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5/08 ICIProi/AccaPrelelRClDaIeDueIndd

IMPROVING THE CHARACTERIZATION OF BREAST LESIONS
USING DCE-MRI AND DTI

By

Tobias Hahn

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Physics

2008

Abstract

IMPROVING THE CHARACTERIZATION OF BREAST LESIONS
USING DCE-MRI AND DTI

By

Tobias Hahn

Breast magnetic resonance imaging (MRI) has evolved to be accepted as an important
lesion diagnosis technique, providing higher sensitivities than other techniques such as
mammography. However, like the other techniques, one main limitation is still a relatively
low specificity. The main goal of this study was to reduce the Type I error of breast MRI
via investigating new methods for the analysis of dynamic contrast-enhanced (DCE) breast
MRI and breast diffusion tensor imaging (DTI). A software for an automatic detection of
breast lesions was developed, tested and demonstrated to be reliable for the detection of the
lesion margin. Then we investigated the kinetic features of breast lesions and introduced
the slope angle as a measure for characterizing the kinetic behavior. The study showed that
the slope angle clearly separated our sample into two groups of benign and malignant and
consequently could be used to significantly reduce the Type I error. Finally, we examined
the usage of breast DTI for improving the characterization of breast lesions. We found
no significant difference in mean diffusivity between the benign and the malignant group.
However, we found a significant difference in relative change of the mean diffusivity, which

could be used as an additional measure for improving the characterization of breast lesions.

ACKNOWLEDGMENTS

The research project described in this thesis would not have been possible without the
support from many people. I am deeply grateful for the incomparable support that I
received from my adviser, Prof. Jie Huang, during my research on this project. I want to
express my thankfulness to Prof. Wolfgang Bauer for providing the opportunity to spend
an inspiring and fruitful time at Michigan State University. I am very grateful for the
technical and financial support granted by Prof. E. James Potchen and the Department
of Radiology at Michigan State University. I want to thank Lori Hoisington and Prof.
Kevin Berger for their commitment in this research project. Thanks to Prof. James Lyon
for reading the manuscript and helpful suggestions. I acknowledge the support of the

Studienstiftung des deutschen Volkes.

I especially want to thank Emanuel Gavartin, Luis Carlos Reyes, my family and in partic-

ular Dr. Matthias Hahn for innumerable ways of supporting and motivating me.

Soli Deo Gloria.

Contents

List of Tables vi
List of Figures vii
1 Introduction 1
2 Overview of Magnetic Resonance Imaging 2
2.1 Historical Overview .............................. 2
2.2 Nuclear Magnetic Resonance ......................... 3

2.3 MR signal detection .............................. 7
2.4 Signal spatial encoding and image reconstruction .............. 9

2.5 The spin echo pulse sequence ......................... 10
2.6 The gradient-recalled echo pulse sequence .................. 12

2.7 Principles of Dynamic Contrast-Enhanced MRI ............... 14

2.8 Principles of Diffusion Tensor Imaging .................... 15
2.8.1 Physical background ......................... 15

2.8.2 Definitions .............................. 16

2.8.3 Measurement of the Diffusion Coefficients ............. 17

3 Breast lesion analysis tool (BLAT) 19
3.1 Introduction .................................. 19

3.2 Image processing ............................... 19
3.2.1 Image reconstruction ......................... 19

3.2.2 Slice fitting for different image types ................ 20

3.2.3 Motion artifact correction ...................... 21

3.2.4 Kinetic feature image creation .................... 21

3.3 Lesion boundary detection .......................... 23
3.3.1 The iterative lesion detection algorithm ............... 24

3.3.2 Test of extreme initial lesion choices ................. 25

3.3.3 Discussion on the choice of the threshold constant c ........ 25

3.3.4 Numerical ID simulation ....................... 25

3.4 Tissue area creation .............................. 27

4 Methods and Materials 32
4.1 MRI ............................... - ....... 32
4.2 Image Data .................................. 33
4.2.1 Discussion of a possibly false negative biopsy result (A) ...... 33

5 Dynamic Contrast-Enhanced Imaging Data Analysis
5.1 DCE motion artifacts .............................
5.2 ROI test ....................................
5.3 Kinetic behavior analysis ...........................
5.4 Combining kinetic information to delineate between malignant tumors and
benign lesions .................................

6 Diffusion Tensor Imaging Data Analysis
6.1 DT'I motion artifacts .............................
6.2 Mean diffusivity calculations .........................
6.3 Fractional anisotropy calculations ......................
6.4 Statistical justification for the introduction of the relative change concept . .
6.4.1 Lesion-tissue correlation analysis ..................
6.4.2 Tissue-tissue correlation analysis ...................
6.5 Introduction of the mean diffusivity relative change model and results .
6.5.1 Detailed DTI subject data ......................

7 Discussion
APPENDICES
A Gyromagnetic ratios

Bibliography

34
34
35

36

41
41
42

45
48

51

53

53

55

3.1

5.1

6.1

6.2

6.3

6.4

List of Tables

One-dimensional example of the iterational steps of the lesion detection
algorithm. The center of the lesion is the pixel with the value 10 and the
initially chosen pixels are the center of the lesion and its two neighboring
pixels. For each iteration step the pixels that are included in the lesion
are written in bold letters. 3 is the threshold value, corresponding to the
specific iteration step .............................. 26

Mean and standard deviation of the slope-angle E for benign and malignant
masses with corresponding p-value. ..................... 37

Mean diffusivity (D) and fractional anisotropy FA for malignant tumors,
benign lesions and their surrounding tissue areas (p :I: a) ........... 43

Relative mean diffusivity and relative fractional anisotropy (,u d: a) for be-
nign and malignant cases ............................ 47

Data of the DTI image analysis with benign cases (1-6) and malignant cases
(7-15) for lesion (l), tissue 1 (t1) and tissue 2 (t2) areas. Mean diffusivity
values are given in 10‘3mm2/s. A denotes the possibly false negative case. 49

Mean diffusivity (D) and relative mean diffusivity (D)r (p i a) of the
distributions given in Figure 6.9 ........................ 49

vi

2.1

2.2
2.3

2.4
2.5
2.6

2.7

3.1

3.2

3.3

3.4

3.5

3.6

List of Figures

Free induction decay with T2* envelope for all spins precessing at the same
Larmor frequency ................................ 9
The basic spin echo pulse sequence. ..................... 1 1
The signal of the spin echo pulse sequence. ................. 12
The basic gradient-recalled echo pulse sequence for a tip angle 6. ..... 13
The signal of the gradient-recalled echo pulse sequence ............ 13
Different kinetic curve shapes. Left: Wash-out behavior. Center: Plateau
behavior. Right: Persistence behavior. .................... 15
Illustrative waveforms for a spin-echo diffusion pulse sequence, defining
the parameters 6, 6 and A for (2.8.31). A, B and C denote magnetic field
gradients, applied in x-axis (A), y-axis (B) and z-axis (C). Figure adapted
from [10]. ................................... 18
Illustration of the different spatial resolution of DTI and DCE images. . . . 20
An exemplary signal intensity kinetic curve for a single pixel with the cor-
responding calculated interpolated function. ................. 22
The slope image I slope for the breast lesion given in Figure 3.10 ....... 23
The iterative lesion boundary detection algorithm: The threshold value .9 is

calculated on the basis of the mean u and the standard deviation 0 of the be-
fore defined lesion ROI. All pixels with values larger than 3 are assembled
to make up the lesion’ ROI ........................... 28

Two differently chosen initial lesion R015 and the corresponding iteration
steps of the boundary detection algorithm. The initial chosen lesion R01 is
marked green and the two boundaries are marked red. The algorithm for
the first initial chosen ROI (first line) converges after four iterations and
the last ROI in the first line is the corresponding final ROI. For the second
initial chosen ROI the algorithm converges after only two iterations. . . . . 29

Two possible initial ROI selections. Left: choice 1. Right: choice 2. The
manually selected lesion area is displayed green, inner and outer bound-
aries are displayed red. ............................ 29

vii

3.7 Final lesion area after convergence of the algorithm for the initially selected
areas shown in Figure 3.6. Left: choice 1. Right: choice 2. .........

3.8 Difference image, showing all pixels that differ between the final lesions in
Figure 3.7 in black. ..............................

3.9 Final lesion ROIs for differently chosen cut-off values. From left to right:
c = 125,15, 1.75, 2, 2.25 ...........................

3.10 An example for a detected lesion and its surrounding tissue areas. The inner
black contour denotes the one pixel wide gap between the lesion and the
tissue 1 area; the middle contour denotes the last pixel layer of the tissue 1
area and the same way the outer contour denotes the last pixel layer of the
tissue 2 area ...................................

5.1 Mean relative change kinetic curves for benign lesions and malignant tu-
mors and their surrounding tissue areas. The error bars denote the standard
error of means. ................................

5.2 The distribution of the mean slopes of the kinetic behavior of the detected
lesions after the first post contrast-enhanced image. A denotes the possibly
false negative case. ..............................

5.3 The slope angle E between the wash-in slope function and the interpolated
slope-function between the first and last post contrast-enhanced image for
an exemplary kinetic curve ...........................

5.4 The distribution of the slope angle 3. A denotes the possibly false negative
case .......................................

6.1 Mean diffusivity distribution for malignant tumors and benign lesions. A
denotes the possibly false negative case. ...................

6.2 Fractional anisotropy distribution for malignant tumors and benign lesions.
A denotes the possibly false negative case ...................

6.3 Mean diffusivity correlation between tissue 1 and lesion area .........
6.4 Fractional anisotropy correlation between tissue 1 and lesion area. .....
6.5 Mean diffusivity correlation between tissue 1 and tissue 2 area ........
6.6 Fractional anisotropy correlation between tissue 1 and tissue 2 area.

6.7 Relative mean diffusivity distribution for malignant tumors and benign le-
sions. A denotes the possibly false negative case. ..............

viii

30

30

31

31

37

38

39

42

43
45
45
46

46

47

6.8 Relative fractional anisotropy distribution for malignant tumors and benign

lesions. A denotes the possibly false negative case. ............. 48

6.9 Normalized mean diffusivity for malignant tumors (A) and benign lesions
(C) and normalized relative mean diffusivity distribution for malignant tu-
mors (B) and benign lesions (D). In (B) the Gaussian distribution according
to the set up statistical model is included. ..................

Figures in this thesis are presented in color.

ix

Chapter 1

Introduction

Breast cancer, the most frequent cancer among women [20], is an increasing threat as the
cases per year increase [12], causing nearly 1% of all deaths worldwide in 2005 [20]. In re-
cent years, breast magnetic resonance imaging (MRI) has evolved into an established tech-
nique for supplementing other lesion diagnosis methods such as mammography and breast
ultrasound. One of the big advantages of breast MRI, in comparison to other techniques,
is its high sensitivity, being 27 — 36% more sensitive than mammography [8]. With cur—
rent technology, the sensitivity of breast MRI almost reached 100% [26]. One of the major
concerns about breast MRI, however, is its low specificity [8]: The Type 1 error, denoting
the false positive rate, is still significant for breast MRI, where the exact specificity values
vary a lot between different studies [26]. Due to small specificity values, many biopsies
are recommended for what prove to be truly benign lesions. Each biopsy, in return, leads
to psychological costs for women. An unnecessary biopsy should be avoided, since it is an
invasive procedure with possible side effects such as infections, altered breast appearance
etc. The crucial task, therefore, is to maintain a high sensitivity, while reducing the Type
1 error and with it the number of unnecessary biopsies. In this work, different approaches
on the basis of dynamic contrast-enhanced (DCE) breast MRI and breast diffusion tensor

imaging (DTI) are described to tackle this task.

Chapter 2

Overview of Magnetic Resonance

Imaging

2.1 Historical Overview

MRI is a non-invasive imaging technique that has been developed during the last century,
whose potential, however, still seems to be far from being fully revealed.

In contrast to other imaging techniques, such as X-ray imaging, MRI is an unequally more
sophisticated method. Where for X-ray less than one year passed between the first obser-
vations of the underlying physical principal and the first image taken (both by Wilhelm
Conrad Roentgen in 1895) for MRI this was a matter of decades.

In 1930, Isidor Isaac Rabi conducted experiments that led to a “resonance method for
recording the magnetic properties of atomic nuclei.”1 After having developed a technique
to measure the magnetic moments of the nuclei of a molecular beam to high precision, he
introduced - according to suggestions by the Dutch physicist Cornelius J. Gorter - a method
to flip nuclear spins of a sample by applying radio waves to this sample. These methods

turned out to be harbingers of the upcoming MRI technology.

 

1The Nobel Prize Committee, 1944.

In 1945 and 1946 Edward Purcell and Felix Bloch independently observed nuclear mag-
netic resonance in bulk matter. Molecular resonance spectroscopy (MRS) was a fruit of
their discoveries; this new technique revealed information about how much of what kind of
molecules was included in the examined sample by exciting the molecular spins according
to their resonance condition. Only in 1973, the known physical principals were applied
for imaging by Paul C. Lauterbur and Peter Mansfield, an accomplishment for which they

were awarded the 2003 Nobel Prize in Physiology or Medicine.

2.2 Nuclear Magnetic Resonance

Magnetic resonance imaging is primarily based on the magnetic field interactions with the
nuclei of a sample2.

According to Maxwell’s theory of magnetic fields, spinning charges induce a magnetic field
and a magnetic moment, respectively. With regard to their specific quark composition,
we can consider both protons and neutrons as spinning charges, having a “spin” angular

momentum S that induces a spin magnetic moment it with
[1 = g—S = 73. (2.2.1)

Hereby, g denotes the particle specific g-factor, '7 the gyromagnetic ratio and m and q the
mass and charge of the particle, respectively. According to their specific proton/neutron
composition, nuclei have a specific spin inducing a magnetic moment that interacts with

external magnetic fields3.

 

2There are certain techniques that make use of the magnetic field interactions with other particles, such
as Electron Spin Resonance Enhanced Magnetic Resonance Imaging (ESREMRI). They are, however, not
subject of this work.

3The spin concept is of fundamentally quantum mechanical nature. It is however more intuitive to regard
the physical principals of MRI from a classical point of view and it can indeed be shown that the classical
description leads to the same results as the Quantum mechanical approach, see e.g. [7]. Therefore we want
to treat the spin as a classical angular momentum.

A magnetic moment [i in an external magnetic field [IQ is affected by a torque A7, given by
N=flx&h can

where the index 0 denotes that the magnetic field is static. This formula can be derived
for the classical magnetic moment of a current loop. For magnetic moments that are not
associated with an angular momentum (like the magnetic moment given by a pair of mag-
netic charges with opposite Sign, in analogy to an electric dipole moment given by two
charges), the torque will simply lead to an alignment of the magnetic moment vector with

the external magnetic field. A magnetic potential energy H, given by
H=—fi&y oz»

is associated with the torque that pushes the magnetic moment vector towards an alignment
with the magnetic field. Following the natural tendency to be in a state of lowest possible
energy, the preferred state, [NIB-*0, has the lowest energy.

If the magnetic moment, however, is associated with an angular momentum - like in the
case of a spin - the resulting torque on an unaligned magnetic moment leads to a precession
of the magnetic moment around the H0 axis.

The fundamental equation of motion for the magnetic moment vector can be found using
(2.2.2) and Newton’s second law, according to which it can be derived that the torque is

equal to the derivative of the angular momentum, yielding

 

(S IWL . .
—=——=N=” B
dt 7m “x
(1;? _, _.
EZE=I“XB' on»

 

 

 

We want to consider now the case of ‘a magnetic moment vector, which is aligned with
the external magnetic field, and introduce the principals of Rabi’s spin flip method that

has already been mentioned above: Spins can be brought out of the alignment with the

3'0 axis into the transverse plane by applying energy to the spins using a radio-frequency
electromagnetic radiation pulse. The tipping is most effective if the radio-frequency (RF)
pulse is tuned to the specific precession frequency of the spins, i.e., if the excitation happens
on-resonant4. A famous analogue for this excitation process is the swing, which is most
effectively excited if an external force excites the swing with the swing specific frequency.
The specific precession frequencies of the spins are the well-known Larmor frequencies
too, which are given by

em = 7130. (2.2.5)

For an omresonant excitation, the pulse energy is given by two, which corresponds to
the energy difference between the excited state and the ground state. In the absence of a
magnetic field, thermal agitation leads to a random orientation of the magnetic moments.
Generally speaking, for a given small volume, the microscopic random orientation results in
a zero macroscopic sum of the magnetic moments. In the presence of an external magnetic
field, however, a preferred direction is given as the magnetic field direction and in the
equilibrium state the number of ground states (N _) prevails the number of excited states

(N+) according to the Boltzmann distribution,

N_ hwo
_ = 1 1 — 2.20
N+ ”7’ ( kT) ’ ( 6)

with the thermal energy ET = kT being usually much larger than hwo. Still, no direction
in the plane perpendicular to the external magnetic field is preferred, leading to a zero
transverse bulk magnetization. However, the slight excess of aligned spins over unaligned
spins leads to a non-zero bulk magnetization in the direction of the BO-field. We introduce
the magnetization III as the magnetic moment per volume V, where V is assumed to be
small enough so that external fields are to a good approximation constant over V [7]:

A7=$Zflia

iEV

 

4Less power is required to flip spins if the exciting field rotates in the same way as the precessing magnetic
moment vector. Therefore for MR applications the commonly used radio frequency field is left—circularly
polarized.

where the index 2' denotes the different protons. A first order approximation of (2.2.6) for a

5

s in 1 s stem returns the Curie Law
P 2 Y

30
M — 2.2.7

revealing the dependence of the equilibrium magnetization MO on the BO-field and the
temperature.

In the absence of interactions between the spins and interactions between the spins and their
surrounding lattice, the fundamental equation of motion (2.2.4) can directly be adapted for

a bulk magnetization system that has been tipped away from the equilibrium state:

.A" a a
1d?! = 7M x BO. (2.2.8)

_. _. an? a
It is M“ x BO = 0 => WEI—I = 0, from which follows that M" remains unchanged, where

117" is the longitudinal magnetization component. For the transverse component, Ml =
My; + 1173,, we get M; x 3'0 aé 0, however the magnitude of M I does not change, but the
transverse magnetization precesses around BIG with the Larmor frequency tug = 780.
However, due to interactions of the system with its surrounding lattice, the longitudi-
nal component of the bulk magnetization recovers, and due to inner-system spin-spin-
interactions, the transverse component decays. Assuming that the external magnetic field
is applied in z-direction, the components obey the equations given in (2.2.9) and (2.2.10):

Spin-lattice interactions lead to

sz 1

= — AI — AL 2.2.9
dt T1( 0 1.) ( )

 

and Spin-spin-interactions change the perpendicular component of (2.2.8) into

dAfi
dt

 

= 71171 x 1?}, — Tim, (2.2.10)
2

where .L denotes the magnetization perpendicular to the 50 axis with 117i = 717;; + 1173,.

 

5In this description we want to stick to spin % systems. The most common NMR-active nuclei 11!, 13C
or 19F are all spin % systems.

Equation (2.2. 10) can be explained by the process of dephasing: As time goes by, the spin
vectors of the spins in the sample start pointing in different directions, caused by the mutual
spin interactions - and according to (2.2.7) [If decreases.

(2.2.9) and (2.2.10) can be combined, resulting in the Bloch equation:

 

(1117i _. .. 1 1 ~
= A.’ B _ A, -— A115. A _ _A'[ _ 2.20 l I

 

 

 

In addition to spin-spin interactions being reflected in T2, magnetic field inhomogeneities

also induce a dephasing. A new parameter, T2*, is introduced according to

1 _1+ 1
T2*—T2 T2”

 

where T2’ takes into account the field inhomogeneity-induced dephasing. For the follow-
ing, T2 has to be replaced by T 2* in the case of present field inhomogeneities.

The solution to (2.2.11) can be written down for each component, given E = B02 and

using (2.2.5):
Mx(t) = (ft/T2 (Ml-(0) cos(w0t) + My(0) sin(w0t)) (2.2.12)
111,,(1) = (it/7‘2 (11,,(0) cos(u20t) — 111,.(0)sin(w01)) (2.2.13)
1113(1) = 1112(0)e*‘/T1 + 1110(1 — art/T1). (2.2.14)

Defining the complex transverse magnetization 11/14. = M); + iMy yields:

111,.(1) = e-Woirt/Tl‘2 111+(0)6. (2.2.15)

2.3 MR signal detection

Mostly, a single coil around the object of interest to be scanned (subject) acts at the same
time as a transmitter and receiver coil (= transceiver) for the radio frequency pulses. We

can tip the magnetization vector away from the [IO-direction by applying a radio frequency

 

6For derivations of the above equations see [7].

pulse onto the subject using the transceiver. Depending on how long the RF pulse is applied
and which amplitude is used, respectively, we can tip the vector by an arbitrary angle.
According to Faraday’s law of induction, the precessing magnetization vector induces a

voltage inside the transceiver coil, given by

(1(1) d

(It dt coil area

UM = 1? - (121’ (2.3.16)

with (I) being the magnetic flux and A the surface vector of the area regarded. This integral
can be transformed - according to the principle of reciprocity - into a volume integral over
the magnetization times the magnetic field per unit current, RT = E / I , that would excite

the magnetization of the sample if B" - I was used for the excitation [11]:
d r r a
Um, = 'E (M - Br) (1' 7‘. (2.3.17)

Equation (2.3.17) makes clear the dependence of the induced voltage on the magnetization

VCCIOI‘.

The measured signal is proportional to Uindr whereat the proportionality factor depends
on the measurement device. We insert the solutions (2.2.14) and (2.2.15) to the Bloch
equation into (2.3.17). Since usually wo >> 1/T1 and um >> 1/T2, the time derivatives in
(2.3.17) - which we can take inside the integrand - of all exponentials that contain 1/T1 or
1 /T2 terms can be neglected, comparing them to the time derivatives of the rug-dependent
exponential functions. Therefore, the contribution of the longitudinal magnetization to
the signal is negligible and this is why the transverse magnetization M+ or its magnitude
Mi = ‘ M13 + M; is also referred to as ’the signal’.

The free induction decay, FID, refers to the signal decay after an RF pulse. After applying
such a pulse due to spin-spin interactions (T2) and field inhomogeneities (T2') the transver-
sal component of the magnetization vector decays and with it the signal, which is shown in

Figure 2.1.

 

 

‘ . —Free induction decay
fl ---T2* envelope

 

 

 

 

 

 

 

 

 

 

 

Signal (a.u.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time (a.u.)

Figure 2.1. Free induction decay with T2* envelope for all spins precessing at the same
Larmor frequency.

2.4 Signal spatial encoding and image reconstruction
Combining (2.3.17) and (2.2.15) yields for the signal 3 at time t:
3(t) = [d3rp(77)ei¢(F’t)e—t/T§, (2.4.18)

where (150“, t) is the accumulated phase at a certain position 1" at a given time t and p the
effective spin density, which includes all sample specific scaling factors7. As long as the
sampling time (or “data acquisition window”) is small in comparison to T2*, eTt/Tg can
be pulled out of the integral as a constant that we want to disregard in the following.

We want to consider a one-dimensional scenario and introduce a spatial linear gradient in

z-direction in addition to the static magnetic field, giving

B,(z,1) = BO + zG(t).

 

7The reader is referred to literature such as [7] for a detailed derivation.

The angular frequency of the spins changes according to

w(z, t) = tug —> w(z, t) = too + w(;(z, t)

= 1.10 + 72cm. (2.4.19)

Given (2.4.19), we have developed a relation between the spatial position of the spins and
their precession frequencies. The spins are said to be frequency encoded (in z-direction).

(2.4.18) is changed to
8(1) : /d:p(z)ei(¢(}(2,t)+¢cmtstl = dep(z)e—ifdlw(z,t)
t
= fd:p(2) eXp [ll—72] dt,G(t’) + $007130] - (2.4.20)
0

owns) denotes a constant phase offset, which can be disregarded at this point. Identifying
t
k(t) = l / dt'G(t')
27r 0

as the spatial frequency changes (2.4.20) into
3(k) = [deflate—2'27”” (2.4.21)

and we recognize the measured signal as the Fourier transform of the spin density of the
sample. In order to retrieve p(z), we change It until the whole k-space is covered, and run
the Fourier transform. In real MRI applications at least three different gradients have to
be applied for two dimensional images: a slice selection gradient to determine the slice
of interest and a frequency- and a phase- encoding gradient to cover the two-dimensional

k-space8.

2.5 The spin echo pulse sequence

In a spin echo pulse sequence - which was used for the acquisition of the below discussed

DTI images (see chapter 6) - first a 90° pulse is applied, flipping the magnetization vector

 

8We refer the interested reader at this point to further reading such as [7, 2].

10

into the plane perpendicular to the external magnetic field and leading to a free induction
decay as in Figure 2.1. The basic idea is now to undo the non-random dephasing due to
field inhomogeneities, quantified by T2', by applying a 180° pulse after a certain time
when the signal has been reduced to a certain extent. We call this time T. The pulse flips
all spins in the plane J. B by 180°, leading to a rephasing of the spins as if we did a time
reversal. The signal is at maximum after the echo time T E = 2T. Multiple 180° pulses can
be applied, each after the repetition time T R- Depending on the chosen TE-and T R-values,
images with different weighting can be acquiredg.
The magnitude of the transverse magnetization for a sampling at the echo time TE is given
by

MATE) = 1110(1 — e-TR/Tl)e‘TE/T2. (25.22)

An illustration of a basic spin echo pulse sequence is given in 2.2. Figure 2.3 shows the

signal time evolution for the sequence.

 

 

 

180°
90°
RF pulse
Echo
Signal I I were!
0 1 TE

 

 

 

Figure 2.2. The basic spin echo pulse sequence.

 

9We refer the interested reader to pertinent literature, such as [7, 2, 27].

ll

 

T2 Envelope

 

. Signal

 

Echo Time

 

Time (a.u.)

Figure 2.3. The signal of the spin echo pulse sequence.

2.6 The gradient-recalled echo pulse sequence

Multiple images, that have been used for this work, had been acquired using the below
described dynamic contrast-enhanced imaging method (see chapter 2.7). This method uses
not the spin echo, but the gradient-recalled echo pulse sequence to acquire the images. As
the name implies, the echo in the gradient-recalled echo pulse sequence is obtained not by
rephasing the spins using a 1800 pulse, but using a gradient.

A variable flip angle can be chosen for the excitation. After exciting the system, a gradient
(spoiler) is applied, which - according to (2.4.19) - changes the precession frequencies of
the nuclei at different spatial locations. This way the spins dephase very quickly. After
the dephasing induced by the spoiler, a different gradient (rewinder) is applied, whose
magnetic field gradient points in the opposite direction than the field gradient of the spoiler.
Naturally, the spins rephase again very quickly and a maximum signal intensity is achieved
at the echo time TE, when an echo signal was formed.

It is an advantage of the gradient-recalled echo pulse sequence that the rephasing process
can be run much quicker than with the 180° pulse in the spin echo pulse sequence case.
Smaller flip angles than 90° also speed up the sequence, since the repetition time T R can
be chosen smaller. Smaller flip angles also lead to a smaller energy deposit in the sample.

However, there is no compensation for magnetic field inhomogeneities in the gradient-

12

recalled echo pulse sequence in contrast to the spin echo pulse sequence, where the 180°
pulse compensates for field inhomogeneities. We characterize the signal decay by a new
time constant T2”, that takes into account all effects included in T2 and in addition the
dephasing due to the field inhomogeneity given by the applied gradient. An illustration of

the basic gradient-recalled echo pulse sequence is given in 2.4. Figure 2.5 shows the signal

time evolution for the sequence.

 

 

 

 

 

I3
RF pulse
Gradient \—
\_/ Echo
Signal I i wellirru
O 1 TE

 

 

 

Figure 2.4. The basic gradient-recalled echo pulse sequence for a tip angle ,6.

 

T2' Envelope

T2“ Envelope

I 'III-

Signal

 

Echo Time

 

 

Time (a.u.)

Figure 2.5. The signal of the gradient-recalled echo pulse sequence.

13

2.7 Principles of Dynamic Contrast-Enhanced MRI

Dynamic contrast-enhanced MRI allows for the study of signal intensity time courses by
injecting an intravenous tracer, such as compounds of Gadolinium, into the patient’s blood-
stream. At room temperature, Gadolinium exhibits highly paramagnetic features, leading
to reduced T1 and T2 values. In a T1-weighted image, a reduced T1 will result in a
bright area. The awaited contrast enhancement shortly after the intravenous injection of a
gadolinium chelate is broadly assumed by researchers to be a key for wreast) MR imaging
[22]. Obtaining a series of post-contrast images after certain time intervals allows for the
calculation of signal intensity curves (kinetic curves) for specific chosen regions of interest
(ROIs). Examples of three distinct possible kinetic curves are given in Figure 2.6.

There is a physiological reasoning for an association of the shape of a kinetic curve for
a specific lesion with its diagnosis. Most of the cancers demonstrate a rapid increase in
gadolinium concentration after the injection of the tracer, most probably due to an increased
vascularity (vessel density) in comparison to benign lesions or normal tissue. However, it
is still not clear what exactly determines the degree of enhancement, since it has been
shown that vessel density cannot be the only contributor [13]. The vascularity increase
is due to an augmented growth of blood vessels (angiogenesis), which is necessary for
tumor expansion. The growing capillaries have been shown to be leaky [13], leading to
an accelerated extravasation of contrast material. Therefore wash-out curves are to a high
extent associated with malignancy.

Aside the kinetic properties, lesion architecture can be used to set up criteria for the his-
tological diagnosis. Among different features to look at, clear versus smooth borders and
rim versus stippled regional enhancement are commonly examined features to distinguish

between malignant and benign lesions [22].

I4

 

 

 

 

Figure 2.6. Different kinetic curve shapes. Left: Wash-out behavior. Center: Plateau
behavior. Right: Persistence behavior.

2.8 Principles of Diffusion Tensor Imaging

Random molecular motion or Brownian motion causes matter transport from one part of a
system to another part of the system. This process of matter transfer is called Diffusion [3].
Diffusion tensor imaging reveals quantitative information about the diffusion properties of
the scanned sample. The most important diffusion properties include mean diffusivity and
anisotropy, which have turned out to possibly constitute quantities to delineate between

malignant and benign breast lesions [6, 21].

2.8.1 Physical background

Tissue in real cases is never uniform; diffusion is generally orientation dependent, given
different concentration gradients in different directions. In this case the diffusion can be

described by a second rank tensor

Dara: Dzy 022
D = Dyx Dyy Dyz
sz Day D22

Fick’s first law states that the transfer rate of diffusing matter - the diffusing flux .7 - is

proportional to the macroscopic concentration gradient VC:

.7 = —DVC. (2.8.23)

15

D is assumed to be symmetric. This assumption is based on the reciprocity theorem and
the principle of microscopic reversibility [18, 19], and is valid for microscopic systems.
However, though dealing with macroscopic quantities, this assumption is also valid for
the MRI applications described in this paper to a high accuracy, which can be verified
by measuring all 9 diffusion coefficients and comparing the off—diagonal elements of
D. Since Diffusion is a measurable physical quantity, it has to be determined by real
values. The Spectral Theorem tells us that any symmetric matrix with real entries can be
diagonalized. The orientation independent eigenvalues (Du, D22, 033) of the matrix D
represent the diffusion coefficients in the principal diffusivity directions, which are given

by the eigenvectors of D.

2.8.2 Definitions

We define four invariants, 11 (trace), 12, 13 (determinant) and 14:

1.1 = D“ + D22 + D33 (2.8.24)

12 = 0111222 + 0111233 + 1222033 (2.8.25)

[3 = 0110221233 (2.8.26)
_ 2 2 2

I4 — Dll + D22 + D33. (2H827)

The first three invariants can be interpreted as physical quantities determining the shape of
a “diffusion ellipsoid.” This ellipsoid can be illustrated with the process of the diffusion of
a spherical ink drop that is being placed inside a water volume: It will form an ellipsoid
that spreads with time. 11 would then describe the sum of the square of the radii of the
ellipsoid, 12 the square of its surface and I 3 the square of its volume [25].

The later used quantities Fractional Anisotropy (FA) and mean diffusivity ((D)) are defined

16

as:

2.8.3 Measurement of the Diffusion Coefficients

(2.8.28)

(2.8.29)

Stejskal related the diffusion coefficients with the echo intensities [24] at the echo time TE

in a spin-echo experiment (see Figure 2.7) by

-‘ 3
A(C)
———=exp— E bx'D-m

with

and the echo intensities

 

Au?) = (/Re(m(o‘))2 +1m(m(c'i))2 and

 

4(0) = (/Re(m(0))2 + Im(m(0))2.

We can also write this as

m((3) = m(0) exp(——b : D),

with m = Aei‘p being the magnetization and G a given gradient at time TE. ’

the scalar generalized tensor product, which is defined as:
3
b: D = Z buoj,
i,j=1
For a derivation of (2.8.33) see [10].

According to (2.8.33), D attenuates the echo intensity.

(2.8.30)

(2.8.31)

(2.8.32)

(2.8.33)

:’ refers to

Taking into account (2.8.30), one can acquire the different components of D by applying

l7

gradients along different directions: Using a gradient pulse sequence with 6 having only a

component in the x-direction for example leads to

A(Ci) _
III [m] — —bg;;ng;g;

with the measurable quantities A((7), A(O) and the known quantity bu.

 

180°
90° I
RF pulse I

 

 

 

 

 

 

Signal I I F

 

 

 

Figure 2.7. Illustrative waveforms for a spin-echo diffusion pulse sequence, defining the
parameters 6, 6 and A for (2.8.31). A, B and C denote magnetic field gradients, applied in
x-axis (A), y-axis (B) and z-axis (C). Figure adapted from [10].

18

 

Chapter 3

Breast lesion analysis tool (BLAT)

3.1 Introduction

BLAT is a software, based on MATLAB (The MathWorks, Natick, MA), that I developed
in the course of the project, which is described in this thesis. Its main goal is the automatic

detection and analysis of breast lesions. The tool divides into four major tasks:

1. Image reconstruction
2. Lesion boundary detection
3. Surrounding tissue area creation

4. Parameter calculation (discussion see chapters 5 and 6)

3.2 Image processing

3.2.1 Image reconstruction

Patient images are available as binary data with a certain header size on a central server.
Given the file name of the patient image of interest, BLAT determines the size of the file

and creates a two-dimensional array (i.e., an image) of 512x512 unsigned 16 bit integer

l9

values (DCE case) or 256x256 values (DTI case).

3.2.2 Slice fitting for different image types

DCE images have a different spatial resolution than the DTI images. The slice thickness
is 4mm for DTI and lm for DCE. The in-plane matrix for DTI is 256x256 and for DCE
512x512. DTI images were expanded to a 512x512 matrix in order to match the DCE
matrix. The resolution difference in the direction perpendicular to the image plane is illus-

trated in Figure 3.1.

DTI DCE

 

slice 1 slice 1
slice 2
slice 3
slice 4

 

MECZ erS

 

 

 

 

Figure 3.1. Illustration of the different spatial resolution of DTI and DCE images.

The analysis of BLAT described here is based on the evaluation of multiple slices. For the
later analysis, the DTI and DCE slices have to match each other: For a specific DTI slice,
say “slice 1” in Figure 3.1, DCE “slice 2” was chosen as the corresponding slice, where the
DTI image acquisition was centered right between the corresponding DCE slices “slice 2”

and “slice 3”.

20

 

3.2.3 Motion artifact correction

In order to quantify the kinetic behavior of a lesion, it is crucial that there is no shift between
the single DCE images corresponding to the same slice. However, due to patient’s motion,
there might be an image shift in the series that becomes clear by comparing the coordinates
of apparent landmarks. A quantitative description of the motion artifacts found in the
course of this work can be found in chapter 5. All DCE images were taken in the axial plane
- which is the plane in which the midriff lies - with the patient’s breast facing downwards,
see chapter 4. Although the patients were always asked not to move, a small amount of, for
example, breathing-induced movement cannot be eliminated, and will result in a (small)
image shift. In order to correct this shift, first a by-eye control should be performed to
ensure that there is no image series with apparent shifts in the direction perpendicular to
the image plane, which would be more difficult to correct. Landmarks like the nipple can
be compared in the image series, and if the landmark doesn’t appear (or appears apparently
smaller) in some images, an off-image-plane shift is detected and the patient data set should
not be included in the study.

BLAT then allows shifting the images by an arbitrary number of pixels in both coordinates
of the image plane. A comparison of the position of certain landmarks inside the lesion
for images of the DCE series allows reducing motion artifacts in the case of apparent shifts
in the axial plane. This shift correction is imperfect, given skewed images as an example.
However, cases with such skewed or unclear motion artifacts should not be included in a

study using BLAT for the quantitative analysis.

3.2.4 Kinetic feature image creation

After allowing the user to manually correct for possible motion artifacts in the DCE image

series, BLAT calculates the wash-in phases for each pixel. For each patient data set, the

21

wash-in image is calculated as the relative change given by the equation

I2—11

Irel = 11 a (3.2.1)

 

where I denotes signal intensity of images and I,- is the 2"“ image in the DCE image time
series. [1 corresponds to the first image of the DCE series, which is the pre-contrast image,
and 12 corresponds to the first phase of the post contrast images.

BLAT also creates images that show the kinetic behavior of the corresponding pixels after
the injection of the contrast agent. The DCE image series in this study consist of six images:
One pre-contrast (11) and five post-contrast images, acquired after fixed time intervals.
Each pixel with x- and y-coordinates at, y of a new image ,Islope’ is assigned the slope of an
interpolated linear function that interpolates the set of dependent values [12(2, 3;), I3(:1:, y),
[4 (x, y), 15(2, y), 16(2', y)] to the set of independent values [2, 3, 4, 5, 6] according to the
least squares method. Figure 3.2 shows an example of a kinetic curve for a single pixel

with the corresponding interpolated function.

—
,av
’
'
'
—
,a
—"‘
'
.‘
a
--
O
-.

.
‘0
.¢
4",
'o
’—

lnterpolated Function

Signal Intensity (a.u.)

 

i 2 53 4 s 6
Image number

Figure 3.2. An exemplary signal intensity kinetic curve for a single pixel with the corre-
sponding calculated interpolated function.

For a better display leading to the best scattered distribution of slopes for both the lesion

22

 

and the surrounding tissue, the slopes are scaled by the factor 1 / 80. (Note that the choice

of the unit for the abscissa is arbitrary). The slopes are then converted into degree by

a = atan(slope)11rfl. An example of an image showing the calculated slopes for the breast

lesion that is given in Figure 3.10 in degree for each pixel is shown in Figure 3.3.

90°
45°
00
-45°
-90°

Figure 3.3. The slope image I slope for the breast lesion given in Figure 3.10.

3.3 Lesion boundary detection

The following general criteria have to be considered for the finding of the cut-off threshold

for the lesion boundary detection:

1. For different patient subjects the same algorithm with the same parameters has to be

used to determine the lesion boundary.
2. Experienced researchers/radiologists have to agree on the detected lesions.

3. The portion of human interference has to be minimized.

23

The algorithm described below accounts for these criteria. The algorithm was tested on
more than 180 different lesions and was found reliable for the detection of lesion margins.

For a reliability test, see chapter 5.

3.3.1 The iterative lesion detection algorithm

The user is asked to specify three regions of interest on the image using the mouse:

0 an inner boundary of the lesion,
0 an outer boundary of the lesion and

c a lesion ROI.

The drawing of an inner and outer bound is included in the software to allow for a manual
control of the algorithm. All pixels outside the outer boundary are disregarded and all
pixels inside the inner boundary are included in the lesion. This way, the final lesion ROI
will be restricted between the outer and the inner boundary. Figure 3.4 shows the individual
steps of the algorithm.
After defining the boundaries and the lesion contour, the mean 11 and standard deviation
0 of the gray-scale values of the pixels inside the lesion area are calculated and a cut-off
threshold 3 of

s=,u—c-o (3.3.2)

is calculated. For this study, we chose a cut-off threshold of u — 1.750, corresponding to a
p-value of p = 0.04 (one-tailed t-test).

All values of the pixels between the outer and inner boundary are then compared to s and
pixels would be included in the lesion if their values are larger than 3. For this new lesion
a new cut-off value is calculated according to (3.3.2) and the algorithm is iterated until the
lesion reaches a stable area, which would represent the final lesion.

Figure 3.5 shows an example of two differently initially chosen lesion ROIs, the corre-

sponding iteration steps and the final lesion R013. The initial selection is hereby marked

24

green, outer and inner boundary are marked red. The final lesion ROIs differ in eight pixels,

which is less than 5% of the lesion area (of the second final lesion).

3.3.2 Test of extreme initial lesion choices

Even for big differences between the initial choices of the lesion ROIs, the algorithm shows
a high reliability in delineating the lesion margin: Figure 3.6 shows two different manual
initial ROI selections (again the initial selection is marked green and the boundaries are
marked red). Figure 3.7 shows the resulting ROIs after the convergence of the algorithm.
The first selected area results in an only slightly larger final lesion area. In figure 3.8 all
pixels that are counted to the lesion starting with the first initial selection, but not counted
to the lesion starting with the second initial selection are set to zero, i.e., they are displayed
black. Although there is a large difference between the initially selected areas, the final

lesions differ only in relatively few pixels.

3.3.3 Discussion on the choice of the threshold constant c

We analyzed the choice of different threshold values. Figure 3.9 shows the final lesions for
the threshold values 1.25, 1.5, 1.75, 2 and 2.25 a without using inner and outer boundary.
As can be seen, the difference between 1.5, 1.75 and 2 o is not dramatic, however 1.25 and

2.25 a show dramatically different results. This result supports the choice of c = 1.75.

3.3.4 Numerical 1D simulation

We want to consider one line of signal intensity values, that could have been taken from an
image of a breast lesion, and apply the iterative algorithm described above to it in order to
point out its effectiveness. Table 3.1 shows the iteration steps and corresponding threshold
values 3 for such a one-dimensional example. The center of the lesion shall be the pixel

with the value 10, and the initially chosen pixels are the center of the lesion and its two

25

 

 

 

 

 

 

 

Iteration Pixel values of the one-dimensional lesion 5
0 (initial choice) 1 l 2 7 8 9 9 10 9 l2 8 7 2 l 1 8.3
l l l 2 7 8 9 9 10 9 12 8 7 2 1 1 7.5
2 l l 2 7 8 9 9 10 9 12 8 7 2 l l 6.9
3 1 l 2 7 8 9 9 10 9 12 8 7 2 l 1 6.0
4 l 1 2 7 8 9 9 10 9 12 8 7 2 1 1 6.0
Convergence

 

Table 3.1. One-dimensional example of the iterational steps of the lesion detection al-
gorithm. The center of the lesion is the pixel with the value 10 and the initially chosen
pixels are the center of the lesion and its two neighboring pixels. For each iteration step
the pixels that are included in the lesion are written in bold letters. 3 is the threshold value,
corresponding to the specific iteration step.

neighboring pixels. For each iteration step, the pixels that are included in the lesion are
written in bold letters. Different initial lesion ROIs may be selected to verify that the

algorithm is not highly sensitive to the initial selection.

Convergence discussion

Generally, the algorithm lets the lesion expand until it finds a relatively large step between
the intensity values of two neighboring pixels, i.e., the difference between these two values
has to be large enough so that the threshold values 5’ and s” of two subsequent iterations
both lie in the interval between the two pixel values. The lesion will continue to increase
from iteration step to step if there is no clear jump of the pixel values at the lesion margin.
In such cases, where it is also by eye hard or impossible to tell where the lesion ends, the
outer boundary comes into play, and we draw it in such a way that we exclude those parts

outside the lesion, within which we are sure that they do not belong.

26

3.4 Tissue area creation

After having found the lesion area, a layer of one pixel width is created as a ’ gap’ between
the lesion area and the tissue areas to be created. The gap accounts for the partial volume
eflect, which has to be taken into account when voxels are covering different areas of in-
terest. Following pixel layers are added to the lesion until the new area, which we want to
call tissue 1, has the same area of the original lesion 1.
Layers are added by including all pixels in the 8-connected neighborhood of the margin
pixels to the last layer. The same way, a second tissue area called tissue 2 is also created,
directly surrounding tissue I .

Figure 3.10 shows an example for a detected lesion with the surrounding tissue areas.
Hereby, the inner black contour denotes the one pixel wide gap between the lesion and

the tissue 1 area; the middle contour denotes the last pixel layer of the tissue 1 area and the

same way the outer contour denotes the last pixel layer of the tissue 2 area.

 

1By adding whole pixel layers at one time, the wanted area is in most cases not exactly obtained. Therefore
the algorithm adds layers until the absolute value of the difference between the lesion area and the tissue 1
area is minimized and then pixels of the margin are taken away or pixels are added at the layer directly
surrounding the margin, respectively, until the areas equal each other.

27

 

1m 1
l

 

/ Read in image /

 

Draw inner 1boundary,
outer boundary and
initial lesion ROI

 

Computel mean (u) and
standard deviation (0) of
initial lesion ROI

 

 

 

I

 

Thresholding
s = 114.750

 

 

 

 

l

 

 

Create lesion’ ROI

 

 

 

Set lesion-ROI = lesion’ ROI

 

       
 

ls lesion'ROI E lesion ROI?

No

 

 

 

final lesion = lesion’ ROI

 

 

 

I

1 1

Figure 3.4. The iterative lesion boundary detection algorithm: The threshold value 3 is
calculated on the basis of the mean u and the standard deviation 0 of the before defined
lesion ROI. All pixels with values larger than 3 are assembled to make up the lesion’ R01.

28

 

 

Figure 3.5. Two differently chosen initial lesion ROIs and the corresponding iteration steps
of the boundary detection algorithm. The initial chosen lesion R01 is marked green and the
two boundaries are marked red. The algorithm for the first initial chosen ROI (first line)
converges after four iterations and the last ROI in the first line is the corresponding final
ROI. For the second initial chosen ROI the algorithm converges after only two iterations.

        

Figure 3.6. TWO possible initial ROI selections. Left: choice 1. Right: choice 2. The
manually selected lesion area is displayed green, inner and outer boundaries are displayed
red.

29

    

Figure 3.7. Final lesion area after convergence of the algorithm for the initially selected
areas shown in Figure 3.6. Left: choice 1. Right: choice 2.

 

Figure 3.8. Difference image, showing all pixels that differ between the final lesions in
Figure 3.7 in black.

30

 

. S
I". ‘1

Figure 3.9. Final lesion ROIs for differently chosen cut-off values. From left to right:
0 = 1.25,1.5,1.75, 2, 2.25.

 

Figure 3.10. An example for a detected lesion and its surrounding tissue areas. The inner
black contour denotes the one pixel wide gap between the lesion and the tissue 1 area; the
middle contour denotes the last pixel layer of the tissue 1 area and the same way the outer
contour denotes the last pixel layer of the tissue 2 area.

31

Chapter 4

Methods and Materials

4.1 MRI

Imaging was performed at a GB 1.5 T clinical scanner (General Electric HealthCare, Mil-
waukee, WI). For the dynamic contrast-enhanced imaging, the contrast agent injection and
the dynamic imaging were synchronized and the time interval between two post-contrast
images was set to 90 seconds. As a contrast agent, gadobenate dimeglumine (Gd-BOPTA,
0.2mL/kg) was used and it was injected at a rate of 3cc/s over 7-10 seconds followed
by a 20—cc saline flush. For the dynamic imaging in the axial plane a 3D fat-suppressed
Tl-weighted fast spoiled-gradient-echo pulse sequence with the following parameters was
used:

TE/TR=2.8/5.9 ms, Field of View (FOV) 320 mm, Matrix 320x320, Flip Angle (FA) 10°,
Slice thickness 2 mm, Number of Excitations (NEX) 0.76 and ZIP2.

The DTI scan was acquired prior to the DCE scan and the following parameters were
used: FOV 320 mm, TE/TR=min/10000ms, matrix 160x160, slice thickness 4mm, gap
0mm, NEX 2, b = 6003/mm2. Diffusion encoding was accomplished in six non-collinear

directions.

32

4.2 Image Data

Anonymous breast MRI data was examined. Sixteen contrast-enhanced lesions were in-
cluded in this study. Among these, ten were grouped as malignant and six as benign, ac-
cording to the pathology reports. The malignant tumors included infiltrating invasive ductal
carcinomas, grades I-IH, and the benign lesions fibroadenomas and fibrocystic changes.

The DCE analysis was based on all 16 masses. For the DTI analysis one malignant case
with a large apparent necrotic area was omitted, since the mean diffusivity and fractional

anisotropy of necrotic areas are awaited to significantly change for necrotic areas.

4.2.1 Discussion of a possibly false negative biopsy result (A)

It is highly probable that one out of the six examined benign cases was truly malignant.
After the MR scan, two subsequent biopsies were performed for this subject and both times
the diagnosis was negative for atypia or malignancy, categorizing the lesion as fibrocystic.
However, a mastectomy with a subsequent examination of the breast was carried out three
months after the last biopsy, finding the whole breast to be exceedingly interspersed with
malignant substance. A malignant lesion (infiltrating ductal carcinoma) was found, which
according to the mastectomy report most probably corresponded to the lesion analyzed at
the two prior biopsies, revealing most probably false negative biopsy results. In this work,
this case has been assigned to the benign group, according to our inclusion criterion of
a negative pathology report. It is however marked in all relevant figures with the special

symbol A.

33

Chapter 5

Dynamic Contrast-Enhanced Imaging

Data Analysis

5.1 DCE motion artifacts

The mean absolute value of the shift in anterior/posterior direction was found to be 0.55
pixels with a shift maximum of 3 pixels. The mean absolute value of the left/right shift was
found to be 0.25 pixels with a shift maximum of 2 pixels. There was no off-image-plane

shift found.

5.2 ROI test

A statistical analysis, based on the DCE images, was performed in order to validate that
the algorithm described in chapter 3.3.1 truly picks up the lesion and separates lesion and
tissue into two groups of significant difference. For the lesions, the signal intensity’s mean
and standard deviation were calculated to 1582 :l: 334; for the tissue 1 area, to 673 i 161;
and for the tissue 2 area, to 583 :1: 142, revealing a significant difference between the lesion
and the tissue 1 area with p < 10-7 (students’ t-test), but no significant difference was

detected between the two tissue areas (p > 0.10), which was the awaited result.

34

In a second step, the uptake signal changes mg for the lesion and the tissue 1 and tissue
2 areas were calculated and compared. r12 is given by the mean relative change value
reflected in the wash-in image, which has been discussed in chapter 3.2.4. The uptake signal
change for the benign lesions was (111 i 39)%, for their surrounding tissues (50 :l: 20)%,
for the malignant tumors (140 :t 33)% and for their surrounding tissues (62 :t 27)%. For
both the benign and the malignant case the difference between lesion and tissue area was
significant (p < 0.009 and p < 10’4, respectively). There was however no significant
difference between the benign lesions and the malignant tumors (p > 0.16). This result is
consistent with the radiologic reports of suspicion for malignancy, taking into account that
it has been reported that most invasive breast cancers show fast strong enhancement and

that benign lesions tend to have lower enhancement rates than the malignant ones [14].

5.3 Kinetic behavior analysis

Mean relative change kinetic curves for the benign lesions, the malignant tumors and the
tissue areas are plotted in Figure 5.1. Note the clearly distinct kinetic behaviors of the
lesions and the tissue areas in Figure 5.1, which furthermore supports the boundary deter-
mination using the presented algorithm. Also, the benign lesions show a slightly different
kinetic behavior than the malignant lesions: the mean uptake rate for the benign lesions is
lower than that for the malignant tumors - however, insignificantly lower, as shown above
- and the kinetic behavior from the first to the last post-contrast enhanced image shows a
persistent behavior for the benign cases in contrast to a plateau or slight wash-out behavior
for the malignant cases. The mean slope m, given as the mean of the pixel values in I slope
(see chapter 3.2.4) of the lesion areas, was calculated for the benign (m = (30.2 :t 10.2)°)
and the malignant case (m = (2.1 i 12.6)°). The difference is significant (p 2 3.9- 10—4),
which demonstrates the potential of the mean slope value of the detected lesions for the

delineation between malignant and benign lesions. Figure 5.2 shows the slope distribution

35

 

200%

160°/o 1“

 

 

 

 

 

 

 

 

a)
8’ 120% ~
(6
.c:
0
g 800/0 1'
.9
(I) / .‘1’ ' ’ — - Benign Lesions
400/0 1 ”/I’ —Malignant Tumors
2’ - - - Tissue 1
— - -Tissue 2
00/0 1 1 1 1 I
0 1.5 3 4.5 6 7.5
Time (min)

Figure 5.1. Mean relative change kinetic curves for benign lesions and malignant tumors
and their surrounding tissue areas. The error bars denote the standard error of means.

for the malignant and the benign cases.

5.4 Combining kinetic information to delineate between
malignant tumors and benign lesions

We introduced a method to combine the kinetic information between the pre-contrast and
the first post contrast-enhanced image, i.e., data given by the wash-in image, and between
the first and the last post contrast-enhanced image, i.e., data given by I slope- It is commonly
accepted that both phases can be used for the delineation between malignant and benign
masses, see e.g. [5, 15]. However, to our knowledge no attempt has been made to date to
(I) combine both phases for a (2) quantitative analysis using (3) the automatically detected
whole lesion ROI instead of the most enhancing area. We show that for our sample a clear
separation between the benign and the malignant group was yielded, using our method
(1) < 3 - 111-4).

We calculated slope wash-in images in conformance with the slope images 1810,36, see 3.2.4.

36

 

50°?

 

° . Benign Lesions
40°— . Malignant Tumors

 

 

 

N
O
o
I

d
O
o
1
D.

 

Mean Slope m
0

-1o°~ .

 

 

 

Figure 5.2. The distribution of the mean slopes of the kinetic behavior of the detected
lesions after the first post contrast-enhanced image. A denotes the possibly false negative
case.

 

Ill

 

malignant (97.9 i l3.4)°
benign (129.6 :1: 11.2)°
p-value 2.7~ 10-4

 

 

 

 

 

Table 5.1. Mean and standard deviation of the slope-angle E for benign and malignant
masses with corresponding p-value.

The correlation coefficient between the mean slopes from I slope and the mean wash-in
slopes was R2 = 0.31 with p < 0.02. A strong uptake rate was therefore correlated with a
strong wash-out, which allowed us to combine the information given by both phases. The
angle 3 between the slope wash-in image and I slope was calculated and we awaited a lower
E for malignant tumors than for benign lesions. Figure 5.3 defines E. The calculation of 5
yielded the results given in table 5.1.

The distribution of E is plotted in Figure 5.4.

Considering the clear separation of the benign and the malignant group, we conclude that

37

 

Signal Intensity (a.u.)

 

 

l-

1 l 1 1 l

1 2 3 4 5 6
Image number

Figure 5.3. The slope angle E between the wash-in slope function and the interpolated
slope—function between the first and last post contrast—enhanced image for an exemplary
kinetic curve.

the mean slope angle clearly provides clinical potential for the delineation of malignant and

benign lesions.

38

 

 

 

 

 

150° . Benign Lesions
° . Malignant Tumors
140“
0
130°:
[I] 2
. O
E. 120
A
“ 110°~ ‘
§ 2
a 100°: ‘
90°:
:
80°*
70°: A
60°

 

 

 

Figure 5.4. The distribution of the slope angle 3. A denotes the possibly false negative
case.

39

Chapter 6

Diffusion Tensor Imaging Data Analysis

So far, we used DCE imaging to improve the characterization of breast lesions. The physi-
ological reasoning for the comparison of kinetic features is hereby the increased vascularity
of malignant tumors (see chapter 2.7). DCE imaging, however, does not reveal direct infor-
mation about lesion cellularity (cell density), which has also been shown to be an important
index of tumor grade [4]. In particular, malignant tumors are known to be hypercellular in
comparison to benign lesions [4].

Brownian motion of water molecules in a tissue is affected by the microscopic structure of
the tissue. A high cell density if therefore expected to reduce the water diffusion because
of the high restriction to the diffusion. It has indeed been observed that the lesion mean dif-
fusivity correlates with tumor cellularity [6], revealing the potential of the mean diffusivity
for a delineation between malignant tumors and benign lesions according to their different
cellularities [6, 23, 16]. However, these studies also revealed that there was a large overlap
between the mean diffusivity values of benign and malignant masses. A recent prelimi-
nary study introduced a method of using relative mean diffusivity changes to establish a
statistical model for quantitatively characterizing breast lesions [9].

In this study, we first examined the mean diffusivity for both the lesions and their sur-

rounding tissues, and a large variation in diffusivity was observed among the subjects. The

40

large tissue variation in mean diffusivity from subject to subject is likely to be a cause for
the large overlap between the benign and the malignant group. To examine this possibil-
ity, we also investigated the correlation between the mean diffusivity of the lesion and the
surrounding tissue, and a correlation was found. This correlation provides a reason for in-
troducing the relative mean diffusivity change that accounts for the variation from subject
to subject.

Subsequently, using the relative mean diffusivity change, we found a significant separation
of the benign and malignant groups (p > 0.006) in contrast to no significant difference
comparing the mean diffusivity (p > 0.23). We also examined the fractional anisotropy

and relative fractional anisotropy of the benign and malignant cases.

6.1 DTI motion artifacts

BLAT allows for the manual correction of shift artifacts between the DCE and DTI images
in the same way as discussed above for the DCE image series. The mean absolute value of
the shift in anterior/posterior direction was found to be 1.60 pixels with a shift maximum
of 6 pixels. The mean absolute value of the left/right shift was found to be 4.00 pixels with

a shift maximum of 11 pixels. There was no off-image-plane shift found.

6.2 Mean diffusivity calculations

The created lesion, tissue 1 and tissue 2 R013 (see chapter 3.3) were applied to the DTI
images to both calculate the mean diffusivity and, later, the fractional anisotropy for the
lesion and tissue R013. The results are given in Table 6.1. The data show that there is a
large tissue variation between subjects, which is awaited and consistent with the common
practice to group tissue into four different types: almost entirely fat, scattered fibroglandu-
lar densities, heterogeneously dense and extremely dense [1]. The difference between the

mean diffusivity of the malignant lesions and their surrounding tissue 1 area is significant

41

 

 

 

(p 2 0.0069); however, the difference between the mean diffusivity of the two tissue areas
is not significant (p c: 0.83). The difference between the mean diffusivity of the benign
lesions and their surrounding tissue is not significant (p r: 0.66 between lesion and tissue
1, p 2 0.70 between tissue 1 and tissue 2). Since lesion cellularity has been shown to
correlate with lesion mean diffusivity [6], we considered that benign lesions might have a
similar cellularity as normal tissue.

The distribution of the mean diffusivity is plotted in Figure 6.1, which shows a huge overlap
between the malignant and the benign group. No significant difference between the two

groups is found (p > 0.23). Therefore, comparing the mean diffusivity was for our sample

1.6
1.5 .
1.4 : o
1.3 ~
12 <
1.1 1 0 ‘
1 1 A
0.9 ~ l
0.8 4 ,
0 Benign Lesions

. 4 .
07 IL A MalignantTumorsj
0.6 ' 7'" ~——

 

 

 

Mean Diflusivity (10'3 mmZ/s)

 

Figure 6.1. Mean diffusivity distribution for malignant tumors and benign lesions. A
denotes the possibly false negative case.

not a reliable method to characterize breast lesions.

6.3 Fractional anisotropy calculations

The fractional anisotropy was calculated for the lesion and tissue areas for both benign and
malignant cases. The results are shown in Table 6.1. Again the data show that there is a

large tissue variation between subjects. The difference between the fractional anisotropy

42

 

 

 

 

 

 

 

 

(D) (10—3mm2/s) FA
Malignant Tumors Benign Lesions Malignant Tumors Benign Lesions
Lesion 1.05 d: 0.16 1.23 :1: 0.30 0.43 :1: 0.08 0.46 :1: 0.13
Tissue 1 1.32 :t 0.20 1.17 :1: 0.20 0.55 :1: 0.10 0.62 :1: 0.12
Tissue 2 1.35 :l: 0.23 1.12 i: 0.19 0.58 :1: 0.12 0.67 i 0.14

 

Table 6.1. Mean diffusivity (D) and fractional anisotropy FA for malignant tumors, benign

lesions and their surrounding tissue areas (p :1: o).

of the malignant lesions and their surrounding tissue 1 area is significant (p 2 0.01); how-

ever, the difference between the fractional anisotropy of the two tissue areas is again not

significant (p 2 0.58). For the benign case we get a significant difference comparing the

tissue 1 and the lesion area (p 2 0.04) and not a significant difference for the tissue area

comparison (p 2 0.56).

The fractional anisotropy distribution is plotted in Figure 6.2. There is no significant dif-

ference between the malignant and the benign masses (p > 0.66). Therefore, the fractional

 

0.7
0.65 1

.°
0:

0.55 h

9
0'1
2

0.45 r

.0
A

0.35 r

Fractional Anisotropy

 

9
to

0.25 ~

 

 

0 Benign Lesions
A Malignant Tumors]

 

0.2

Db Db

Db

 

Figure 6.2 Fractional anisotropy distribution for malignant tumors and benign lesions. A
denotes the possibly false negative case.

anisotropy is also not sensitive enough to delineate between malignant tumors and (suspi-

cious) benign lesions for our sample.

43

 

 

6.4 Statistical justification for the introduction of the rel-

ative change concept

6.4.1 Lesion-tissue correlation analysis

In order to quantify the possible dependence between the tissue and the lesion properties,
we drew scatter plots with linear trend lines of the lesion and tissue 1 mean diffusivity and
fractional anisotropy, respectively (see Figures 6.3 and 6.4). The equations for the linear
trend lines are given in the figures. For the mean diffusivity, the correlation coefficient
R2 was calculated to RID) = 0.21 with p < 0.09 and for the fractional anisotropy we
got R3714 = 0.44 with p < 0.01. The fractional anisotropy shows a significant correlation
between the tissue and the lesion area. This correlation may be used to possibly reduce the
large variation from subject to subject. Using the common significance level of 5%, there
is no significant correlation between the lesion and tissue mean diffusivity. However, since
the p-value is not much bigger than the commonly accepted significance level threshold

value, we still assumed a linear dependency. Additional studies with larger samples are

needed to examine further the correlation between lesion and tissue mean diffusivity.

6.4.2 Tissue-tissue correlation analysis

We analyzed the correlation between tissue 1 and tissue 2. Figure 6.5 and 6.6 show the
linear correlation between tissue 1 and tissue 2 areas for both the mean diffusivity (p <
7 - 10‘7) and fractional anisotropy (p < 2 - 10’7). From the trend line equations given in
both figures it becomes clear that the two tissue areas show always about the same behavior.
Accordingly, either the tissue 1 area or the tissue 2 area could be taken as a reference that
most probably reflects the mean normal breast tissue values of (D) and FA, respectively,

of the specific subject. For this study, we chose the tissue 1 area as a reference.

 

1.8
1.6

I

14 . , y=0.5101x+0.4823

O

1.2

l

0.8 °

I

0.6 _

 

 

04 1 1 1 1
0.8 1 1.2 1.4 1.6 1.8
Mean Diffusivity Tissue 1 (10'3 mm2/s)

 

Mean Diffusivity Lesion (10'3 mmz/s)
0

Figure 6.3. Mean diffusivity correlation between tissue 1 and lesion area.

0.7

 

.
0.6 I y = 0.5932x + 0.096

0.4 ~

 

0.3 r

0.2 r

 

 

Fractional Anisotropy Lesion

0 1 1 1 1
0.3 0.4 0.5 0.6 0.7 0.8

Fractional Anisotropy Tissue 1

 

Figure 6.4. Fractional anisotropy correlation between tissue 1 and lesion area.

6.5 Introduction of the mean diffusivity relative change

model and results

We introduce the relative change X r as

X. = (fl—£2, (6.5.1)

45

 

 

1.9

1-7 F y=1.0319x - 0.0443

    

1.3 r

1.1 ~

0.7 —

 

 

 

05 L 1 1 1 g 1
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9

Mean Diffusivity Tissue 1 (10'3 mmz/s)

Mean Diffusivity Tissue 2 (10‘3 mmZ/s)

Figure 6.5. Mean diffusivity correlation between tissue 1 and tissue 2 area.

 

N 0.9
0.8 .
0.7 1
> 0.6 —

Tissue

9.0.0
004501
fil

 

9.0
dN
l

 

 

Fractional Anisotrop

I 1 1

O

 

o 0.2 0.4 0.6 0.8
Fractional Anisotropy Tissue 1

Figure 6.6. Fractional anisotropy correlation between tissue 1 and tissue 2 area.

where X denotes a quantity such as the mean diffusivity or the fractional anisotropy and
the index l denotes the lesion area and t the tissue 1 area.

Figure 6.7 shows the distribution of the relative mean diffusivity values of the lesions. Their
corresponding means, standard deviations and p-value are given in Table 6.2. As can be

seen, the introduction of the relative mean diffusivity change significantly separates the

46

 

(0),. FAT

malignant —0.197 :1: 0.114 —0.211 :1: 0.068
benign 0.049 :1: 0.141 —0.272 :t 0.126
-values 0.006 0.41

 

 

 

 

 

 

 

Table 6.2. Relative mean diffusivity and relative fractional anisotropy (p :1: a) for benign
and malignant cases.

malignant distribution from the benign distribution, thus revealing clinical potential for the
delineation of benign and malignant masses. However, there is still an overlap between the
groups.

The relative mean diffusivity of the benign lesions is distributed around the tissue values
(i.e., around zero), as awaited, since the benign lesions show similar behavior as their

surrounding tissue (see discussion above).

 

 

 

 

 

 

 

 

0.3
O
A? 0.2
.2
a)
3 _, 0
SE 0.1 .
D 0
g A
a)
2 -o.1 . A A
a) O
>
a: . 1
w -0 2 ‘
E
CC .03 A o Benign Lesions A
A Malignant Tumors
-0.4 W"

Figure 6.7. Relative mean diffusivity distribution for malignant tumors and benign lesions.
A denotes the possibly false negative case.

Figure 6.8 shows the distribution of the relative fractional anisotropy change values, FAT.
Their corresponding means, standard deviations and p-value are also given in Table 6.2.
Fractional anisotropy and relative fractional anisotropy seem to be not sensitive enough for

a reliable delineation between malignant and benign masses.

47

 

0.05
o
-o.os ~
-o.1 «
41.15 ~ A A
02 ~ ‘
0.25 ~ A
03 4 A
-o.35 - 8

-0.4 ~
0 Benign Lesions

"0'45 A a Malignant Tumors .
-0.5

I)

 

 

Relative Fractional Anisotropy

 

 

 

 

 

 

Figure 6.8. Relative fractional anisotropy distribution for malignant tumors and benign
lesions. A denotes the possibly false negative case.

6.5.1 Detailed DTI subject data

The individual subject DTI data is given in Table 6.3.

Figure 6.9 shows the normalized mean diffusivity distribution for all malignant (A) and
benign (C) lesions and the normalized relative mean diffusivity distribution for malignant
(B) and benign (D) lesions. We set up a statistical model for the malignant tumors, given
the mean and standard deviation of the relative mean diffusivity distribution. The corre-
sponding Gaussian distribution is plotted in Figure 6.9(B). Means and standard deviations
for the four distributions in Figure 6.9 are given in Table 6.4. The standard deviation of
the mean diffusivity distributions is larger than that of the relative mean diffusivity distri—
bution, which supports the assumption that the normal tissue mean diffusivity biases the
mean diffusivity distribution and that the introduction of the relative change corrects for

this distortion.

48

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(Dz) (Du) (012) (Dir FA1 F1411 FA12 F Ar

1 1.395 1.031 1.031 0.245 0.447 0.690 0.758 —0.353
2 0.830 0.958 0.911 —0.134 0.642 0.756 0.790 —0.150
3 1.099 1.010 0.963 0.088 0.470 0.710 0.799 —0.338
4 1.538 1.375 1.390 0.118 0.291 0.525 0.544 -—0.446
5 1.547 1.439 1.264 0.075 0.544 0.588 0.633 —0.074
A 0.987 1.093 1.177 —0.097 0.336 0.461 0.472 —0.271
7 0.904 1.286 1.483 —0.297 0.298 0.379 0.343 —0.213
8 1.257 1.689 1.793 —0.256 0.508 0.589 0.610 —0.137
9 0.915 1.211 1.200 —0.244 0.380 0.537 0.616 —0.292
10 0.923 1.021 1.046 —0.096 0.364 0.582 0.676 —0.374
I] 1.069 1.534 1.520 —0.303 0.509 0.598 0.537 —0.148
12 1.092 1.119 1.131 —0.025 0.452 0.737 0.767 -0.388
13 1.067 1.378 1.338 —0.225 0.527 0.526 0.598 0.001
14 1.344 1.385 1.314 —0.030 0.380 0.434 0.499 —0.126
15 0.920 1.301 1.299 —0.293 0.435 0.559 0.560 —0.222

 

 

 

 

 

 

 

 

 

 

 

 

Table 6.3. Data of the DTI image analysis with benign cases (1-6) and malignant cases
(7-15) for lesion (1), tissue 1 (11) and tissue 2 (t2) areas. Mean diffusivity values are given
in 10‘3mm2/s. A denotes the possibly false negative case.

 

 

 

 

 

 

(D) (10—3mm2/s) (D).
malignant 1.11 :t 0.33 —0.15 :1: 0.25
benign 1.22 1: 0.41 0.03 :1: 0.28

 

Table 6.4. Mean diffusivity (D) and relative mean diffusivity (D),~ (p :1: a) of the distribu-
tions given in Figure 6.9.

49

 

1.5

0.5"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.5

0.5'

 

 

will

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

111111 .[1

 

 

Figure 6.9. Normalized mean diffusivity for malignant tumors (A) and benign lesions (C)
and normalized relative mean diffusivity distribution for malignant tumors (B) and benign
lesions (D). In (B) the Gaussian distribution according to the set up statistical model is

included.

50

 

1.5’

0.5’

 

 

 

 

 

 

 

 

 

 

1.5*

0.5-

 

“hf!

 

 

 

 

 

 

-1

 

 

 

 

 

 

 

Chapter 7

Discussion

The breast lesion analysis software that was created in the course of this work was vali-
dated, and it presented a reliable method to identify lesions. A method using combined
kinetic inforrnations was introduced and it revealed potential for later clinical applications
for the delineation between malignant and benign breast masses.

The recently evolving diffusion tensor imaging technique was used and examined for us-
ability for the characterization of breast lesions. So far, it seems to bear less potential for
a reliable delineation criterion than dynamic contrast-enhanced imaging. However, a sta-
tistical justification for the introduction of the relative change concept was found, and the
relative mean diffusivity change was demonstrated to significantly improve the separation
of the benign and malignant group in comparison to the approach using the mean diffusiv-
ity. Further studies have to be done in order to evaluate the clinical usability of DTI for the

characterization of breast lesions, in particular with regard to the fractional anisotropy.

51

 

 

APPENDICES

52

Appendix A

Gyromagnetic ratios

'7 /27r (MHZ/T)
IH (proton) 42.576
electron 28024.954

 

neutron 29.165
7L1 16.546
13C 10.705
14N 3.0766
15N -4.3156
170 -5.7716
23Na 1 1.262
319 17.235

 

(Values for electron and neutron from [l7]. All other values from [2]).

53

 

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5. !

 

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