Diffusion Imaging and Computational Anatomy Studies

1
Diffusion Imaging and Computational Anatomy
Studies
Patrick A. Helm, Ph.D. University of Virginia

• Raimond L. Winslow, Ph.D. , Institute of
  Computational Medicine, JHU
• Michael I. Miller, Ph.D., Center for Imaging
  Science, JHU
• Elliot McVeigh, Ph.D., Laboratory of Cardiac
  Energetics, NIH
• Frederick Epstein, Ph.D., Department of
  Radiology, UVA

University of Virginia Charlottesville, VA
Johns Hopkins University Baltimore, MD
2
Background and Significance

• Heart failure is a disease in which electrical
  conduction and mechanical abnormalities lead
• Reduced cardiac output
• Increased risk for arrhythmias
• Heart failure is a leading cause of death in the
  US
• Heart failure currently affects 4.7 million
  Americans
• It is associated with a poor prognosis 1 in 5
  people with heart failure will die within one
  year of diagnosis

3
Importance of Anatomic Remodeling in Heart Disease

• The cardiac ventricles undergo significant
  remodeling during development of heart disease.
• Remodeling may include
• Electrophysiological Remodeling (altered
  expressions of genes/proteins)
• Structural Remodeling (chamber geometry,
  material properties, fiber architecture)
• Remodeling is known to impact the
  electro-mechanical functioning of the heart
  during disease.

4
Examples of Remodeling in Disease
5
Animal Models of Heart Failure Aid the Study of
Remodeling

• Swine, Canine, Murine etc.
• Canine Model
• Dyssynchronous failure model
• Non-ischemic model of failure
• Left Bundle Branch Block followed by 4-6 weeks of
  tachypacing
• Physiologic/Pathologic alterations mimic those in
  human dilated cardiomyopathy
• Elevated end diastolic volume and pressure
  (EDV,EDP)
• Reduced contractile function
• Dyssynchronous contraction due to
  intraventricular conduction defect

(Helm et al.)
6
Remodeling Impacts Function of Ventricles
Function assessed using tagged MRI
Dyssynchronous
Normal
Dyssynchronous
Normal
7
Outline

• Part I. Review DTMRI techniques for high
  resolution 3D reconstruction of ventricular
  geometry and fiber orientation.
• Part II. Define computational methods adapted
  from the field of Computational Anatomy to
  quantify variability of ventricular structures.
  Present results obtained by applying these
  techniques to the study of dyssynchronous failing
  heart.
• Part III. Briefly, discuss future work in the
  field of Computational Cardiac Anatomy .

8
Histological Reconstruction of Cardiac
Ventricular Geometry and Fiber Architecture
Whole Heart Reconstruction
Gross and Histological Dissections
McCallum et al (1900) Johns Hopkins Hosp Rep
9307 Streeter et al (1969) Circ Res 24339 Fox
and Hutchins (1972). Johns Hopkins Med. J.
130(5) 289-299
Nielsen et al (1991) Am. J. Physiol. 260 H1365
9
Diffusion Tensor Imaging (DTI) Permits
Non-Invasive Assessment of Tissue Structure
Demonstration that ?1 aligns with fiber direction
Principles of DTMRI
(Auckland group)

• DTMRI 3x3 diffusion tensor D(x)
• Hypothesis The primary eigenvector of D(x), ?1
  is aligned with fiber direction.

Scollan DF. et al (1998). Am. J. Physiol. 275
H2308 Holmes A. (2000). Magn. Res. Med., 44157
10
Diffusion Tensor Imaging (DTI) Enables Rapid
Reconstruction of Primary Fiber Structure
DTMRI Reconstruction of Ex-Vivo Canine Ventricles

• Spatial resolution of
• 350 x 350 x 800 ?m

Apical Spiral
11
Primary Eigenvector Disarray Within an Infarct
1 week post- MI
Helm, PA. et al. (unpublished data)
12
Variance of Estimated D as a function of B and
Actual Diffusivity
13
Possible Relationship Between Higher Order
Diffusion Eigenvectors and Laminar Organization
of the Heart
Cardiac Histology
Scollan DF. et al. Am. J. Physiol. (1998). 275
H2308.
14
Challenge - Identifying Secondary and Tertiary
Eigenvectors of the Diffusion
Types of diffusion that may occur
Distribution of Eigenvalues for Normal Heart

• Isotropic (Spherical)
• ?1 ?2 ?3
• v1, v2, v3 uniformly distributed about sphere
• Transversly Isotropic (Cylindrical)
• ?1 gt ?2 ?3
• v2, v3 uniformly distributed about disc
• Anisotropic (Planar)
• ?1 gt ?2 gt ?3
• v3 has preferred direction

15
Hypothesis testing procedure for distinguishing
anisotropic diffusion
Hypothesis test D 0
Types of diffusion that may occur
Within an ROI define D ds dt
(ideal difference) z l2 - l3
(measured difference) v3 are tertiary
eigenvectors vn is orthogonal vector to
v1

• Isotropic (Spherical)
• ?1 ?2 ?3
• v1, v2, v3 uniformly distributed about sphere
• Transversly Isotropic (Cylindrical)
• ?1 gt ?2 ?3
• v2, v3 uniformly distributed about disc
• Anisotropic (Planar)
• ?1 gt ?2 gt ?3
• v3 has preferred direction

Eigenvalue Based Test
Eigenvector Based Test
F?(t) empirical cumulative distribution function
of ?
Helm PA., et al MRM. (2005) 54(4)850-9.
16
Characterization of Tests, Rc and Tc
Null Hypothesis ?0
Define ? ds dt (ideal difference)
? ?2 - ?3 (actual difference)
Power defined as scores above critical value /
total samples
Helm PA., et al MRM. (2005) 54(4)850-9.
17
Statistically Significant Regions in a Pooled
Population of Normals
Values highlighted in red indicate statistically
anisotropic regions (rejection of the null
hypothesis)
Helm PA., et al MRM. (2005) 54(4)850-9.
18
Relation between Diffusion Tensor and Laminar
Structure
Orientation of Tertiary eigenvector of DT
Epi Sub. Epi. Mid.
Sub. Endo. Endo.
APEX
Two Hearts
Helm PA., et al. MRM. (2005) 54(4)850-9.
Pooled from 8 Hearts
Numerical Models and Histological measurements of
sheets
Arts et al (2001). Am. J. Physiol., 280H2222
19
Improved Visualization of Tensors using Glyphs
Superquadric Glyphs
Ellipsoids
Kindlmann G. Proc. IEEE TVCG/EG Symp Vis (2004),
147-154 Ennis D. et al. MRM (2005) 53 169-176
Westin CF et al Med Image Anal 20026(2)93-108
20
Diffusion Tensor Shape
Uniaxial Diffusion
Equibiaxial Diffusion
?1gt? 2?3
?1? 2gt?3
Ennis D. (Stanford)
(Auckland group)
21
Visualization of Transmural Variation of Tensors
using Ellipsoids
Epicardium
Ennis D. (Stanford)
22
Visualization of Transmural Variation of Tensors
using Glyphs
Epicardium
Ennis D. (Stanford)
23
Right ventricular insertion structure
Ennis D. et al. MRM. (2005) 53 169-176
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Anterior papillary muscle structure
LV Base
Epicardium
LV Apex
Ennis D. et al. MRM. (2005) 53 169-176
25
Anterior papillary muscle structure
Epicardium
Endocardium
Ennis D. et al. MRM. (2005) 53 169-176
26
Application of DTMRI Reveals Structural
Differences Between Normal and Failing
N
N
F
Experiments Completed

• 11 normal, 7 failing canine hearts
• 1 normal human heart
• 3 normal, 3 infarcted rhesus monkey / canine
  hearts
• Data available at www.ccbm.jhu.edu

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Method for Registering Anatomies

• Resample hearts to a common isotropic
  resolution
• Select Template and Target anatomies
• Rigid body translation and rotation of
  template based on a sparse set of landmarks
• Apply a high-order transformation to template
  so that every voxel on the template maps to a
  voxel on the target

Coordinate Transformation
Template (Atlas)
Target (Patient Specific)
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Large Deformation Diffeomorphic Metric Mapping
(LDDMM)

• Transformations are
• 11
• Invertible
• Smooth and yield best fit

• I1 is uniquely determined by I0 and initial v
• time does not represent cardiac phase rather a
  time point in the evolution of the template

Beg, M.F., et al. Int. J. Comput Vis. (2005)
61139-157 Beg, M.F., et al. MRM. (2004)
521167-1174
29
Demonstration of Evolving One Heart into Another
using V0
Method

• Match the normal heart to the failing heart using
  rigid body transformation
• For the normal heart, compute an initial velocity
  vector field using LDDMM that deforms it into the
  failing heart at t1

Normal Heart
Failing Heart
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Average Geometric Configuration using Evolution
of the Template
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Procrustes Alignment to Estimate Mean Geometry
Variation about Procrustes mean defines
population variability
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Variation about Geodesic Mean using PCA on Vector
Fields
v is (3 x pixels) X N
Principle Direction of Variation Normal Hearts
N is the population size P is the number of
voxels in the vector field vi(u) (vi(u)1,
vi(u)2, vi(u)3)T, where i 1,N
Principle Direction of Variation Failing Hearts
33
Principle Components Analysis of Within and
Between Class Variation
- Normal Population - Within Class Variability
- Normal to Failing -Between Class
- Failing Population - Within Class Variability
?n, ?f are primary eigenvectors of momentum
across population (these vectors point in the
direction of highest geometric variability)
Helm PA., et al. Circ. Res. (2006) 98(1) 125-32
34
Evolution of Principle Directions - Animations
- Normal Population - Within Class Variability
- Normal to Failing -Between Class
- Failing Population - Within Class Variability
Helm PA., et al. Circ. Res. (2006) 98(1) 125-32
35
Techniques for Analysis of Fiber Structure
DT-MRI data is non-scalar and thus requires
addition consideration when mapping. Proper
procedure requires pixel mapping plus
re-orientation of the directional vectors.
Two Solutions

• Transform diffusion tensor with Jacobian of
  transformation
• First, reference fiber architecture to
  un-deformed geometry. Second, transform geometry
  using LDDMM carrying scalar information of fiber
  architecture.

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Remodeling in the Dyssynchronous Failing Heart
Normal
Failing
60

• Significant Findings in Failure
• Regional wall thinning
• Increased rate of transmural fiber rotation
• Remodeling of laminar structure

Helm PA., et al. Circ. Res. (2006) 98(1) 125-32
37
Remodeling of Transverse Angle in Failure
Computational Anatomy
Significance of Transverse Angle
Normal
Circumferential-radial shear deformation reduced
in base and apex by non-zero transverse angle
Frangi A.F. et al. (Eds.) FIMH 2005, LNCS 3504
314-324 Bovendeerd, PH., J Biomech (1994)
27(7)941-51
Failing
35o
0o
Helm PA., et al. in Progress
38
Extension of Results using Fiber Tracking of
Principle Eigenvector
Line Propagation Technique

• Tracking halted when
• fibers deviated gt 45 degrees
• Anisotropy lt 0.15

Xue R. et al., MRM 421123-1127
39
Fiber Tracking Reveals Continuity of Fiber
Architecture through the Apex and Base
Basal Loop
Apical Loop
Helm PA., et al. in progress
40
Pathways are Very Similar to Gross Dissections of
Cardiac Ventricular
Torrent-Guasp et al (1980) Rev. Esp. Cardiol.
33(3)265
41
Quantitative Assessment of Vector Pathways Reveal
Continuous Helixes
Helm PA., et al. in progress
42
Future Applications of Computational Anatomy

• Mapping of diffusion eigenvectors and/or tensors
• Mapping cardiac phase from CINE MRI
• Mapping mechanical function from DENSE MRI

43
Diffeomorphisms on Non-Scalar Fields
Cao Y., et al. IEEE Trans Med Imag. (2005) 98(1)
125-32
44
Diffeomorphisms on Time Evolving Fields
CINE / Tagged -MRI
DENSE -MRI
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Acknowledgements

• Raimond L. Winslow, Ph.D.
• Laurent Younes, Ph.D.
• Michael I. Miller, Ph.D.
• Elliot McVeigh, Ph.D
• Susumu Mori, Ph.D.
• M. Faisal Beg, Ph.D.
• Daniel B. Ennis, Ph.D
• Reza Mazhari, Ph.D.
• David Kass, M.D.
• Christophe Leclerq, M.D.