Marko VESELINOVIC1, Dalibor STEVANOVIC1, Miroslav TRAJANOVIC1, Miodrag MANIC1, Stojanka ARSIC2, Milan TRIFUNOVIC1, Dragan MISIC1
1Faculty of Mechanical Engineering, Universityof Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia
2Faculty of Medicine, Universityof Nis, Blvd. Dr Zorana Djindjica 81, 18000 Nis, Serbia
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Abstract: This paper presents the application of geometric modeling techniques in the process of creating 3D surface model of the human tibia. In order to create valid CAD (computer-aided design)model, the accurate definition of geometry and topology of tibia’s entity is essential. Therefore, geometrical model was created based on anatomical and morphological properties of the human tibia.Proposed process of creation tibia’s geometrical model contains several steps: importingand editing the CT (computer tomography) model in CAD software, recognition and defining of geometrical entities, and creation of adequate surface model. From the morphometric point of viewthis approach allows creation of more accurate models than the use of standard modeling techniques.
Key words: 3D surface model, tibia, reverse modeling, reverse engineering, CAD
- INTRODUCTION
In orthopedic surgery, but alsoin all other sub-branches of surgery, where the needfor creation of customized implants or fixators exists, there is a specific requirement to know the exact geometrical model of the human bone. Therefore, it is very important to create geometry of the bone rapidly and accurately. Usually, the techniques of reversemodeling (RM) are used to define the exact geometrical model of bones. Having such models, it is possible to build customized bone implants and fixators using rapid prototyping technologies.
There are few different approaches for creating 3D surface model of human bones. Some of them are applied for creating 3D surface model of bones other than tibia, e.g. femur. Nevertheless, they are presented in this paper, because method used for one human bone, can be used for some other.
First approach is based on deforming the sample of thehuman bone shape according to an input X-ray image. In this example template shape is solid model, but the same method could be used for creating 3D surface model.Disadvantages ofthis method are about dealing with X-ray images, e.g. inaccuratepatient positioning, and possible less accurate 3D model than by using CT [7,8].3D model (solid or surface) created with this approach does not have precisely defined geometric entities (points, planes, spline curves, etc.). This is the main disadvantage of this method compared with method used in this paper. Furthermore, using method with defined geometric entities, accuracy of the 3D surface modelcan be controlled(if there are more planes for cross-sections, more spline curves will be created, and obtained model will be more precise).
Secondapproach for creating 3D surface model is by using curves which are in relation with CT slices [9,10]. This is disadvantage of the second approach compared with method from this paper, which can use differently oriented curves (curves which are not strictly linked to CT slices).
For creating 3D model of femur, approach defined in [11] use curves obtained from different cross-sections. In this paper curves are obtained from cross-sections which are in relation with mechanical axis and 3 main parts of tibia (proximal end, tibial shaft or distal end).
In this paper the method of characteristic regions for creating 3D surface model of the human tibiais presented.This method is based on anatomical and morphological properties of the bone.
- INPUT DATA
The radiology image of the bone, which is often called rawdatain CAD terminology, represents input data for RM.The sample of tibia wasscanned by CT in resolution of 0.5mm.The raw data, that is coordinates of the points of scanned bone, were imported into appropriate CAD software for reverse modeling. The CT scans were obtained fast, but in a low resolution (in terms of RM). That affected on accuracy of some details in the 3D digital model, but not on accuracy of the total bone morphology. In addition, CT scans contained internal bone tissue structures,as well as the other type of the surrounding soft tissues.That is the reason why these scans required considerable time for model post processing (“for cleaning and healing the model”).
- REVERSE MODELING
Reverse modeling of a human bone’s geometry using CAD software means generating digital 3Dmodel of bone’s geometry from radiology image (X-Ray, CT, MRI).In this particular case, CATIA V5 R19 CAD software and its modules were used. Importing the rawdata into the CAD system results in generating ofone or more clouds of points (discrete points of the bone, which are scanned by some of radiology methods). In the next phases of reverse modeling, thegeometrical features of higher order (curves and surfaces) are designed.
The process of creating model of tibia was based on the processes that are described in [1,2].
- Importing and editing (filtering, aligning, etc.) of clouds of points.
- Tessellation of polygonal model (mesh) bycreating a huge number of small triangularplanar surfaces between the points in thecloud, as well as editing of polygonal model.
- Recognition and defining theReferential Geometrical Entities(RGEs)and it’scorrelation with tibia anatomy(Fig. 2).
- Creating anatomical points and spline curves in the defined planes (Fig. 3).
- Creating the 3D surface model oftibia using obtained spline curves (Fig. 4).
- THE 3D SURFACE MODEL OF THE HUMAN TIBIA
Situated at the medial side of the leg, tibia, excepting the femur, is the longest bone of the skeleton. It has a body and two extremities,proximal and distal. Proximal end of the tibia has a broad superior articular surface which articulates with the femur. The shaft has prismoid shape with three surfaces and three margins. The anterior margin, the most prominent of the three, commences above at the tuberosity, and ends below at the anterior margin of the medial malleolus. Distal end of the tibia, much smaller than the upper,is prolonged downward on its medial side as a strong process, the medial malleolus.Its inferior articular surface is quadrilateral, and smooth for articulation with the talus [3,4] (Fig. 1).
4.1.Recognition and defining the RGEs
In the case of the tibia, the mechanical axis is a line from the center of the tibial plateau (interspinous intercruciate midpoint) extending distally to the center of the tibial plafond. [5]
The tibial plateau (proximal/superior articular surface) was approximated with ellipse, which was best solution compared with all other tested entities: circles, spline curves, etc. The first point of mechanical axis is center of the ellipse, which is approximately equal with center of tibial spines notch [5]. Second point is center of the tibial plafond (distal/inferior articular surface) which was approximated with adequate lower cross-section of distal end of tibia (Fig. 2).
Next step was creation of ten planes based on mechanical axis and anatomical landmarksof tibia. These planes were used for the creation of the cross-sections.
a)b)
Fig.1. Right tibia and fibula, a)Anterior view, 1. Medial condyle, 2. Lateral condyle, 3. Tibial tuberosity, 4. Lateral surface, 5. Anterior margin of tibia, 6. Medial surface, 7. Lateral margin of tibia, b) Posterior view, 1. Intercondylar tubercles of intercondylar eminence, 2. Fibula, 3. Medial margin of tibia, 4. Posterior surface, 5. Medial malleolus, 6. Lateral malleolus [3]
Fig.2. RGEson polygonal model of theright tibia
4.2.Creating anatomical points and spline curves
The intersections of planes and polygonal model of tibiaproduces contour curves (cross-section contour).These curves wereused for creating points and spline curves (Fig. 3).
Obtained spline curves were used for creation of the proximal end of tibia surface model(Fig. 4).The expanded proximal end is a bearing surface for body weight, which is transmitted through the femur. It consists of medial and lateral condyles, with intercondylar eminence and anterior and posterior intercondilar area between and the tibial tuberosity, on the anterior surface [6].
The same procedure was applied for creation of 3D surface model for thedistal end of tibia (Fig. 6).The slightly expanded distal end of the tibia has anterior, medial, posterior, lateral and distal surfaces. It projects inferomedially as the medial malleolus. The distal end of the tibia, when compared to the proximal end, is laterally rotated (tibial torsion). The short thick medial malleolus has a smooth lateral surface with a crescentic facet that articulates with the medial surface of the talus [6].
For tibial shaft (Fig. 5), set of nineteen planes was used. These planes are perpendicular to themechanical axis.The shaft is triangular on the cross section and has three surfaces: medial, lateral and posterior, separated with three margins: anterior, lateral and medial [6].
Fig.3. Points and spline curves on proximal end of tibia
Fig.4. Creation of the 3D surface model of the proximal end of tibia
Fig.5. 3D surface of shaft of tibia
Fig.6. 3D surface of the distal endof tibia
4.3.Creating 3D surface model of tibia
3D surface model of tibia was created by merging 3D surfaces of proximal end, shaft and distal end of tibia (Fig. 7).
Problem whit this approach is alignment of these tibial parts during merging. This requires approximations of 3D surface modelsof tibial parts on places where they should be connected.
- CONCLUSION
Reverse modeling and reverse engineering provide all necessarytools for design of 3D surface model of bone and rapid prototyping of customizedimplants and fixators.
Application of bone reverse modeling method based onRGEs, enables building of high quality 3D surface model usingCT scans as raw data. It is necessary to know anatomy of the bone for recognition and defining the RGEs.
Disadvantage of the method of characteristic regions is bad alignment of created 3D surface models of tibial parts during merging.
a) b)
Fig.7. 3D surface model of the right tibia, a) anterior view, b) posterior view
ACKNOWLEDGMENTS
This paper is part of project III41017 Virtual human osteoarticular system and its application in preclinical and clinical practice, funded by the Ministry of Education and Science of Republic of Serbia, for the period of 2011-2014.
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