Computational and Mathematical Methods in Medicine

Volume 2015, Article ID 574132, 10 pages

http://dx.doi.org/10.1155/2015/574132

## The Parametric Model of the Human Mandible Coronoid Process Created by Method of Anatomical Features

^{1}Faculty оf Mechanical Engineering, University of Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia^{2}University of Qadisiya, Diwaniya, Iraq^{3}Faculty of Medicine, University of Niš, Dr. Zorana Đinđića 81 Boulevard, 18000 Niš, Serbia

Received 11 January 2015; Accepted 15 April 2015

Academic Editor: Ezequiel López-Rubio

Copyright © 2015 Nikola Vitković et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Geometrically accurate and anatomically correct 3D models of the human bones are of great importance for medical research and practice in orthopedics and surgery. These geometrical models can be created by the use of techniques which can be based on input geometrical data acquired from volumetric methods of scanning (e.g., Computed Tomography (CT)) or on the 2D images (e.g., X-ray). Geometrical models of human bones created in such way can be applied for education of medical practitioners, preoperative planning, etc. In cases when geometrical data about the human bone is incomplete (e.g., fractures), it may be necessary to create its complete geometrical model. The possible solution for this problem is the application of parametric models. The geometry of these models can be changed and adapted to the specific patient based on the values of parameters acquired from medical images (e.g., X-ray). In this paper, Method of Anatomical Features (MAF) which enables creation of geometrically precise and anatomically accurate geometrical models of the human bones is implemented for the creation of the parametric model of the Human Mandible Coronoid Process (HMCP). The obtained results about geometrical accuracy of the model are quite satisfactory, as it is stated by the medical practitioners and confirmed in the literature.

#### 1. Introduction

Geometrical models of human bones are of great importance in today’s medicine, as well as in anthropology and other related disciplines. Computer-Assisted Surgery (CAS) is one of the most common applications of computer generated geometrical models, as stated by Adams et al. in [1]. The application of geometrically precise models enables surgeons to properly prepare and perform interventions with use of suitable computer software tools and/or other techniques, and it lessens the possibility of error occurrence. The comparison of conventional methods and CAS is presented in [2] by Bäthis et al., where the Total Knee Arthroplasty (TKA) process is shown. Based on the facts stated in [2], we can conclude that the new technique of performing surgical procedures, that is, surgical interventions, may significantly improve both the quality of the procedure itself and the patients’ convalescence.

The preoperative planning of surgical procedures and interventions is an important part of CAS. Preoperative planning most often implies the use of suitable human organ models in specific software which enables a surgeon to plan the course of surgical procedure up to a specific level defined by limitations of the applied software. The application of preoperative planning in the case of mandible reconstruction is presented in [3] by Essig et al. and in [4] by Chapius et al.

Geometrical models of human bones created as aforementioned may find their use in the area of virtual anthropology (VA). VA is an area which extends comparative morphology but implies introducing and establishing interconnection among anthropology, mathematics, statistics, engineering, and other areas of science and technology directed to digitalization of observed objects fossil specimens (e.g., bones). Students of anthropology, as well as practitioners, can learn necessary information from precise geometrical models of bones. A detailed description of virtual anthropology, along with the description of methods and techniques applied in this area of research, is provided in [5] by Weber and in [6] by Benazzi et al., in the case of mandible reconstruction.

The basic mandible reconstruction can be performed based on volumetric methods of scanning (Computed Tomography (CT), Magnetic Resonance Imaging (MRI), etc.) as presented in [5, 6] as well as by direct methods of Computer Aided Design (CAD) [5].

Volumetric methods of scanning imply the use of scanner to form volumetric model by the application of different techniques and methods described in detail in [6]. Basically, this is the reverse engineering procedure and contains multiple actions. The first step is to form 2D image (slice) of human body on volumetric scanner. By superposition of provided slices a volumetric image of scanned object (patient) is formed, comprised of volumetric elements (voxels). By further process of segmentation, a detailed bonding of anatomical entities along the whole volume of the scanned model is performed, as shown in [7] by Archipa et al. Segmentation can be a very complex process, and lots of studies have been done to solve problems with feature extraction, like it is described in [8] by Huang et al. for the automatic extraction of the vertebral column from the SPECT (Single-Photon Emission Computed Tomography) scan of the whole body. Through an adequate process of volumetric rendering, a reconstructed 3D model of the scanned object is acquired [9]. Volumetric rendering implies shading of projected 3D scalar field (cloud of points) onto 2D, that is, the computer screen, and it is applied in various areas of computer graphics, as described in [10] by Li et al. Based on created 3D scalar field (initially segmented volumetric model comprised of voxels), by application of an adequate algorithm, such as marching cubes algorithm which is described in [11] by Lorensen and Cline, a polygonal model (mesh) of scanned object can be constructed. Polygonal model can be further used in CAD software packages for creation of surface and volume models, as presented in [12] by Tufegdžić et al. Such models are constructed based on geometry of a specific patient, and, thus, they can be used to create implants and fixators adjusted to the patient, in preoperative planning, intraoperational navigation, and so forth.

Direct modeling implies the creation of models by use of technical elements of CAD software packages. This sort of modeling does not use scanned models; modeling is performed based on information in the form of images, instructions, and presentational models (models of bone and joint system). The geometrical and anatomical accuracy of the models created by the application of these methods is less than the accuracy of models created by the reverse engineering methods. Thus created models can be used for training students and medical practitioners, for the creation of presentational models by use of additive technologies, which are described in [13] by Salmoria et al. and in all other applications where there is no need for geometrical models of great precision.

Creation of geometrical models of human bones, mandible included, can be performed based on predictive models. Predictive models (most often parametric models) are models whose geometry and topology can be adjusted to a specific patient, based on specific parameters (most commonly morphometric, but also others, such as height and weight). Morphometric parameters are acquired from 2D images (X-ray) or from volumetric models obtained by a volumetric scanning method (CT, MRI) [5, 6]. Such models can be very precise, if a number of parameters are adequate and the model structure itself is well chosen (e.g., containing parametric surfaces like NURBS surfaces). These models can be used for many purposes: creation of implants and fixators, preoperative planning, creating geometrical models of the missing parts of bones, and so forth.

It is important to mention that predictive models are created not only for the human bones, but also for the other parts of the human body (or even whole body). In [14] by Li et al. prediction of the deformations and movements of body organs/tissues and skeletal structures using patient-specific nonlinear biomechanical modeling from whole body CT image registration is presented. Besides volumetric internal scanning methods (CT, MRI, etc.), there is a possibility of creating predictive human body or parts of the body models based on the various types of the 3D measurements, like it is shown in [15] by Wuhrer and Shu and also by Leong et al. in [16]. These research studies enable feature extraction and prediction of the shape of the human body’s anatomical section, as demonstrated in the example of reconstruction of the human torso in [16]. Deformable statistical whole body model which can be adapted to the single 2D image is presented in [17] by Chen et al. Model presented in [17] can be applied for the creation of whole body meshes or clothed 3D meshes for different people, neither of which appears in the training dataset.

In this paper Method of Anatomical Features (MAF), which was introduced in [18] by Vitković et al. and in [19] by Majstorovic et al., is implemented for the creation of the parametric (predictive) model of the Human Mandible Coronoid Process (HMCP). The MAF was originally applied for the development of the parametric and surface models of the human femur and tibia, and the results are quite satisfactory, as presented in [18, 19]. The main objective of this research is to show that MAF can be applied for other types of human bones, not just for the long bones. The HMCP was chosen because of its complex geometric and topological properties, and it is adequate anatomical section for the creation of prototype (test) parametric model. MAF was tested on prototype model and the results are more than promising. The research will be continued for the creation of the parametric model of the whole human mandible, so that the geometrical and anatomical correctness of the whole model can be confirmed.

#### 2. Material and Methods

For the geometry analysis of the human mandible, ten (10) mandible samples were scanned (input training set). The samples were made by 64-slice CT (MSCT) (Aquilion 64, Toshiba, Japan), according to the standard protocol recording: radiation of 120 kVp, current of 150 mA, rotation time of 0.5 s, exposure time of 500 ms, rotation time 0.5 s, thickness of 0.5 mm, image resolution 512 × 512 px, and pixel size approximately 0.36–0.42 mm, 16 bits allocated and stored. The samples came from Serbian adults, intentionally including different gender and age: six male samples aged 25–67 and four women samples aged 22–72, of different height and weight, which have been previously scanned (because of trauma or some disease). It was assumed that this diverse set of samples could present quite a diverse morphology of the very same bone. These samples are used for the creation of the parametric model of the human mandible. The process of creation of parametric model for femur and tibia by using MAF is presented in [18, 19] in detail, but here the short introduction of the method is shown.

The process of creation of parametric model of the human bone (MAF method) is presented in Figure 1 and it contains several steps:(i)Creation of anatomical model, morphologically and anatomically defined descriptive model of human bone. This model defines where some anatomical feature on the physical model of the bone is and its morphometrical and geometrical relations to other anatomical features.(ii)RGE creation. The basic prerequisite for successful reverse modelling of a human bone’s geometry is identification of referential geometrical entities (RGEs). Usually, these RGEs include characteristics, points, directions, planes, and views, as presented in [18, 19].(iii)Creation of spline curves. Spline curves are created by the use of RGEs and additional geometry. How curves are created depends on the shape of anatomical feature and its relation to other anatomical features.(iv)Creation of anatomical points. Anatomical points can be created on spline curves and/or anatomical landmarks. Anatomical points created on spline curves can be positioned in two distinctive ways. First, they can be distributed evenly on the curve or they can be positioned in correspondence to some anatomical landmark. For example, anatomical point can be placed on gnathion of mandible.(v)Measurement of anatomical points coordinates values for defined number of specimens. Values of coordinates are measured on each sample of mandible model in 3D. Values of morphometric parameters (defined in the step of anatomical model creation) are measured on the same 3D models.(vi)The measured data which is processed in mathematical software by using multilinear regression as the tool for statistical analysis.(vii)Parametric equations (functions) which define relations between morphometric parameters and coordinate values. The created parametric model which consists of a set of parametric equations is a predictive model. This means that, for every next patient, it is enough to measure the same morphometric parameters on scanned mandible and to calculate coordinates of points. The resulting model is cloud of calculated anatomical points which can be imported in any CAD software (e.g., CATIA).