New Techniques for New Techniques for Visualizing and Evaluating Visualizing and Evaluating

Left Ventricular PerformanceLeft Ventricular Performance

Burkhard Wünsche1 & Alistair Young2

1Division for Biomedical Imaging & VisualizationDepartment of Computer Science

2Department of Anatomy with RadiologyUniversity of Auckland

New Zealand

IntroductionIntroduction

• Heart diseases remain the biggest Heart diseases remain the biggest killer in the western world.killer in the western world.

• An improved understanding of An improved understanding of cardiac mechanics might advance cardiac mechanics might advance the diagnosis and treatment of heart the diagnosis and treatment of heart diseases.diseases.

• This presentation explains how This presentation explains how myocardial deformation can be myocardial deformation can be measured and visualized.measured and visualized.

Overview Overview

• Myocardial strainMyocardial strain

• A left-ventricular finite element A left-ventricular finite element modelmodel

• Computing ventricular performance Computing ventricular performance measuresmeasures

• Visualizing myocardial strainVisualizing myocardial strain

• ConclusionConclusion

Myocardial StrainMyocardial Strain

• Regional altered myocardial Regional altered myocardial mechanics have been originally mechanics have been originally determined by measuring wall determined by measuring wall thickening.thickening.

• A full description of the myocardial A full description of the myocardial deformation is given by the strain deformation is given by the strain tensor which is mathematical tensor which is mathematical represented by a 3x3 matrix.represented by a 3x3 matrix.

Finite Element ModellingFinite Element Modelling

( ) ( )k ki i

i k

Bx ξ v ξ

The geometry of an element is defined The geometry of an element is defined by specifying coordinates, coordinate by specifying coordinates, coordinate derivatives and interpolation functions.derivatives and interpolation functions.

Material Coordinates World Coordinates

Finite Element Model of the Finite Element Model of the Left VentricleLeft Ventricle• Developed by Alistair A. Young et. al., 1994/95 University

of Pennsylvania.

Measuring Myocardial StrainMeasuring Myocardial Strain

• Use tagged MRI data setUse tagged MRI data set• Compute displacement field from points Compute displacement field from points

on tag lineson tag lines• Compute strain tensor from displacement Compute strain tensor from displacement

gradient tensorgradient tensor

Computing Volume Computing Volume MeasuresMeasures• Substitution rule for multi-dimensional integration Substitution rule for multi-dimensional integration

[Heuser 1981][Heuser 1981]

- - ΩΩ i is the domain of the finite elements the domain of the finite element- f- f is the identity function is the identity function - x- x((ξξ) is the mapping from material to world coordinates.) is the mapping from material to world coordinates.

• Efficiently evaluated using Gaussian Quadrature. Efficiently evaluated using Gaussian Quadrature.

Myocardial VolumeMyocardial Volume

• Select all elements and sum up their volumeSelect all elements and sum up their volume

• Volume reduction higher than expected due to Volume reduction higher than expected due to underestimation of wall thickening caused by underestimation of wall thickening caused by the limited tag line resolution in radial direction.the limited tag line resolution in radial direction.

Ventricular VolumeVentricular Volume

• Construct new elements modelling the Construct new elements modelling the ventricular cavity.ventricular cavity.

Computing Area MeasuresComputing Area Measures

The Visualization of Myocardial The Visualization of Myocardial StrainStrain

Principal Strains

Any 3-dimensional symmetric tensor T has 3 eigenvalues i and 3 mutually perpendicular eigenvectors vi such that

The eigenvalues of a strain tensor E are called the principal strains and the corresponding eigenvectors are called the principal directions.

iii vTv 1,...,3i

Tensor EllipsoidsTensor Ellipsoids

Hyperstreamlines – Maximum Hyperstreamlines – Maximum Principal StrainPrincipal Strain

Hyperstreamlines – Minimum Hyperstreamlines – Minimum Principal StrainPrincipal Strain

Hyperstreamlines – Minimum Hyperstreamlines – Minimum Principal StrainPrincipal Strain

Line Line IntegralIntegral

ConvolutioConvolutionn

Colour Mapped Surfaces and Colour Mapped Surfaces and IsosurfacesIsosurfaces

• Separate regions of Separate regions of expanding and expanding and compressive strain.compressive strain.

ConclusionConclusion

• 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 WorkFuture Work

• Further investigations necessary to find Further investigations necessary to find the relationship between degenerate the relationship between degenerate points in the strain field, the myocardial points in the strain field, the myocardial fiber structure and the ventricular fiber structure and the ventricular anatomy.anatomy.

• Explore applications for diagnosis and Explore applications for diagnosis and surgical planning.surgical planning.

• Visualize other data sets, in particular Visualize other data sets, in particular models of ischemic myocardium.models of ischemic myocardium.

AcknowledgementsAcknowledgements

• Dr. Richard White of the Cleveland Clinic, Dr. Richard White of the Cleveland Clinic, Cleveland, Ohio, USA, for providing the Cleveland, Ohio, USA, for providing the tagged MRI data of a heart diagnosed with tagged MRI data of a heart diagnosed with dilated cardiomyopathy.dilated cardiomyopathy.