Download Dr-Amini

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
Louisville, KY 40292
Amir Kabir University, April 24, 2006
Useful Links/Contact Information
• Amir Amini [email protected] until July 15
•
[email protected]
• 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/
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
Minimum Admissions Requirements
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GPA > 80%
GRE > 1800
TOEFL > 600
Students who have finished their M.S. are
given preference.
• If GPA > 90%, GRE > 2000, and class rank in
top 5 students will be considered for a
prestigious university fellowship
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 1990’s with the
AbioCor Implantable Replacement Heart
Cardiovascular Innovations Institute
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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
CII’s new 4 story building will open in December of 2006
Cardiac Imaging and Image Processing is an important component of CII
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
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.
Anatomic Orientation
Yale Center for Advanced Instructional Media
Coronary Arteries
Yale Center for Advanced Instructional Media
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.
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 magnet’s fixed coordinate
system
SPAMM Tagged MRI Sequence
R
a
-a
a
RF
Gz
Gx
Gy
y
x
Tagged MRI: Short-Axis
Patient with
old healed
inferior MI
R
R
R
•••
1000
Tagged MRI: Long-Axis
R
R
R
•••
0 32 64 96 128 160
1000
Acquisition of Short-Axis Slices
•••
Acquisition of Long-Axis Slices
•••
B-Spline Models of Tag Planes
Periodic B-Splines
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
4-D Cartesian B-Spline Model
w
v
Tustison and Amini, IEEE Trans. On Biomedical Engineering, 50(8), Aug. 2003
4-D B-Spline Model
 After 4-D B-Spline fitting to tag data, we can
easily extract
Myocardial beads
3-D Displacement fields
Myocardial strains
Myocardial Beads: Results
Displacement Fields
To generate displacement field, we subtract the 3-D
solid at t = 0 from the 3-D solid at t = τ.
V  S (u, v, w, ) - S (u, v, w,0)  (  , ,  )
Tustison and Amini, IEEE Trans. On Biomedical Engineering, (50)8, Aug. 2003
Myocardial Strain
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.
Myocardial Strain
Myocardial Strain
Myocardial Strain
Differential Element of Length
z
q : ( x  dx, y  dy, z  dz )
Q : ( X  dX , Y  dY , Z  dZ )
(  , ,  )
P : ( X ,Y , Z )
x
p : ( x( X , Y , Z )), y( X , Y , Z ), z ( X , Y , Z ))
y
Strain Calculation

 x

1
    yx
2
1
  zx
2
1
 xy
2
y
1
 zy
2
1 
 xz 
2 
1 
 yz
2 

z 

 L  nnT
n=e1: radial
n=e2:circumferential
n=e3: longitudinal
Strain Calculation
Motion field: V  (  , ,  )






1 2
 x  x  x x2  x2
2
1 2
2
2
 y  y  y y   y
2
1 2
2
2
 z   z  z  z  z
2
 xy   yx   x   y   x  y   x y   x y
 xz   zx   x   z   x  z   x z   x z
 yz   zy   y   y   y  z   y z   y z
Displacement Fields
Radial Strain
Circumferential Strains
Longitudinal Strains
Torsion: k2
Radial Thickening: k1
Simulated Tagged MRI Movie
Circumferential Strains
Displacement Fields
Strain Results – k1
+0.30
0.0
Radial Strain
Circumferential Strain
-0.30
Sixteen Segment Model
Average Normal Strains
Diamonds: radial
Circles: circumferential
Squares: longitudinal
Average Normal Strains
Diamonds: radial
Circles: circumferential
Squares: longitudinal
Normal Strain Plots for Patient
with old MI
Diamonds: radial
Circles: circumferential
Squares: longitudinal
Normal Strain Plots in Patient
with old MI
Diamonds: radial
Circles: circumferential
Squares: longitudinal
www.amazon.com
www.borders.com
Intravascular Pressures from PhaseContrast MR Velocities
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.
Given 3-D pulsatile velocity data how
can we determine pulsatile pressures ?
* Robust to noise
* Computationally efficient
Pressure and Velocity Field Relations
---- Navier-Stokes’ Equation
Pulsatile term
Viscous Forces
Pressure
Convective Inertial Forces Body force term
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
Phase-Contrast velocities in a 90% area stenosis phantom
Motion Induced Phase Shifts
PC-MRI
ignore
Phase Contrast Sequence
a
RF
flow encode 1
Gz
Gx
Gy
signal
A/D
Phase Contrast Sequence
a
RF
flow encode 2
Gz
Gx
Gy
signal
A/D
From Navier-Stokes to Pressure
1. Apply Navier-Stokes to noisy velocities to yield
2. 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
From Noisy Gradient to Pressure
• Orthogonally project
onto an integrable subspace where it can be integrated
Integrable sub-space
Orthogonal Projection
: true gradient vector field
Two Approaches to Orthogonal
Projection
• Iterative solution to pressure-Poisson equation
• Direct harmonics-based orthogonal projection
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.
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.
New Approach to Pressure Calculation:
Harmonics-Based Orthogonal Projection
Shape from Shading
1. Determine surface orientations
from image
brightness
2. 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
Expansion of Noisy Gradients With
Integrable Basis Functions
Set of basis functions satisfying the
integrability constraint
Where:
Computing Pressure From
Integrable Pressure Gradients
Following Frankot and Chellappa:
When using Fourier
basis functions
Using FFT
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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
Specific Problem in Computation of
Intravascular Pressure
• Irregular geometry of blood vessels
Discontinuities
along blood
vessel
boundaries
Discontinuities
at in-flow and
out-flow
boundaries
Concentric and Eccentric Stenosis
Geometries
90% Area Stenosis Phantoms
• 50%, 75%, 90% concentric area stenosis phantoms have been
fabricated
• These exact geometries are used in FLUENT CFD code for flow
simulation
Experimental Flow System
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.
Validation
---- on 3-D Axisymmetric FLUENT Velocities
Relative RMS Error (RError) between calculated pressures using
Fluent velocities with Fluent pressures (%) – no noise, constant flow
Q=10 Q=15 Q=20
Model (ml/s) (ml/s) (ml/s)
50% 3.24 5.10 6.31
Q=10 Q=15 Q=20
Model (ml/s) (ml/s) (ml/s)
50% 7.13 4.29 3.71
75%
4.12
5.26
5.95
75%
10.68
10.60
9.60
90%
6.79
7.26
7.53
90%
5.11
7.55
8.92
Harmonics-Based Orthogonal Projection
Iterative Solution to Pressure-Poisson Equation
Validation
---- on 3-D Axisymmetric FLUENT Velocities
CPU time on a Sun SPARC 10 when computing pressures (seconds):
Q=10 Q=15 Q=20
Q=10 Q=15 Q=20
Model (ml/s) (ml/s) (ml/s) Model (ml/s) (ml/s) (ml/s)
50% 3.30 3.23 3.23
50% 7.91 10.81 13.87
75%
4.25
4.23
3.25
75%
7.18
5.93
5.82
90%
3.25
3.27
3.26
90%
154.3
154.5
154.3
Harmonics-Based Orthogonal Projection
Iterative Solution to Pressure-Poisson Equation
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, Q=20 ml/s (constant flow)
0.02
RError of nonRError of
iterative method iterative method
13%
11.32%
0.04
18%
14.67%
0.06
28.14%
23.86%
0.4
49.97%
299.72%
0.6
71.42%
N/A
In-Vitro Pressure Profiles (from MRI) Along the Axis
of Symmetry of Stenosis Phantoms: Constant Flow
Q=10 ml/s
50%
75%
90%
Center of
Stenoses
Q=15 ml/s
Q=20 ml/s
Pulsatile Flow
Simulation performed by Juan Cebral using FEFLO
Noise Test on 3-D+t Simulated
Pulsatile Velocity Data
Relative RMS Error (RError) between calculated pressures
using noise corrupted FEFLO pulsatile velocities with
FEFLO pressures
= 0.03
Stenosis Model
RError of nonRError of
Iterative Method Iterative Method
75% eccentric
13.00%
32.91%
75% concentric
10.20%
23.87%
90% eccentric
10.29%
17.23%
90% concentric
13.73%
22.58%
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.
Geometry from Level-Set Evolution
Chen and Amini, IEEE Trans. On Medical Imaging, Vol. 23, No. 10, Oct. 2004
Level-Set Segmentation
• Perform 3-D level set evolution, using a speed
function derived from the enhanced image
Conclusions
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
Acknowledgements
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Nasser Fatouraee
Nick Tustison
Jian Chen
Abbas Moghaddam
Geoff Behrens
• NIH, BJH Foundation
Useful Links/Contact Information
• Amir Amini [email protected] until July 15
•
[email protected]
• 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/