目前脊椎內固定器已廣泛地使用在治療脊椎外傷、病變及退化等手術，其中椎弓足螺絲為脊椎內固定器的重要元件之一。但從醫學臨床中發現，在治療過程中脊椎內固定器發生失效（failure）的模式為椎弓足螺絲發生破裂（breakage），以及椎弓足螺絲與椎體產生鬆脫（loosening），而不同的骨螺絲幾何，也會影響骨螺絲之彎曲強度以及與椎體的結合強度，因此可以找出同時保有彎曲強度與拉出強度的椎弓足螺絲幾何是脊椎內固定器的設計重點之一。
本研究將利用有限元素法使用最壞情況（worst-case）來模擬骨螺絲的破壞與鬆脫情況，使用田口品質工程法與L25直交表來探討椎弓足螺絲幾何的重要參數，接著將使用線性迴歸與類神經網路來求得所需之彎曲強度與拉出強度之目標函數，並導入遺傳演算法中，利用適應方程式合併此兩種目標函數找出每個參數的最佳化範圍，本研究的目的為找出最佳化設計之椎弓足螺絲，並利用生物力學測試與四種市售椎弓足螺絲進行比較。
本研究結果顯示，單獨針對彎曲強度而言，圓錐起始位置與內徑為其重要的設計參數，若針對抗拉出強度而言，內徑、近端根部弧角半徑及節距是重要的設計參數；由類神經網路所求得之彎曲強度與拉出強度性質之目標函數，較線性迴歸所求得之目標函數，有較低的誤差，且與有限元素結果相關係數都相當接近1；經遺傳演算法的最佳化演算後，圓錐起始位置的最佳值為0mm、內徑為3.8mm∼4.06mm、近端根部弧角半徑為0.4mm、節距為3.3mm、近端傾斜半角為5°、螺牙厚度為0.1mm；於生物力學測試部分，最佳化椎弓足螺絲有最高的降伏強度（1085N）與疲勞壽命（大於一百萬次），其次為A-Spine骨螺絲（1008N，46529 cycle），且有限元素模擬之總應變能與降伏強度之相關係數為-0.866、最大張應力與疲勞壽命之相關係數為-0.909；而於拉出強度部分，Synthes骨螺絲於0.16 g/cm3及 0.32 g/cm3 密度之人造假骨中有最高的拉出強度（1014N，2148N），其次為A-Spine骨螺絲（975N，2068N），再其次為最佳化骨螺絲（826N，2009N），且與有限元素模擬之總反作用力之相關係數為0.929與0.988；由本研究所找出之最佳化椎弓足螺絲可以同時保有90％以上的彎曲強度與拉出強度，且本研究所建立之有限元素模型可以有效的預測生物力學測試。
關鍵字：椎弓足螺絲、有限元素法、田口品質工程法、線性迴歸、類神經網路法、遺傳演算法、生物力學測試

Spinal instrumentations have been widely used to treat spinal trauma, diseases, and degradation. Clinically, breakage and loosening of the pedicle screws are the most important problems for fixation failure. Pedicle screw design can affect the bending and the pullout strength substantially. Therefore design of the pedicle screws should consider both bending strength and pullout strength simultaneously.
The bending strength and pullout strength were contradictory to each other. The purpose of this study was to find the optimal design of the pedicle screw by multiobjective optimization methods. The worst case scenario in clinical conditions was simulated using finite element analyses. Taguchi method and L25 orthogonal array were used to create the set of learning data for artificial neural network (ANN) and then the contribution of each design parameter was calculated by analysis of variance (ANOVA). Artificial neural network (ANN) and Multiple Linear Regression (MLR) were used to develop two objective functions. Then genetic algorithm (GA) was used to obtain the optimal design of the screws. Then mechanical tests were conducted on four different commercial screws to validate the results of mathematical analyses.
The results showed that for bending strength, the initial position of conical angle (IP) was the most important factor and the second was inner diameter (ID). For pullout strength, the inner diameter (ID), proximal root radius (PRR) and pitch (Pi) were the most important design factors. As the objective functions, ANN could achieve better results for both bending and pullout strength than MLR. In GA section, the optimal values or ranges were 0 mm for IP, 3.8∼4.06 mm for ID, 0.4 mm for PRR, 3.3 mm for Pi, 5°for proximal half angle and 0.1 mm for thread width. The results of mechanical experiments showed the optimal screw had the highest yielding strength（1085N）and fatique life （over than one million cycle）, the second was A-Spine（1008N,46529 cycle）, total strain energy and maximal tensile stress in finite element analysis were closely related to yielding strength（r = -0.86）and fatique life（r = -0.909）.For pullout strength in 0.16 g/cm3 and 0.32 g/cm3 foam bone, Synthes screw was the highest （1014N, 2148N）and the second was A-spine （975N, 2068N）, and the optimal screw was the third（826N, 2009N）respectively. And the total reaction force in finite element analysis was closed relate to the pullout strength（r = 0.929 and r = 0.988 for different foam densities）.
The optimal screw from our method had a high performance for both the bending strength and pullout strength, over than 90% of the highest value. The finite element analyses could reliably predict the results of mechanical test.

Key Words: Pedicle Screw, Finite Element Analysis, Taguchi method, Linear regression, Artificial Neural Networks, Genetic Algorithms, Biomechanical test

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