A Survey of Three-Dimensional Modeling Techniques for Quantitative Functional Analysis of Cardiac Images - Advance Image Processing in Magnetic Resonance Imaging - page 294

local offset either in nonparametric [7] or parametric [8] form, and (c) a local
deformation in the form of a polyhedrization. The thick-walled superquadric repre-
sents a high-level abstraction model of the myocardium that is further refined by the
local offsets. Altogether, these two parts constitute the rest model of the myocardium
that is rigidly scaled to the dimensions of a new data set. The local deformation field
is responsible for capturing the detailed shape variability of different data sets. Park
et al. [5] have extended their LV surface model [6] to a superellipsoid model with
parameter functions. The model is fitted to tagged MR images, providing a compact
and comprehensive description of motion. Radial and longitudinal contraction, twist-
ing, long-axis deformation, and global translation and rotation are readily available
from the parameter functions. Alternatively, standard strain analysis can be carried
out. It is also possible to estimate other volumetric parameters such as SV, CO, LVV,
and LVM. In order to fit the model, a set of boundary points is manually delineated
and a set of tags semiautomatically tracked along the cardiac cycle using the algo-
rithm of Young et al. [81]. Therefore, the accuracy of all volumetric measurements
depends on the manual outlining.
Haber, Metaxas, and Axel [164] have developed a model of biventricular
geometry using FEs in a physics-based modeling context. The 3-D motion of the
RV is analyzed by defining external forces derived from spatial modeling of
magnetization (SPAMM) MR tagging data [165,166]. Recently, Hu, Metaxas,
and Axel [168] have developed a biomechanically based image analysis frame-
work for the estimation of the in vivo material properties and the stress and strain
distributions in both ventricles. A similar aim has motivated Shi et al. [192] to
develop a stochastic FE framework for the simultaneous estimation of kinematic
and material parameters from the heart in vivo. Creswell et al. [161] and Pirolo
et al. [162] describe a mathematical (biventricular) model of the heart built from
3-D MR scans of a canine specimen. Manual contour delineation of the epicardial,
and LV and RV endocardial boundaries provides a set of points that is approxi-
mated with cubic nonuniform rational B-splines (NURBS) [228]. From this
representation, a hexahedral FE model is built in order to generate a realistic
geometric model for biomechanical analysis.
Shi et al. [167] have introduced an integrated framework for volumetric
motion analysis. This work extends the surface model of Shi et al. [142] by
combining surface motion extracted from MR magnitude images, and motion
cues derived from MR phase-contrast (velocity) images. The latter provide
motion information inside the myocardial wall but are known to be less accurate
at the boundaries [94]. The two sources of motion evidence (boundary and
midwall motion) are fused by solving the discretized material constitutive law
of the myocardium, assuming a linear isotropic elastic material. In this frame-
work, the measured boundary and midwall motion estimates at two consecutive
frames are used as the boundary and the initial conditions of an FE element
formulation. An advantage of this method with respect to physically based
techniques is that material properties can be set based on experimental knowl-
edge about myocardial mechanical properties, and not on a virtual mechanical
analog, which usually leads to ad hoc parameter settings.