34th INTERNATIONAL CONFERENCE ON
PRODUCTION ENGINEERING
28. - 30. September 2011, Niš, Serbia
University of Niš, Faculty of Mechanical Engineering
METHOD FOR CREATING 3D SURFACE MODEL OF THE HUMAN TIBIA
Marko VESELINOVIC1, Dalibor STEVANOVIC1, Miroslav TRAJANOVIC1, Miodrag MANIC1, Stojanka
ARSIC2, Milan TRIFUNOVIC1, Dragan MISIC1
1
Faculty of Mechanical Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia
2
Faculty of Medicine, University of Nis, Blvd. Dr Zorana Djindjica 81, 18000 Nis, Serbia
veselinovic_marko@yahoo.com, dalibor.stevanovic85@gmail.com, traja@masfak.ni.ac.rs,
miodrag.manic@masfak.ni.ac.rs, stojanka@medfak.ni.ac.rs, draganm@masfak.ni.ac.rs
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: importing and 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 view this 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
1. INTRODUCTION
In orthopedic surgery, but also in all other sub-branches
of surgery, where the need for 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
reverse modeling (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 the
human 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 of this method are about dealing with Xray images, e.g. inaccurate patient 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 model can be
controlled (if there are more planes for cross-sections,
more spline curves will be created, and obtained model
will be more precise).
Second approach 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 tibia is presented.
This method is based on anatomical and morphological
properties of the bone.
2. INPUT DATA
The radiology image of the bone, which is often called
raw data in CAD terminology, represents input data for
RM. The sample of tibia was scanned 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”).
3. REVERSE MODELING
Reverse modeling of a human bone’s geometry using
CAD software means generating digital 3D model 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 raw
data into the CAD system results in generating of one 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, the geometrical 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].
1. Importing and editing (filtering, aligning, etc.) of
clouds of points.
2. Tessellation of polygonal model (mesh) by creating a
huge number of small triangular planar surfaces
between the points in the cloud, as well as editing of
polygonal model.
3. Recognition and defining the Referential Geometrical
Entities (RGEs) and it’s correlation with tibia anatomy
(Fig. 2).
4. Creating anatomical points and spline curves in the
defined planes (Fig. 3).
5. Creating the 3D surface model of tibia using obtained
spline curves (Fig. 4).
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]
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 landmarks of tibia. These planes were
used for the creation of the cross-sections.
Fig.2. RGEs on polygonal model of the right tibia
4.2. Creating anatomical points and spline curves
The intersections of planes and polygonal model of tibia
produces contour curves (cross-section contour). These
curves were used 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 the distal 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 the mechanical 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.5. 3D surface of shaft of tibia
Fig.3. Points and spline curves on proximal end of tibia
Fig.6. 3D surface of the distal end of 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 models of tibial parts on places where they should
be connected.
5. CONCLUSION
Fig.4. Creation of the 3D surface model of the proximal
end of tibia
Reverse modeling and reverse engineering provide all
necessary tools for design of 3D surface model of bone
and rapid prototyping of customized implants and
fixators.
Application of bone reverse modeling method based on
RGEs, enables building of high quality 3D surface model
using CT 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 20112014.
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