Generation of Three Dimensional Finite Element Bone Models From CT Scan Datasets Kieran M. Pearse, Michael A. McCarthy
[email protected],
[email protected] Mechanical & Aeronautical Engineering Department, University of Limerick, Limerick, Ireland.
Abstract Taken as a contiguous set CT scans are essentially three dimensional even though an individual scan is two dimensional. Therefore by applying surface detection methods to a set of scans a true three dimensional geometry model of a scanned internal human body structure of interest can be produced. This current research addresses this issue and outlines a program capability developed at the University of Limerick to extract bone geometry from CT scan datasets for the purpose of creating three dimensional finite element bone models. The program developed is called LIMEX and runs on a Silicon Graphics workstation platform. It enables the bone boundary to be detected in the individual scans by surface extraction techniques, and outputs this bone geometry in the form of a session file to interface with the finite element pre-processor Patran.
1. Introduction Computerised tomography or CT is an imaging modality that creates transverse slices of the human body by means of a CT scanner. CT scans are essentially three dimensional when taken as a contiguous set even though each scan is two dimensional. By applying surface detection methods to a set of scans a three dimensional geometric model of an internal body structure of interest such as a bone can be produced. This paper addresses this problem and outlines a capability to extract bone geometry from CT scan datasets for the purpose of creating three dimensional finite element bone models. Such a capability was devised at Cornell University in 1989 by McCarthy [1] to run on a Silicon Graphics workstation (SGI) platform. However since then the SGI operating system has changed considerably and the abilities of CT scanners have been enhanced greatly. Therefore this research was undertaken to re-investigate some of the issues involved in geometry extraction from CT and to create a facility at the University of Limerick to extract bone geometry from CT scan datasets which would be available to bioengineering researchers at the University of Limerick. This geometry extraction program is known as LIMEX. The medical and non-medical related applications of this potential to create three dimensional models are numerous. The main purpose of providing the facility at the University of Limerick is for computational studies of body structures. Finite element models of body parts using CT images is not a new concept and have become more and more common especially with the development of computational capabilities [2]. The main advantage of using CT in building these models is that it gives a very accurate definition of geometry. However the application potential of a program such as LIMEX is not restricted to finite element modelling. The ability to use CT scans to generate three dimensional models for the design of custom implants is an important concept in biomedical engineering. Such procedures have been reported widely from orthopaedic centres such as the Royal Orthopaedic Hospital [3]. Another potential use is as a tool in preoperative surgical planning. This has been demonstrated by Caponetti et al. [4]. Outside the field of medicine, such techniques have
application in the field of non-destructive evaluation of expensive components such as rocket nozzles. These numerous applications highlight the capabilities of a potential to generate three dimensional models from CT scan datasets such as that provided by LIMEX and are motivating factors for this research.
2. Surface Extraction Method Implemented Surface extraction in LIMEX is performed using a 2-dimensional region based method. As outlined by Rosenfeld [5], the following steps are generally necessary to perform regionbased surface extraction: (a) Initial Segmentation, (b) Decomposition or Region Growing, (c) Representation. Segmentation is the process that subdivides an image into constituent parts or objects. Thresholding is one of the most common approaches to image segmentation and was the method implemented in LIMEX. The second step in region-based surface extraction is region growing. Region growing is a procedure that groups pixels into connected regions. The approach used to perform region growing was that proposed by Rosenfeld and Pfaltz [6]. The algorithm operates as follows: Each line of the thresholded binary image is scanned from left to right and labels are assigned to pixels with a value of 1. (i.e. region values). This is illustrated by considering two lines of a binary image: line r-1 line r
x x
x c
b a
x x
x x
Given that the pixel labelled a is a 1, a is assigned a label according to the following rules. if
b = c = 0 then a is given the next available label; if
is given c’s label; if
b≠0
b=0
c = 0 then a is given b’s label; if
c ≠ 0 then a b≠0
c≠0
then a is given the smaller of the two labels and b’s label and c’s label are marked as equivalent When this scan of the image S is complete, each pixel of S has a label, and no points belonging to different connected components have the same label. However it is quite possible that the points belonging to the same component have different labels, whose equivalence was not discovered until later in the scan. To eliminate these superfluous labels, the list of recorded equivalencies is processed, and for each label, the smallest label that is equivalent to it is determined. The image is then scanned again, and each label is replaced by its smallest equivalent label. After this second scan is finished, the points of each connected component all have the same label. The final step is representation and one algorithm for finding a simple two-dimensional boundary is that described by Rosenfield [7]. The image is scanned beginning at the top, left, and proceeding down each column in turn, until the first boundary pixel on the region of interest is found. The second boundary pixel is found by checking the eight neighbours of the first boundary pixel, beginning with the pixel to the left of the first boundary pixel and proceeding clockwise. Once a boundary pixel is found, the search is interrupted and the
newly found pixel is made current. Finding subsequent boundary pixels involves checking the neighbours of the current boundary pixel, beginning with the pixel which is one position clockwise of the previous boundary pixel and proceeding clockwise. As boundary pixels are found they are marked to prevent them being found again. The criterion to decide if a pixel with co-ordinates (x,y) is a boundary pixel is: if (x,y) is a member of the region of interest and any of its four-connected neighbours (x-1,y), (x+1,y), (x,y-1) or (x,y+1) are zero and not all are zero then (x,y) is a boundary pixel. Once a failure to find a boundary pixel among the neighbours of the current boundary pixel occurs, that boundary record is terminated and the image is scanned again for a start pixel for a new boundary. The process ends when no further start boundary pixels can be found. The main problem with this procedure is that it does not actively seek closed boundaries, so that boundaries are often terminated in an unclosed state. Other problems are related to the fact that when seeking internal as well as external boundaries, the region width sometimes reduces to only one pixel wide. The method used to overcome these problems is outlined in the next section.
3. LIMEX Program The code for LIMEX was written to run on a Silicon Graphics platform and Figure 1 provides a flow chart of the program. The steps involved will now be outlined in more detail. S ta rt
S e le c t S e t o f S ca n s
R e a d in F irst S ca n
Z o o m in o n A re a o f In te re st
S ca le A re a o f In te re st
A p p ly Im a g e F ilte r a n d E d it Im a g e if N e c e ssa ry
T h re sh o ld
S ca n n in g R e g io n G ro w e r
F in d L a rg e st R e g io n
R e a d in N e xt S c a n , A u to zo o m & A u to sc a le S ca le Im a g e b y th re e
B o u n d a ry F o llo w in g A lg o rith m
F in d O u te r B o u n d a ry o r In n e r a n d O u te r B o u n d a ry a s re q u ire d
O u tp u t G e o m e try to S e ssio n F ile
No L a st S c a n
Yes
En d
Figure 1 :
Flow Chart of LIMEX Program
The first step in extracting bone geometry from CT scans is to select a set of CT scans which contains the bone of interest. When the first scan is opened it is possible to zoom in on the area of interest. It is also possible to scale the area of interest to provide a better visual view of the bone of interest. The next step is to extract the bone geometry from the loaded scan image. The extraction of the geometry is carried out using a region based method. The image is first thresholded as an initial segmentation process. This is to segment bone pixels of the bone of interest from surrounding tissue. Figure 2 displays an example of a scan before and after thresholding. Sometimes it is difficult to select a threshold value that will segment bone from surrounding tissue. This is most evident in skeletal regions of joints. In such cases it is sometimes necessary to apply image filters to enhance the image. Two broad categories of image enhancement techniques are implemented in LIMEX: spatial domain methods and frequency domain methods. Processing techniques in the first category refer to the image plane itself, and approaches in this category are based on direct manipulation of the pixels in an image. The frequency domain filters are based on modifying the Fourier transform of an image. Even with the aid of filters it may still be necessary to edit an image manually to provide segmentation in such regions. Therefore manual editing is a built in feature of LIMEX.
Figure 2 :
Thresholding an Image
Having segmented the bone of interest from other tissue region growing is then performed as outlined in the previous section. This algorithm uses the concept of 4-connectedness to perform region growing. The result of the algorithm is a number of connected regions each with a different label. To decide which region is the region of interest some prior knowledge must be available about the region of interest. The region growing algorithm can provide information such as region area as a by-product. This results in several regions each with a different label. By choosing the region of interest carefully in the earlier step to select as closely as possible only the bone of interest, it can be assumed that the region with the largest area is the area of interest. Therefore this region is selected as the region of interest and pixels in other regions are given a value of zero. The resulting image is then scaled by three to overcome the problem of one element region width and others outlined in Section 2. This image is then scanned until the first member of the largest region which is judged to be a boundary pixel is found and the boundary follower
outlined previously is applied. This finds all the boundaries of the region of interest. However in extracting bone geometry for the purpose of this research, in general the boundary of interest is the outside boundary. This boundary is deemed to be the boundary which spans the greatest sum of pixels in the x and y directions. The co-ordinates of these boundary pixels are then output in the form of a “Session” file which can interface with the commercially available finite element post and pre-processor Patran (McNeal USA). This process is then repeated for each scan in the set. The outputted session file can then be ran within Patran to create the geometry of the bone of interest.
4. Results An example of a 3-dimensional geometry model of an in-vivo femur created with the aid of LIMEX is shown in Figure 3. A pelvic model among others has also been created.
Figure 3 :
Geometry Model of Femur Created Using LIMEX
5. References 1. McCarthy, M. A., 1989. Bone Geometry from CAT Scans for Finite Element Analysis, Image Processing Considerations and Modelling Effects. PhD Thesis, Cornell University, Ithaca, NY. 2. Prendergast, P. J., 1997. “Finite element models in tissue mechanics and orthopaedic implant design.” In: Clinical Biomechanics, vol. 12. 3. Crawford, H.V., P. S. Unwin, P. S. Walker, 1992. “The CADCAM Contribution to Customized Orthopaedic Implants”, In: IMechE, Vol. 206. 4. Caponetti, L., A. M. Fanelli, 1993. “Computer Aided Simulation for Bone Surgery”, In: IEEE Computer Graphics and Applications. 5. Rosenfeld, A., 1978. “Algorithms for Image Vector Conversion”, In: Computer Graphics (ACM) 12 (3). 6. Rosenfeld, A., J. L. Pfaltz, 1966. “Sequential Operations in Digital Picture Processing”, In: J. Assoc. Comput. Mach. 12 (4), 471-494. 7. Rosenfeld, A., 1968. “Picture Processing by Computer”, In: New York: Academic Press.
