Proc. SPIE. 6918, Medical Imaging 2008: Visualization, Image-Guided Procedures, and Modeling
KEYWORDS: Visual process modeling, Optical spheres, Magnetic resonance imaging, Image segmentation, Heart, 3D modeling, Algorithm development, 3D image processing, Cardiovascular magnetic resonance imaging, Anisotropy
This paper presents a novel method for the generation of a four-chamber surface model from segmented cardiac
MRI. The method has been tested on 3D short-axis cardiac magnetic resonance images with strongly anisotropic
voxels in the long-axis direction. It provides a smooth triangulated surface mesh that closely follows the endocardium
and epicardium. The surface triangles are close-to-regular and their number can be preset. The input
to the method is the segmentation of each of the four cardiac chambers. The same algorithm is independently
used to generate the surface mesh of the epicardium and of the endocardia of the four cardiac chambers. For
each chamber, a sphere that includes the chamber is centered at its barycenter. A triangulated surface mesh
with almost perfectly regular triangles is constructed on the sphere. Then, the Laplace equation is solved over
the region bounded by the segmented chamber surface and the sphere. Finally, each vertex from the triangulated
mesh on the sphere is mapped from the sphere to the chamber surface by following the gradient flow of
the solution of the Laplace equation. The proposed method was compared to the marching cubes algorithm.
The proposed method provides a smooth mesh of the heart chambers despite the strong voxel anisotropy of the
3D images. This is not the case for the marching cubes algorithm, unless the mesh is significantly smoothed.
However, the smoothing of the mesh shrinks it, which makes it a less accurate representation of the chamber
surface. The second advantage is that the mesh triangles are more regular for the proposed method than for the
marching cubes algorithm. Finally, the proposed method allows for a finer control of the number of triangles
than the marching cubes algorithm.
This paper presents a method for automated deformation recovery of the left and right ventricular wall from a time sequence of anatomical images of the heart. The deformation is recovered within the heart wall, i.e. it is not limited only to the epicardium and endocardium. Most of the suggested methods either ignore or approximately model incompressibility of the heart wall. This physical property of the cardiac muscle is mathematically guaranteed to be satisfied by the proposed method. A scheme for decomposition of a complex incompressible geometric transformation into simpler components and its application to cardiac deformation recovery is presented. A general case as well as an application specific solution is discussed. Furthermore, the manipulation of the constructed incompressible transformations, including the computation of the inverse transformation, is computationally inexpensive. The presented method is mathematically guaranteed to generate incompressible transformations which are experimentally shown to be a very good approximation of actual cardiac deformations. The transformation representation has a relatively small number of parameters which leads to a fast deformation recovery. The approach was tested on six sequences of two-dimensional short-axis cardiac MR images. The cardiac deformation was
recovered with an average error of 1.1 pixel. The method is directly
extendable to three dimensions and to the entire heart.