Generation of a 3D Finite Element Mesh of the Rat
Spinal Cord from Magnetic Resonance Images
Zhen Qian, Jason T. Maikos, Ting Chen, Dimitris Metaxas, David I. Shreiber
Department of Biomedical Engineering, Rutgers, the State University of New Jersey
617 Bowser Road, Piscataway, NJ, United States 08854-8014
Objectives
We are conducting a biomechanical analysis of spinal cord
injury in the rat using finite element methods to identify tissue
tolerances for mechanical loading. In this project, our objective
is to generate an anatomically accurate, 3-dimensional, finite
element mesh of the rat spinal cord from a set of 3dimensional spin echo magnetic resonance images (MRI). This
model will assist the future research on simulating and
evaluating of the mechanical response of the spinal cord to
trauma.
Experimental settings
We adopted the IMPACTOR, a universally-accepted
experimental model of spinal cord injury, as the experiment
protocol. For the mesh-generating purpose, a fresh rat spinal
cord column between T8 to T11 is excised and fixed within a
custom built solenoid coil in a 4T magnetic resonance imaging
system. To determine in vivo material properties of the rat
spinal cord, an anaesthetized rat is fixed on a plastic board
with the T13-14 spinal cord column exposed after a T9-T10
laminectomy. The impact site is at T9-T10 vertebral level. As
shown in figure 1, we develop a device that accurately controls
the extruding depth of the compressing rod. The solenoid coil
is designed to fit the spinal cord anatomically well. We sew up
the coil into the laminectomy area and extrude the rod to
compress the exposed spinal cord. The deformation of the
spinal cord is captured by MRI equipment.
The MRI raw data are in frequency domain. In the data
parsing step, we transform the data with an inverse fast Fourier
transform. At the same time, the parsed images undergo
preprocesses such as histogram adjustment and recentering. In
the 2D segmentation step, because of the MR images’ high noise
level and irregular shape of the white matter and gray matter,
human intervention is a must. We use a 2D deformable model
(snake) plus human intervention to do segmentation. The inner
force of the snake insures the segmented boundary smooth. The
external force of the snake comes from intensity information and
human interactions. The imaging sampling rates in z direction is
much lower than those in x or y direction. So after we get the 2D
contours, we linearly interpolate in the z direction to achieve
uniform spacing. The set of interpolated 2D results are combined
to form a 3D binary mask, and the marching cubes method is
used to create a 3D surface mesh based on the mask. One
hexahedron element was created for each 3D grid assigned to
the object. The hexahedron elements were connected to form the
final volumetric model. The volumetric model of the gray matter
consists of 41755 nodes and 32810 elements. The volumetric
model of the white matter has altogether 151891 nodes and
138854 elements. We are currently validating the mesh and
simulating in vivo IMPACTOR experiments.
Results
Figure 3
Figure 2
Figure 1, The experimental settings. (a, b): The rat is fixed on
the plastic board and the coil is mounted on the rat’s back. (c)
is the tunable capacitors of the solenoid coil. (d) is the device
that controls the extruding rod.
Figure 3 are the parsed MR images of
the compressed rat spinal cord. The
star indicates the location of the
compressing rod. (A-D) are intact
results. (E-H) are deformed results
with different compressing depths.
Methods
After acquiring the MRI raw data, we did the following steps:
MRI
raw
data
Data parsing
(2D IFFT,
histogram
correction,
recentering)
2D image
segmentation of
the white and
gray matter.
(Snake + user
intervention)
3D mesh
generation
(Marching
cubes,
smoothing)
Interpolating the
2D contours in
the z direction
to achieve
uniform spacing
Figure 2 are the parsed MR images of
the excised rat spinal cord. There are
totally 30 slices along z direction. We
do linear interpolation to generate 90
slices along z direction to achieve
uniform sampling rates in x, y, z
directions.
Figure 4
Figure 4 are the 3D mesh generation
results. (A) is the complete 3D mesh
of the gray matter. (B) and (C) are 2D
views of the mesh structure at
different z positions. (D) is a short 3D
mesh of both white and gray matter
that consists of only a few slices for
better readability.
Acknowledgements
This work was supported by the CDC (R49CCR 221744-01).
The assistance of Michael Brennick, Steve Pickup, and Mitch
Schnall at the University of Pennsylvania is greatly appreciated.