Implementation and validation of robust Dixon methods for abdominal imaging at 3T

43 Pages·2011·4 MB·English

by  Henric Rydén

Implementation and validation of
robust Dixon methods for abdominal
imaging at 3T

M. Sc. Thesis in Medical Physics
Henric Rydén

Supervisors:
Thomas Lange
Department of Radiology, University Medical Center Freiburg, Germany

Maja Sohlin
Department of Radiation Physics, Sahlgrenska Academy at the
University of Gothenburg, Sweden

2011-02-25
Table of Contents
1 INTRODUCTION .................................................................................................. 2
2 THEORY .............................................................................................................. 3
2.1 Fat-water frequency shift .......................................................................... 3

2.2 Standard two-point Dixon ....................................................................... 5

2.3 Partially-opposed phase (POP) ................................................................. 7

2.4 ASR ....................................................................................................... 10

2.5 Graph-cut based method (GC) ............................................................... 14

3 MA TERIALS AND METHODS ................................................................................ 19
3.1 Dixon reconstruction tool ...................................................................... 19

3.2 Image quality assessment ........................................................................ 21

3.3 POP optimization .................................................................................. 22

3.4 ASR optimization .................................................................................. 24

3.5 GC optimization .................................................................................... 24

3.6 Method comparison ............................................................................... 25

4 RES ULTS ............................................................................................................ 26
4.1 Subcutaneous fat ratio measurement ....................................................... 26

4.2 POP ...................................................................................................... 26

4.3 ASR ....................................................................................................... 29

4.4 GC ........................................................................................................ 31

4.5 Method comparison ............................................................................... 35

5 DIS CUSSION ...................................................................................................... 36
6 CONCLUSIONS ................................................................................................... 40
7 REFERENCES ...................................................................................................... 41

1
1 Introduction
Due to the short T1relaxation time of fat, it often appears hyper-intense in T1-weighted MR

images and consequently, it can conceal pathologies. Dixon imaging can be used to suppress this
high-intensity fat signal or for pathological examinations of fatty tissues. Other applications
include separation and quantification of visceral and subcutaneous fat.

The aim of this work was to implement a robust Dixon method at 3T for accurate fat
quantification. Numerous Dixon methods have been proposed in the literature, of which many
have shown good results at 1.5T (1). While 1.5T is the most common field strength, the use of
3T MR scanners has increased rapidly during the past years due to their higher SNR. One of the
disadvantages of higher field strengths is that a homogenous magnetic field is harder to
obtain. Thus, Dixon imaging at 3T requires field map estimation to handle the larger B
0
inhomogeneities compared to 1.5T. Three advanced Dixon methods with intrinsic B
0
inhomogeneity estimation were investigated in this work. The methods, which are sensitive to
various sequence and reconstruction parameters, were optimized and validated at 3T.

The Dixon method with the best performance will be used in a forthcoming study on obese
children (2). The study will explore a possible correlation between liver fat content, measured
with MR spectroscopy (MRS), and visceral fat in the abdominal region measured with Dixon
imaging. Therefore, the objective was to find a robust Dixon method allowing for reliable fat
quantification.

2
2 Theory
In the past, various methods have been proposed for selective fat/water imaging. The majority are
based on inversion recovery, selective excitation or chemical shift (Dixon) imaging.

The concept of inversion recovery is based on the difference in T1relaxation time between fat

and water. By applying a 180° followed by a 90° RF pulse when the longitudinal fat (water)
magnetization component is zero, a fat (water)-suppressed image is obtained. The disadvantages
of inversion recovery sequences are low SNR, high SAR, long scan times, and sensitivity to B
1
inhomogeneities. In addition, T1 values for fat (water) generally varies within the field of view,
yielding residual fat (water) signal in the image. Their main advantage is their independence of
main magnetic field (B ) inhomogeneities.
0

Selective excitation exploits the chemical shift difference of water and lipid protons, using a
narrow-bandwidth RF-pulse for exclusive excitation of either water or fat. It can also be used to
suppress fat by applying a narrow spin-selective pulse followed by gradient spoiling and
subsequent excitation with a broad non-selective pulse. Selective excitation pulses increase scan
time and their performance can be impaired by B inhomogeneities. Another requirement is that
1
the fat-water frequency shift is significantly larger than the shift caused by B inhomogeneities in
0
the field of view.

Similar to selective excitation, Dixon methods also rely on the frequency shift between fat and
water. Multiple images are acquired, each with a different echo time. With prior knowledge of
the frequency shift, it is possible to reconstruct fat and water images. Some reconstruction
algorithms use only two echoes while other, often more advanced, Dixon methods can use a
variable number of echoes.

2.1 Fat-water frequency shift
Fat and water have different molecule structures, shielding the external magnetic field to a
different degree. This causes the Larmour frequency of hydrogen nuclei in water and fat to be
slightly offset with respect to each other. Additionally, fat itself consists of several molecular
groups (CH , CH , etc.) which all have different structures and unique resonance frequencies.
3 2
3
The measured MR signal from a voxel k that contains only water and fat can be described as
follows if signal decay and eddy current effects are ignored (1):

 M 
S(k,TE)=W(k)+∑F (k)ei2π∆fmTEeiΦ(k,TE)eiΦ0(k) [1.1]
m
 
m=1

where TE is the echo time. W and F are the magnitudes of the water and fat magnetization
vectors, respectively. ∆f is the chemical shift of fat component m relative to water. Φ is the
m
phase offset caused by main field (B ) inhomogeneities:
0

Φ(k,TE)=∆B (k)⋅γ⋅TE [1.2]
0

Φ is the phase offset caused by system imperfections such as RF-pulse (B ) inhomogeneities.
0 1
Note that Φ varies spatially but is time-invariant. The magnetization vectors and the error
0
phasors are illustrated in Figure 1.

Φ
0
Φ
W
F S

Figure 1 – Illustration of complex signal vectors and the phase offsets in a voxel. W and F represent the water and
fat signal vectors, respectively. S is the measured signal. B0 inhomogeneities cause a phase error proportional to
the echo time, shown as Φ. There is also a time-invariant phase offset Φ caused by system imperfections.
0

For simplicity, it is often assumed that fat consists only of methylene as the majority of the signal
originates from this component (3). Methylene has a chemical shift difference ∆σ of about
3.3 ppm compared to water, slightly depending on the water temperature. From now on, the
phasors will be denoted P(Φ) where its argument represents its corresponding phase (e.g.
P(Φ)=eiΦ(k,TE)). In addition, the signal components spatial and/or temporal dependency will not
be explicitly written. Instead, entire images will be considered unless specifically stated. Note that
all error phasors are spatially dependent. The images can be described as
4
I=(W+FP(α))P(Φ)P(Φ ) [1.3]
0

where α represents the phase arising from the fat-water frequency shift.

2.2 Standard two-point Dixon
With the standard two-point Dixon (2PD) method, two echoes are acquired with echo times
chosen such that the water and fat magnetization vectors are in phase (IP) in one echo and
opposed (OP) in the other (4).

With an external magnetic field strength of 3T, the frequency shift between water and fat is

Bγ∆σ
∆f = 0 ≈420 Hz [2.1]
2π

Therefore, at TE =1.19 msthe fat and water magnetization vectors are opposed (α=180°). At
1
TE=0, the magnetization vectors are in phase. The images at these echo times are

I =(W+F)P(Φ )
IP 0
[2.2]
I =(W−F)P(Φ)P(Φ )
OP 0

This means that I and I are completely opposed only if there are no B inhomogeneities, i.e.
OP IP 0
P(Φ)=1. At TE =2.38 ms, the fat and water magnetization vectors are in phase again.
2
Figure 2 illustrates the signal vectors in this case. If this assumption is valid, W and F can be
solved by summation and subtraction of the complex images:

I +I
W = IP OP
2
[2.3]
I −I
F= IP OP
2

Magnitudes are taken to avoid any imaginary signal component due to P(Φ ). If there are
0
inhomogeneities present, the signal vectors are not opposed, as illustrated in Figure 3. A solution
5
to this problem was proposed in Dixon’s original paper (4), where the magnitude of each image is
taken before addition and subtraction:
I + I
I = IP OP
B 2
[2.4]
I − I
I = IP OP
S 2

In phase Opposed phase
S W
IP
Φ
0
F
Φ0 W

S
OP
F

Figure 2 –Magnetization vectors in a voxel without B0-inhomogeneity. The signal vectors are completely
opposed in the two echoes. The phase offset Φ from system imperfections affects both echoes equally and its
0
effect is cancelled by taking the magnitude of the W and F estimates in Eq. [2.3]. α represents the phase arising
from the frequency shift between fat and water.

Opposed phase
In phase
F
Φ
0
Φ
S 2
ÌP S
Φ OP
0 W
Φ
1 F
W

Figure 3 - Magnetization vectors in a voxel with B0 inhomogeneities. The in-phase echo is acquired W and F are
in phase. The signal vectors SIP and SOP, measured at TE1=1.19 and TE2=2.38 ms, are not opposed. A
reconstruction based on Eq. [2.3] will cause incorrect estimations of the fat and water contents. α represents the
phase arising from the frequency shift between fat and water.

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While this gets rid of all error phasors, the sign of the signal in all voxels are lost. It is then
impossible to distinguish a voxel where, for instance (F,W)=(0.2,0.8) from another voxel with
(F,W)=(0.8,0.2) as they will have the same signal magnitude. The water and fat images will
only be correct in voxels where W≥F. Instead, I and I are images where each voxel represents
B S
the biggest and smallest signal component, and there is an uncertainty as to which corresponds to
water and fat:

(F,W)∈{(S,B),(B,S)} [2.5]

In reality, an echo time of zero is not attainable. The in-phase echo must therefore be acquired
when α=360°⋅n (n=1,2,...). Consequently, the B inhomogeneities will also affect the in-
0
phase echo. However, this is not a problem as the magnitude operation in Eq.[2.3] removes any
phase offset that equally affects both echoes. The only remaining error phase Φ −Φ will be
2 1
caused by B inhomogeneities during the echo time spacing TE −TE (Figure 3). This is
0 2 1
sometimes referred to as a differential error phasor:

P(∆Φ)=P(Φ )P(Φ ) [2.6]
2 1

where the bar symbolizes the complex conjugate operator.

For these reasons, it is clear that B inhomogeneities must be taken into consideration when
0
reconstructing fat and water images using a Dixon-based method.

2.3 Partially-opposed phase (POP)
The partially-opposed phase (POP) Dixon method used in this work was developed by Xiang and
is described in more detail in his original paper (5). In order to understand the reconstruction
parameters for this method, a short explanation of the method is given here. The method is based
on a two-echo acquisition. The difference between POP and 2PD is that one echo is acquired
when the fat and water magnetization vectors are only partially opposed (e.g. α=150°). The two
images are

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I =(W+F)P(Φ )P(Φ )
IP 1 0
[3.1]
I =(W+FP(α))P(Φ )P(Φ )
POP 2 0

where α is the POP angle. As described by Eq. [2.6], P(Φ )=P(Φ )P(∆Φ). The magnitudes of
2 1
both images are taken such as in the standard 2PD reconstruction. Since the signals are not
completely opposed, finding solutions for I and I requires use of the cosine theorem:
B S

1 2 I 2 − I 2(1+cosα)
I = I + POP IP
B 2 IP 1−cosα
[3.2]
1 2 I 2 − I 2(1+cosα)
I = I − POP IP
S 2 IP 1−cosα

2.3.1 Removal of common error phasors
By multiplying I with the complex conjugate of the in-phase signal, the common error
POP
phasors are removed from I . To reduce noise, the fact that B inhomogeneities are in general
POP 0
spatially smooth is utilized and I is filtered with a mean filter F before its multiplication with
IP 1
I . The kernel size is a reconstruction parameter, and its impact on the resulting water and fat
POP
images is investigated in this thesis. The magnitude of I is taken to remove its error phasors,
IP
and the following images are formed:

I =W+F
IP
[3.3]
J =I IF1 =(W+FP(α))P(∆Φ)
POP POP IP

The superscript marks that the image has been filtered with F . Because of the magnitude
1
operations in Eq.[3.2] there are two possible solutions for P(∆Φ), in analogy to the ambiguity
explained by Eq.[2.5]:
J
P = POP
v (I +I P(α))
B S
[3.4]
J
P = POP
u (I +I P(α))
S B
8
2.3.2 Regional Iterative Phasor Extraction (RIPE)
The problem of estimating F and W is reduced to determining the correct P(∆Φ) in every voxel,
which is done through an iterative procedure called RIPE:

P +P
P = v u [3.5]
0 2

P if P −PF2 < P −PF2
 u u n v n

P =P if P −PF2 < P −PF2 [3.6]
n+1 v v n u n

 0 if Pu −PnF2 = Pv −PnF2

where the subscript denotes the current iteration number. Initially, a seed P is generated from an
0
average of the two candidates. P is thereafter filtered with a mean filter F . The filtering is
0 2
performed separately on the real and imaginary part of P . For every voxel, the smoothed P ,
0 n
PF2, is compared with its two candidates in Eq.[3.4]. The candidate that differs least from PF2 is
n n
chosen as P (Eq. [3.6]).
n+1

This procedure can be considered as a local phasor choice within the convolution kernel. Since
the B inhomogeneities are spatially smooth, the voxels within the kernel experience more or less
0
the same inhomogeneity and the correct P should be chosen. The size of F is a reconstruction
n+1 2
parameter, and its impact on the resulting water and fat images is investigated in this work.

Subsequently, a new iteration begins where P (the formerP ) is used as a seed. It is filtered and
n n+1
a new decision is made. The process is repeated until the number of voxels that have changed
their phasor P is zero. Finally, the resulting P is chosen as P(∆Φ).
n n

2.3.3 Estimation of fat and water
The RIPE procedure described above yields P(∆Φ). To remove any discontinuities, P(∆Φ) is
filtered with a mean filter F and normalized to unit magnitude. The size of F is a reconstruction
3 3
parameter, and its impact on the resulting water and fat images is investigated in this work. J
POP
is multiplied by PF3(∆Φ) to remove the error phasor in Eq.[3.3]. This gives an image corrected
9