Image Analysis of Cardiovascular MR Data

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Image Analysis of Cardiovascular MR Data
Amir A. Amini, Ph.D. Endowed Chair in
Bioimaging Professor of Electrical and Computer
Engineering The University of Louisville Louisvil
le, KY 40292
Amir Kabir University, April 24, 2006
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Useful Links/Contact Information

• Amir Amini amini_at_wustl.edu until July 15
• shams1000_at_sbcglobal.net
• General information about ECE and forms
• http//www.ece.louisville.edu/gen_forms.html 
• On-line application for doctoral degree
  http//graduate.louisville.edu/app/

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ECE Dept. Highlights
Paul B. Lutz Hall

• 20-25 faculty covering all areas of research and
  teaching in ECE
• Strong group in nanotechnology including an
  8.5M clean room
• Strong group in signal and image processing
  including 3 faculty
• with interests in computer vision, medical
  imaging, and neural networks

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Minimum Admissions Requirements

• GPA gt 80
• GRE gt 1800
• TOEFL gt 600
• Students who have finished their M.S. are given
  preference.
• If GPA gt 90, GRE gt 2000, and class rank in top 5
  students will be considered for a prestigious
  university fellowship

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Cardiovascular Innovations at UofL
Univ. of Louisville surgeons Laman Gray and
Robert Dowling performed the very first totally
artificial heart implant in a human in the world
in the late 1990s with the AbioCor Implantable
Replacement Heart
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Cardiovascular Innovations Institute

• Almost 400,000 people are diagnosed with heart
  failure in the US alone per year
• Mission is to perform research in advanced
  technologies to help patients
• So far 50 Million has been donated as initial
  budget for the institute
• CIIs new 4 story building will open in December
  of 2006
• Cardiac Imaging and Image Processing is an
  important component of CII

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Overview of Projects

• Tagged MRI for assessment of cardiac function
  Non-invasive measurement of 3-D myocardial
  strains, in-vivo
• Analysis of MRA data Phase-Contrast MRI for
  non-invasive measurement of intravascular
  pressure distributions

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Myocardial Strains from Tagged MRI
E. Zerhouni et al., Human Heart Tagging with
MR Imaging A Method for Non-invasive
Assessment of Myocardial Motion, Radiology,
Vol. 169, pp. 59-63, 1988.
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Anatomic Orientation
Yale Center for Advanced Instructional Media
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Coronary Arteries
Yale Center for Advanced Instructional Media
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Motivation

• Lack of blood flow to the myocardium due to
  coronary artery disease leads progressively to
  ischemia, infarction, tissue necrosis, and tissue
  remodeling
• When blood flow is diminished to tissue,
  generally, its contractility is compromised
• Echocardiography is a very versatile imaging
  modality in measurement of LV contractility.
  But, it lacks methods for determining intramural
  deformations of the LV. The advantage of
  echocardiography however is that it is
  inexpensive.

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Tagged MRI

• Prior to conventional imaging, tissue
  magnetization is perturbed by application of RF
  and gradient pulses, resulting in saturation of
  signal from selected tissue locations
• Tag lines appear as a dark grid on images of soft
  tissue
• Data collection is synchronized with the ECG.
• As standard in MRI, image slices are acquired at
  precise 3-D locations relative to the magnets
  fixed coordinate system

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SPAMM Tagged MRI Sequence
R
a
a
-a
RF
Gz
Gx
Gy
y
x
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Patient with old healed inferior MI
R
R
R
1000
0 32 64 96 128 160
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R
R
R
0 32 64 96 128 160
1000
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Acquisition of Short-Axis Slices
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Acquisition of Long-Axis Slices
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Cubic polynomial in u

• Locality Since each basis function has local
  support, movement of any control point only
  affects a small portion of the curve
• Continuity Cubic B-spline curves are
  continuous everywhere

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w
u
v
Tustison and Amini, IEEE Trans. On Biomedical
Engineering, 50(8), Aug. 2003
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• After 4-D B-Spline fitting to tag data, we can
  easily extract
• Myocardial beads
• 3-D Displacement fields
• Myocardial strains

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To generate displacement field, we subtract the
3-D solid at t 0 from the 3-D solid at t t.
Tustison and Amini, IEEE Trans. On Biomedical
Engineering, (50)8, Aug. 2003
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• Strain is a directionally dependent measure of
  percent change in length of a continuous
  deformable body

• Positive strains correspond to elongation whereas
  negative strains correspond to compression.

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Myocardial Strain
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Myocardial Strain
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Myocardial Strain
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ne1 radial ne2circumferential ne3
longitudinal
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Motion field
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Radial Strain
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Circumferential Strains
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Longitudinal Strains
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Torsion k2
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Radial Strain
Circumferential Strain
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Sixteen Segment Model
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Average Normal Strains
Diamonds radial Circles circumferential Squares
longitudinal
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Average Normal Strains
Diamonds radial Circles circumferential Squares
longitudinal
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Normal Strain Plots for Patient with old MI
Diamonds radial Circles circumferential Squares
longitudinal
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Normal Strain Plots in Patient with old MI
Diamonds radial Circles circumferential Squares
longitudinal
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www.amazon.com www.borders.com
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Intravascular Pressures from Phase-Contrast MR
Velocities
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Hemodynamic Significance of Arterial Stenoses

• Percent diameter stenosis does not generally
  translate to a measure of a stenosis
  significance
• Knowledge of pressure drop across a stenosis is
  the gold standard but is currently obtained
  invasively with a pressure catheter under X-ray
  angiography
• MRI has the tools for potentially determining
  pressure drops across vascular stenoses,
  accurately, and non-invasively.

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Given 3-D pulsatile velocity data how can we
determine pulsatile pressures ? Robust to
noise Computationally efficient
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Pressure and Velocity Field Relations----
Navier-Stokes Equation
Pulsatile term
Viscous Forces
Pressure
Convective Inertial Forces
Body force term
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Phase-Contrast MRI

• An effective tool for blood flow quantification
• Phase-Contrast MRI may be used to acquire
  velocity images
• (a) At precise 3D slice locations
• (b) Can quantify different components
  of
• 3D velocities

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Phase-Contrast velocities in a 90 area stenosis
phantom
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Motion Induced Phase Shifts
PC-MRI
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Phase Contrast Sequence
a
RF
Gz
Gx
Gy
signal
A/D
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Phase Contrast Sequence
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From Navier-Stokes to Pressure

• Apply Navier-Stokes to noisy velocities to yield
• Can it be integrated to yield pressure ?

Noise-corrupted velocities in a straight pipe
is path-dependent
Can not be a true gradient vector field and
therefore can not be integrated
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From Noisy Gradient to Pressure

• Orthogonally project onto an integrable
  sub-space where it can be integrated

Integrable sub-space
Orthogonal Projection
true gradient vector field
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Two Approaches to Orthogonal Projection

• Iterative solution to pressure-Poisson equation
• Direct harmonics-based orthogonal projection

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Iterative Solution to Pressure-Poisson Equation
According to the calculus of variations,
should satisfy the pressure-Poisson equation
For interior points
Subject to natural boundary conditions.
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Previous Work

• Song, et al. 1994, Yang, et al. 1996, Tyszeka et
  al. 2000, Thompson et al. 2003, and Moghaddam et
  al. 2004 all use iterative solution to the
  Pressure-Poisson equation to determine pressures
  from velocity data
• Predominantly, an iterative implementation based
  on the Gauss-Seidel iteration was used
• Moghaddam et al. used SOR to speed-up
  computations.

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New Approach to Pressure Calculation
Harmonics-Based Orthogonal Projection
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Shape from Shading

• Determine surface orientations from
  image brightness
• To ensure integrability, noisy surface
  orientations are orthogonally projected into an
  integrable subspace

See for example, Ch. 11, Robot Vision by Horn
Frankot and Chellappa, IEEE PAMI, July
1988 Adopted a far more efficient basis function
approach
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Expansion of Noisy Gradients With Integrable
Basis Functions
Set of basis functions satisfying the
integrability constraint
Where
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Computing Pressure From Integrable Pressure
Gradients
Following Frankot and Chellappa
When using Fourier basis functions
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Using FFT

• STEP 1 perform FFT of to determine
• STEP 2 perform FFT of to determine
• STEP 3 Combine to determine
• STEP 4 Perform inverse FFT of to determine
  the relative pressure

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Specific Problem in Computation of Intravascular
Pressure

• Irregular geometry of blood vessels

Discontinuities at in-flow and out-flow
boundaries
Discontinuities along blood vessel boundaries
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Concentric and Eccentric Stenosis Geometries

• 50, 75, 90 concentric area stenosis phantoms
  have been fabricated
• These exact geometries are used in FLUENT CFD
  code for flow simulation

90 Area Stenosis Phantoms
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Experimental Flow System
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Validations
1. Used FLUENT CFD package to generate velocity
fields and pressure maps for geometries and flow
rates of interest. 2. Varying amounts of additive
noise was added to FLUENT velocities and then
fed to the algorithm. Calculated pressures were
compared with FLUENT pressures. 3. In-vitro PC MR
data from an experimental flow system were
collected and fed to the algorithm. Calculated
pressure maps were compared with FLUENT pressures.
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Validation ---- on 3-D Axisymmetric FLUENT
Velocities
Relative RMS Error (RError) between calculated
pressures using Fluent velocities with Fluent
pressures () no noise, constant flow
Harmonics-Based Orthogonal Projection
Iterative Solution to Pressure-Poisson Equation
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Validation ---- on 3-D Axisymmetric FLUENT
Velocities
CPU time on a Sun SPARC 10 when computing
pressures (seconds)
Harmonics-Based Orthogonal Projection
Iterative Solution to Pressure-Poisson Equation
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Noise Test on 3-D Axisymmetric FLUENT Data
Relative RMS Error (RError) between calculated
pressures using Fluent velocities with Fluent
pressures for the 90 area stenosis phantom,
Q20 ml/s (constant flow)
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In-Vitro Pressure Profiles (from MRI) Along the
Axis of Symmetry of Stenosis Phantoms Constant
Flow
Q10 ml/s Q15 ml/s Q20
ml/s
50 75 90
Center of Stenoses
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Pulsatile Flow
Simulation performed by Juan Cebral using FEFLO
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Noise Test on 3-Dt Simulated Pulsatile Velocity
Data
Relative RMS Error (RError) between calculated
pressures using noise corrupted FEFLO pulsatile
velocities with FEFLO pressures 0.03
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Percent stenosis can be quantified from the MIP.
The goal of this project is to determine whether
the stenoses are hemodynamically significant
requiring invasive surgery/intervention.
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Geometry from Level-Set Evolution
Chen and Amini, IEEE Trans. On Medical Imaging,
Vol. 23, No. 10, Oct. 2004
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Level-Set Segmentation

• Perform 3-D level set evolution, using a speed
  function derived from the enhanced image

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• Tagged MRI
• Non-invasive measurement of myocardial strain
  maps
• Visualization of myocardial beads

• Phase-Contrast MRI
• Non-invasive measurement of intravascular
  pressures from Phase-Contrast MRI

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Acknowledgements

• Nasser Fatouraee
• Nick Tustison
• Jian Chen
• Abbas Moghaddam
• Geoff Behrens

• NIH, BJH Foundation

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Useful Links/Contact Information

• Amir Amini amini_at_wustl.edu until July 15
• shams1000_at_sbcglobal.net
• General information about ECE and forms
• http//www.ece.louisville.edu/gen_forms.html 
• On-line application for doctoral degree
  http//graduate.louisville.edu/app/