Modeling of Kinematic Parameters of a Healthy Tibia by PLS

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1 , pp Modeling of Kinematic Parameters of a Healthy Tibia by PLS Haiyan Qiang 1, Jiangwei Wu 1, Yougang Sun 1, 2 and Yuhui Shen 3 1 Logistics Engineering College, Shanghai Maritime University, Shanghai, School of Mechanical Engineering, Tongji University, Shanghai, Ruijin Hospital affiliated to Shanghai Jiaotong University, Shanghai, hyqiang@shmtu.edu.cn Abstract. Body of a human being is an etremely complicated system and the knee joint is the biggest joint in human s body. In this paper, attention will be mainly paid on the tibia of the knee joint. RSA method is a new way to get the kinematic parameters in three-dimensional directions. PLS method is applied to find the relationship between the knee joint and the skin markers and a regression model had been built. Keywords: Tibia, RSA, Multi-variable, PLS regression method 1 Introduction Body of a human being is an etremely complicated system. There are many researches on the 3D modeling and skeleton kinematics of human beings. Delp et al. [1] had built a model of the lower musculoskeleton. EM Aronold [2] built a new model of the lower musculoskeleton based on Delp s model. Tang G [3] [4] simulated and analyzed biomechanics for typical movements of human. Meanwhile much attention has also been paid on 3D modeling and kinematical analysis of knee joint which is the biggest the joint in human s body. MJ Sun et al. [5] had already measured the geometric dimension of the knee joint. Y Wang et al. [6] had built a 3D model for the knee joint. Sonia Duprey [7] had built kinematics estimation from skin markers on lower limb. But thorough understanding of the knee joint is still incomplete. In this paper, attention will be mainly paid on the tibia of the knee joint. 2 RSA and PLS Methods Roentgen Sterephotogrammetric Analysis (RSA)[8] combined with finite element method is a new way on knee joint researches and the kinematic parameters of the knee joint and the skin markers can be got in three-dimensional directions. Then, the partial least square (PLS) method is applied to fine the relationship between the knee joint and the skin markers and a regression model can be built. The RSA method helps to obtain the positional information of the bones and the skin markers while the ISSN: ASTL Copyright 2016 SERSC

2 PLS method helps to simplify and obtain the relationship between the bones and the skin makers. The regression model can predict the situation of the bones in the knee joint by the kinematic parameters collecting from the skin markers. 3 Eperimental Procedures A healthy male volunteer (age: 32 years; height: 1.76 m; mass: 72.5kg) participated in this study. The volunteer s right tibia was chosen to be a research object. Si skin markers were mounted onto the tibia which was shown in Fig. 1. In order to improve accuracy, markers were divided into groups. In the process of the eperiment, marker12 lost some data and focus will be paid on the marker 7, marker 8 and marker 9. A RSA correction bo was used to capture the continuous motion of the tibia and the si markers while bending and stretching by thirty eposures per second with eposure time of 0.1ms each time. (Figure 2) Fig. 1. Position of the markers Fig. 2. Eposed by X ray 132 Copyright 2016 SERSC

3 4 Computational Methods and Data Analysis 4.1 Parameter Set The motion of tibia in X, Y and Z directions can be defined as response variables and can be denoted as y 1, y2 and y 3. The motion of skin markers in X, Y and Z directions can be defined as predictor variables and can be denoted as 1, 2, 3, 4, 5, 6, 7, 8 and 9. There would be nine predictor variables which would do harm to the regression model. So, the center of gravity of spatial triangles had been found to simplify the predictor variables by the data in the eperiment. And the new variables are c 1, c2 and c3. The parameters with different units and magnitude should be standardized to eliminate the influence of dimension, which would make the parameter analysis more reasonable. The motion parameters were standardized by equation 1. * ij j i 1,2, L, b ij, j 1,2, L, p s j (1) 4.2 Regression Model Regression model of can be list in equation 2. (2) A function can be created by the former standardized variable t h. and component (3) The PLS regression model can be built as follow. (4) Where rh represents the regression coefficient. Copyright 2016 SERSC 133

4 5 Results To improve the accuracy of the regression equation model was taken as coordinate value to draw the prognostic map of all sample points. was the kth variable, was the predicted value of the ith sample point. As it was shown in Fig 3 and Fig 5, the asterisk was a two-dimensional point combined with the eperimental value and the fitted value. It was clear that the asterisks were not equally distributed and the imitative effect of the equation was not satisfactory. The accuracy of the model should be improved. As it was shown in Fig. 4, it was clear that the asterisks were equally distributed and the imitative effect of the equation was satisfied. The accuracy of the model was quite ideal. Fig. 3. Predicted value in X direction Fig. 4. Predicted value in Y direction 134 Copyright 2016 SERSC

5 Fig. 5. Predicted value in Z direction 6 Conclusions PLS method was applied in this paper, and it had solved the modeling problem of muti-response variables to multi-predictor variables. The structure of the data had been simplified and the multi-dimensional data can be observed in two-dimensional data. Acknowledgements. Part of this work is supported by Shanghai Natural Science Foundation Project (10ZR ), medical-engineering cross fund of Jiaotong University (YG2011MS10). The authors acknowledge the support from the students, Gaoiang Yuan, Wenjia Hua for their assistance in the eperiments and measurements. References 1. Delp, S.L., Loan, J. P., Hoy, M. G.: An interactive graphics-based model of the lower etremity to study orthopaedic surgical procedures [J]. IEEE Transactions on Biomedical Engineering 1990, 37(8), Arnold, E., Ward, S., Lieber, R.: A Model of the Lower Limb for Analysis of Human Movements [J]. Annals of biomedical engineering 2010, 38(2), Tang, G.: biomechanics simulation analysis for typical movements of human [D]. Shanghai: Jiaotong University, 2011: Tang, G.: A muscle-path-plane method for representing muscle contraction during joint movement. Computer Methods in Biomechanics and Biomedical Engineering. 2010, 13(6): Sun, MJ., Wang, HL., Zhang, Y.: Measurement and geometric parameter for Chinese people s knee joint., Journal of Med Chin PLA, 2002;27(12): Wang, Y., Zhou, FH., Zhoul, YG.: 3D measurement and related researches on Chinese people s knee joint.,journal of Chin Orthopedic Surgery. 2004;12(8): Copyright 2016 SERSC 135

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