 | 1.11 | 119.9 | <2.0 × 10−16 | *** |
Cartil_E | 1 | 10.27 | 10.27 | 1112.5 | <2.0 × 10−16 | *** |
Cartil_μ | 1 | 0.84 | 0.84 | 91.0 | <2.0 × 10−16 | *** |
Residuals | 123 | 1.14 | 0.01 |
Lateral Bending Bulge Posterior | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.26 | 0.26 | 53.7 | 2.84 × 10−11 | *** |
C0 | 1 | 0.12 | 0.12 | 25.5 | 1.59 × 10−6 | *** |
Annulus_E | 1 | 0.06 | 0.06 | 11.8 | 8.21 × 10−4 | *** |
Annulus_μ | 1 | 2.34 | 2.34 | 478.3 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 17.71 | 17.71 | 3624.2 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 0.23 | 0.23 | 47.1 | 3.06 × 10−10 | *** |
Residuals | 121 | 0.59 | 0.00 |
Lateral Bending Stiffness | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.08 | 0.08 | 1.9 | 1.68 × 10−1 | |
Annulus_E | 1 | 0.11 | 0.11 | 2.6 | 1.10 × 10−1 | |
Annulus_μ | 1 | 11.63 | 11.63 | 265.9 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 56.69 | 56.69 | 1295.7 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 1.15 | 1.15 | 26.3 | 1.11 × 10−6 | *** |
Residuals | 122 | 5.34 | 0.04 |
Flexion Bulge Lateral | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.00012 | 0.00012 | 15.7 | 1.25 × 10−4 | *** |
C0 | 1 | 0.00005 | 0.00005 | 6.2 | 1.38 × 10−2 | * |
Fiber12 | 1 | 0.00004 | 0.00004 | 5.0 | 2.74 × 10−2 | * |
Annulus_E | 1 | 0.00002 | 0.00002 | 3.0 | 8.73 × 10−2 | . |
Annulus_μ | 1 | 0.00313 | 0.00313 | 416.0 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 0.00316 | 0.00316 | 420.0 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 0.00012 | 0.00012 | 15.5 | 1.42 × 10−4 | *** |
Residuals | 120 | 0.00090 | 0.00001 |
Flexion Bulge Posterior | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.024 | 0.024 | 2130.8 | <2.2 × 10−16 | *** |
C0 | 1 | 0.011 | 0.011 | 949.1 | <2.2 × 10−16 | *** |
Annulus_E | 1 | 0.003 | 0.003 | 264.3 | <2.2 × 10−16 | *** |
Annulus_μ | 1 | 0.016 | 0.016 | 1429.9 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 0.000 | 0.000 | 43.1 | 1.36 × 10−9 | *** |
Residuals | 122 | 0.001 | 0.000 |
Flexion Stiffness | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.059 | 0.059 | 13.0 | 4.45 × 10−4 | *** |
C0 | 1 | 0.027 | 0.027 | 5.9 | 1.68 × 10−2 | * |
Annulus_E | 1 | 0.093 | 0.093 | 20.5 | 1.39 × 10−5 | *** |
Annulus_μ | 1 | 5.643 | 5.643 | 1243.7 | <2.2 × 10−16 | *** |
Cartil_E | 1 | 5.706 | 5.706 | 1257.6 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 0.044 | 0.044 | 9.6 | 2.42 × 10−3 | ** |
Residuals | 121 | 0.549 | 0.005 |
Torsion Stiffness | ||||||
---|---|---|---|---|---|---|
Var. | Df | Sum of Sq. | Mean Square | F Value | p-Value | Significance Code |
C10 | 1 | 0.032 | 0.032 | 21.0 | 1.13 × 10−5 | *** |
C0 | 1 | 0.010 | 0.010 | 6.8 | 1.03 × 10−2 | * |
Fibra34 | 1 | 0.032 | 0.032 | 20.9 | 1.22 × 10−5 | *** |
Fiber56 | 1 | 0.016 | 0.016 | 10.6 | 1.47 × 10−3 | ** |
Fiber78 | 1 | 0.102 | 0.102 | 66.8 | 3.84 × 10−13 | *** |
Annulus_E | 1 | 1.056 | 1.056 | 691.1 | <2.2 × 10−16 | *** |
Annulus_μ | 1 | 1.049 | 1.049 | 685.9 | <2.2×10−16 | *** |
Cartil_E | 1 | 5.539 | 5.539 | 3623.7 | <2.2 × 10−16 | *** |
Cartil_μ | 1 | 0.087 | 0.087 | 56.9 | 1.04 × 10−11 | *** |
Residuals | 118 | 0.180 | 0.002 |
Errors and Correlations | Comp_BulgeA | Comp_BulgeL | Comp_BulgeP | Comp_Stiff | Shear_Stiff |
Correlation | 99.189 | 96.861 | 99.180 | 98.784 | 99.636 |
MAE | 3.384 | 7.353 | 2.839 | 5.166 | 1.740 |
RMSE | 3.710 | 7.786 | 3.433 | 5.228 | 2.190 |
Exte_BulgeL | Exte_BulgeP | Exte_Stiff | LBend_BulgeL | LBen_BulgeP | |
Correlation | 84.457 | 64.532 | 48.035 | 95.663 | 98.603 |
MAE | 11.141 | 13.241 | 13.973 | 8.023 | 4.176 |
RMSE | 17.393 | 19.936 | 21.812 | 9.483 | 5.135 |
LBend_Stiff | Flex_BulgeL | Flex_BulgeP | Flex_Stiff | Tors_Stiff | |
Correlation | 96.376 | 93.817 | 98.757 | 97.709 | 98.881 |
MAE | 8.956 | 8.864 | 3.203 | 6.036 | 3.257 |
RMSE | 9.072 | 9.840 | 3.607 | 6.441 | 3.997 |
Errors and Correlations | Comp_BulgeA | Comp_BulgeL | Comp_BulgeP | Comp_Stiff | Shear_Stiff |
Correlation | 98.801 | 95.648 | 95.429 | 97.603 | 94.763 |
MAE | 5.998 | 12.781 | 8.063 | 4.835 | 6.320 |
RMSE | 6.792 | 14.106 | 9.167 | 6.031 | 7.802 |
Exte_BulgeL | Exte_BulgeP | Exte_Stiff | LBend_BulgeL | LBend_BulgeP | |
Correlation | 92.228 | 82.880 | 69.068 | 88.825 | 91.281 |
MAE | 6.595 | 5.537 | 9.807 | 8.575 | 8.315 |
RMSE | 7.574 | 6.884 | 11.204 | 11.663 | 10.359 |
LBend_Stiff | Flex_BulgeL | Flex_BulgeP | Flex_Stiff | Tors_Stiff | |
Correlation | 87.637 | 92.933 | 96.930 | 94.031 | 64.698 |
MAE | 9.122 | 6.981 | 2.8642 | 5.594 | 10.067 |
RMSE | 11.125 | 8.152 | 3.193 | 6.883 | 19.505 |
Var. | Goal | Value | Desirability |
---|---|---|---|
C10 | inRange → 0.125 | 0.102 | 1.000 |
C0 | inRange → 0.03 | 0.015 | 1.000 |
Fiber12 | inRange → 532.5 | 518.133 | 1.000 |
Fiber34 | inRange → 509 | 500.083 | 1.000 |
Fiber56 | inRange → 479 | 517.692 | 1.000 |
Fiber78 | inRange → 431.5 | 463.054 | 1.000 |
Fiber910 | inRange → 384 | 366.794 | 1.000 |
Annulus_E | inRange → 4.1 | 3.951 | 1.000 |
Annulus_μ | inRange → 0.35 | 0.201 | 1.000 |
Cartil_E | inRange → 39 | 42.121 | 1.000 |
Cartil_μ | inRange → 0.35 | 0.430 | 1.000 |
Comp_bulgeA | target → 0.5 | 0.265 | 0.262 |
Comp_bulgeL | target → 0.35 | 0.097 | 0.244 |
Comp_bulgeP | target → 0.75 | 0.650 | 0.651 |
Comp_stiff | target → 810 | 826.143 | 0.983 |
Shear_stiff | target → 300 | 298.124 | 0.964 |
Exte_bulgeL | target → 0.1 | 0.100 | 1.000 |
Exte_bulgeP | target → 0.24 | 0.490 | 0.711 |
Exte_stiff | target → 1.53 | 2.167 | 0.867 |
LBend_bulgeL | target → 2.11 | 1.235 | 0.534 |
LBend_bulgeP | target → 1.13 | 1.459 | 0.792 |
LBend_stiff | target → 2 | 1.465 | 0.634 |
Flex_bulgeL | target → 0.07 | 0.074 | 0.873 |
Flex_bulgeP | target → 0.73 | 0.375 | 0.381 |
Flex_stiff | target → 1.18 | 1.357 | 0.880 |
Tors_stiff | target → 2.1 | 3.401 | 0.451 |
Overall Desirability | 0.625 |
Var. | Goal | Value | Desirability |
---|---|---|---|
C10 | inRange → 0.125 | 0.105 | 1.000 |
C0 | inRange → 0.03 | 0.015 | 1.000 |
Fiber12 | inRange → 532.5 | 541.867 | 1.000 |
Fiber34 | inRange → 509 | 500.123 | 1.000 |
Fiber56 | inRange → 479 | 458.643 | 1.000 |
Fiber78 | inRange → 431.5 | 396.291 | 1.000 |
Fiber91 | inRange → 384 | 421.320 | 1.000 |
Annulus_E | inRange → 4.1 | 3.952205 | 1.000 |
Annulus_μ | inRange → 0.35 | 0.2269 | 1.000 |
Cartil_E | inRange → 39 | 45.575 | 1.000 |
Cartil_μ | inRange → 0.35 | 0.2756 | 1.000 |
Comp_bulgeA | inRange → 0.5 | 0.262 | 1.000 |
Comp_bulgeL | inRange → 0.35 | 0.089 | 1.000 |
Comp_bulgeP | inRange → 0.75 | 0.628 | 1.000 |
Comp_stiff | target → 810 | 900.147 | 0.907 |
Shear_stiff | target → 300 | 300.000 | 1.000 |
Exte_bulgeL | inRange → 0.1 | 0.105 | 1.000 |
Exte_bulgeP | inRange → 0.24 | 0.605 | 1.000 |
Exte_stiff | target → 1.53 | 1.530 | 0.999 |
LBend_bulgeL | inRange → 2.11 | 0.895 | 1.000 |
LBend_bulgeP | inRange → 1.13 | 1.270 | 1.000 |
LBend_stiff | target → 2 | 1.984 | 0.989 |
Flex_bulgeL | inRange → 0.07 | 0.076 | 1.000 |
Flex_bulgeP | inRange → 0.73 | 0.363 | 1.000 |
Flex_stiff | target → 1.18 | 1.518 | 0.772 |
Tors_stiff | target → 2.1 | 3.456 | 0.428 |
Overall Desirability | 0.817 |
Var. | Goal | Value | Desirability |
---|---|---|---|
C10 | inRange → 0.125 | 0.102 | 1.000 |
C0 | inRange → 0.03 | 0.015 | 1.000 |
Fiber12 | inRange → 532.5 | 559.341 | 1.000 |
Fiber34 | inRange → 509 | 512.790 | 1.000 |
Fiber56 | inRange → 479 | 443.243 | 1.000 |
Fiber78 | inRange → 431.5 | 396.348 | 1.000 |
Fiber91 | inRange → 384 | 348.282 | 1.000 |
Annulus_E | inRange → 4.1 | 3.951 | 1.000 |
Annulus_μ | inRange → 0.35 | 0.214 | 1.000 |
Cartil_E | inRange → 39 | 36.933 | 1.000 |
Cartil_μ | inRange → 0.35 | 0.429 | 1.000 |
Comp_bulgeA | target → 0.5 | 0.277 | 0.298 |
Comp_bulgeL | target → 0.35 | 0.101 | 0.257 |
Comp_bulgeP | target → 0.75 | 0.673 | 0.730 |
Comp_stiff | inRange → 810 | 821.981 | 1.000 |
Shear_stiff | inRange → 300 | 287.011 | 1.000 |
Exte_bulgeL | target → 0.1 | 0.103 | 0.947 |
Exte_bulgeP | target → 0.24 | 0.481 | 0.722 |
Exte_stiff | inRange → 1.53 | 2.403 | 1.000 |
LBend_bulgeL | Target → 2.11 | 1.314 | 0.576 |
LBend_bulgeP | target → 1.13 | 1.595 | 0.706 |
LBend_stiff | inRange → 2 | 1.288 | 1.000 |
Flex_bulgeL | target → 0.07 | 0.075 | 0.846 |
Flex_bulgeP | target → 0.73 | 0.373 | 0.378 |
Flex_stiff | inRange → 1.18 | 1.315 | 1.000 |
Tors_stiff | inRange → 2.1 | 3.311 | 1.000 |
Overall Desirability | 0.554 |
Parameters | Criteria 1 | Criteria 2 | Criteria 3 | Experiments | Error |
---|---|---|---|---|---|
FEM | FEM | FEM | Standard Test | Normalized MAE | |
Comp_bulgeA | 0.266 | 0.262 | 0.269 | 0.50 | 0.469 |
Comp_bulgeL | 0.096 | 0.090 | 0.095 | 0.35 | 0.732 |
Comp_bulgeP | 0.624 | 0.602 | 0.625 | 0.75 | 0.177 |
Comp_stiff | 915.640 | 944.360 | 922.740 | 810 | 0.125 |
Shear_stiff | 302.925 | 304.920 | 299.090 | 300 | 0.010 |
Exte_bulgeL | 0.106 | 0.099 | 0.106 | 0.10 | 0.041 |
Exte_bulgeP | 0.527 | 0.559 | 0.538 | 0.24 | 0.539 |
Exte_stiff | 1.634 | 1.678 | 1.645 | 1.53 | 0.073 |
LBend_bulgeL | 0.997 | 0.871 | 0.977 | 2.11 | 0.551 |
LBend_bulgeP | 1.282 | 1.173 | 1.263 | 1.13 | 0.085 |
LBend_stiff | 1.489 | 2.175 | 1.493 | 2.00 | 0.183 |
Flex_bulgeL | 0.077 | 0.080 | 0.076 | 0.07 | 0.096 |
Flex_bulgeP | 0.380 | 0.373 | 0.373 | 0.73 | 0.486 |
Flex_stiff | 1.488 | 1.524 | 1.500 | 1.18 | 0.213 |
Tors_stiff | 3.550 | 3.549 | 3.506 | 2.10 | 0.404 |
Normalized MAE | 0.2782 | 0.2795 | 0.2788 |
© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Gómez, F.S.; Lorza, R.L.; Bobadilla, M.C.; García, R.E. Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method. Materials 2017, 10, 1116. https://doi.org/10.3390/ma10101116
Gómez FS, Lorza RL, Bobadilla MC, García RE. Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method. Materials. 2017; 10(10):1116. https://doi.org/10.3390/ma10101116
Chicago/Turabian StyleGómez, Fátima Somovilla, Rubén Lostado Lorza, Marina Corral Bobadilla, and Rubén Escribano García. 2017. "Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method" Materials 10, no. 10: 1116. https://doi.org/10.3390/ma10101116
APA StyleGómez, F. S., Lorza, R. L., Bobadilla, M. C., & García, R. E. (2017). Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method. Materials, 10(10), 1116. https://doi.org/10.3390/ma10101116