Diffusion Imaging and
Computational Anatomy Studies
Patrick A. Helm, Ph.D.
University of Virginia
Raimond L. Winslow, Ph.D. ,
Michael I. Miller, Ph.D.,
Elliot McVeigh, Ph.D.,
Frederick Epstein, Ph.D.,
Johns Hopkins University
Baltimore, MD
Institute of Computational Medicine, JHU
Center for Imaging Science, JHU
Laboratory of Cardiac Energetics, NIH
Department of Radiology, UVA
University of Virginia
Charlottesville, VA
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
IPAM Feb, 2006
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.
IPAM Feb, 2006
Examples of Remodeling in Disease
IPAM Feb, 2006
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.)
IPAM Feb, 2006
Remodeling Impacts Function of Ventricles
Function assessed using tagged MRI
Normal
Normal
IPAM Feb, 2006
Dyssynchronous
Dyssynchronous
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 .
IPAM Feb, 2006
Histological Reconstruction of Cardiac Ventricular
Geometry and Fiber Architecture
Gross and Histological Dissections
McCallum et al (1900) Johns Hopkins Hosp Rep 9:307
Streeter et al (1969) Circ Res 24:339
Fox and Hutchins (1972). Johns Hopkins Med. J.
130(5): 289-299
IPAM Feb, 2006
Whole Heart Reconstruction
Nielsen et al (1991) Am. J. Physiol. 260: H1365
Diffusion Tensor Imaging (DTI) Permits Non-Invasive
Assessment of Tissue Structure
Demonstration that 1 aligns with
fiber direction
Principles of DTMRI
x
(Auckland group)
 s
ln    BD
 s0 
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., 44:157
IPAM Feb, 2006
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
IPAM Feb, 2006
Primary Eigenvector Disarray Within an Infarct
1 week
post- MI
IPAM Feb, 2006
Helm, PA. et al. (unpublished data)
Variance of Estimated D as a function of B
and Actual Diffusivity
IPAM Feb, 2006
Possible Relationship Between Higher Order Diffusion
Eigenvectors and Laminar Organization of the Heart
Cardiac Histology
Primary
Secondary
Tertiary
IPAM Feb, 2006
Scollan DF. et al. Am. J. Physiol. (1998). 275: H2308.
Challenge - Identifying Secondary and Tertiary
Eigenvectors of the Diffusion
Distribution of Eigenvalues for
Normal Heart
Types of diffusion that may occur
Isotropic (Spherical)
1 = 2 = 3
v1, v2, v3 uniformly distributed
about sphere
Transversly Isotropic (Cylindrical)
1 > 2 = 3
v2, v3 uniformly distributed
about disc
Anisotropic (Planar)
1 > 2 > 3
v3 has preferred direction
IPAM Feb, 2006
Hypothesis testing procedure for
distinguishing anisotropic diffusion
Types of diffusion that may occur
Isotropic (Spherical)
1 = 2 = 3
v1, v2, v3 uniformly distributed
about sphere
Transversly Isotropic (Cylindrical)
1 > 2 = 3
v2, v3 uniformly distributed
about disc
Anisotropic (Planar)
1 > 2 > 3
v3 has preferred direction
Hypothesis test: D = 0
Within an ROI define:
D = ds – dt (ideal difference)
 = 2 - 3 (measured difference)
v3 are tertiary eigenvectors
vn is orthogonal vector to v1
Eigenvalue Based Test
mdn( )
T
  mdn( )
Eigenvector Based Test
  cos 1 V3 Vn 


R  max   F ( ) 
  0,2   


F(t) empirical cumulative
distribution function of 
IPAM Feb, 2006
Helm PA., et al MRM. (2005) 54(4):850-9.
Characterization of Tests, Rc and Tc
Define: D = ds – dt (ideal difference)
 = 2 - 3 (actual difference)
Null Hypothesis: D=0
Power defined as # scores above critical value / total samples
IPAM Feb, 2006
Helm PA., et al MRM. (2005) 54(4):850-9.
Statistically Significant Regions in a Pooled
Population of Normals
Epicardium
SubEpicardium
Mid-Wall
SubEndocardium
Endocardium
Anterior
Base
2.40 ± 0.11
2.79 ± 0.16
2.96 ± 0.19
3.22 ± 0.43
2.96 ± 0.30
Lateral
Base
2.55 ± 0.11
2.76 ± 0.13
3.00 ± 0.20
2.90 ± 0.21
2.94 ± 0.31
Posterior
Base
2.66 ± 0.20
2.65 ± 0.28
2.84 ± 0.33
3.06 ± 0.36
2.92 ± 0.24
Anterior
Apex
2.65 ± 0.20
3.19 ± 0.66
3.64 ± 0.68
3.51 ± 0.50
2.98 ± 0.33
Lateral
Apex
2.59 ± 0.17
3.49 ± 0.84
3.43 ± 0.56
2.83 ± 0.16
2.74 ± 0.19
Posterior
Apex
2.74 ± 0.19
3.09 ± 0.49
3.59 ± 0.87
3.28 ± 0.50
3.10 ± 0.30
T-value
Values highlighted in red indicate statistically anisotropic
regions (rejection of the null hypothesis)
IPAM Feb, 2006
Helm PA., et al MRM. (2005) 54(4):850-9.
Relation between Diffusion Tensor and Laminar
Structure
Orientation of Tertiary eigenvector of DT
APEX
Epi
Sub. Epi.
Mid.
Sub. Endo.
Endo.
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., 280:H2222
IPAM Feb, 2006
Improved Visualization of Tensors using Glyphs
Superquadric Glyphs
Ellipsoids
1 > 2 > 3
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 2002;6(2):93-108
Diffusion Tensor Shape
Uniaxial
Diffusion
1> 2=3
IPAM Feb, 2006
Orthotropic
Diffusion
Equibiaxial
Diffusion
1> 2>3
1= 2>3
(Auckland group)
Ennis D. (Stanford)
Visualization of Transmural Variation of
Tensors using Ellipsoids
Epicardium
IPAM Feb, 2006
Ennis D. (Stanford)
Visualization of Transmural Variation of
Tensors using Glyphs
Epicardium
IPAM Feb, 2006
Ennis D. (Stanford)
Right ventricular insertion structure
Ennis D. et al. MRM. (2005) 53: 169-176
IPAM Feb, 2006
Anterior papillary muscle structure
Epicardium
LV Base
LV Apex
Ennis D. et al. MRM. (2005) 53: 169-176
IPAM Feb, 2006
Anterior papillary muscle structure
Epicardium
Anterior
Papillary
Muscle
Endocardium
Ennis D. et al. MRM. (2005) 53: 169-176
IPAM Feb, 2006
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
IPAM Feb, 2006
Method for Registering Anatomies
Resample hearts to a common isotropic
resolution
Select Template and Target anatomies
Coordinate Transformation
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
Template (Atlas)
IPAM Feb, 2006
Target (Patient Specific)
Large Deformation Diffeomorphic Metric
Mapping (LDDMM)
1
2
1
0
V
2
E ( )    t dt 
E1


2
I 0 ( y ) ˆ1,0 ( y )  I1 ( y ) dy
E2
Transformations are:
1:1
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
IPAM Feb, 2006
Beg, M.F., et al. Int. J. Comput Vis. (2005) 61:139-157
Beg, M.F., et al. MRM. (2004) 52:1167-1174
Demonstration of Evolving One
Heart into Another using V0
Method
1) Match the normal heart to the
failing heart using rigid body
transformation
2) For the normal heart, compute an
initial velocity vector field using
LDDMM that deforms it into the
failing heart at t=1
Normal Heart
IPAM Feb, 2006
Failing Heart
Average Geometric Configuration using
Evolution of the Template
Targets
Template
I0
I1
V0(1)
^
I1
I2
V0(2)
^
I2
V0(1) + V0(2)
2
IPAM Feb, 2006
I1 + I 2
Procrustes Alignment to Estimate Mean Geometry
Variation about Procrustes mean defines population variability
IPAM Feb, 2006
Variation about Geodesic Mean using PCA
on Vector Fields
Kv 
N
1
N
T
ˆ
ˆ



v

v
v

v
 i
i
i 1
~
K v  vT v
vT v~   ~
j
j
j
vvT v~ j    j v~ j 
Kv is [(3 x pixels)X(3 x pixels)]
~
Kv is [N X N], N is # of patients
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
Variation –
3)T, where i of
vi(u) =(vi(u)1Principle
, vi(u)2, vi(u)Direction
= 1,…N
IPAM Feb, 2006
Failing Hearts
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)
IPAM Feb, 2006
Helm PA., et al. Circ. Res. (2006) 98(1): 125-32
Evolution of Principle Directions Animations
- Normal Population Within Class Variability
- Normal to Failing Between Class
- Failing Population Within Class Variability
IPAM Feb, 2006
Helm PA., et al. Circ. Res. (2006) 98(1): 125-32
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:
1) Transform diffusion tensor with Jacobian of
transformation
2) First, reference fiber architecture to un-deformed
geometry. Second, transform geometry using LDDMM
carrying scalar information of fiber architecture.
IPAM Feb, 2006
Remodeling in the Dyssynchronous Failing Heart
Normal
Failing
Normal
Significant Findings in Failure:
Regional wall thinning
Increased rate of transmural fiber
rotation
Remodeling of laminar structure
Failing
+ 60
0
- 60
Epi.
Endo.
Epi. Endo.
Helm PA., et al. Circ. Res. (2006) 98(1): 125-32
IPAM Feb, 2006
Remodeling of Transverse Angle in Failure
Significance of Transverse Angle
Computational Anatomy
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
IPAM Feb, 2006
Helm PA., et al. in Progress
Extension of Results using Fiber Tracking
of Principle Eigenvector
Line Propagation Technique
•
Tracking halted when
– fibers deviated > 45 degrees
– Anisotropy < 0.15
IPAM Feb, 2006
Xue R. et al., MRM 42:1123-1127
Fiber Tracking Reveals Continuity of Fiber
Architecture through the Apex and Base
Apical Loop
IPAM Feb, 2006
Basal Loop
Helm PA., et al. in progress
Pathways are Very Similar to Gross Dissections of
Cardiac Ventricular
RV
LV
Torrent-Guasp et al (1980) Rev. Esp.
Cardiol. 33(3):265
IPAM Feb, 2006
Quantitative Assessment of Vector
Pathways Reveal Continuous Helixes
IPAM Feb, 2006
Helm PA., et al. in progress
Future Applications of Computational
Anatomy
 Mapping of diffusion eigenvectors and/or tensors
 Mapping cardiac phase from CINE MRI
 Mapping mechanical function from DENSE MRI
IPAM Feb, 2006
Diffeomorphisms on Non-Scalar Fields
2
2
1
1
E (v)   Vt dt  2  I 0  ˆ1, 0  I1 dy
0

V


 

E1
E2
D1, 0 1, 0 I 0  1, 0 I 0  1, 0  I1
2
E (v)   Vt dt  c1 
 c2  I 0  1, 0  I1  dx
0

V

D

I





1, 0 1, 0 0
1, 0
E3
E1



1
2
2
E2
IPAM Feb, 2006
Cao Y., et al. IEEE Trans Med Imag. (2005) 98(1): 125-32
Diffeomorphisms on Time Evolving Fields
CINE / Tagged -MRI
IPAM Feb, 2006
DENSE -MRI
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.
IPAM Feb, 2006