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Location of lesions on postmortem brain by co-registering corresponding MRI and postmortem slices
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Location of lesions on postmortem brain by co-registering corresponding MRI and postmortem slices
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Content
LOCATION OF LESIONS ON POSTMORTEM BRAIN BY CO-REGISTERING
CORRESPONDING MRI AND POSTMORTEM SLICES
by
Amrita Rajagopalan
A Thesis Presented to the
FACULTY OF THE VITERBI SCHOOL OF ENGINEERING
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(BIOMEDICAL ENGINEERING)
December 2006
Copyright 2006 Amrita Rajagopalan
ii
Acknowledgments
I would like to express my gratitude to my advisor, Dr. Manbir Singh, whose expertise,
understanding, and patience, added considerably to my graduate experience. I would like
to thank the other members of my committee, Dr. Krishna Nayak, and Dr. Jean-Michel
Maarek for the assistance they provided at all levels of my thesis. I also thank Dr. Chris
Zarow, Dr. Ae-Young Lee, Dr. Helena Chui , Dr. Xiao-Ling, Darryl Hwang and who
were part of the research team for this project for being very supportive and co-operative.
Very special thanks go to Dr. Sungheon Kim, Dr. Tae-Seong Kim and Nilesh Gunghre
who were responsible for laying the foundations of this project. I recognize that this
research would not have been possible without the financial assistance of the NIH grants
(NIA-NIH1P01AG12453 and NIA-NIH P50AG05142).
iii
Table of Contents
Acknowledgments........................................................................................................... ii
List of Tables ..................................................................................................................v
List of Figures................................................................................................................ vi
Abstract.......................................................................................................................... ix
0.1 Introduction to Magnetic Resonance Imaging (MRI)......................................... 1
0.1.1 Principle ..............................................................................................................1
0.2 What is Registration?.......................................................................................... 5
0.3 Application of Image Registration in Medicine.................................................. 5
0.3.1 Registration in Multimodality Imaging .............................................................. 6
0.3.2 Problems related to Multimodality Imaging....................................................... 7
0.4 General Approaches to the Registration Problem [1]......................................... 7
0.5 Objective.............................................................................................................9
0.6 Challenges in Co-registration...........................................................................10
0.7 Co-registration..................................................................................................11
0.8 Block Diagram..................................................................................................12
0.9 Preprocessing....................................................................................................13
0.9.1 Preparation and Preprocessing of the postmortem brain slices: ....................... 13
0.9.2 Preprocessing of in-vivo MR images................................................................ 15
0.10 Volume Matching.............................................................................................17
0.11 Image Registration............................................................................................19
0.12 Transferring information from MR images to postmortem Images.................. 29
0.13 Validation..........................................................................................................33
0.14 Conclusion........................................................................................................35
iv
Bibliography ................................................................................................................. 36
v
List of Tables
Table 1: Comparison between single slice and multiple slice co-registration.
27
Table 2: The 3D Euclidean distances between the centroids of the lesions
identified by co-registration and by histology.
34
vi
List of Figures
Figure 1: (a) The orientation of spins in the absence of an external
magnetic field. (b) The orientation of spins in the presence of
an external magnetic field B
0.
(c) The tipping of the net
Magnetic moment M on the application of an RF field in a
rotating frame of reference.
3
Figure 2: (a) The relaxation of M
z
on the removal of RF field. (b) The
relaxation of M
xy
on the removal of the RF field.
4
Figure 3: An outline of the project.
12
Figure 4: The digital photograph of a postmortem slice.
13
Figure 5: (a) The selection of control points: the cross wire points to one
of the control points. (b) The locations of control points from
all the slices before realignment. (c) The locations of control
points from all the slices after realignment. Note that the
corresponding control points overlap.
14
Figure 6: The segmented postmortem slice.
15
Figure 7: The T1 weighted coronal MR Image (slice at the center of the
volume).
16
Figure 8: The MR image on applying BSE algorithm (slice at the center
of the volume).
16
Figure 9: The MR image after removal of the midbrain region (slice at
the center of the volume).
17
Figure 10: Right hemisphere of the MRI brain image (slice at the center
of the volume).
17
vii
Figure 11: (a) The postmortem brain volume: four views. (b) Postmortem
slices. (c) The MRI volume before reorientation: four views.
(d) The MRI slices before reorientation. (e) The MRI volume
after reorientation: four views. (f) The MRI slices after
reorientation.
18
Figure 12: (a) Selection of a slice from the postmortem volume. (b) The
warped slices from the reoriented MR volume obtained by
changing the polynomial coefficients.
21
Figure 13: Co-registration results with stacks of varying sizes. The first
row consists of postmortem slices, while the corresponding
registered MRIs and the difference images are in the second
row and the third rows respectively. (a) The results with stacks
of single slice. (b) The results with stacks of four slices. (c)
The results with stacks of eight slices. (d) The results with a
stack consisting of the entire volume.
24
Figure 14: The co-registration results with stacks of four slices. The first
and the third rows show the post mortem slices, while the
corresponding registered MRI slices are in the second and the
fourth rows.
28
Figure 15: (a) The T2 weighted image. (b) The T2 weighted image with
the lesion that was identified by a radiologist. (c) Image with
only the lesion (extracted from (b)).
29
Figure 16: (a) The T1 weighted volume. (b The T2 weighted volume. (c)
The T2 weighted volume registered with T1 weighted volume.
30
Figure 17: (a) The T2 weighted volume with the lesion. (b) The volume,
which is matched with the T1 volume, with only the lesion.
The cross wires that point at the lesion in both the volumes,
indicate that the lesions are at the same location in both the
volumes.
31
viii
Figure 18: (a) Reoriented and resliced T2 weighted volume with the
lesion identified on it. (b) Reoriented and resliced Lacune
volume.
32
Figure 19: (a) A postmortem slice. (b)The slice in (a) with the lesion that
is identified by co-registration. (c) The registered MRI slice
corresponding to the slice in (a). (d) The MRI slice in (c) with
the lesion that is identified by the radiologist.
32
Figure 20: Shows the histology results (a) Histology slide with the lesion
location marked by the histologist. (b) The magnified
microscopy image of the region that is encircled in (a). (c) A
magnified portion of (b).
33
Figure 21: Shows a histology slide that is manually registered to the
postmortem slice. The black circle shows the lesion that is
identified histologically and the dark grey region beneath is the
region that is identified by the co-registration procedure.
34
ix
Abstract
Brain vascular abnormalities like lacunar infarcts and perivascular spaces cannot be
readily identified on MRI images but can be recognized on postmortem slices. We
present a method for transferring information from MRI images to the corresponding
postmortem images in order to validate the diagnosis of vascular lesions from MRI. We
achieve this by co-registering the in-vivo MRI with digital photographs of the
postmortem brain and transferring marked lesions from the registered MRI to the
postmortem images. Relatively larger samples of the postmortem slices around these
marks are extracted and sent to a pathologist to identify abnormalities by histological
methods. To validate the co-registration, the histologically identified regions are
manually registered to the original postmortem images. Results reveal that the co-
registration identifies the locations of 11 lesions in 7 subjects within an error of 7.6 ± 2.6
mm.
1
0.1 Introduction to Magnetic Resonance Imaging (MRI)
MRI is a non-invasive medical imaging modality, which gives two dimensional
and three dimensional images of the body. It is a powerful diagnostic tool, which offers a
wide range of parameters that can be modified to control the image content as required.
For example, images of fat and water can be acquired separately by varying the imaging
parameters. Since it does not involve ionizing radiations, MRI is considered safer than
other imaging modalities like Computed Tomography (CT), Positron Emission
Tomography (PET) and Single Photon Emission Computed Tomography (SPECT). MR
images have superior soft tissue contrast and can be used for anatomical and
physiological imaging. Shortcomings of the MR machine include the expense and the
sophisticated hardware.
0.1.1 Principle
Atoms with an odd number of protons or neutrons possess a nuclear spin angular
momentum. These spinning nuclei can be visualized as spinning charged particles that
have a magnetic moment, which is essential to MRI. Since 70 % of the human body
constitutes of water molecules, hydrogen nuclei emits the largest MR signal. Thus,
hydrogen atoms are generally used for MR imaging. In the absence of an external
magnetic field these magnetic moments are randomly oriented and the net macroscopic
magnetic moment (M) is zero.
2
When a strong external magnetic field (B
0
) is applied, say along the z-axis, these
nuclei align themselves parallel or anti-parallel to the applied field. Thus, the body has a
net magnetic moment (M
0
) in the direction of B
0
. The nuclei precess about B
0
with a
characteristic frequency ( ω
0
), called the Larmor frequency, according to the following
relationship
0
0
B γ ω = (1)
Here γ is a dimensionless quantity called the gyromagnetic ratio ( γ). Since gyromagnetic
ratio varies among atomic nuclei, so does the Larmor frequency.
Application of a radio frequency (RF) field at Larmor frequency, perpendicular to
B
0
, increases the energy of the polarized nuclei resulting in resonance. The macroscopic
magnetic moment tips away from B
0
while precessing about B
0
. Upon the removal of the
RF field, the nuclei return to their low energy states accompanied by the emission of
radio waves at Larmor frequency, which are detected by RF receiving coils. The emitting
nuclei can be characterized by analyzing the resulting frequency spectrum. In the absence
of the RF field, M
returns to its initial state M
0
. This phenomenon is called relaxation.
The amplitude of the MR signal depends on the MR parameters such as proton density
( ρ), longitudinal time constant (T
1
), and the transverse time constant (T
2
). By choosing
appropriate scanning parameters, one can modify the extent of this dependency. T
1
is the
time taken for the z component of the net magnetic moment (M) to relax to 63.2 % of its
initial value (M
0
). T
2
is the time taken for the xy component of the net magnetic moment
to relax to 36.7 % of its initial value (M
0
). By applying a gradient
3
magnetic field along B
0
, the frequencies can be localized to reconstruct an image from
the MR signal.
M
Figure 1: (a) The orientation of spins in the absence of an external magnetic field. (b)
The orientation of spins in the presence of an external magnetic field B
0.
(c) The
tipping of the net Magnetic moment M on the application of an RF field in a rotating
frame of reference.
(c)
Rotating frame of reference
Z
Y’
X’
RF
B
0
No external magnetic field
(a)
Presence of an external magnetic field
B
0
(b)
4
(a)
Figure 2: (a) The relaxation of M
z
on the removal of RF field. (b) The relaxation of M
xy
on the removal of the RF field.
(b)
X’
M
B
0
Z
X’
Y’
M
xy
relaxation- due to the
dephasing of individual magnetic
moments
Rotating frame of reference
RF field removed
Mxy
M
xy
Z
B
0
Y’
Rotating frame of reference RF field removed
M
z
going back to its initial
value – T
1
relaxation.
5
0.2 What is Registration?
Registration [1] & [2] is a fundamental task in image processing which is used to
match two or more pictures. The images could be taken at different times, with different
sensors, or from different viewpoints. Images are registered for the purpose of combining
or comparing the information that is associated with them. To register different images,
one finds an optimal geometrical transformation that brings the source image in precise
spatial correspondence with the target image.
Linear transformations such as rotation, scaling, reflection and translation are
used for cases where there is only a global difference between the target and the source
image. But while comparing images that have many local variations, transformations
such as uniform and non-uniform scaling, shearing and non linear warping become
necessary.
Different techniques of image registration have been developed for various types
of data and problems. Merits and relationships between the wide varieties of existing
techniques have to be understood before selecting the most suitable technique for a
specific problem.
0.3 Application of Image Registration in Medicine
Image registration [2] has significant applications in the field of medical sciences.
Specific situations include: combining images of the same subject acquired using
different modalities, aligning temporal sequences of images of the same subject to
compensate for motion in between scans, relating the video images that are obtained in an
6
image guided surgery to the preoperatively obtained diagnostic scans, in clinical studies
for the generalization of individual results to a population by transferring them to a
population template, etc. The latter procedure is termed-normalization. Medical image
registration also plays a crucial role in the diagnosis of breast cancer, colon cancer,
cardiac studies, study of inflammatory diseases and different neurological disorders
including brain tumors, Alzheimer's disease and schizophrenia.
0.3.1 Registration in Multimodality Imaging
Two basic types of medical images are: functional body images (such as SPECT
or PET scans), which provide physiological information, and structural images (such as
CT or MRI), which provide an anatomic map of the body. Different medical imaging
techniques may provide scans with complementary and occasionally conflicting
information. Combining images obtained from different modalities can give valuable
additional clinical information that may not be apparent in the separate images. However,
the functional images often do not have enough anatomical detail. To determine the exact
anatomical location of an activity in a functional image, it is registered to a structural
image, and the registered image is subsequently overlaid on the structural image. This
enables the identification of the exact location of an abnormality that was originally
diagnosed from the functional image. For example, functional SPECT or PET images
could be registered with structural magnetic resonance images (MRI) or X-ray computed
tomography (CT) images. This provides complementary anatomic and physiological
information that is of great importance to research, diagnosis, and treatment.
7
0.3.2 Problems related to Multimodality Imaging
The problems related to multimodality imaging can be classified into two groups; a)
registration, and b) visualization of the composite images that are obtained after
registration.[1]
• Registration
Scanning parameters may vary depending on the imaging modality. These
parameters include pixel or voxel size, matrix size, and orientation. For example,
one of the first steps in registering SPECT images with MRI or CT images is to
expand the 64x64 SPECT image to a 256x256, or even to 512x512 matrix. To
preserve the quality of images during the aforementioned enlargement, certain
interpolation schemes become necessary.
• Visualization
In order to combine and utilize information, a composite image is
generated after registering images from different modalities. During this
procedure, one should retain as much information as possible. The way this is
implemented depends on the particular clinical application at hand.
0.4 General Approaches to the Registration Problem [1]
• Control-point based registration methods
Control-points are the features that are unique to a set of images. They are
indicators to the transformation that matches the source and the target images.
8
They can be extrinsic, intrinsic, or a combination of both. They can be internal
anatomic landmarks such as the rib cage, ventricles, bone surfaces, external point
sources attached to the patient, or external fiducial markers in stereotactic studies.
Once the transformation is determined from the control-points it is applied to the
entire image.
• Moment-based registration
In the previous method, the registration process depends on the location
and correspondence of the control points. Since the landmarks could be
distributed in complicated patterns, which are difficult to characterize
mathematically, methods of registration that employ control-points become
difficult to automate. The method of Moment-based registration is based on
features that can be derived from the image. For example, center of gravity,
principal axis and more complex moments. Noise tolerance is weak for moment-
based registration techniques since noise can lead to imperfect moment estimates
and hence large errors in parameter determination. These techniques usually do
not permit robust registration and its use is restricted to the matching of pairs of
simple objects.
• Edge-based registration methods
This method is applied to images that have well defined contours.
Extraction of contours from a noisy image is a non-trivial task. Resulting contours
must be properly characterized before applying a matching algorithm. This
9
technique has potential use in the field of medical imaging, because in most
instances edge information is the only common feature found in each image.
• Optimization of a similarity measurement as a registration method
In this technique, the source image is iteratively transformed and the
similarity is measured until, the best fit is achieved. We employ this method in
our project. The measures of similarity can be in the form of mutual information,
correlation coefficient, or a sum of absolute differences. This method can lead to
misregistration in some cases. For instance, a misregistration could occur if one of
the images that are being registered shows a tumor while the other does not.
0.5 Objective
Abnormalities such as white matter lesions, hippocampal and cortical atrophy,
and lacunar infarcts are often manifested in patients who are suffering from small vessel
ischemia or Alzheimer’s Disease [3]. At times, MR images lead to an incorrect diagnosis
of these abnormalities. The only way to validate the diagnosis is through histology
studies [4-7]. Correlating the MRI images with the postmortem images enables the
transfer of such lesions onto the postmortem brain.
The objective of this project is to extract information about the location of the
abnormality from MR images and transfer it on to the postmortem brain slice. We
achieve this by co-registering the in-vivo MR images with the postmortem images of the
same person. Once this is done, the abnormality may be removed for histological
10
examinations to provide better understanding of the disease and its pathological
mechanism.
0.6 Challenges in Co-registration
• The acquisition time gap between the postmortem images and the MR
images
There is a large interval (2-3 years) between the acquisition of the MR
images and the postmortem images. As a result, there are structural discrepancies
between the two sets of images. One way to evade this is to use postmortem MRI
rather than in-vivo MRI. But it is known that the MRI signals change
significantly after death [8] & [9]. It has been shown that the T2 signal decays
within 90 hours of death [10]. Moreover, the fixative agents cause the white
matter and gray matter to have similar intensities in T1 and T2 weighted images.
Hence, we use in-vivo MR images for this project.
• The slices of postmortem brain are prone to distortions
The procedure of extraction of the brain from the cranial vault leads to
multiple deformations such as collapse of the ventricles during extraction,
distortions while slicing, and deformations due to dehydration.
• Non-uniformity of the postmortem slices
The postmortem brain is sliced with a meat chopper. During this
procedure, it is difficult to maintain an even planar thickness and a constant slice
11
orientation with respect to a single reference point. This hinders the 3D
reconstruction of the brain volume.
0.7 Co-registration
Co-registration begins with preprocessing the postmortem and the MRI brain
volumes. The MR volume is then roughly matched with the postmortem volume by
applying transformations such as scaling, rotation and translation. The reoriented MR
volume is resliced using a second order polynomial, whose parameters are iteratively
varied until the slices match the postmortem brain slices. The information about the
lesion locations (marked by a radiologist on the MR images) are transferred to the post
mortem slices from the registered MR images. To validate our findings a relatively larger
region around the identified location is sent to a histologist for stained microscopy. The
histologist identifies regions of abnormality on these substrates. The Euclidean distances
between these locations and those previously obtained by co-registration are calculated.
These are indicators of accuracy of the co-registration procedure.
12
0.8 Block Diagram
Overlaid
Postmortem
brain volume
MRI(T1)
brain volume
Processed
Postmortem
brain volume
Processed MRI
brain volume
MRI(T2) brain volume
with lacune marks
Co registration
using SPM2
Lacune volume
Co registered Lacune
volume
Volume matching: MR volume is
transformed to match the postmortem
CO REGISTRATION-2
nd
order polynomial
Reoriented
MRI brain volume
Co-registered
MR slices
Reoriented Lacune
volume
Co registered Lacune
volume
Postmortem
brain slices with transferred
lacune locations
Pre-processing
Pre-processing
Registration
parameters
Reorientation
parameters
Overlaid on postmortem slices
Registration parameters
Figure 3: An outline of the project.
13
0.9 Preprocessing
The postmortem brain images and the MRI images are preprocessed before co-
registration.
0.9.1 Preparation and Preprocessing of the postmortem brain slices:
The postmortem brain is fixed in 10% neutral formalin for at least two weeks. It is
then cut into 25 to 30 coronal slices, 5mm thick each, with a motor-driven rotary slicer. A
very thin tissue called corpus callosum holds the two hemispheres of the brain together.
Hence, it is very difficult to maintain the relative distance between them while slicing. To
circumvent this, the two hemispheres are separated and registered separately. For better
registration it is essential to minimize the local and global geometrical distortions. To
ensure this the brain slices are embedded in 5% agar gel. Four to six glass rods are also
embedded in the gel, as external registration markers. These serve as control points. Each
slice is then digitally photographed (resolution: 3072 X 2048) (Figure 4).
Gel
Postmortem
brain
Figure 4: The digital photograph of a postmortem slice.
Control point
Right hemisphere
14
These postmortem images are loaded and processed in matlab using software developed
by our research group called pipe1. The required sections of the images are cropped and
saved for further processing. The control points in each image are selected (Figure 5-a)
and their locations are saved in a .mat file. The individual slices are realigned such that
the corresponding control points in each slice overlap (Figure 5-b & c). To realign, the
controls points are translated and rotated till the Euclidean distance between the
corresponding control points of the current slice and the previous slice is minimized.
(c)
Figure 5: (a) The selection of control points: the cross wire points to one of the control
points. (b) The locations of control points from all the slices before realignment. (c)
The locations of control points from all the slices after realignment. Note that the
corresponding control points overlap.
(a)
(b)
(c)
15
The unwanted regions (i.e., anything other than the brain tissue) in the image are
eliminated by thresholding (Figure 6). The threshold parameter is chosen by trial and
error so as to preserve the relevant detail.
A three dimensional volume is reconstructed from the gray scale images (Figure 11-a).
0.9.2 Preprocessing of in-vivo MR images
Coronal T1-weighted, transaxial Proton Density (PD), and transaxial T2-weighted
MRIs are acquired on a GE 1.5T Signa system. Lacunes are best detected on both
transaxial proton density images and T2 weighted images. Certain structures like the
hippocampus are detected more clearly on thin coronal T1 weighted images. Hence, we
use the T1 weighted coronal images for co-registration, while the transaxial T2 weighted
images and proton density images are used for diagnosis. The T1-weighted 3D coronal
images are acquired using a gradient-echo (SPGR) sequence with TR=24ms, TE=5ms,
flip angle=45
o
, and field of view=24x24cm
2
(resolution: 0.86x0.86mm
2
in plane
resolution, slice thickness=1.5mm). The PD and T2-weighted images are acquired using a
Figure 6: The segmented postmortem slice.
Right
side
16
dual echo turbo spin echo (TSE) sequence with TR=45ms, TE1=14ms, and TE2=85ms
(resolution: slice thickness=3mm, 1.0x1.0 mm
2
in plane resolution).
The coronal T1-weighted MR images are loaded into matlab using pipe1 (Figure
7). The skull and the scalp regions are stripped off from the MR images using a
morphological algorithm called the Brain Surface Extraction algorithm (BSE) that was
developed by Sander and Leahy [11] & [12] (Figure 8). BSE identifies the brain using
anisotropic diffusion filtering, Marr-Hildreth edge detection, and morphological
operations. Anisotropic diffusion filtering enhances the edges in the MRI images. The
Marr-Hildreth edge detector identifies the brain-skull boundary. The brain is then
identified and refined using a sequence of morphological operations.
Figure 7: The T1 weighted coronal
MR Image (slice at the center of the
volume).
Figure 8: The MR image on applying
BSE algorithm (slice at the center of
the volume).
Right
side
Left
side
Right
side
Left
side
17
The postmortem brain slices do not have the pons and cerebellum regions. Therefore,
these regions are manually removed from the in-vivo MR images (Figure 9). Since the
two hemispheres of the postmortem brain are separated before registration, the MR brain
volume, which is extracted using BSE, is cut into two hemispheres through the inter-
hemisphere fissure (Figure 10).
A three dimensional volume is reconstructed from these images (Figure 11-c).
0.10 Volume Matching
The 3D MR volume is transformed to match the postmortem volume (Figure 11),
using rotations, scalar multiplications and translations. These transformations are
performed iteratively until the mean squared error between the postmortem volume and
Right
side
Left
side
Figure 9: The MR image after removal
of the midbrain region (slice at the
center of the volume).
Figure 10: Right hemisphere of the
MRI brain image (slice at the center
of the volume).
Right
side
Right
side
Left
side
18
the MR volume is minimized. This takes care of differences in resolution and orientation
between the postmortem and the MR images. An example is illustrated in figure 11.
Figure 11-a and figure 11-c depicts the different views of the postmortem volume and the
MRI volume respectively before reorientation. Figure 11-b and figure 11-d show the
coronal slices of the postmortem volume and the MR volume respectively before
reorientation. From figure 11 –a, b, c and d, it is seen that the orientations of the
postmortem slices and the MR slices differ. Hence, prior to registration, the MR volume
is reoriented to approximately match the orientation of the postmortem volume (Figure
11-e). Figure 11-f shows the reoriented MR slices.
(b) (a)
Figure 11: (a) The postmortem brain volume: four views. (b) Postmortem slices.
19
0.11 Image Registration
There are various image registration techniques that are based on pixel intensity
or model matching strategies. Application of these existing registration methods to our
context is limited by the problems of pixel-voxel size matching, global and local
Figure 11: Continued . (c) The MRI volume before reorientation: four views. (d) The
MRI slices before reorientation. (e) The MRI volume after reorientation: four views. (f)
The MRI slices after reorientation.
(f)
(e)
(c) (d)
20
geometrical distortions, and coarsely reconstructed postmortem brain volume [13] &
[14]. For instance, model-based approaches generally require geometrical representation
of structures based on points, curves, and surfaces. However, identifying these features
requires the assistance of experienced anatomists and it is often difficult to identify the
exact same features in repeated trials.
This work improves upon a method, which is a non linear registration technique
involving a second order polynomial that is described in [15-17]. Note that, due to severe
local deformations, rigid transformations alone are not sufficient. Another concern is that
the postmortem photographs do not reflect the three dimensional voxel information, but
they only represent the surface optical reflectance variations (two dimensional). Hence,
direct volume to volume registration is difficult. Here we use a pixel to voxel coordinate
transformation, which employs a second order polynomial that incorporates warping
(equation 2). We do not employ higher order polynomials since; for the amount of
additional computation time it takes there is no significant improvement in the results.
Details of the convergence of the algorithm w.r.t different initial conditions and the
performance of different polynomial order are given in [15] & [16].
The second order polynomial is given below:-
2
5 4
2
3 2 1 0
2
5 4
2
3 2 1 0
2
5 4
2
3 2 1 0
j c ij c i c j c i c c w
j b ij b i b j b i b b v
j a ij a i a j a i a a u
+ + + + + =
+ + + + + =
+ + + + + =
(2)
21
Here, (i, j) are the pixel coordinates within a postmortem image(u, v, w) are new voxel
coordinates in a 3D MRI. a
1
,
b
1
,
c
1
are the image coordinate transformation coefficients or
co-registration coefficients.
These equations transform the pixel coordinates of the postmortem slices to the
voxel coordinates of the MRI volume. The polynomials represent a surface. The location
and the shape of the surface can be varied by changing the co-registration coefficients.
Hence, by varying the registration coefficients we extract an MRI slice from the MR
volume that best matches the post mortem slice (Figure 12).
For a given postmortem slice, the approximate location of the corresponding MR slice is
calculated as follows:-
Figure 12: (a) Selection of a slice from the postmortem volume. (b) The warped slices from
the reoriented MR volume obtained by changing the polynomial coefficients.
Fit postmortem slice to warped
MRI volume
(b) (a)
22
mri
pm pm
pm
z
z n
w
) ( ×
=
Where,
w
pm
is the slice location in the 3D MRI volume
pm
n is the postmortem slice number i.e.
pm
n
th
postmortem brain slice
pm
z is the slice thickness of a postmortem slice.
mri
z is the slice thickness of a MRI slice
The transformations that are applied on the MR volume during the volume matching
procedure are applied on w
pm
to get the approximate slice location.
A stack of postmortem slices is selected (we use stacks of four slices each). The
approximate locations of the slices in the stack are evaluated using the procedure that was
previously discussed.
The initial values of the co-registration parameters are:-
This implies,
Substituting these initial values in equation 2 we get,
=
=
=
=
=
=
0
2
1
5 4 3 2 1
5 4 3 1 0
5 4 3 2 0
1
1
0 , , , ,
0 , , , ,
0 , , , ,
c
b
a
c c c c c
b b b b b
a a a a a
approximate location of the MRI slice
=
=
=
w
j v
i u
approximate location of the MRI
slice
23
The values of the co-registration coefficients are varied iteratively. In each iterative step,
the similarity between the postmortem slices and the extracted MRI slices is evaluated.
The co-registration parameters are varied to optimize the sum of the cost functions for the
four slices. Here we employ a two-step registration process. In the first step, the co-
registration coefficients are estimated by using Pearson Cross Correlation (PCC) as the
cost function. In the second step, we assign the parameters from the previous step as the
initial values, and Mutual Information (MI) [18-21] is used to further improve the
registration by matching internal structures and intensity distribution. We use the optimal
registration coefficients thus obtained as the initial condition for the immediate next stack
of slices to be registered. However, the value of c
0
is incremented by
z
z
mri
pm
n × . Here
‘n’ is the difference between the index of the first slice of the current stack and the index
of the first slice in the stack to be co-registered. This speeds up the estimation of the
registration coefficients, since two consecutive postmortem slices have similar
deformations.
We have analyzed the co registration results by varying the number of
postmortem slices in the stack. Co registration was performed with stacks of single slice,
four slices, eight slices, and the whole brain volume. Figure 13 shows the co registration
results with stacks of one , four, eight, and all the slices. To evaluate the reliability and
accuracy of co-registration, we determine the mutual information between the
postmortem and the corresponding registered MR slices (given in Table 1). In addition,
visual identification of common anatomical landmarks (e.g., anterior commissure, pillars
24
of fornix, perivascular spaces, and optic chiasm) by experienced anatomists was used to
verify co-registration. To visualize the differences, we normalize the images and subtract
the corresponding slices to get the difference images. The pixels having intensities less
than 30% of the maximum are considered as zero in the difference image. A threshold of
30% was selected since the intensity of the ventricles in the MRI images are 30% higher
than in the postmortem images. This ensures that if the ventricles of the corressponding
slices overlap, they evaluate to zero in the difference image as shown in figure 13.
(a)
(b)
(a)
Co-registration with single slice – Right hemisphere
Figure 13: Co-registration results with stacks of varying sizes. The first row consists of
postmortem slices, while the corresponding registered MRIs and the difference images
are in the second row and the third rows respectively. (a) The results with stacks of single
slice.
25
Co-registration with stacks of four slices– Right hemisphere
(b)
(c)
Figure 13: Continued. Co-registration results with stacks of varying sizes. The first row
consists of postmortem slices, while the corresponding registered MRIs and the
difference images are in the second row and the third rows respectively. (b) The results
with stacks of four slices. (c) The results with stacks of eight slices. (d) The results with
a stack consisting of the entire volume.
Co-registration with stacks of eight slices– Right hemisphere
26
It is observed that the co-registration with stacks of eight slices and the whole
volume is inaccurate. This is because they do not account for local deformations. The
best results were observed with single slice registration. But the accuracy of co-
registration with stack of four postmortem slices is quite close to that of single slice
registration and for some slices it is even better. However, single slice registration has a
disadvantage. It is possible for two consecutive slices to match up with the same MR
slice. This risk is lower in co registration with a stack of four slices, since we optimize
sum of the cost function of the four slices as opposed to the individual cost functions of
(d)
Co-registration with a stack of the entire volume- Right Hemisphere
Figure 13: Continued. Co-registration results with stacks of varying sizes. The first row
consists of postmortem slices, while the corresponding registered MRIs and the
difference images are in the second row and the third rows respectively. (d) The results
with a stack consisting of the entire volume.
27
the slices . Also, the co-registration with four slices processed simultaneously tends to be
faster.
Table 1: Comparison between single slice and multiple slice co-registration.
Mutual Information
Slice Stack of Stack of
Stack
of Stack of
Number 1 slice 4 slice 8 slice whole volume
1 0.7177 0.7225 0.7019 0.5698
2 0.781 0.7777 0.7572 0.6312
3 0.8132 0.8138 0.7902 0.6701
4 0.8378 0.8337 0.812 0.7046
5 0.8986 0.9002 0.8735 0.7462
6 0.9384 0.9313 0.8993 0.7693
7 0.9835 0.9741 0.9288 0.7998
8 1.0214 1.0165 0.9698 0.8301
9 1.1025 1.0964 1.0375 0.8822
10 1.1394 1.1218 1.0676 0.9215
11 1.1352 1.1206 1.0709 0.9408
12 1.1013 1.0867 1.0354 0.9143
13 1.0843 1.0598 1.0094 0.9109
14 1.0663 1.0664 1.0014 0.9167
15 1.0233 1.0338 0.9706 0.8936
16 1.0363 1.0229 0.9806 0.9009
17 0.9926 0.9681 0.9796 0.9044
18 1.0126 0.9843 0.9917 0.9146
19 0.9406 0.9509 0.95 0.8766
20 0.9107 0.9224 0.9204 0.8447
Average= 0.976835 0.9702 0.93739 0.827115
28
Figure 14: The co-registration results with stacks of four slices. The first and the third
rows show the post mortem slices, while the corresponding registered MRI slices are in
the second and the fourth rows.
29
0.12 Transferring information from MR images to postmortem Images
Lacunes are best seen on transaxial T2-weighted images, which are relatively
thick, and proton density images. A radiologist identifies the lacunes by analyzing the
T1-weighted, T2-weighted, and proton density images. These locations are marked on the
transaxial T2-weighted images (Figure 15 b). The lacunes are extracted from this volume
and stored in a sparse 3D grid of the same dimension as the T2-weighted MR volume
(Figure 15 c).
The T1 and T2 weighted MRI volumes (Figure 16- a, b & c) are co-registered using
SPM2 (http://www.fil.ion.ucl.ac.uk/spm/). The lacune volume is transformed using these
registration parameters.(Figure 17-a & b). This ensures that the locations of the lesions
coincide in the three volumes (T1 weighted volume, T2 weighted volume, and the
volume with only the lesion).
(b)
(a)
(c)
Figure 15: (a) The T2 weighted image. (b) The T2 weighted image with the lesion that
was identified by a radiologist. (c) Image with only the lesion (extracted from (b)).
(a) (b)
30
(c)
Figure 16: (a) The T1 weighted volume. (b The T2 weighted volume. (c) The T2
weighted volume registered with T1 weighted volume.
(b)
31
The transformations that were previously applied on the T1-weighted MR volume to
match it roughly with the postmortem volume are now applied on the registered Lacune
volume (Figure 18 b). This reoriented lacune volume is resliced with the second order
polynomial given in equation 2. We employ the registration coefficients that were
obtained by optimizing the cost functions while registering the T1-weighted MR slices
with the postmortem slices. These lacune slices are then superimposed on the registered
coronal T1-weighted MRI slices and the corresponding postmortem slices (Figure 19).
(b)
Figure 17: (a) The T2 weighted volume with the lesion. (b) The volume, which is
matched with the T1 volume, with only the lesion. The cross wires that point at the
lesion in both the volumes, indicate that the lesions are at the same location in both the
volumes.
(a) (b)
32
Figure 18: (a) Reoriented and resliced T2 weighted volume with the lesion identified
on it. (b) Reoriented and resliced Lacune volume.
Lesion
(a) (b)
(a)
Figure 19: (a) A postmortem slice. (b)The slice in (a) with the lesion that is identified by
co-registration. (c) The registered MRI slice corresponding to the slice in (a). (d) The
MRI slice in (c) with the lesion that is identified by the radiologist.
(a)
(b)
(c)
(d)
33
0.13 Validation
A relatively larger section of the postmortem brain around the lacune, which is
identified by the co-registration process, is sent to a histologist for stained microscopy.
Our results are not revealed to the histologist. The substrate is sliced to 20 micron
sections. The regions of abnormality, which are identified by histology, are marked on
the slide. The photographs of the results are sent back to us (Figure 20-a). Figures 20-b
and c show the microscopically magnified photographs of the histologically identified
region. These are manually registered to the postmortem images (Figure 21). The 3D
Euclidean distance between the centroids of the locations that are identified by co-
registration and the histology is calculated to quantify the accuracy of this procedure.
Table 2 lists these Euclidean distances for seven cases.
(c)
Figure 20: Shows the histology results (a) Histology slide with the lesion location
marked by the histologist. (b) The magnified microscopy image of the region that is
encircled in (a). (c) A magnified portion of (b).
(b)
Location marked by the histologist
(a)
(c)
34
Figure 21: Shows a histology slide that is manually registered to the postmortem slice.
The black circle shows the lesion that is identified histologically and the dark grey
region beneath is the region that is identified by the co-registration procedure.
Sno: Case Number Lesion 3D Euclidean
Name Number Distance(cm)
1 FP87M04 1 0.8766
2 0.5399
2 HP86F02 1 0.8743
2 0.5772
3 WG1M03 1 1.0556
2 1.0634
4 V097F02 1 0.42
5 PF84F03 1 0.307
6 DL72M03 1 0.7087
2 0.963
7 JS85M03 1 0.8822
Average= 0.751627273
Standard deviation= 0.258217393
Table 2: The 3D Euclidean distances between the centroids of the lesions identified by
co-registration and by histology.
35
0.14 Conclusion
We developed a technique to transfer lesion information from the MRI images to
the postmortem slices. The technique relies on co-registering MRI brain images to its
corresponding postmortem images. The accuracy of the procedure was quantified by
evaluating the 3D Euclidean distances between the centroids of the lesions identified by
our procedure and those that were identified by the histologist. The mean 3D distance for
7 subjects, 11 lesions was 7.5 ± 2.6mm. This method is efficient and cost effective.
36
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Abstract (if available)
Abstract
Brain vascular abnormalities like lacunar infarcts and perivascular spaces cannot be readily identified on MRI images but can be recognized on postmortem slices. We present a method for transferring information from MRI images to the corresponding postmortem images in order to validate the diagnosis of vascular lesions from MRI. We achieve this by co-registering the in-vivo MRI with digital photographs of the postmortem brain and transferring marked lesions from the registered MRI to the postmortem images. Relatively larger samples of the postmortem slices around these marks are extracted and sent to a pathologist to identify abnormalities by histological methods. To validate the co-registration, the histologically identified regions are manually registered to the original postmortem images. Results reveal that the co-registration identifies the locations of 11 lesions in 7 subjects within an error of 7.6±2.6 mm.
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Asset Metadata
Creator
Rajagopalan, Amrita
(author)
Core Title
Location of lesions on postmortem brain by co-registering corresponding MRI and postmortem slices
School
Viterbi School of Engineering
Degree
Master of Science
Degree Program
Biomedical Engineering
Publication Date
10/30/2006
Defense Date
10/17/2006
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
OAI-PMH Harvest,polynomial registration,postmortem brain
Language
English
Advisor
Singh, Manbir (
committee chair
), Maarek, Jean-Michel (
committee member
), Nayak, Krishna S. (
committee member
)
Creator Email
arajagop@usc.edu
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https://doi.org/10.25549/usctheses-m115
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Tags
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