Deformable Image Registration with Hyperelastic Warping - Biomedical Image Analysis - page 502

to be more difficult. Toward this end, the following study was designed to exam-
ine the feasibility of using Hyperelastic Warping to determine the displacements
of the ossicular chain from high-resolution CT images. These displacements
would in turn provide the boundary conditions for FE models of the individual
bones of the ossicular chain. This secondary analysis would be used to deter-
mine the stress distributions within bones of the middle ear. High-resolution
computed tomography (CT) images (1024 × 1024 × 1024 isotropic image ma-
trix, 14.1 mm FOV, 10 µ m isotropic resolution) were taken of the external and
middle ear of an anesthetized gerbil. The images were acquired on a Skyscan
1072 80 kV micro-CT tomograph. An image data set was acquired with the tym-
panic membrane under no external pressure load other than atmospheric pres-
sure. The second image set was acquired while a 3.0 kPa pressure load was
placed on the external surface of the tympanic membrane. The images were
cropped (270 × 270 × 172 voxels) to include only the tympanic membrane and
the malleus bone of the middle ear. The image obtained under atmospheric load-
ing was defined as the template image while the image under a pressure load of
3 kPa was defined as the target image. A 41 × 41 × 27 rectilinear finite element
mesh was constructed that included the entire cropped image domain (11,767
elements). This deforming template mesh was modeled as a neo-Hookean hyper-
elastic material with a shear modulus of 450 Pa and a bulk modulus of 400 Pa.
A fixed flat spatial filter (3 × 3 × 3 pixel mask) [38] was used in the warping
analysis. The FE mesh was rezoned twice during the analysis to determine the
displacements of the malleus.
Subsequent to the deformable registration analysis, a finite element model
was created to represent the malleus bone. The external boundary of the malleus
was manually segmented from the template image data set. B-spline curves were
fitted to the points generated by the segmentation and these curves were used to
define the exterior surface of the malleus. A tetrahedral mesh (42,391 elements)
was generated from this surface definition. The malleus was modeled as a linear
elastic material using properties (elastic modulus E = 20 . 0 GPa, Poisson's Ratio,
ν = 0 . 3) from the literature [41, 45].
The surface of the malleus model was loaded using the displacements de-
termined from the deformable image registration analysis. The displacements
for each surface node of the malleus model were defined by interpolating
nodal displacements determined from the warping analysis using the rectilinear
(Warping) mesh trilinear shape functions. The NIKE3-D nonlinear finite ele-
ment program [46] was used to analyze the malleus model and determine the