1. Department of Physics and Astronomy
University of Heidelberg
Bachelor Thesis in Physics
submitted by
Luca Jan Schmidtke
born in Speyer (Germany)
2016
2.
3. Optimization of a 3D CEST sequence for imaging the human
brain at 3 Tesla
This Bachelor Thesis has been carried out by Luca Jan Schmidtke at the
German Cancer Research Center in Heidelberg
under the supervision of
Prof. Dr. Peter Bachert
4.
5. Optimization of a 3D CEST sequence for imaging the human brain at 3 Tesla Chemical
Exchange Saturation Transfer (CEST) employs the proton transfer between low concentrated
solutes and bulk water to prepare enhanced saturation of the water signal. Presaturation
of solute protons by a series of frequency-selective rf pulses is followed by detection of the
modified water proton signal for each voxel by a conventional MR imaging sequence. The
strong dependence of the proton exchange processes on physiological conditions may lead to a
better differentiation of normal and pathologic tissue.
However, despite its unique contrast, CEST is still not incorporated into clinical routine.
In this study, the flip angle and the signal-to-noise ratio (SNR) of a CEST sequence at B0 = 3 T
could be optimized for signals mediated by so-called exchange-relayed Nuclear Overhauser effects
(rNOE). The CEST pulse sequence was realized by a saturation phase interleaved by 3D fast
gradient echo imaging. Herein, one segment consists of a certain number of saturation pulses
and a corresponding amount of acquired k-space lines and is repeated until the entire image
can be reconstructed. Additionally, the impact of different segmentation schemes on the rNOE
signals was investigated. No significant difference was observed although smaller numbers of
saturation pulses are generally recommended due to specific-absorption-rate (SAR) limitations
of clinical MR tomographs.
Optimierung einer 3D CEST Sequenz f¨ur die Bildgebung des menschlichen Gehirns bei
3 Tesla Chemical Exchange Saturation Transfer (CEST) nutzt den Protonentransfer zwis-
chen niedrig konzentrierten gel¨osten Moleklen und Wasser, um eine st¨arkere S¨attigung des
Wassersignals zu erhalten. Die S¨attigung der gel¨osten Protonen durch eine Serie von Frequenz-
selekiven Rf-Pulsen wird gefolgt von der Detektion des Wassersignals durch konventionelle MR-
Bildgebung. Die starke Abh¨angigkeit der Protonenauschtausch-Prozesse von physiologischen
Bedingungen k¨onnte zu einer besseren Unterscheidbarkeit von normalem und pathologischem
Gewebe f¨uhren.
Allerdings ist CEST trotz des einzigartigen Kontrastes noch nicht in der klinischen Routine
integriert.
In dieser Arbeit konnte der Flipwinkel und das Signal-zu-Rausch Verh¨altnis (SNR) einer CEST-
Sequenz bei B0 = 3 T f¨ur Signale optimiert werden, die durch die sogenannten exchange-
relayed Nuclear Overhauser Effekte (rNOE ) entstehen. Die CEST Sequenz wurde mit
einer S¨attigungsphase implementiert, die mit einer schnellen 3D Gradienten-Echo-Sequenz ver-
schachtelt wurde. Hierin besteht ein Segment aus einer bestimmten Menge von S¨attigungspulsen
und der dazugeh¨origen Anzahl von ausgelesenen k-Raum-Linien. Dieses wird wiederholt, bis das
komplette Bild rekonstruiert werden kann. Es wurde zus¨atzlich untersucht, welchen Einfluss ver-
schiedene Segmentierungen auf die rNOE-Signale haben. Es konnte kein deutlicher Unterschied
festgestellt werden, allerdings ist eine kleinere Anzahl von S¨attigungspulsen mehr zu empfehlen,
da klinische MR-Tomographen durch die Spezifische Absorptionsrate (SAR) limitiert sind.
9. 1 Introduction
The theoretical foundation for Nuclear Magnetic Resonance has been laid in the early 20th
century when the particle spin was discovered as a result of the Stern-Gerlach-Experiment [1].
Since then, many discoveries and developments, especially those by Bloch [2],Hahn [3], Pur-
cell [4] or Lauterbur [5] have led to the powerful imaging technology that Magnetic Resonance
Imaging (MRI) is today. MRI is nowadays an essential part of clinical diagnostic routine all
over the world. The contrasts enabled by the longitudinal (T1) and transverse (T2) relaxation
times offer an excellent imaging modality for noninvasive imaging in-vivo.
While conventional techniques rely on the detection of 1H water protons, newly proposed
methods utilize complex magnetization transfer mechanisms. Chemical Exchange Saturation
Transfer MRI (CEST-MRI) focuses on exchanging protons of dilute molecules and the sur-
rounding water pool in order to enable a more sophisticated metabolic contrast without the
necessity of radioactive tracers or other injected agents. The metabolites can be indirectly
detected through their effect on the spin population of water protons. The basic principle of
CEST involves the following steps: First, the magnetization of the smaller pool of metabolites
is selectively saturated by radiofrequency pulses which leave the larger water pool unaffected.
Due to the proton exchange of both pools, saturation is transferred to the water system and ef-
fectively leads to a detectable decrease in proton magnetization. The signal of the water proton
magnetization is then measured with a conventional imaging sequence. These steps are repeated
with varying radiofrequency irradiation which finally leads to the acquisition of a spectrum in
which characteristic peaks define the contrast of CEST.
It has been demonstrated previously that numerous molecules such as Amides and Amines
within proteins as well as exchange relayed Nuclear Overhauser effects (rNOEs) can offer a
unique CEST contrast in-vivo [6] [7] [8]. However, CEST phenomena are entangled by a series
of compromising effects like spillover from direct water saturation or macromolecular magneti-
zation transfer (MT) [9].
It remains an open challenge to successfully incorporate CEST into the clinical routine of
MRI. One approach is to apply saturation pulses of different shapes and interleave this scheme
with a low flip angle 3D GRE imaging sequence. With 3D acquisition, the data truly reflects
the spatial distribution of spins within the human body and therefore allows the reconstruction
of three dimensional images. The higher SNR due to a signal contribution from one additional
spatial dimension and the ability to sample the data more densely make 3D imaging generally
desirable. This also applies to CEST imaging. The interleaved approach can be characterized
by so called segments, which are repeated sections comprised of partial saturation and read-
out. For instance the reconstruction of one slice usually requires 128 k-space lines. With a
segmentation scheme set to 2 saturation pulses per 4 k-space line acquisitions, the segment will
be repeated 32 times. In-vivo, different segmentation schemes might have an impact on CEST
effects.
The goal of this work was optimize the unique contrast that CEST has to offer by means
of rNOEs. In all measurements, the asymmetry of the Z-spectrum was evaluated as a func-
tion of different parameters including flip angle, signal-to-noise ratio (SNR) and segmentation
scheme. Several experiments regarding the optimization of readout parameters were already
performed [10] in phantoms, but still need to be investigated in-vivo.
1
10.
11. 2 Physical background
The following chapter will offer a brief overview of the thereotical background of Nuclear Mag-
netic Resonance (NMR) and Magnetic resonance imaging (MRI). More information can be
found in [11].
2.1 Basics of NMR
In this section, the basics of Nuclear magnetic resonance (NMR) are displayed.
2.1.1 Nuclear Spin in quantum mechanics
The mathematical description of spin is analogous to that of angular momentum in quantum
mechanics. The Spin operator
ˆ
S = ( ˆSx, ˆSy, ˆSz) obeys the same commutation relations:
ˆSi, ˆSj = ijki¯h ˆSk (2.1)
ˆSi,
ˆ
S2
= 0 (2.2)
Therefore, the eigenvectors of
ˆ
S2 and ˆSz expressed in the basis of
ˆ
S are:
ˆ
S2
|s, ms = ¯hs(s + 1) |s, ms (2.3)
ˆSz |s, ms = m¯h |s, ms (2.4)
With the spin quantum number s = 0, 1
2, 1, 3
2 etc. and the magnetic spin number ms =
−s, −(s − 1), ..., s.
NMR is governed by the properties of atoms with a nuclear spin other than zero. The total
atomic angular momentum (protons and neutrons) is the superposition of orbital momentum
ˆ
L
and intrinsic spin
ˆ
S:
ˆ
I =
ˆ
L +
ˆ
S (2.5)
The analogous algebra applies to this operator. Following the eigenvalue approach from above
its discrete value is:
|I| =
ˆ
I2 = ¯h I(I + 1) (2.6)
The discretization along an arbitrary z-direction is of particular interest:
Iz = ˆIz = m¯h (2.7)
with I = 0, 1
2, 1, 3
2 etc. and m = mI = −I, −(I − 1), ..., I.
Due to the extremely high abundance of water within the human body, the most prominent
nucleus of interest is 1H. The hydrogen atom is described by its nuclear spin of I = 1
2.
The particle possesses a magnetic moment associated with its total atomic angular momentum:
ˆµ = γ
ˆ
I (2.8)
3
12. 2 Physical background
The constant γ is called gyromagnetic ratio and is written in units of (rad · s−1 · T−1). For
protons , γ has a value of 2.6752 · 108 Hz T−1
or in more common units
γ
2π
= 42.58 MHz T−1
.
2.1.2 The spin within an external magnetic field
To continue the path within the quantum mechanical picture, consider a particle with spin s=
1
2 at rest and with an orbital angular momentum of L = 0 in a constant, external magnetic
field B = (0, 0, B0) along the arbitrary z-direction. The Hamiltonian describes the interaction
between field and particle:
ˆH = −ˆµB = − ˆµzB0 (2.9)
ˆH can be represented in the basis of its eigenvectors |ψ with corresponding eigenvalues in form
of discretized energy levels En:
ˆH |ψ = En |ψ (2.10)
In this case one obtains:
ˆH |ψ = − ˆµzB0 |ψ = −γ ˆIzB0 |ψ = −γ ˆSzB0 |ψ = −γ
¯h
2
1 0
0 −1
B0 |ψ (2.11)
Using the so called larmor frequency ω0 = γB0 yields:
ˆH |ψ =
−
1
2
¯hω0 0
0
1
2
¯hω0
|↑ or |↓ (2.12)
with |↑ =
1
0
and |↓ =
0
1
It immediately follows that the energy difference between the spin-up and spin-down state
is
∆E = ¯hω0 (2.13)
It will follow later (2.1.4) that an oscillating external magnetic field with frequency ω0 will
provide the energy needed to induce a transition between the two states.
2.1.3 The Precessional motion of the magnetic moment
In this section, the motion of the physical spin vector around an external magnetic field will be
derived and analyzed. The Ehrenfest Theorem justifies a transition into the classical picture:
d
dt
ˆµ =
i
¯h
ˆH, ˆµ (2.14)
This equation can be transformed with the help of the commutation relations of the angular
momentum operator (and therefore also the spin operator
ˆ
S) from equations 2.1 and 2.2:
i
¯h
ˆH, ˆµ j
= γ2 i
¯h
Bi
ˆSj, ˆSi = γ kijµkBi (2.15)
The result is the quantum mechanical representation of the classical equation of motion for a
magnetic moment µ in an external magnetic field:
d
dt
ˆµ = ˆµ × γB (2.16)
4
13. 2.1. Basics of NMR
Therefore, the classical representation of this equation with euclidean vectors can be applied:
d
dt
µ = µ × γB (2.17)
As a result of the equation of motion above, the magnetic moment vector will start to precess
around the z-axis with an angular frequency ω0 = γB0 similar to that defined in (2.1.2)
2.1.4 Rotating reference frame and excitation
In the case of NMR, it is practical to perform a coordinate transformation into a cartesian
coordinate frame which rotates around the fixed z-axis. The external magnetic field B points
along the z-axis. Let the coordinates of that system be x , y , z . As a result of the rotation
with angular velocity Ω pointing along the z-axis, the equation of motion for a single magnetic
moment transforms into:
d
dt
µ =
3
i=1
dµi
dt
ˆei = γµ × Beff with Beff = B −
Ω
γ
(2.18)
In order to measure an oscillating signal induced in a coil, the magnetic moment vector has to
be tipped into the transverse plane. Therefore, a radiofrequency field is applied:
B1(t) = B1
cos(ωrf t)
sin(ωrf t)
(2.19)
Let the angular velocity defining the rotating frame be Ω = ωrf ˆez. This can be seen as a
transition from the laboratory system into that of the applied oscillating B1 field. The equation
of motion in the rotating frame therefore becomes:
d
dt
µ = µ × γ
B1
0
B0 −
ωrf
γ
(2.20)
Effectively, µ will precess around the vector of the effective field Beff with an angular frequency
ωeff = (ω0 − ωrf )2 + ω2
1 with ω1 = γB1.
In the special case of resonance, the applied radiofrequency ωrf matches the Larmor frequency
ω0:
ωrf = ω0 −→
d
dt
µ = µ × γ
B1
0
0
(2.21)
This will result in a precession around the x -axis. Effectively, a resonant radiofrequency field
applied for a certain amount of time will rotate the magnetic moment in the z y -plane. Since
µ now precesses with angular frequency ω1 = γB1, the flip angle φ after a certain amount of
time can be derived:
φ(t) = ω1t = γB1t (2.22)
An applied B1-field for a certain amount of time is also called ’pulse’. A 90◦-pulse for instance
is a timed application of radiofrequency that will result in a flip angle of 90◦.
5
14. 2 Physical background
2.1.5 Macroscopic magnetization
Until now, the interaction of a single spin 1
2 particle with an external magnetic field has been
discussed. However, in MRI proton spins in numbers of 1023 are excited within a small volume
of tissue. Therefore, the concept of macroscopic magnetization will be introduced in order to
describe the following phenomena. The macroscopic magnetization vector M is defined as:
M =
1
V
N
i=1
ˆµ i (2.23)
The value M0 can be seen as the projection of M onto the axis of the applied external magnetic
field B0 = (0, 0, B0) before excitation. The spin system grows into an equilibrium state between
the lowest possible potential energy (which corresponds to the alignment with the B0-field) and
higher states given by the ability of the spins to interact on a thermal level. The Boltzmann
distribution describes the population probability of a certain energy state Em in a large system
of particles with temperature T:
P(Em) =
e−Em/kbT
I
−I e−Em/kbT
(2.24)
The possible energy states for spin 1
2 are Em = ±1
2¯hω0 according to (2.12) and the Boltzmann
constant is given by kb = 1.38 · 10−23JK−1
. The expectation value for the z-component of the
magnetic moment therefore can be written as:
ˆµz = γ ˆIz = γ¯h
m
−m
P(Em)m (2.25)
For M0 follows:
M0 =
1
V
N
i=1
ˆµz i =
Nγ¯h
2V
P(E−1/2) + P(E1/2) =
Nγ¯h
2V
e
¯hω0
2kbT − e
−
¯hω0
2kbT
e
¯hω0
2kbT + e
−
¯hω0
2kbT
(2.26)
The exponential terms can be developed in a Taylor series: e
¯hω0
2kbT = 1 +
¯hω
0
2kbT + O2(...)... Since
¯hω0 << 2kbT, we can neglect the higher order terms which leads to the high temperature
approximation:
Nγ¯h
2V
e
¯hω0
2kbT − e
−
¯hω0
2kbT
e
¯hω0
2kbT + e
−
¯hω0
2kbT
≈
N
V
γ2
¯h2 B0
4kbT
(2.27)
The resulting term describes the magnetization after the spin population has been immersed
into an external magnetic field. The excess of spins aligned parallel to B0 is extremely low:
N↑ − N↓
N↑ + N↓
=
∆N
N
≈ 10−5
(2.28)
However, the number of proton spins N is in the order of 1023 within a few grams of tissue.
Therefore, a macroscopic magnetization can measured.
2.1.6 Spin relaxation and the Bloch equations
A spin system will undergo relaxation processes after it has been flipped into the transverse
plane by an excitation pulse. Two distinct effects can be observed: The longitudinal compo-
nent M or Mz will grow back into its equilibrium state M0 after excitation. The transverse
6
15. 2.1. Basics of NMR
component M⊥ will decay.
This is described by a set of phenomenological differential equations for each component of
M:
dMx(t)
dt
= γ(M(t) × B)x −
Mx
T2
(2.29)
dMy(t)
dt
= γ(M(t) × B)y −
My
T2
(2.30)
dMz(t)
dt
= γ(M(t) × B)z −
Mz − M0
T1
(2.31)
T1 and T2 are called longitudinal and transverse relaxation times, respectively. Other commonly
used terms are ’spin-lattice’ and ’spin-spin’ relaxation times. T1 is a parameter for longitudinal
relaxation due to interactions of the spins with the surrounding lattice. T2 on the other hand
describes collective dephasing caused by interactions between individual spins. Both relaxation
times are essential variables of an NMR experiment and vary depending on molecular structure
and therefore different types of tissue.
By defining Mc = Mx + iMy, the solutions for the above equations 2.29, 2.30 and 2.31 with
t = 0 after an excitation pulse can be written as:
Mc(t) = e
−
t
T2 M⊥(0)e−ω0t+φ0
(2.32)
Mz(t) = Mz(0)e
−
t
T1 + M0(1 − e
−
t
T1 ) (2.33)
With M⊥ = Mx(0)2
+ My(0)2
and φ = arctan
My
Mx
.
However, a different transverse relaxation time T∗
2 has to be introduced in order to reflect
reality. External field inhomogeneities cause an additional dephasing of the magnetization
(characterized by a separate decay time T2) in the transverse plane. T∗
2 (which is much shorter
than T2) is defined as:
1
T∗
2
=
1
T2
+
1
T2
(2.34)
2.1.7 The NMR signal
According to Faraday’s law, the precessing magnetization in the transverse plane induces a
voltage in a coil:
U = −
d
dt
Φ(t) = −
d
dt
M(r, t) · Breceive(r) d3
r (2.35)
Where B = B(r)
I denotes the magnetic field produced in the coil divided by the current I. It
can be shown that the signal S is formed as following:
S(t) ∝ ω0ΛB⊥ e
t
T2 M⊥(r, 0)ei(Ω−ω0)t+φ(r,t)
d3
r (2.36)
Λ is a constant including electronic gain factors, initial phases of the magnetization and the
receive field direction. The term Ω − ω0 as well as the complex notation corresponds to a
signal demodulation carried out in the real and imaginary channel. The angle φ = − ω(r, t)dt
describes the accumulated precessional phase.
7
16. 2 Physical background
2.2 Basics of MRI
In this section, the basic principles of Magnetic Resonance Imaging (MRI) are discussed.
2.2.1 Frequency encoding
In order to obtain an image, a linear gradient field Gx = ∂Bz
∂x in arbitrary direction (in this case
along the x-axis) is applied. The spins along that axis will precess with different frequencies
according to (12):
ω(x, t) = ω0 + γGx · x (2.37)
In order to simplify the equation, the effective projected spin density ρ is introduced:
ρ(x) = ω0ΛB⊥M⊥(r, 0)dy dz (2.38)
After demodulation with frequency Ω = ω0 and application of Gx the signal S transforms into:
S(t) = ρ(x)e−iγ Gx(t)dt·x
dx (2.39)
The spatial frequency k is introduced:
k(t) =
γ
2π
G(t)dt (2.40)
Therefore, equation 2.39 becomes:
S(k) = ρ(x)e−i2πk·x
dx (2.41)
The image ρ(x) can be obtained by an inverse Fourier Transformation:
ρ(x) = s(k)ei2πk·x
dk (2.42)
2.2.2 Phase encoding
In order to obtain an image in all three spatial dimensions, additional information is required.
This is achieved by the application of so called ’phase-encoding’ gradients in y and z-direction
before the readout along x. This will result in different phases along these axes.
2.2.3 k-space
The raw data is acquired in the spatial frequency domain, the so called ’k-space’. Frequency-
and phase-encoding gradients can be seen as paths through k-space:
∆k =
γ
2π
G · ∆t (frequency-encoding or readout) (2.43)
∆k =
γ
2π
∆G · t (phase-encoding) (2.44)
Every readout line contains information about the whole image, which is why all data has to
be acquired before an image can be formed. The data is read out along x in finite time steps
∆t. After every readout line, the phase-encoding gradient’s amplitude is increased by ∆G in
order to cover the next line in k-space.
8
17. 2.2. Basics of MRI
2.2.4 Slice selection
It is possible to only excite slices of finite thickness within the body. This is achieved by applying
a gradient and a rf pulse with bandwidth ∆f. Let the gradient be applied along the z-axis.
Therefore, the spins along z will experience different larmor frequencies depending on their
position (2.1.7). In order to excite a slice of thickness ∆z, the necessary frequency bandwidth
is:
∆f = 2π∆ω = γGz∆z (2.45)
2.2.5 Gradient echo
An applied frequency encoding gradient can be seen as an external field inhomogeinity. There-
fore, the signal decays rapidly according to (2.1.6). This effect can be reversed with a sequence
that consists of a dephasing gradient followed by a rephasing gradient with opposite polarity in
order to form a so called ’gradient echo’.
Figure 2.1: Schematics of a gradient echo readout with dephasing and rephasing gradient lobe
∝ e
t
T∗
2
time [ms]
signal
Te
The signal is enveloped by an exponential decay proportional to e
t
T∗
2 and the maximum signal
is usually acquired in the middle of the rephasing gradient lobe.
2.2.6 Fast low angle shot
This readout can be combined with low flip angles and a so called spoiler gradient along all
spatial dimensions. A spoiler gradient destroys any remaining transverse magnetization after
the readout. The combination of these elements allows very short repetition times Tr (the time
that is needed for excitation and readout). The longitudinal magnetization Mz partially relaxes
according to T1 before it gets flipped towards the transverse plane again. Due to the large
number of repetitions, Mz is driven into a steady state and the measured spin density ρ0 be
described the FLASH (Fast low angle shot) equation [12].
ρFLASH = ρ0 · sin(α)) ·
1 − e
−Tr
T1
1 − e−Tr
T1
· cos(α)
· e
−
Te
T∗
2 (2.46)
9
18. 2 Physical background
With α = flip angle, Tr =repetition time, T∗
2 = transverse relaxation time and Te = echo time.
The function ρFLASH(α) has a maximum, the so called Ernst angle:
αErnst = arccos(e
−
Tr
T1 ) (2.47)
2.2.7 Chemical shift
Protons bound to other molecules than water experience a different external magnetic field.
This is due to a local magnetic field caused by the motion of electrons within the molecular
orbitals. This local field can be described with a shielding constant σ:
Blocal = B0(1 − σ) (2.48)
This will lead to another larmor frequency of these protons:
ω0 = γB0(1 − σ) = ω0(1 − σ) (2.49)
This change in larmor frequency can be described relative to a reference frequency ω0 of the
corresponding nucleus:
δ[ppm] =
ω − ω0
ω0
· 106
(2.50)
The unit ppm stands for ’parts per million’ and 0 ppm corresponds the a reference frequency.
10
19. 3 Magnetization transfer
Until now, only a homogeneous population of water protons has been considered. However, in-
vivo systems include various types of molecules within a larger water environment. Hydrogen
protons can not only be found in water, but also in solute molecules. Between these different
spin systems magnetization can be transferred. This will be further discussed in the following
section.
3.1 Pool model
The transfer of magnetization in-vivo can be described by a multi-pool model:
Figure 3.1: The different pools (MT = macromolecular magnetization transfer, NOE= Nuclear
Overhauser Effect) exchange magnetization with rates kai and kia from the water
to the solute (ai) and vice versa (ia) and i = A, B, C, D
Pool A: Water
Pool B Pool C Pool D Pool E
kab kba kac kca kad kda kae kea
MTAmides NOE Amines
The transfer of magnetization is governed by three different processes:
• Dipole-dipole interactions between water protons and protons of macromolecules
• Exchange of water molecules between metabolites and macromolecules
• Chemical exchange of free water protons and labile protons of solute metabolites
Mathematically, the Dipole-dipole interactions can be described by equations formulated by I.
Solomon [13]. The exchange of water molecules as well as the chemical exchange is character-
ized by the Bloch - McConnell equations [14]. It is possible to show that both formulations are
equivalent and here, only the Bloch-McConnell equations are considered.
3.1.1 Bloch-McConnell equations
The Bloch-McConnell equations describe the dynamics of two different spin systems under the
influence of a static magnetic field and rf irridiation. In this case, only two poos are considered
for the sake of simplicity. However, the system can easily expanded to multiple pools as employed
11
20. Chapter 3. Magnetization transfer
by Patrick Sch¨uke [15]. The two pools a and b exchange saturation characterized by the exchange
rates kba from pool b to pool a and kab vice versa. The backwards exchange can be calculated
with the equilibrium magnetizations M0,a and M0,b of pool a and b.
kab = fbkb, with f =
M0,b
M0,a
(3.1)
Consider a two pool system in a static magnetic field B = (0, 0, B0) with longitudinal (R1A/B =
1/T1A/B) and transversal (R2A/B = 1/T2A/B) relaxation rates of pools a and b. The frequency
ω1 = γB1 defines the rf amplitude and ∆ωa/b = Ω−ω0,a/b describes the frequency offset between
rf frequency Ω and the larmor frequency ω0,a/b of the corresponding pool.
d
dt
Mxa = − ∆ωaMya − R2aMxa +kbaMxb − kabMxa (3.2)
d
dt
Mya = + ∆ωaMxa − R2aMya − ω1Mza +kbaMyb − kabMya (3.3)
d
dt
Mza = + ω1Mya − R1a(Mza − Mza,0) +kBaMzb − kabMza (3.4)
d
dt
Mxb = − ∆ωbMyb − R2aMxb −kbaMxb + kabMxa (3.5)
d
dt
Myb = + ∆ωbMxb − R2aMyb − ω1Mzb −kbaMyb + kabMya (3.6)
d
dt
Mzb = + ω1Myb − R1A(Mzb − Mzb,0) −kbaMzb + kabMza (3.7)
These first order coupled linear equations cannot be solved analytically without making several
approximations. This can be further understood by reading [9].
3.2 Chemical Exchange Saturation Transfer (CEST)
Labile protons of certain functional groups such as Amides or Amines can be exchanged with
water protons. This results in an effective magnetization transfer between the different popula-
tions which is mainly governed by the exchange rates and the relative concentration of the water
and solute pool [16]. As mentioned in section 2.2.7, spins within different chemical environments
will exhibit different larmor frequencies and relaxation behaviors according to section (2.2.7).
Therefore, one can selectively irradiate certain solutes without directly affecting the water pro-
ton population. The two populations will exchange protons and hence, exchange spins and the
corresponding magnetization. This picture can also be applied to saturation, which means driv-
ing the macroscopic magnetization of a spin system to zero by radiofrequency irradiation. The
spin exchange between the saturated solute system and the water system will result in a transfer
of saturation. This transfer caused by chemical exchange is the essential principle of Chemical
Exchange Saturation Transfer (CEST) and offers an opportunity to indirectly measure very low
concentrated solute molecules. This enables an unique contrast within different types of tissue
that can be utilized in different medical issues such as tumor detection. Three different cases
of CEST can be distinguished depending on the magnitude of the exchange rates in relation to
the frequency offset:
• fast exchange limit: k ∆ω
• intermediate exchange limit: k ≈ ∆ω
• slow exchange limit: k ∆ω
12
21. 3.3. Observable effects in the Z-spectrum in vivo
3.2.1 CEST data acquisition
In principle, every CEST sequence includes the following basic steps: First, the spin system is
irradiated by a number of saturation pulses with a frequency offset ∆ω from the water proton
resonance. In order to obtain the thermal equilibrium magnetization M0 for the normalization of
the spectrum, the first offset is in the far off resonant region of -300 ppm. This step is followed by
a conventional image sequence consisting of excitation and k-space acquisition. This is repeated
for different offsets, usually symmetric around the water peak at 0 ppm. A whole image is
acquired for each single offset and the normalized z-component of the magnetization (figure
(3.2). is plotted against ∆ω (in ppm). This results in a z-spectrum for each pixel of the slice of
interest. Due to the large amount of offsets in the range of 20 to 100 it is necessary to image
as fast as possible without compromising the CEST effect in order to achieve acceptable overall
acquisition times in-vivo.
Figure 3.2: The general principle of CEST data acquisition
3.3 Observable effects in the Z-spectrum in vivo
Several effects casued by different molecules can be observe in the Z-spectrum. These will be
discussed in the following section.
3.3.1 Direct water saturation and macromolecular MT
A typical Z-spectrum of a human brain is shown in figure (3.3). The dominating peak around 0
ppm is caused by direct water saturation while the baseline (the large negative shift of the whole
spectrum on the y-axis) corresponds to the so called semi-solid macromolecular magnetization
transfer or simply ’macromolecular MT’. This effect is caused by protons which are bound to
the surface of macromolecules and protons in water molecules bound to ’the macromolecular
matrix’, e.g protein surfaces and cell membranes. The MT effect has large line-widths of several
kHz, which is why the it is scattered across the whole range of the z-spectrum [9]. The MT can
also be asymmetric, which can compromise other CEST effects.
13
22. Chapter 3. Magnetization transfer
3.3.2 Nuclear Overhauser effects (NOE)
Nuclear Overhauser effects are mediated by Dipole-dipole interactions between close spins. In
in-vitro and in-vivo systems, effects between protons in proteins and water protons in the range
of -2 to -5 ppm can be observed [17] [7].
3.3.3 Amides and Amines
A CEST effect of amide and amine protons in the human brain in the range of +3.5 and +2
ppm , respectively, has been reported by multiple groups [8], [6].
3.3.4 Spillover-Dilution
The CEST effects can become diluted due to the direct saturation of the water pool. Less
water magnetization is left for preparation by saturation transfer. This effect is called spillover
dilution [9].
Figure 3.3: A typcial Z-spectrum of the human brain at 7 T
14
23. 4 Material and Methods
This chapter offers a brief overview over the material and methods used to acquire and interpret
the data.
4.1 Data acquisition
4.1.1 The 3D gradient echo sequence
In order to acquire 3D data, not only a slice, but a so called slab (covering the whole volume
of interest)is excited by a rf pulse with broader bandwidth. After that, an additional phase
encoding step in z-direction makes it possible to collect data within a threedimensional k-space.
Each slice (which corresponds to a two dimensional data set) within the slab is completed
before the z-gradient changes and another slice can be acquired. It is worth to note, that in this
context (contrary to 2D imaging) a slice refers to a plane within k- and not euklidian space.
The sequence timing diagram is shown in figure (4.1).
Figure 4.1: The 3D Gradient Echo Timing Diagram
α
rf
Te
Gz
Tr
α
Spoiler
Gy
Spoiler
Gx
ADC
Spoiler
time
15
24. Chapter 4. Material and Methods
4.1.2 The 3D gradient echo interleaved with saturation pulses
CEST sequences can be carried out in sequential or interleaved fashion. In the sequential case,
the whole image is acquired after the saturation phase. However, in this thesis, the interleaved
principle is applied and optimized. Figure(4.2) shows the CEST imaging scheme which was
applied and further optimized in-vivo. After ns saturation pulses, nk k-space lines are acquired.
This scheme is repeated until a complete 2D k-space data set is completed. After that, another
slice can be imaged until the whole 3D volume is covered. Lastly, the whole sequence is repeated
for each offset. The first slices are not fully saturated and eventually reach a steady state between
relaxation, saturation and readout.
Figure 4.2: The interleaved CEST sequence scheme
... Readout ...Readout
tp td
ns saturation pulses
nk k-space lines
4.1.3 Parameters
The sequence parameters can be divided into two general categories:
• CEST
– No. of Pulses (np)
– Pulse duration (tp)
– B1: amplitude of the saturation pulse
– Duty Cycle (DC): The DC is defined as DC =
tp
tp+td
(td = pause between pulses)
– Pulse type
– Offset: The maximum offset of the spectrum in ppm
– Recover Time: Time between saturation and imaging
– Number of Measurements: Number of acquired offsets
• Imaging
– Segments (nk)
– Flip angle
– Te (always chosen to be minimal)
– Tr (always chosen to be minimal)
16
25. 4.2. Scanning System
4.1.4 Numerical Simulation
The Bloch-McConnell equations can be numerically solved and the results can be utilized to
simulate z-spectra with a wide range of selectable parameters. The MATLAB code was written
by Patrick Sch¨unke and the general approach can be read and understood in [15].
4.1.5 Expansion to imaging
Christian David expanded the numerical simulation by also considering saturation interleaved
with excitation and readout [10]. After n saturation pulses, the simulated longitudinal magne-
tization Mz is instantaneously flipped by an angle of α:
Mz = cos(α)Mz (4.1)
This process is repeated nread times. The whole block consisting of np saturation pulses and
nread readouts is repeated nblocks times. Additional parameters are Tr,read (the repetition time
of the readout), Te,read (the echo time of the readout) and read pause (a pause between readout
and saturation).
4.2 Scanning System
4.2.1 Scanner and coils
Examinations were performed on a Biograph mMR MR-PET scanner and a Magnetom 7T
from Siemens (Siemens Healthcare, Erlangen, Germany) with static magnetic field strengths of
B0 = 3 T and B0 = 7 T, respectively.
Figure 4.3: Biograph mMR , DKFZ Heidelberg
17
26. Chapter 4. Material and Methods
Figure 4.4: Magnetom 7 T, DKFZ Heidelberg
4.2.2 Shimming
The z-spectrum and the observable effects of CEST depend on a homogeneous B0-field. How-
ever, due to varying susceptibilities and inaccuracies of the scanning system, this is not the
case. In order to improve this situation, additional shimming coils with adjustable currents are
utilized in order to compensate for these inhomogeneities.
4.3 Postprocessing of the CEST data
The images were stored in the DICOM format and copied to a PC, where further analyzation
was carried out using MATLAB (The Mathworks, Natick, Massachusetts) software written by
M.Zaiss.
4.3.1 Normalization
The obtained data is normalized pixel-wise by dividing every value of Mz by the value M0 of
the M0-measurement acquired at the beginning of the scan. The result of this step is the so
called Z-value:
Z(∆ω) =
Mz(∆ω)
M0
(4.2)
4.3.2 B0 correction
Despite the shimming, a locally varying B0 shift remains in each pixel. This can be internally
corrected by the following steps:
• Creation of an internal ∆B0-map:
– The spectrum is interpolated with a smoothing spline and the intrinsic minimum is
found and assumed to be at the position at 0 ppm
– This intrinsic minimum is compared with the actual minimum at 0 ppm. The B0
shift can then be calculated for each pixel: ∆B0 = γ∆ω0
• Correction of the spectrum
18
27. 4.4. In-vivo measurements
– The shift is rounded to 0.01 ppm
– The spectrum is shifted according to ∆B0
– The data points at the edge of the spectrum are excluded and linearly extrapolated
4.3.3 Asymmetry
CEST effects can be quantified by a an asymmetry analysis. This is performed by substracting
the positive from the negative offset of the normalized z-spectrum symmetrically around 0 ppm:
MTRasym(∆ω) =
Mz(−∆ω) − Mz(+∆ω)
M0
(4.3)
However, this method is problematic in-vivo and should be applied with caution due to the
following reasons:
• The asymmetric MT scattered across the whole spectrum
• Different effects on opposite sides of the spectrum can lead to a overall reduced asymmetry.
For instance, the amide proton resonance at +3.5 ppm can be superimposed by a larger
NOE effect in the range of -2 to -5 ppm in the human brain.
• The normalization of the spectrum with M0 leads to seemingly larger asymmetries when
the signal of M0 is reduced in another measurement.
4.4 In-vivo measurements
All measurements were performed on a total of five healthy probands in the age between 21 and
26 including four males and one female. The data was analyzed by taking the mean in a ROI
of white matter as well as grey matter.
4.5 Acquisition time
If the saturation would be carried out with a duty cycle (DC) of 100% (which means that there
would be no pauses between the pulses), the overall acquisition time of every segmentation
scheme would remain exactly the same. However, due to scanner regulations only a DC of
50% could be used resulting in different acquisition times. The 32/16 (32 acquired k-space
lines paired with 16 saturation pulses) scheme will result in a longer acquisition time because
there are more pauses in between the saturation pulses. This is compensated by adding a
pause after the readout for the lower segmentation schemes. The overall acquisition times of
each measurement were simulated with the sequence developer environment IDEA provided by
Siemens in order to find the right values for the pause. This is illustrated in figure (4.5).
19
28. Chapter 4. Material and Methods
Figure 4.5: The 2/1 and 4/2 segmentation schemes in comparison: S stands for saturation pulse
and R four readout pulse. The pulse train consisting of 2 pulses has an additional
pause due to the duty cycle and is therefore more time consuming. tpause > tpause.
This was done to keep the repetition time tr constant.
td
time
time
tpause
tpause
tr
S S
S S
R R R R
R R R R
20
29. 5 Results
This chapter deals with the results of various in-vivo measurements. Three values MTRasym
were summed up around the offset of 3.5 ppm and plotted as a function of different parameters
including the segmentation scheme, the flip angle as well as the SNR.
5.1 Optimization of the segmentation scheme
The aim of the first measurement was to find an optimum in observable CEST effects including
Amines, Amides and NOE as a function of the segmentation scheme explained in section (4.1.2).
Therefore, a total of 6 measurements on two healthy volunteers were performed in the following
steps:
• 2 k-space lines / 1 saturation pulse
• 4 k-space lines / 2 saturation pulses
• 8 k-space lines / 4 saturation pulses
• 16 k-space lines / 8 saturation pulses
• 32 k-space lines / 16 saturation pulses
In the following, the segmentation schemes will be given by the tupel (nk/np). The 8/4 and 4/2
segmentation schemes were measured with both probands. The overall number of saturation
pulses remains the same because the number of readout lines changes accordingly. An overview
of the chosen parameters can be found in table (5.1). An empty field represents the same value
as the one before. In each measurement, 16 slices were acquired and the spectrum was internally
corrected for B0 inhomogeneities (4.3.2).
21
30. Chapter 5. Results
Table 5.1: Overview of experimental parameters for the optimization of the segmentation scheme
Proband 1 Proband 2
tp [ms] 15
B1 [µT] 0.7
DC 50%
Pulse Type Gaussian
Maximal offset [ppm] 4
Recover Time [ms] 0
Number of Offsets 24
Flip Angle 10
Te [ms] 3.82
Tr [ms] 56 112 197 205 384 742
nk 2 4 8 8 16 32
np 1 2 4 4 8 16
ROI # 1
0.8
0.9
1
−4−2024
0
0.5
1
Offset [ppm]
Z
Mean Z-spectrum with standard deviation in ROI
−4−2024
0
0.5
1
Offset [ppm]
Z
ROI # 2
0.8
0.9
1
Figure 5.1: Z-spectrum and contrast obtained with a 2/1 segmentation scheme in slice 6 for
white matter (ROI = (region of interest) 1) and grey matter (ROI 2) at the offset
of -3.6 ppm, internal B0 correction
No actual CEST peaks can be observed in the spectrum of the white and grey matter ROIs in
figure (5.1). However,the spectrum shows a slight asymmetry due to the broad NOE effect on
the right of the water peak. Further optimization was based on MTRasym in white matter.
22
31. 5.1. Optimization of the segmentation scheme
In the following, MTRaysm will be defined as:
MTRaysm =
3
i=0
MTRaysm,i(∆ω) (5.1)
where MTRaysm,i(∆ω) are three different values around the offset of ∆ω = 3.5 ppm.
The values of MTRaysm for all following plots were obtained by taking the mean of the ROI.
The errors were calculated by dividing the standard deviation of the ROI by the square root of
the number of the pixels within. This step is justified due to the fact that the tissue within the
ROI could be considered homogeneous. In the region of interest, there was no more than 5%
deviation from the mean value obtained from the M0 measurement.
2/1 4/2 8/4 16/8 32/16
−0.15
−0.1
−5 · 10−2
Segmentation scheme (np / nk)
MTRasym
Proband 1
Proband 2
Figure 5.2: MTRasym plotted against different segmentation schemes in slice 6. A maximum
can be observed for 8/4 in both measurements.
Figure (5.2) displays MTRasym’ plotted against different segmentation schemes. The values
are summed up because the NOE peak is broader than 1 ppm. A maximum value for both
probands can be observed for 8 k-space lines paired with 4 saturation pulses. However, the
different values are normalized with different M0 measurements and therefore, MTRasym seems
higher for smaller M0. This has to be corrected in the following way: The lowest average value
of M0 (in the same ROI as used for the evaluation of MTRasym) is chosen as the reference
magnetization M0,0. MTRasym is renormalized to this reference:
MTR∗
asym = MTRasym ·
M0,i
M0,0
(5.2)
Where M0,i stands for the corresponding M0 value obtained for each segmentation scheme.
23
32. Chapter 5. Results
2/1 4/2 8/4 16/8 32/16
−0.16
−0.14
−0.12
−0.1
−8 · 10−2
−6 · 10−2
nk / np
MTR∗
asym
Proband 1
Proband 2
Figure 5.3: MTR∗
aysm as a function of the segmentation scheme (proband 1 and 2) within slice
6
2/1 4/2 8/4 16/8 32/16
−0.16
−0.14
−0.12
−0.1
−8 · 10−2
nk / np
MTR∗
asym
Proband 1
Proband 2
Figure 5.4: MTR∗
aysm as a function of the segmentation scheme (proband 1 and 2) within slice
8
In slice 6 (5.3), the 8/4 segmentation scheme in both probands yields the highest asymmetry.
However, this changes in slice 8 (5.4). In proband 1, 4/2 is at the maximum while in proband
2, 32/16 shows the highest asymmetry. Further measurements were performed with the 8/4
segmentation scheme as it seems to create maximal asymmetry in at least one slice near the
middle of the slab (In all measurements, 16 slices were acquired).
5.2 Optimization of the flip angle
The next step was to optimize the flip angle of the excitation pulse together with the 8/4
segmentation scheme. Once again, the parameters are shown in the following table:
24
33. 5.2. Optimization of the flip angle
Table 5.2: Overview of experimental parameters for the optimization of the flip angle
Proband 3
tp [ms] 15
B1 [µT] 0.7
DC 50
Pulse Type Gaussian
Maximal offset [ppm] 4.5
Recover Time [ms] 0
Number of offsets 28
Flip angle 6 8 10 15
Te [ms] 3.82
Tr [ms] 197
nk 8
np 4
In figure (5.5) MTR∗
asym was plotted against different flip angles. An optimum of 8◦ can be
observed in slice 6 and 8. In order to theoretically verify this result, the unnormalized MTRasym
(Z(−∆ω)-Z(+∆ω))(3.5 ppm) as a function of the flip angle was simulated and plotted with the
code provided by Christian David (4.1.5) in figure (5.6). The parameters are summarized in
the following tables:
Table 5.3: Parameters for the simulation of the unnormalized asymmetry as a function of the
flip angle (with interleaved imaging)
B0 [T] Pulse type Pulse length [ms] Number of pulses Pools
3 Gauss 15 4 W, Ad, An, MT, NOE
Te,read [ms] Tr,read [ms] read pause [ms] nblocks
3.8 7.6 4.5 16
6 8 10 15
−0.16
−0.14
−0.12
−0.1
−8 · 10−2
−6 · 10−2
Flip angle [degrees]
MTR∗
asym
slice 8
slice 6
Figure 5.5: MTR∗
aysm as a function of the flip angle (proband 3) within slices 6 and 8
25
34. Chapter 5. Results
0 2 4 6 8 10 12
−3
−2
−1
·10−3
Flip angle [degrees]
M(-∆ω)-M(∆ω)(3.5ppm)
Figure 5.6: Simulated unnormalized Asymmetry at the offset of 3.5 ppm as a function of the
flip angle. In this case, only one value (at 3.5 ppm) is obtained
The experimental data in figure (5.5) follows the curve provided by the numerical simulation
(figure 5.6), but with a maximum shifted to the left. Further measurements were performed
with a flip angle of 8◦.
5.3 SNR
In the next step, the signal-to-noise ratios (SNR) of the M0 - measurements with different flip
angle were compared and plotted in figure (5.7). The SNR was calculated in the following way:
SNR =
Signal - Noise
Standard deviation of noise
(5.3)
For the signal, the mean value of a ROI inside of the brain was calculated. The same was done
within a region outside of the brain where it can safely be assumed that any signal contribution
comes from the background noise. An error of overall 5% was assumed due to the standard
deviation within the signal-ROI.
6 8 10 15
80
100
120
140
Flip angle [degrees]
SNR
Figure 5.7: SNR of the M0 measurement plotted against the flip angle (proband 2)
26
35. 5.4. Trend with varying B1
0.8
0.9
1
0.8
0.9
1
Figure 5.8: Z contrast obtained at flip angles 8◦ and 10◦ and at the offset of -3.8 ppm
As can be seen in figure (5.7), the maximum SNR can be achieved with a flip angle of 10◦.
However, the comparison of contrasts in figure (5.8) shows no significant decrease of image
quality for 8◦. Grey and white matter structures can be distinguished in both pictures.
5.4 Trend with varying B1
The amplitude B1 of the saturation pulse cannot be optimized for different CEST agents and
effects at the same time, because the optimal value largely depends on the chemical exchange
rates. It should be noted that an increase in B1 will compromise other effects such as that of
Amides and Amines. However, several measurements were made in order to verify the general
trend which can be observed in numerical 5 pool simulations. The parameters were chosen as
follows:
Table 5.4: Parameters for the simulation of MTRasym (3.5 ppm) as a function of B1 (without
interleaved imaging)
B0 [T] Pulse type Pulse length [ms] Number of pulses Pools
3 Gauss 15 100 W, Ad, An, MT, NOE
Table 5.5: Overview of experimental parameters for measurements with varying B1
Proband 3
tp [ms] 15
B1 [µT] 0.5 0.7 0.9 1.1
DC 50
Pulse Type Gaussian
Maximal offset [ppm] 4.5
Recover Time [ms] 0
Number of offsets 28
Flip angle 8
Te [ms] 3.82
Tr [ms] 197
nk 8
np 4
27
36. Chapter 5. Results
0.5 0.7 0.9 1.1
−0.15
−0.1
−5 · 10−2
B1 [µT]
MTRasym
Figure 5.9: MTR∗
aysm as a function of B1
0 0.5 1 1.5 2 2.5
−0.25
−0.2
−0.15
−0.1
−5 · 10−2
B1[µT]
MTRasym(3.5ppm)
Figure 5.10: The simulated MTRaysm at ∆ω = 3.5 ppm plotted as a function of B1. 5 Pools
were simulated including Water, MT, NOE, Amdides and Amines.
The general trend of increasing negative asymmetry around the offset of 3.5 ppm for increasing
values of B1 in figures 5.9 and 5.10 complies qualitatively with the numerical simulation of
MTRasym of a 5 pool system (Water (w), Amides (Ad), Amines (An), MT, NOE). Note that
in the simulation, only one value of MTRasym at 3.5 ppm is displayed. However, this has no
impact on the trend of the curve.
5.5 Comparison with 7 T
Figure (5.11) shows Z-spectra and the MTRasym contrast obtained at 3.8 ppm (3 T) and 3.6
ppm (7 T) of the 3D sequence measured with B0 = 3 and 7 T from two different probands. Two
ROIs, one in white and one in grey matter were analyzed in slice 6, respectively. The imaging
and saturation parameters were the same (except for a higher number of offsets at 7 T).
28
37. 5.5. Comparison with 7 T
# 1
#2
−0.1
−5 · 10−2
0
−4−2024
0
0.5
1
offset [ppm]
Z
Mean Z-spectrum with std in ROI @ 3 T
ROI #1
ROI #2
# 1
# 2
−4
−2
0
2
4
·10−2
−4−2024
0
0.5
1
offset [ppm]
Z
Mean Z-spectrum with std in ROI @ 7 T
ROI #1
ROI #2
Figure 5.11: Comparison of Z-spectra and the MTRasym contrast at the offset of 3.8 (3 T) and
3.6 (7 T) ppm.
A comparison of MTRasym contrasts in figure (5.11) already demonstrates the superiority of
higher static field strengths. White and grey matter can clearly be distinguished. In the Z-
spectrum, the amide peak around +3.5 ppm and the broad NOE peak at -2 to -4ppm are very
prominent compared to those visible at B0 = 3T.
29
38.
39. 6 Discussion
In-vivo CEST measurements remain a challenge, especially at lower field strenghts. The goal of
this work was to optimize combined saturation and imaging parameters of a 3D CEST sequence
on a 3 T scanner. The optimization was carried out in regard to the negative asymmetry caused
by the NOE around -3.5 ppm of the Z-spectrum. The segmentation could only be optimized
for single slices and a global optimum was not found. The optimal flip angle on the other hand
was found rather easily.
However, the image contrast due to MTRasym remained low in all probands and could only
be improved by measuring with a higher field strength of 7 T. The same observation was
made for the general appearance of the z-spectrum. At 3 T, no actual amide or amine peaks
were observable with different saturation amplitudes of B1 = (0.5, 0.7, 0.9, 1.1) µT. This is in
accordance to other publications, in which the Amide proton transfer (APT) caused a positive
asymmetry due to different saturation and readout sequences, but no visible peaks in the Z-
spectrum or a specific contrast in healthy tissue [8], [6]. It seems that to observe these peaks
selectively, the transition to 7 T has to be made.
6.1 General note on the asymmetry analysis
As already mentioned in (4.3.3), the evaluation involving MTRasym and the associated potential
errors including asymmetric MT (3.3.1), spillover dilution (3.3.4) and competing resonances
(4.3.3) should lead to cautious assumptions when quantifying CEST effects. These effects
can be compensated for with the employment of a post-processing method called AREX or
apparent-exchange-depended relaxation [9] as well as Lorentz-fitting of the Z-spectra [18].
Additionally, the asymmetry analysis could be compromised by lipid artifacts [19]. The reso-
nance frequencies of protons in mobile lipids such as fatty acids are shifted by around -3.5 ppm
from the water proton resonance and hence could contribute to a CEST effect. This can be
avoided by selective fat saturation before the readout [19].
6.2 Optimization of the segmentation
In the first measurements with probands 1 and 2 the maximal offset was set to 4 ppm which
can be considered close to the position of interest at 3.5 ppm. In this case, the internal B0
correction could be the origin of a potential error. According to (4.3.2), the values at the edge
of the Z-spectrum are linearly extrapolated and do not necessarily reflect the actual measure-
ment. This can lead to wrong evaluations of MTRasym especially near the water peak due to
the higher gradient of the extrapolated function.
However, a comparison between corrected and uncorrected spectra obtained from the measure-
ments shows that in this case, the linear extrapolation reflects reality. Furthermore, the analysis
was also carried out with the uncorrected data and provides the same results. All following mea-
surements were performed with a maximal offset of 4.5 ppm and thus the possibility of this error
was avoided.
Different measurements with varying segmetation schemes (number of k-space lines / number
31
40. Chapter 6. Discussion
of saturation pulses) were performed. A maximum in asymmetry could be found for the 8/4
segmentation scheme in two measurements with different probands within slice 6. This seems
to contradict the results of the numerical simulation and other experimental findings [10], where
there was no impact on the asymmetry.
However, the offsets were summed up over three values of MTRasym and the difference between
segmentation schemes did not exceed one percent for single offsets. The same analysis (seg-
mentations 2/1, 4/2 and 8/4) was repeated for slice 8 and showed different results with an
optimal segmentation scheme of 4/2. This raises the question whether the system had been
fully saturated within slice 6. However, this possibility can be ruled out by the fact that the
asymmetry effect does not increase significantly from slice 6 to 8. Furthermore, the overall num-
ber of saturation time was more than After each slice, the same amount of saturation pulses
were applied regardless of the segmentation. Due to the very small changes in asymmetry and
different results for two different slices no clear conclusion can be drawn.
For the sake of clarity, a larger number of probands has to be measured. The acquisition times
were kept constant by the implementation of a pause after the readout (4.5). Without this
pause, lower segmentation schemes are generally faster and the time gain could be used to:
• increase the SNR by averaging
• increase the ratio between saturation and readout (for example 2/2)
• increase the length of the saturation pulses
Longer saturation pulses would be beneficial if slices further away from the center slice are also
required to yield a CEST contrast. This is due to the fact that the steady state in saturation
would be reached faster. To quantify these statements, different segmentation schemes were
simulated with IDEA:
Table 6.1: The simulated acquisition time for different segmentation schemes assuming the ac-
quisition of 16 slices with 2 different offsets
nk / np 2/1 2/2 8/4 32/16
Acquisition time [min:sec] 10:12 20:00 13:27 18:43
For this simulation, the acquisition of 16 slices with 32 offsets was assumed. All parameters
(except the segmentation) remained the same. The general conclusion is that lower segmenta-
tions within the range from one to four saturation pulses per segment are more favorable due
to the time advantage that can be invested to increase SNR or saturation as discussed before.
6.3 Optimization of the Flip angle and SNR
A total of four measurements with varying flip angles (6◦, 8◦, 10◦ and 15◦) were performed. The
maximal asymmetry was observed with 8◦. The SNR was obtained from the M0-measurement.
The highest SNR was found for a flip angle of 10◦.
These results are in compliance with the numerical simulation. Quantitavely, the curve behaves
according to the equation of the ernst angle (2.47) but with a maximum shifted to the left.
This further verifies the numerical simulation of the interleaved scheme developed by Christian
David [10], where the same observations could be made. Hwoever, this is not surprising due to
the fact that CEST effects have a very little impact on the overall longitudinal magnetization.
32
41. 6.4. Trend with varying B1
6.4 Trend with varying B1
As already mentioned earlier, B1 needs to be optimized individually for the desired CEST effect.
Nonetheless, the experimental results qualitavely follow the curve predicted by the numerical
simulation. It remains a scientific challenge to truly isolate CEST effect of each metabolite. Due
to the asymmetric magnetization transfer across the whole spectrum, competing resonances,
and spillover dilution. However, there are different proposed approaches like AREX or Lorentz-
fitting in order to deal with these problems [9], [18].
6.5 Higher field strengths
Two measurements with the same parameters at static field strengths of 3 and 7 Tesla were
compared in 5.5. In the Z-spectrum of the 7 T measurement, clear peaks of Amides as well as
Amines and a negative asymmetry of up to 10% in the NOE region are very prominent compared
to those measured at 3 T. On top of that, the contrast obtained by MTRasym is clearly stronger
at 7 T. The conclusion of these measurements is that CEST largely benefits from higher static
field strengths. This is due to the following reasons:
• The SNR is generally higher because of a higher thermal equilibrium magnetization
• Because of higher resonance frequencies of all nuclei, the spectral distance between peaks
increases while the relative spectral width decreases, which makes them better distinguish-
able
• In the steady state, longer T1-relaxation times leave more time for the labeled state to
transfer into the water pool
Due to these reasons, it is highly desirable to perform CEST experiments at higher field
strengths. However, this transition is accompanied by a different set of challenges. Both B0 and
B1 inhomogeneities increase and make correct shimming and correction even more important.
6.6 Outlook
CEST imaging at 3T remains a challenge. However, the search for methods to enhance the
specific contrast of healthy as well as pathogenic tissue should be continued. In order to verify
the method in a medical and clinical context, a larger amount of patients needs to be imaged.
Although field strengths of 7 T will soon be incorporated into clinical practice, the availability
in the following years will remain low compared to 3 T scanners. The following approaches
might further improve CEST imaging at lower field strengths:
• The usage of adiabatic pulses could lead to a more effective selective saturation of CEST
pools and thus enhance the overall effect. Several measurements were already performed
during this work, but the acquired data was still compromised by oscillation artifacts near
the water resonance
• CEST involves the acquisition of the same slice for a relatively large number of different
offsets. A faster image acquisition with EPI or a radial sequence paired with image
reconstruction result in the overall reduction of the acquisition time. The time advantage
could be used to increase the SNR by averaging. However, this time gain would be rather
small because saturation is the dominant factor when it comes to acquisition time.
33
42. Chapter 6. Discussion
Furthermore, the expected advantage of saturation and interleaved 3D imaging over 2D acqui-
sition needs to be verified by direct comparison of the two methods.
34
43. 7 Conclusion
In the course of this thesis, a CEST sequence consisting of saturation interleaved with a 3D-
GRE-sequence for imaging was optimized by the means of segmentation and flip angle. The
following results were found:
• No significant differences in form of an asymmetry in the z-spectrum were found for varying
schemes. This supports the findings of numerical simulations and phantom experiments
[10]. However, lower segmentation schemes are generally more desirable due to the time
advantage caused by a Duty cycle = 100%.
• The flip angle could sucessfully be optimized and the trend resembles the behaviour of the
FLASH signal equation with a shift to smaller optimal values. This also verifies findings
of the numerical simulation [10].
• Higher static field strengths lead to an increase of CEST effects and greatly enhance the
desired specific contrast. However, due to the higher availability of 3 T scanners, the
search for better methods at lower field strengths needs to be continued.
35
44.
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38
47. List of Figures
2.1 Schematics of a gradient echo readout . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 Pool model in-vivo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 CEST data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Z-spectrum of the human brain at 7 T . . . . . . . . . . . . . . . . . . . . . . . . 14
4.1 The 3D Gradient Echo Timing Diagram . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 The interleaved CEST sequence scheme . . . . . . . . . . . . . . . . . . . . . . . 16
4.3 3 T scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.4 7 T scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.5 The 2/1 and 4/2 segmentation schemes in comparison . . . . . . . . . . . . . . . 20
5.1 Z-spectrum and contrast @ -3.6 ppm . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2 MTRasym as a function of the segmentation (slice 6) . . . . . . . . . . . . . . . . 23
5.3 MTR∗
aysm as a function of the segmentation . . . . . . . . . . . . . . . . . . . . . 24
5.4 MTR∗
aysm as a function of the segmentation scheme (slice 8) . . . . . . . . . . . . 24
5.5 MTR∗
aysm as a function of the flip angle . . . . . . . . . . . . . . . . . . . . . . . 25
5.6 Simulated unnormalized Asymmetry @ 3.5 ppm as a function of the flip angle . . 26
5.7 SNR of the M0 measurement as a function of the flip angle . . . . . . . . . . . . 26
5.8 Z-contrast obtained at flip angles 8◦ and 10◦ @ -3.8 ppm . . . . . . . . . . . . . 27
5.9 MTR∗
aysm as a function of B1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.10 The simulated MTRaysm @ 3.5 ppm plotted as a function of B1 . . . . . . . . . . 28
5.11 Comparison of 3 T and 7 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
39
48.
49. List of Tables
5.1 Experimental parameters for the optimization of the segmentation scheme . . . . 22
5.2 experimental parameters for the optimization of the flip angle . . . . . . . . . . . 25
5.3 Parameters for the simulation of the unnormalized asymmetry as a function of
the flip angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.4 Parameters for the simulation of MTRasym (3.5 ppm) as a function of B1 . . . . 27
5.5 Experimental parameters for measurements with varying B1 . . . . . . . . . . . . 27
6.1 The simulated acquisition time for different segmentation schemes assuming the
acquisition of 16 slices with 2 different offsets . . . . . . . . . . . . . . . . . . . . 32
41
50.
51. Erkl¨arung
Ich versichere, dass ich diese Arbeit selbstst¨andig verfasst und keine anderen als die angegebe-
nen Quellen und Hilfsmittel benutzt habe.
Heidelberg, den 21.03.2016.
43
52.
53. Danksagung
An dieser Stelle m¨ochte ich allen danken, die mir das Verfassen dieser Arbeit erm¨oglicht haben.
• Herrn Prof. Dr. Bachert danke ich f¨ur die M¨oglichkeit, in dieser Arbeitsgruppe selb-
stst¨andig geforscht haben zu d¨urfen.
• Herrn Prof. Dr. Schlegel danke ich f¨ur die Zweitbeurteilung meiner Arbeit.
• Ein ganz besonderes Dankesch¨on geht an Moritz. Seine einzigartige Leidenschaft f¨ur die
Forschung hat mich jeden Tag motiviert. Außerdem ist er halt einfach ein cooler Typ mit
dem man immer lachen kann. (Mal abgesehen davon, dass er ein ziemlich genialer Kopf
ist)
• Das gleiche gilt fr Jan: Ich hoffe er hat nicht zu viele Stunden mit der Korrektur verbracht.
• Dankesch¨on an die Probandinnen und Probanden Pascal, Nico, Leo (er hat w¨ahrend der
gesamten Untersuchung nicht geschluckt), Bente und Alex.
• Danke auch an den Rest der Truppe: Steffen, Johnny, Christian, Johannes, Sebastian,
Patrick, Cornelius und Andi (der mir mit seinen Pr¨asentationen gezeigt hat, dass ich
noch l¨angst nicht alles kapiert habe, was mit MR Bildgebung zu tun hat.)
• Mein Dank richtet sich auch an meine Mathe- und Physiklehrer Herrn Sch¨atzle und Herrn
Piffer, die mich f¨ur die Naturwissenschaft begeistert haben. (Und das, obwohl ich doch
eigentlich Journalist werden wollte)
• Danke an die 21-E-Street. F¨ur die bisher geilste Zeit meines Lebens.
• Nat¨urlich danke ich an letzter Stelle meiner Familie: Meiner Mutter, meinem Vater und
meinem Bruder, die nicht nur w¨ahrend meines Studiums, sondern in allen Lebenslagen zu
mir gehalten haben.
45
