Download The Visualization of Two-Dimensional Second

New Techniques for Visualizing
and Evaluating Left Ventricular
Performance
Burkhard Wünsche1
& Alistair Young2
1Division
for Biomedical Imaging & Visualization
Department of Computer Science
2Department of Anatomy with Radiology
University of Auckland
New Zealand
Introduction
• Heart diseases remain the biggest killer in
the western world.
• An improved understanding of cardiac
mechanics might advance the diagnosis
and treatment of heart diseases.
• This presentation explains how myocardial
deformation can be measured and
visualized.
Overview
• Myocardial strain
• A left-ventricular finite element model
• Computing ventricular performance
measures
• Visualizing myocardial strain
• Conclusion
Myocardial Strain
• Regional altered myocardial mechanics
•
have been originally determined by
measuring wall thickening.
A full description of the myocardial
deformation is given by the strain tensor
which is mathematical represented by a
3x3 matrix.
Finite Element Modelling
The geometry of an element is defined
by specifying coordinates, coordinate
derivatives and interpolation functions.
x(ξ)   v B (ξ)
k
i
i
k
i
k
Material Coordinates
World Coordinates
Finite Element Model of the Left
Ventricle
• Developed by Alistair A. Young et. al., 1994/95 University of
Pennsylvania.
Measuring Myocardial Strain
• Use tagged MRI data set
• Compute displacement field from points on tag
•
lines
Compute strain tensor from displacement
gradient tensor
Computing Volume Measures
• Substitution rule for multi-dimensional integration [Heuser
1981]
- Ω is the domain of the finite element
- f is the identity function
- x(ξ) is the mapping from material to world coordinates.
• Efficiently evaluated using Gaussian Quadrature.
Myocardial Volume
• Select all elements and sum up their volume
• Volume reduction higher than expected due to
underestimation of wall thickening caused by the
limited tag line resolution in radial direction.
Ventricular Volume
• Construct new elements modelling the ventricular
cavity.
Computing Area Measures
The Visualization of Myocardial Strain
Principal Strains
Any 3-dimensional symmetric tensor T has 3
eigenvalues i and 3 mutually perpendicular
eigenvectors vi such that
Tv i  i v i
i  1,...,3
The eigenvalues of a strain tensor E are called
the principal strains and the corresponding
eigenvectors are called the principal directions.
Tensor Ellipsoids
Hyperstreamlines – Maximum
Principal Strain
Hyperstreamlines – Minimum
Principal Strain
Hyperstreamlines – Minimum
Principal Strain
Line Integral
Convolution
Colour Mapped Surfaces and
Isosurfaces
• Separate regions of
expanding and
compressive strain.
Conclusion
• Visualizing the strain field improves the understanding
•
•
•
•
of the complex deformation of the heart muscle.
Using techniques new to the biomedical field offers
additional insight.
Tensor ellipsoids and hyperstreamlines make it possible
to visualize complex deformation in a single image.
Line integral convolution uncovered the presence of
degenerate points at which the principal strain suddenly
changes direction.
Visual information can be supplemented by computing
ventricular performance measures.
Future Work
• Further investigations necessary to find the
•
•
relationship between degenerate points in the
strain field, the myocardial fiber structure and
the ventricular anatomy.
Explore applications for diagnosis and surgical
planning.
Visualize other data sets, in particular models
of ischemic myocardium.
Acknowledgements
• Dr. Richard White of the Cleveland Clinic,
Cleveland, Ohio, USA, for providing the tagged
MRI data of a heart diagnosed with dilated
cardiomyopathy.