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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 Louisville, KY Amir Kabir University, April 24, 2006

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Useful Links/Contact Information Amir Amini until July General information about ECE and forms On-line application for doctoral degree

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ECE Dept. Highlights Paul B. Lutz Hall 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 > 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

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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 1990’s 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 CII’s 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 , 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 magnet’s fixed coordinate system

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SPAMM Tagged MRI Sequence GxGxGxGx RF GyGyGyGy GzGzGzGz R x y

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Tagged MRI: Short-Axis Patient with old healed inferior MI RR R 1000

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Tagged MRI: Long-Axis RR R 1000

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Acquisition of Short-Axis Slices

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Acquisition of Long-Axis Slices

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B-Spline Models of Tag Planes

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Periodic B-Splines 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 Cubic polynomial in u

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4-D Cartesian B-Spline Model Tustison and Amini, IEEE Trans. On Biomedical Engineering, 50(8), Aug u v w

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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

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Myocardial Beads: Results

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Displacement Fields To generate displacement field, we subtract the 3-D solid at t = 0 from the 3-D solid at t = τ. Tustison and Amini, IEEE Trans. On Biomedical Engineering, (50)8, Aug. 2003

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Myocardial Strain Positive strains correspond to elongation whereas negative strains correspond to compression. Strain is a directionally dependent measure of percent change in length of a continuous deformable body

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Myocardial Strain

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Differential Element of Length

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Strain Calculation n=e 1 : radial n=e 2 :circumferential n=e 3 : longitudinal

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Strain Calculation Motion field:

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Displacement Fields

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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 Thickening: k 1

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Simulated Tagged MRI Movie

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Circumferential Strains

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Displacement Fields

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Strain Results – k Radial StrainCircumferential 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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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 Convective Inertial Forces Body force term Viscous Forces Pressure Pulsatile 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 ignore PC-MRI

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Phase Contrast Sequence flow encode 1 A/D GxGxGxGx RF GyGyGyGy GzGzGzGz signal

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Phase Contrast Sequence flow encode 2 A/D GxGxGxGx RF GyGyGyGy GzGzGzGz signal

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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

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From Noisy Gradient to Pressure Orthogonally project onto an integrable sub- space where it can be integrated Integrable sub-space : true gradient vector field Orthogonal Projection

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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 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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Frankot and Chellappa, IEEE PAMI, July 1988: Adopted a far more efficient basis function approach 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

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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 along blood vessel boundaries Discontinuities at in-flow and out-flow boundaries

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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

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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 Model Q=10 (ml/s) Q=15 (ml/s) Q=20 (ml/s) 50% % % Relative RMS Error (RError) between calculated pressures using Fluent velocities with Fluent pressures (%) – no noise, constant flow Model Q=10 (ml/s) Q=15 (ml/s) Q=20 (ml/s) 50% % % Harmonics-Based Orthogonal Projection Iterative Solution to Pressure-Poisson Equation

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Validation ---- on 3-D Axisymmetric FLUENT Velocities Model Q=10 (ml/s) Q=15 (ml/s) Q=20 (ml/s) 50% % % CPU time on a Sun SPARC 10 when computing pressures (seconds): Model Q=10 (ml/s) Q=15 (ml/s) Q=20 (ml/s) 50% % % Harmonics-Based Orthogonal ProjectionIterative 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, Q=20 ml/s (constant flow) RError of non- iterative method RError of iterative method % 11.32% % 14.67% % 23.86% % % % N/A

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In-Vitro Pressure Profiles (from MRI) Along the Axis of Symmetry of Stenosis Phantoms: Constant Flow 50% 75% 90% Q=10 ml/s Q=15 ml/s Q=20 ml/s Center of Stenoses

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Pulsatile Flow Simulation performed by Juan Cebral using FEFLO

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Noise Test on 3-D+t Simulated Pulsatile Velocity Data Stenosis Model RError of non- Iterative Method RError of 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% 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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Conclusions Phase-Contrast MRI Non-invasive measurement of intravascular pressures from Phase-Contrast MRI Tagged MRI Non-invasive measurement of myocardial strain maps Visualization of myocardial beads

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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 until July General information about ECE and forms On-line application for doctoral degree

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