An Advanced Approach for Computer Modeling and Prototyping of the Human Tooth KUANG-HUA CHANG, 1 SHEETALKUMAR MAGDUM, 1 SATISH C. KHERA, 2 and VIJAY K. GOEL 3 1 School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK; 2 Department of Operative Dentistry, College of Dentistry, The University of Iowa, Iowa City, IA; and 3 Department of Bioengineering, 5051C Nitschke Hall, The University of Toledo, Toledo, OH (Received 9 April 2002; accepted 17 February 2003) Abstract—This paper presents a systematic and practical method for constructing accurate computer and physical models that can be employed for the study of human tooth mechanics. The proposed method starts with a histological section prepa- ration of a human tooth. Through tracing outlines of the tooth on the sections, discrete points are obtained and are employed to construct B-spline curves that represent the exterior contours and dentino-enamel junction DEJ of the tooth using a least square curve fitting technique. The surface skinning technique is then employed to quilt the B-spline curves to create a smooth boundary and DEJ of the tooth using B-spline surfaces. These surfaces are respectively imported into SolidWorks via its application protocol interface to create solid models. The solid models are then imported into Pro/MECHANICA Struc- ture for finite element analysis FEA. The major advantage of the proposed method is that it first generates smooth solid models, instead of finite element models in discretized form. As a result, a more advanced p-FEA can be employed for struc- tural analysis, which usually provides superior results to tradi- tional h-FEA. In addition, the solid model constructed is smooth and can be fabricated with various scales using the solid freeform fabrication technology. This method is especially useful in supporting bioengineering applications, where the shape of the object is usually complicated. A human maxillary second molar is presented to illustrate and demonstrate the proposed method. Note that both the solid and p-FEA models of the molar are presented. However, comparison between p- and h-FEA models is out of the scope of the paper. © 2003 Biomedical Engineering Society. DOI: 10.1114/1.1568117 Keywords—Geometric modeling, Solid freeform fabrication, Finite element analysis, Human tooth. INTRODUCTION Many studies investigating the mechanical behavior of biological structures require the construction of three- dimensional 3D computer-aided design CAD and fi- nite element models. One of the most commonly em- ployed approaches in constructing 3D models is to digitize histological section images for discrete points and convert the data points to solid and finite element models using geometric modeling techniques. The sec- tion images can be obtained from different methods, in- cluding magnetic resonance imaging, computer tomogra- phy CT, or photographing the milled surface of a cast. 3,4,14,24 These methods have been applied to various bioengineering applications, including human spine 13,26 middle ear, 5 tooth, 8 etc. However, the validity of the 3D model constructed depends significantly on the geometric modeling technique employed, especially the accuracy and smoothness of the biomedical models it creates. Most of the previous work focused on creating h-version finite element models directly from the digitized data. The complexity of the modeling approach multiplies when it is applied to study human teeth, where the geo- metric shape of the dentino-enamel junction DEJ plays a critical role in determining the tooth strength and mechanics. 8 In tooth mechanics, it is critical to study the DEJ area where two very dissimilar tissues approximate each other and are bonded biologically. Though these tissues are very different, they do compliment and protect each other from the abuses of heavy and functional mastica- tory loads and yet, provide a cushioning type of sub- structure for absorbing the stresses and protect the vital pulpal tissue from bacterial attack by providing a selec- tively impermeable covering in the form of enamel. A study on the effect of the variation of the DEJ contour to stress distribution strongly suggested a relationship of the DEJ contour to the development of cervical lesions. 8 In Ref. 8, hexagonal solid finite elements of an h-version finite element analysis h-FEA software ANSYS 2 were used for creating the 3D tooth model. Instead of creating C 0 -continuous piece-wise linear surfaces in h-FEA for representing the exterior and DEJ geometric shapes of a human tooth, p-FEA will provide much smoother surfaces that represent the tooth geom- etry more accurately. Therefore, the p-FEA is especially attractive for applications with sophisticated geometry. One important reason is that there is no need to refine Address correspondence to Kuang-Hua Chang, PhD, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019. Electronic mail: khchang@ou.edu Annals of Biomedical Engineering, Vol. 31, pp. 621–631, 2003 0090-6964/2003/315/621/11/$20.00 Printed in the USA. All rights reserved. Copyright © 2003 Biomedical Engineering Society 621