A New Method to Develop the Finite Element Model
of the Bones in the Hand from CT Scans

Suneel Battula, Glen O. Njus
The University of Akron
325 Buchtel Ave
Akron, OH 44325
Abstract— There is a need for biomechanical computer models
that can qualitatively and quantitatively generate an accurate
representation of the patient’s condition. Such a model of the
hand was developed using Computerized Axial Tomography (CT)
scans from a cadaver hand. CT and Magnetic Resonance (MR)
scans of a cadaver hand glued to a polycarbonate box were
acquired in the axial orientation. The bones from the CT images
were segmented using edge detection technique. The point cloud
of the individual bones in millimeter coordinates was fitted with
curves. A solid surfaces fitted to the curves were assembled to
build a Finite Element (FE) model comprising of the bones of the
hand.
model, Fig. 2, are: (a) to acquire the CT and MR images of the
cadaver hand, (b) to segment the phalanges, carpals,
metacarpals, radius and ulna, (c) to create a solid model from
the segmented objects and (d) to fit a finite element model to
the solid surface model.
I. INTRODUCTION
The injuries of the hand often result in the reduction of the
functionality of the hand. The complexity of the hand makes it
difficult to predict the consequences of these injuries. Thus,
there is a need for biomechanical computer models that can
predict the consequences of the hand injuries by relating
individual anatomical structures and the interactions between
them [1].
A. Significance of the Study
The physicians need a quantitative model that outputs an
accurate representation of the patient’s condition. The
quantitative model is better than a qualitative model because
the computer interprets the results from the CT and MR
images and comes up with an output, which is more
reproducible than human interpretation. The model may have
its applications in surgical planning, medical treatment and
rehabilitation strategies.
B. Anatomy of the Hand
The skeleton of the upper extremity consists arm, forearm
and the hand. The hand is the manual part of the upper limb
distal to the forearm. The forearm consists of ulna and the
radius and the hand consists of carpals in the wrist,
metacarpals in the hand proper and phalanges in the digits,
Fig. 1, [2].
C. Model Development
The significant steps involved in the development of the
Fig.1. Basic skeletal anatomy of the hand [2]
II. METHODS
A. Image Acquisition
A cadaver hand, of an African-American of unknown age,
approved by an orthopedic surgeon to be with normal anatomy
with no rheumatoid was selected for image acquisition. CT
scans, in axial orientation, with 3.75mm slice thickness were
obtained from the cadaver hand glued to the polycarbonate
box.
B. Segmentation
“Image segmentation is the separation of the structures of
interest from the background and from each other” [3]. The
regions of interest in our research are the bones that have a
distinct intensity value. The objective of the segmentation can
be defined as to obtain the segmented edges of the bones of
Specimen
Image
Acquisition
Finite
Element
Model
Solid Surface
Model
Segmentation
Curve Fitting
Fig. 2. Steps involved in the development of the model
the hand.
(a)
1
1
1
1
-2
1
-1
-1
-1
(b)
(c)
Fig. 3. (a) A slice of the original CT scans. (b) One of the “Templates” or the
masks used for the edge detection [4]. (c) Segmented (edge detected) image.
(a)
(b)
Fig 5 “Lofting” the curves using IDEAS (a) Wire-frame fitted to the
curves (b) Solid surface model fitted to the wire-frame
The bones were separated from the background, Fig. 3(a, c),
using edge detection techniques, as these are the simplest
methods to separate an object from its background. The
technique utilizes the masks, also called templates, and the
neighborhood of a pixel to determine the intensity value of that
pixel, Fig. 3(b) [4]. The neighborhood of a pixel is defined as
a 3 x 3 region with the concerned pixel at the center. The
resultant pixel intensity can be calculated as:
E. Finite Element Model
All the bones were assembled together, Fig. 6(a), to define
the solid surface model of the skeletal anatomy. Joints between
the bones were then developed using the loft feature of
IDEAS. Each of the bones and joints were assigned with
material properties based on the following equation:
q 9
(1)
G   i p  mq
q 1
C. Curve Fitting
The edges of the bones in each slice comprised of the x and
y coordinates making them two-dimensional data points. To
represent these two-dimensional data points in a threedimensional coordinate system a z-coordinate was assigned to
each of the slices as a multiple of slice thickness Fig. 4(a).
The data points were then fitted with Freeform Closed Curves
based on the Non-uniform Rational B-Spline (NURBS)
mathematics Fig. 4(b). There were some knots and intersecting
lines in the curves that had to be eliminated by not considering
the data points causing them during the curve fitting. This was
necessary as the knots and intersecting lines would cause
errors during the surface fitting.
D. Surface Fitting
The curves were then imported to SDRC-IDEAS (CAD
software), which has a powerful library of functions, using the
loft function. Wire-frame structure, Fig. 5(a), was fitted with
the loft function using splines to interconnect the curves. Solid
surfaces were fitted to the wire-frame to check for jagged
edges and unfilled gaps in the surface Fig. 5(b).
E  2G (1   )
(2)
A solid mesh of three-dimensional tetrahedral elements was
then fitted to each of the regions representing the bones and
joints, Fig. 6(b). Model equations were solved and a FE model
was simulated.
(a)
(b)
Fig. 6. (a) Wire-frame structure of the assembly of bones. (b) FE Model
of a finger fitted with a solid mesh and assigned with material properties.
III. FUTURE WORK AND LIMITATIONS
The above model does not incorporate the ligaments,
tendons and other soft tissue as the MR scans acquired were
not satisfactory. In the future, high-resolution MR images can
be used to incorporate the above structures. The bones were
only assigned with cortical bone material properties, in the
future cancellous bone properties can also be incorporated.
IV. REFERENCES
J.B.Antoine Maintz and Max A. Veirgever, “A survey of Medical image
registration,” Medical Image Analysis, Vol. 2, No. 1, p 1-36, 1998.
[2] Gerard J. Tortora and Sandra R. Grabowski, Principles of Anatomy and
Physiology, Biological Sciences Textbooks, Inc., A & P Textbooks,
Inc.,  1995 John Wiley & Sons, Inc.
[3] Nicholas Ayache, “Epidaure Research Project,” INRIA Sophia
Antipolis, France  2002.
[4] Werner Frei and Chung Chen, “ Fast Boundary Detection: A
Generalization and a New Algorithm,” IEEE Transactions on
Computers, October 1977.
[1]
(a)
(b)
Fig. 4. (a) Slices assigned with three-dimensional coordinates. (b) Freeform
Closed Curves (NURBS) fitted to the data points representing the bone edges