Multiobjective Optimization Design of Spinal Pedicle Screws Using Neural Networks and Genetic Algorithm: Mathematical Models and Mechanical Validation

Table 1

Design variables of the pedicle screws, FE analytical results and ANN models.

No.	BP (mm)	ID (mm)	PRR (mm)	P (mm)	PHA (°)	TW (mm)	MTS-FE (MPa)	MTS-ANN (MPa)	TRF-FE (N)	TRF-ANN (N)
1	0	3.80	0.40	2.60	5.00	0.10	464.49	464.71	39.93	39.99
2	0	4.23	0.55	2.95	8.75	0.15	416.30	415.05	38.40	38.59
3	0	4.65	0.70	3.30	12.50	0.20	399.83	392.63	35.56	35.75
4	0	5.08	0.85	3.65	16.25	0.25	377.19	382.49	31.37	31.26
5	0	5.50	1.00	4.00	20.00	0.30	380.56	377.39	26.36	26.48
6	9	3.80	0.55	3.30	16.25	0.30	452.25	457.14	38.37	38.38
7	9	4.23	0.70	3.65	20.00	0.10	415.59	419.10	36.48	36.57
8	9	4.65	0.85	4.00	5.00	0.15	404.94	405.94	33.66	33.72
9	9	5.08	1.00	2.60	8.75	0.20	432.04	427.96	33.96	33.82
10	9	5.50	0.40	2.95	12.50	0.25	393.19	404.48	35.67	35.54
11	18	3.80	0.70	4.00	8.75	0.25	468.89	468.30	36.74	36.80
12	18	4.23	0.85	2.60	12.50	0.30	576.54	574.13	37.94	37.90
13	18	4.65	1.00	2.95	16.25	0.10	444.50	437.91	35.72	35.71
14	18	5.08	0.40	3.30	20.00	0.15	429.80	416.79	36.65	36.33
15	18	5.50	0.55	3.65	5.00	0.20	391.64	397.72	33.37	33.49
16	27	3.80	0.85	2.95	20.00	0.20	608.56	617.34	37.47	37.15
17	27	4.23	1.00	3.30	5.00	0.25	532.07	529.34	36.37	36.23
18	27	4.65	0.40	3.65	8.75	0.30	491.02	481.84	36.73	36.58
19	27	5.08	0.55	4.00	12.50	0.10	460.59	463.83	34.67	34.41
20	27	5.50	0.70	2.60	16.25	0.15	463.35	469.46	35.14	35.44
21	36	3.80	1.00	3.65	12.50	0.15	919.85	918.26	35.19	35.31
22	36	4.23	0.40	4.00	16.25	0.20	787.66	789.04	34.90	35.05
23	36	4.65	0.55	2.60	20.00	0.25	770.40	765.61	36.66	36.90
24	36	5.08	0.70	2.95	5.00	0.30	605.92	611.19	35.97	36.01
25	36	5.50	0.85	3.30	8.75	0.10	527.13	526.30	33.54	33.46
26	25.4	4.7	0.748	3.1	9.53	0.255	488.62	483.69	36.59	36.41
27	0.5	5.093	0.885	3.59	5.68	0.183	375.29	380.79	31.47	31.64
28	31.05	5.144	0.624	3.947	18.07	0.11	504.19	510.02	34.01	33.62
29	16.87	4.3	0.774	3.507	8.95	0.156	444.71	436.37	36.46	36.73
30	25.02	5.46	0.546	3.347	6.58	0.3	429.47	427.33	34.48	34.43
31	10.24	3.87	0.577	3.135	9.515	0.28	447.07	465.53	38.51	38.73
32	6.696	4.79	0.448	3.241	18.58	0.152	412.10	401.96	37.189	37.16
33	23.25	4.39	0.463	2.86	6.16	0.187	495.95	506.34	38.365	38.56
34	21.55	5.334	0.745	2.943	17.91	0.115	420.82	424.14	34.036	34.89
35	31.64	5.49	0.543	3.528	14.39	0.294	476.86	472.29	34.167	33.80

No. 1–25, learning set; No. 26–35, testing set. MTS represents maximum tensile stress. TRF represents total reaction force.