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Department of Physics and Astronomy University of Heidelberg Bachelor Thesis in Physics submitted by Luca Jan Schmidtke born in Speyer (Germany) 2016

Bachelor Arbeit

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Department of Physics and AstronomyUniversity of Heidelberg

Bachelor Thesis in Physicssubmitted by

Luca Jan Schmidtke

born in Speyer (Germany)

2016

Optimization of a 3D CEST sequence for imaging the humanbrain at 3 Tesla

This Bachelor Thesis has been carried out by Luca Jan Schmidtke at theGerman Cancer Research Center in Heidelberg

under the supervision ofProf. Dr. Peter Bachert

Optimization of a 3D CEST sequence for imaging the human brain at 3 Tesla ChemicalExchange Saturation Transfer (CEST) employs the proton transfer between low concentratedsolutes and bulk water to prepare enhanced saturation of the water signal. Presaturationof solute protons by a series of frequency-selective rf pulses is followed by detection of themodified water proton signal for each voxel by a conventional MR imaging sequence. Thestrong dependence of the proton exchange processes on physiological conditions may lead to abetter 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 Tcould 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 fastgradient echo imaging. Herein, one segment consists of a certain number of saturation pulsesand a corresponding amount of acquired k-space lines and is repeated until the entire imagecan be reconstructed. Additionally, the impact of different segmentation schemes on the rNOEsignals was investigated. No significant difference was observed although smaller numbers ofsaturation pulses are generally recommended due to specific-absorption-rate (SAR) limitationsof clinical MR tomographs.

Optimierung einer 3D CEST Sequenz fur die Bildgebung des menschlichen Gehirns bei3 Tesla Chemical Exchange Saturation Transfer (CEST) nutzt den Protonentransfer zwis-chen niedrig konzentrierten gelosten Moleklen und Wasser, um eine starkere Sattigung desWassersignals zu erhalten. Die Sattigung der gelosten Protonen durch eine Serie von Frequenz-selekiven Rf-Pulsen wird gefolgt von der Detektion des Wassersignals durch konventionelle MR-Bildgebung. Die starke Abhangigkeit der Protonenauschtausch-Prozesse von physiologischenBedingungen konnte zu einer besseren Unterscheidbarkeit von normalem und pathologischemGewebe fuhren.Allerdings ist CEST trotz des einzigartigen Kontrastes noch nicht in der klinischen Routineintegriert.In dieser Arbeit konnte der Flipwinkel und das Signal-zu-Rausch Verhaltnis (SNR) einer CEST-Sequenz bei B0 = 3 T fur Signale optimiert werden, die durch die sogenannten exchange-relayed Nuclear Overhauser Effekte (rNOE ) entstehen. Die CEST Sequenz wurde miteiner Sattigungsphase implementiert, die mit einer schnellen 3D Gradienten-Echo-Sequenz ver-schachtelt wurde. Hierin besteht ein Segment aus einer bestimmten Menge von Sattigungspulsenund der dazugehorigen Anzahl von ausgelesenen k-Raum-Linien. Dieses wird wiederholt, bis daskomplette Bild rekonstruiert werden kann. Es wurde zusatzlich untersucht, welchen Einfluss ver-schiedene Segmentierungen auf die rNOE-Signale haben. Es konnte kein deutlicher Unterschiedfestgestellt werden, allerdings ist eine kleinere Anzahl von Sattigungspulsen mehr zu empfehlen,da klinische MR-Tomographen durch die Spezifische Absorptionsrate (SAR) limitiert sind.

Contents

1 Introduction 1

2 Physical background 32.1 Basics of NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Nuclear Spin in quantum mechanics . . . . . . . . . . . . . . . . . . . . . 32.1.2 The spin within an external magnetic field . . . . . . . . . . . . . . . . . . 42.1.3 The Precessional motion of the magnetic moment . . . . . . . . . . . . . . 42.1.4 Rotating reference frame and excitation . . . . . . . . . . . . . . . . . . . 52.1.5 Macroscopic magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.6 Spin relaxation and the Bloch equations . . . . . . . . . . . . . . . . . . . 62.1.7 The NMR signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Basics of MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Frequency encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Phase encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.3 k-space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.4 Slice selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.5 Gradient echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.6 Fast low angle shot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.7 Chemical shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Magnetization transfer 113.1 Pool model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Bloch-McConnell equations . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Chemical Exchange Saturation Transfer (CEST) . . . . . . . . . . . . . . . . . . 12

3.2.1 CEST data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Observable effects in the Z-spectrum in vivo . . . . . . . . . . . . . . . . . . . . . 13

3.3.1 Direct water saturation and macromolecular MT . . . . . . . . . . . . . . 133.3.2 Nuclear Overhauser effects (NOE) . . . . . . . . . . . . . . . . . . . . . . 143.3.3 Amides and Amines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3.4 Spillover-Dilution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Material and Methods 154.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.1.1 The 3D gradient echo sequence . . . . . . . . . . . . . . . . . . . . . . . . 154.1.2 The 3D gradient echo interleaved with saturation pulses . . . . . . . . . . 164.1.3 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.1.4 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.1.5 Expansion to imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2 Scanning System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2.1 Scanner and coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2.2 Shimming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3 Postprocessing of the CEST data . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.1 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.2 B0 correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.3 Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.4 In-vivo measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.5 Acquisition time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Results 215.1 Optimization of the segmentation scheme . . . . . . . . . . . . . . . . . . . . . . 215.2 Optimization of the flip angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3 SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.4 Trend with varying B1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.5 Comparison with 7 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6 Discussion 316.1 General note on the asymmetry analysis . . . . . . . . . . . . . . . . . . . . . . . 316.2 Optimization of the segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.3 Optimization of the Flip angle and SNR . . . . . . . . . . . . . . . . . . . . . . . 326.4 Trend with varying B1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.5 Higher field strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.6 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7 Conclusion 35

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 ResonanceImaging (MRI) is today. MRI is nowadays an essential part of clinical diagnostic routine allover the world. The contrasts enabled by the longitudinal (T1) and transverse (T2) relaxationtimes offer an excellent imaging modality for noninvasive imaging in-vivo.

While conventional techniques rely on the detection of 1H water protons, newly proposedmethods utilize complex magnetization transfer mechanisms. Chemical Exchange SaturationTransfer 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 thenecessity of radioactive tracers or other injected agents. The metabolites can be indirectlydetected through their effect on the spin population of water protons. The basic principle ofCEST involves the following steps: First, the magnetization of the smaller pool of metabolitesis 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 protonmagnetization is then measured with a conventional imaging sequence. These steps are repeatedwith varying radiofrequency irradiation which finally leads to the acquisition of a spectrum inwhich characteristic peaks define the contrast of CEST.

It has been demonstrated previously that numerous molecules such as Amides and Amineswithin proteins as well as exchange relayed Nuclear Overhauser effects (rNOEs) can offer aunique CEST contrast in-vivo [6] [7] [8]. However, CEST phenomena are entangled by a seriesof 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 ofMRI. One approach is to apply saturation pulses of different shapes and interleave this schemewith a low flip angle 3D GRE imaging sequence. With 3D acquisition, the data truly reflectsthe spatial distribution of spins within the human body and therefore allows the reconstructionof three dimensional images. The higher SNR due to a signal contribution from one additionalspatial dimension and the ability to sample the data more densely make 3D imaging generallydesirable. This also applies to CEST imaging. The interleaved approach can be characterizedby 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 asegmentation scheme set to 2 saturation pulses per 4 k-space line acquisitions, the segment willbe repeated 32 times. In-vivo, different segmentation schemes might have an impact on CESTeffects.The goal of this work was optimize the unique contrast that CEST has to offer by meansof 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 segmentationscheme. Several experiments regarding the optimization of readout parameters were alreadyperformed [10] in phantoms, but still need to be investigated in-vivo.

1

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 befound 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 ~S = (Sx, Sy, Sz) obeys the same commutation relations:[Si, Sj

]= εijkihSk (2.1)[

Si, ~S2]

= 0 (2.2)

Therefore, the eigenvectors of ~S2 and Sz expressed in the basis of ~S are:

~S2 |s,ms〉 = hs(s+ 1) |s,ms〉 (2.3)

Sz |s,ms〉 = mh |s,ms〉 (2.4)

With the spin quantum number s = 0, 12 , 1,

32 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 ~L

and intrinsic spin ~S:

~I = ~L+ ~S (2.5)

The analogous algebra applies to this operator. Following the eigenvalue approach from aboveits discrete value is:

|~I| =√〈~I2〉 = h

√I(I + 1) (2.6)

The discretization along an arbitrary z-direction is of particular interest:

Iz = 〈 Iz〉 = mh (2.7)

with I = 0, 12 , 1,

32 etc. and m = mI = −I,−(I − 1), ..., I.

Due to the extremely high abundance of water within the human body, the most prominentnucleus 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:

~µ = γ~I (2.8)

3

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 unitsγ

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=12 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 interactionbetween field and particle:

H = −~µ ~B = −µzB0 (2.9)

H can be represented in the basis of its eigenvectors |ψ〉 with corresponding eigenvalues in formof discretized energy levels En:

H |ψ〉 = En |ψ〉 (2.10)

In this case one obtains:

H |ψ〉 = −µzB0 |ψ〉 = −γIzB0 |ψ〉 = −γSzB0 |ψ〉 = −γ h2

(1 00 −1

)B0 |ψ〉 (2.11)

Using the so called larmor frequency ω0 = γB0 yields:

H |ψ〉 =

−1

2hω0 0

01

2hω0

|↑〉 or |↓〉 (2.12)

with |↑〉 =

(10

)and |↓〉 =

(01

)It immediately follows that the energy difference between the spin-up and spin-down stateis

∆E = hω0 (2.13)

It will follow later (2.1.4) that an oscillating external magnetic field with frequency ω0 willprovide 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 bederived and analyzed. The Ehrenfest Theorem justifies a transition into the classical picture:

d

dt〈~µ〉 =

i

h〈[H, ~µ

]〉 (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 ~S) from equations 2.1 and 2.2:

i

h

[H, ~µ

]j

= γ2 i

hBi[Sj , Si

]= γεkijµkBi (2.15)

The result is the quantum mechanical representation of the classical equation of motion for amagnetic moment ~µ in an external magnetic field:

d

dt〈~µ〉 = 〈~µ〉 × γ ~B (2.16)

4

2.1. Basics of NMR

Therefore, the classical representation of this equation with euclidean vectors can be applied:

d

dt~µ = ~µ× γ ~B (2.17)

As a result of the equation of motion above, the magnetic moment vector will start to precessaround 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 cartesiancoordinate frame which rotates around the fixed z-axis. The external magnetic field ~B pointsalong the z-axis. Let the coordinates of that system be x′, y′, z′. As a result of the rotationwith angular velocity ~Ω pointing along the z-axis, the equation of motion for a single magneticmoment transforms into:(

d

dt~µ

)′=

3∑i=1

dµ′idte′i = γµ× ~Beff with ~Beff = ~B −

γ(2.18)

In order to measure an oscillating signal induced in a coil, the magnetic moment vector has tobe 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 ez. This can be seen as a

transition from the laboratory system into that of the applied oscillating ~B1 field. The equationof motion in the rotating frame therefore becomes:(

d

dt~µ

)′= ~µ× γ

B1

0B0 −

ωrf

γ

(2.20)

Effectively, ~µ will precess around the vector of the effective field ~Beff with an angular frequency

ωeff =√

(ω0 − ωrf )2 + ω21 with ω1 = γB1.

In the special case of resonance, the applied radiofrequency ωrf matches the Larmor frequencyω0:

ωrf = ω0 −→

(d

dt~µ

)′= ~µ× γ

B1

00

(2.21)

This will result in a precession around the x′-axis. Effectively, a resonant radiofrequency fieldapplied 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 oftime 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 instanceis a timed application of radiofrequency that will result in a flip angle of 90.

5

2 Physical background

2.1.5 Macroscopic magnetization

Until now, the interaction of a single spin 12 particle with an external magnetic field has been

discussed. However, in MRI proton spins in numbers of 1023 are excited within a small volumeof tissue. Therefore, the concept of macroscopic magnetization will be introduced in order todescribe the following phenomena. The macroscopic magnetization vector ~M is defined as:

~M =1

V

N∑i=1

〈~µ〉i (2.23)

The value M0 can be seen as the projection of ~M onto the axis of the applied external magneticfield ~B0 = (0, 0, B0) before excitation. The spin system grows into an equilibrium state betweenthe lowest possible potential energy (which corresponds to the alignment with the ~B0-field) andhigher states given by the ability of the spins to interact on a thermal level. The Boltzmanndistribution describes the population probability of a certain energy state Em in a large systemof particles with temperature T :

P (Em) =e−Em/kbT∑I−I e

−Em/kbT(2.24)

The possible energy states for spin 12 are Em = ±1

2 hω0 according to (2.12) and the Boltzmannconstant is given by kb = 1.38 · 10−23JK−1. The expectation value for the z-component of themagnetic moment therefore can be written as:

〈µz〉 = γ〈Iz〉 = γhm∑−m

P (Em)m (2.25)

For M0 follows:

M0 =1

V

N∑i=1

〈µz〉i =Nγh

2V

(P (E−1/2) + P (E1/2)

)=Nγh

2V

ehω02kbT − e−

hω02kbT

ehω02kbT + e

− hω02kbT

(2.26)

The exponential terms can be developed in a Taylor series: ehω02kbT = 1 +

hω02kbT

+ O2(...)... Sincehω0 << 2kbT, we can neglect the higher order terms which leads to the high temperatureapproximation:

Nγh

2V

ehω02kbT − e−

hω02kbT

ehω02kbT + e

− hω02kbT

≈ N

Vγ2h2 B0

4kbT(2.27)

The resulting term describes the magnetization after the spin population has been immersedinto 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 transverseplane 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

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 commonlyused terms are ’spin-lattice’ and ’spin-spin’ relaxation times. T1 is a parameter for longitudinalrelaxation due to interactions of the spins with the surrounding lattice. T2 on the other handdescribes collective dephasing caused by interactions between individual spins. Both relaxationtimes are essential variables of an NMR experiment and vary depending on molecular structureand therefore different types of tissue.

By defining Mc = Mx + iMy, the solutions for the above equations 2.29, 2.30 and 2.31 witht = 0 after an excitation pulse can be written as:

Mc(t) = e− tT2M⊥(0)e−ω0t+φ0 (2.32)

Mz(t) = Mz(0)e− tT1 +M0(1− e−

tT1 ) (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 reflectreality. External field inhomogeneities cause an additional dephasing of the magnetization(characterized by a separate decay time T ′2) in the transverse plane. T ∗2 (which is much shorterthan T2) is defined as:

1

T ∗2=

1

T2+

1

T ′2(2.34)

2.1.7 The NMR signal

According to Faraday’s law, the precessing magnetization in the transverse plane induces avoltage in a coil:

U = − d

dtΦ(t) = − d

dt

∫~M(~r, t) · ~Breceive(~r) d3r (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⊥

∫etT2M⊥(~r, 0)ei(Ω−ω0)t+φ(~r,t) d3r (2.36)

Λ is a constant including electronic gain factors, initial phases of the magnetization and thereceive field direction. The term Ω − ω0 as well as the complex notation corresponds to asignal demodulation carried out in the real and imaginary channel. The angle φ = −

∫ω(~r, t)dt

describes the accumulated precessional phase.

7

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 frequenciesaccording 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·xdx (2.39)

The spatial frequency k is introduced:

k(t) =γ

∫G(t)dt (2.40)

Therefore, equation 2.39 becomes:

S(k) =

∫ρ(x)e−i2πk·xdx (2.41)

The image ρ(x) can be obtained by an inverse Fourier Transformation:

ρ(x) =

∫s(k)ei2πk·xdk (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-directionbefore 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

2πG ·∆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 tobe 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 inorder to cover the next line in k-space.

8

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 applyinga 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 theirposition (2.1.7). In order to excite a slice of thickness ∆z, the necessary frequency bandwidthis:

∆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 sequencethat consists of a dephasing gradient followed by a rephasing gradient with opposite polarity inorder to form a so called ’gradient echo’.

Figure 2.1: Schematics of a gradient echo readout with dephasing and rephasing gradient lobe

∝ etT ∗2

time [ms]

sign

al

Te

The signal is enveloped by an exponential decay proportional to etT ∗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 allspatial dimensions. A spoiler gradient destroys any remaining transverse magnetization afterthe readout. The combination of these elements allows very short repetition times Tr (the timethat is needed for excitation and readout). The longitudinal magnetization Mz partially relaxesaccording to T1 before it gets flipped towards the transverse plane again. Due to the largenumber of repetitions, Mz is driven into a steady state and the measured spin density ρ0 bedescribed the FLASH (Fast low angle shot) equation [12].

ρFLASH = ρ0 · sin(α)) · 1− e−TrT1

1− e−TrT1· cos(α)

· e− TeT ∗

2 (2.46)

9

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−TrT1 ) (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 molecularorbitals. 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 thecorresponding 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

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. Hydrogenprotons can not only be found in water, but also in solute molecules. Between these differentspin systems magnetization can be transferred. This will be further discussed in the followingsection.

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= NuclearOverhauser Effect) exchange magnetization with rates kai and kia from the waterto 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 areequivalent 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 theinfluence of a static magnetic field and rf irridiation. In this case, only two poos are consideredfor the sake of simplicity. However, the system can easily expanded to multiple pools as employed

11

Chapter 3. Magnetization transfer

by Patrick Schuke [15]. The two pools a and b exchange saturation characterized by the exchangerates kba from pool b to pool a and kab vice versa. The backwards exchange can be calculatedwith 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 frequencyω1 = γB1 defines the rf amplitude and ∆ωa/b = Ω−ω0,a/b describes the frequency offset betweenrf frequency Ω and the larmor frequency ω0,a/b of the corresponding pool.

d

dtMxa =−∆ωaMya −R2aMxa +kbaMxb − kabMxa (3.2)

d

dtMya = + ∆ωaMxa −R2aMya − ω1Mza +kbaMyb − kabMya (3.3)

d

dtMza = + ω1Mya −R1a(Mza −Mza,0) +kBaMzb − kabMza (3.4)

d

dtMxb =−∆ωbMyb −R2aMxb −kbaMxb + kabMxa (3.5)

d

dtMyb = + ∆ωbMxb −R2aMyb − ω1Mzb −kbaMyb + kabMya (3.6)

d

dtMzb = + ω1Myb −R1A(Mzb −Mzb,0) −kbaMzb + kabMza (3.7)

These first order coupled linear equations cannot be solved analytically without making severalapproximations. 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 withwater 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 waterand solute pool [16]. As mentioned in section 2.2.7, spins within different chemical environmentswill 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 thecorresponding 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. Thespin exchange between the saturated solute system and the water system will result in a transferof saturation. This transfer caused by chemical exchange is the essential principle of ChemicalExchange Saturation Transfer (CEST) and offers an opportunity to indirectly measure very lowconcentrated solute molecules. This enables an unique contrast within different types of tissuethat can be utilized in different medical issues such as tumor detection. Three different casesof CEST can be distinguished depending on the magnitude of the exchange rates in relation tothe frequency offset:

• fast exchange limit: k ∆ω

• intermediate exchange limit: k ≈ ∆ω

• slow exchange limit: k ∆ω

12

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 isirradiated by a number of saturation pulses with a frequency offset ∆ω from the water protonresonance. In order to obtain the thermal equilibrium magnetization M0 for the normalization ofthe spectrum, the first offset is in the far off resonant region of -300 ppm. This step is followed bya conventional image sequence consisting of excitation and k-space acquisition. This is repeatedfor different offsets, usually symmetric around the water peak at 0 ppm. A whole image isacquired 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 ofinterest. Due to the large amount of offsets in the range of 20 to 100 it is necessary to imageas fast as possible without compromising the CEST effect in order to achieve acceptable overallacquisition 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 bediscussed 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 0ppm is caused by direct water saturation while the baseline (the large negative shift of the wholespectrum on the y-axis) corresponds to the so called semi-solid macromolecular magnetizationtransfer or simply ’macromolecular MT’. This effect is caused by protons which are bound tothe surface of macromolecules and protons in water molecules bound to ’the macromolecularmatrix’, e.g protein surfaces and cell membranes. The MT effect has large line-widths of severalkHz, which is why the it is scattered across the whole range of the z-spectrum [9]. The MT canalso be asymmetric, which can compromise other CEST effects.

13

Chapter 3. Magnetization transfer

3.3.2 Nuclear Overhauser effects (NOE)

Nuclear Overhauser effects are mediated by Dipole-dipole interactions between close spins. Inin-vitro and in-vivo systems, effects between protons in proteins and water protons in the rangeof -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 +2ppm , 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. Lesswater magnetization is left for preparation by saturation transfer. This effect is called spilloverdilution [9].

Figure 3.3: A typcial Z-spectrum of the human brain at 7 T

14

4 Material and Methods

This chapter offers a brief overview over the material and methods used to acquire and interpretthe 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 volumeof interest)is excited by a rf pulse with broader bandwidth. After that, an additional phaseencoding 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 completedbefore the z-gradient changes and another slice can be acquired. It is worth to note, that in thiscontext (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

GySpoiler

Gx

ADC

Spoiler

time

15

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 interleavedprinciple is applied and optimized. Figure(4.2) shows the CEST imaging scheme which wasapplied 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, anotherslice can be imaged until the whole 3D volume is covered. Lastly, the whole sequence is repeatedfor each offset. The first slices are not fully saturated and eventually reach a steady state betweenrelaxation, 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

4.2. Scanning System

4.1.4 Numerical Simulation

The Bloch-McConnell equations can be numerically solved and the results can be utilized tosimulate z-spectra with a wide range of selectable parameters. The MATLAB code was writtenby Patrick Schunke 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 interleavedwith 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 andnread readouts is repeated nblocks times. Additional parameters are Tr,read (the repetition timeof the readout), Te,read (the echo time of the readout) and read pause (a pause between readoutand saturation).

4.2 Scanning System

4.2.1 Scanner and coils

Examinations were performed on a Biograph mMR MR-PET scanner and a Magnetom 7Tfrom Siemens (Siemens Healthcare, Erlangen, Germany) with static magnetic field strengths ofB0 = 3 T and B0 = 7 T, respectively.

Figure 4.3: Biograph mMR , DKFZ Heidelberg

17

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 thecase. In order to improve this situation, additional shimming coils with adjustable currents areutilized 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 analyzationwas carried out using MATLAB (The Mathworks, Natick, Massachusetts) software written byM.Zaiss.

4.3.1 Normalization

The obtained data is normalized pixel-wise by dividing every value of Mz by the value M0 ofthe M0-measurement acquired at the beginning of the scan. The result of this step is the socalled 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 internallycorrected by the following steps:

• Creation of an internal ∆B0-map:

– The spectrum is interpolated with a smoothing spline and the intrinsic minimum isfound 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

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 substractingthe 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 thefollowing 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 largerNOE 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 whenthe 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 and26 including four males and one female. The data was analyzed by taking the mean in a ROIof 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 therewould be no pauses between the pulses), the overall acquisition time of every segmentationscheme would remain exactly the same. However, due to scanner regulations only a DC of50% could be used resulting in different acquisition times. The 32/16 (32 acquired k-spacelines paired with 16 saturation pulses) scheme will result in a longer acquisition time becausethere are more pauses in between the saturation pulses. This is compensated by adding apause after the readout for the lower segmentation schemes. The overall acquisition times ofeach measurement were simulated with the sequence developer environment IDEA provided bySiemens in order to find the right values for the pause. This is illustrated in figure (4.5).

19

Chapter 4. Material and Methods

Figure 4.5: The 2/1 and 4/2 segmentation schemes in comparison: S stands for saturation pulseand R four readout pulse. The pulse train consisting of 2 pulses has an additionalpause due to the duty cycle and is therefore more time consuming. t′pause > tpause.

This was done to keep the repetition time tr constant.

td

time

time

t′pause

tpause

tr

S S

S S

R R R R

R R R R

20

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 parametersincluding 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 includingAmines, 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 followingsteps:

• 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 4/2segmentation schemes were measured with both probands. The overall number of saturationpulses remains the same because the number of readout lines changes accordingly. An overviewof the chosen parameters can be found in table (5.1). An empty field represents the same valueas the one before. In each measurement, 16 slices were acquired and the spectrum was internallycorrected for B0 inhomogeneities (4.3.2).

21

Chapter 5. Results

Table 5.1: Overview of experimental parameters for the optimization of the segmentation scheme

Proband 1 Proband 2

tp [ms] 15B1 [µT ] 0.7DC 50%Pulse Type GaussianMaximal offset [ppm] 4Recover Time [ms] 0Number of Offsets 24Flip Angle 10Te [ms] 3.82Tr [ms] 56 112 197 205 384 742nk 2 4 8 8 16 32np 1 2 4 4 8 16

ROI # 1

0.8

0.9

1

−4−20240

0.5

1

Offset [ppm]

Z

Mean Z-spectrum with standard deviation in ROI

−4−20240

0.5

1

Offset [ppm]

Z

ROI # 20.8

0.9

1

Figure 5.1: Z-spectrum and contrast obtained with a 2/1 segmentation scheme in slice 6 forwhite matter (ROI = (region of interest) 1) and grey matter (ROI 2) at the offsetof -3.6 ppm, internal B0 correction

No actual CEST peaks can be observed in the spectrum of the white and grey matter ROIs infigure (5.1). However,the spectrum shows a slight asymmetry due to the broad NOE effect onthe right of the water peak. Further optimization was based on MTRasym in white matter.

22

5.1. Optimization of the segmentation scheme

In the following, MTR′aysm will be defined as:

MTR′aysm =

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 ofthe number of the pixels within. This step is justified due to the fact that the tissue within theROI 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)

MT

R′ asy

m

Proband 1Proband 2

Figure 5.2: MTR′asym 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 valuesare summed up because the NOE peak is broader than 1 ppm. A maximum value for bothprobands can be observed for 8 k-space lines paired with 4 saturation pulses. However, thedifferent values are normalized with different M0 measurements and therefore, MTRasym seemshigher for smaller M0. This has to be corrected in the following way: The lowest average valueof M0 (in the same ROI as used for the evaluation of MTRasym) is chosen as the referencemagnetization M0,0. MTRasym is renormalized to this reference:

MTR∗asym = MTR′asym ·M0,i

M0,0(5.2)

Where M0,i stands for the corresponding M0 value obtained for each segmentation scheme.

23

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

MT

R∗ asy

m

Proband 1Proband 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

MT

R∗ asy

m

Proband 1Proband 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 proband2, 32/16 shows the highest asymmetry. Further measurements were performed with the 8/4segmentation scheme as it seems to create maximal asymmetry in at least one slice near themiddle 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 8/4segmentation scheme. Once again, the parameters are shown in the following table:

24

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] 15B1 [µT ] 0.7DC 50Pulse Type GaussianMaximal offset [ppm] 4.5Recover Time [ms] 0Number of offsets 28Flip angle 6 8 10 15Te [ms] 3.82Tr [ms] 197nk 8np 4

In figure (5.5) MTR∗asym was plotted against different flip angles. An optimum of 8 can beobserved 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 thecode provided by Christian David (4.1.5) in figure (5.6). The parameters are summarized inthe following tables:

Table 5.3: Parameters for the simulation of the unnormalized asymmetry as a function of theflip 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] nblocks3.8 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]

MT

R∗ asy

m

slice 8

slice 6

Figure 5.5: MTR∗aysm as a function of the flip angle (proband 3) within slices 6 and 8

25

Chapter 5. Results

0 2 4 6 8 10 12

−3

−2

−1

·10−3

Flip angle [degrees]

M(-

∆ω

)-M

(∆ω

)(3.

5p

pm

)

Figure 5.6: Simulated unnormalized Asymmetry at the offset of 3.5 ppm as a function of theflip 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 performedwith a flip angle of 8.

5.3 SNR

In the next step, the signal-to-noise ratios (SNR) of the M0 - measurements with different flipangle 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 donewithin a region outside of the brain where it can safely be assumed that any signal contributioncomes from the background noise. An error of overall 5% was assumed due to the standarddeviation within the signal-ROI.

6 8 10 1580

100

120

140

Flip angle [degrees]

SN

R

Figure 5.7: SNR of the M0 measurement plotted against the flip angle (proband 2)

26

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 imagequality 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 andeffects at the same time, because the optimal value largely depends on the chemical exchangerates. It should be noted that an increase in B1 will compromise other effects such as that ofAmides and Amines. However, several measurements were made in order to verify the generaltrend which can be observed in numerical 5 pool simulations. The parameters were chosen asfollows:

Table 5.4: Parameters for the simulation of MTRasym (3.5 ppm) as a function of B1 (withoutinterleaved 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] 15B1 [µT ] 0.5 0.7 0.9 1.1DC 50Pulse Type GaussianMaximal offset [ppm] 4.5Recover Time [ms] 0Number of offsets 28Flip angle 8Te [ms] 3.82Tr [ms] 197nk 8np 4

27

Chapter 5. Results

0.5 0.7 0.9 1.1

−0.15

−0.1

−5 · 10−2

B1 [µT]

MT

Rasy

m

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]

MT

Rasy

m(

3.5

pp

m)

Figure 5.10: The simulated MTRaysm at ∆ω = 3.5 ppm plotted as a function of B1. 5 Poolswere simulated including Water, MT, NOE, Amdides and Amines.

The general trend of increasing negative asymmetry around the offset of 3.5 ppm for increasingvalues of B1 in figures 5.9 and 5.10 complies qualitatively with the numerical simulation ofMTRasym of a 5 pool system (Water (w), Amides (Ad), Amines (An), MT, NOE). Note thatin the simulation, only one value of MTRasym at 3.5 ppm is displayed. However, this has noimpact 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 3.6ppm (7 T) of the 3D sequence measured with B0 = 3 and 7 T from two different probands. TwoROIs, one in white and one in grey matter were analyzed in slice 6, respectively. The imagingand saturation parameters were the same (except for a higher number of offsets at 7 T).

28

5.5. Comparison with 7 T

# 1

#2

−0.1

−5 · 10−2

0

−4−20240

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

−4−20240

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) and3.6 (7 T) ppm.

A comparison of MTRasym contrasts in figure (5.11) already demonstrates the superiority ofhigher 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 veryprominent compared to those visible at B0 = 3T.

29

6 Discussion

In-vivo CEST measurements remain a challenge, especially at lower field strenghts. The goal ofthis work was to optimize combined saturation and imaging parameters of a 3D CEST sequenceon a 3 T scanner. The optimization was carried out in regard to the negative asymmetry causedby the NOE around -3.5 ppm of the Z-spectrum. The segmentation could only be optimizedfor single slices and a global optimum was not found. The optimal flip angle on the other handwas found rather easily.However, the image contrast due to MTRasym remained low in all probands and could onlybe improved by measuring with a higher field strength of 7 T. The same observation wasmade for the general appearance of the z-spectrum. At 3 T, no actual amide or amine peakswere observable with different saturation amplitudes of B1 = (0.5, 0.7, 0.9, 1.1) µT . This is inaccordance to other publications, in which the Amide proton transfer (APT) caused a positiveasymmetry 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 peaksselectively, 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 potentialerrors 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 effectscan be compensated for with the employment of a post-processing method called AREX orapparent-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 ppmfrom the water proton resonance and hence could contribute to a CEST effect. This can beavoided 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 whichcan 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 edgeof 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 tothe 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 analysiswas 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 errorwas avoided.

Different measurements with varying segmetation schemes (number of k-space lines / number

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Chapter 6. Discussion

of saturation pulses) were performed. A maximum in asymmetry could be found for the 8/4segmentation scheme in two measurements with different probands within slice 6. This seemsto contradict the results of the numerical simulation and other experimental findings [10], wherethere was no impact on the asymmetry.However, the offsets were summed up over three values of MTRasym and the difference betweensegmentation 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 anoptimal segmentation scheme of 4/2. This raises the question whether the system had beenfully saturated within slice 6. However, this possibility can be ruled out by the fact that theasymmetry 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 pulseswere applied regardless of the segmentation. Due to the very small changes in asymmetry anddifferent 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 timeswere kept constant by the implementation of a pause after the readout (4.5). Without thispause, 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 alsorequired to yield a CEST contrast. This is due to the fact that the steady state in saturationwould be reached faster. To quantify these statements, different segmentation schemes weresimulated 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 32/16Acquisition 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 dueto 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. Themaximal 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 behavesaccording 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 ChristianDavid [10], where the same observations could be made. Hwoever, this is not surprising due tothe fact that CEST effects have a very little impact on the overall longitudinal magnetization.

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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 numericalsimulation. It remains a scientific challenge to truly isolate CEST effect of each metabolite. Dueto 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 werecompared in 5.5. In the Z-spectrum of the 7 T measurement, clear peaks of Amides as well asAmines and a negative asymmetry of up to 10% in the NOE region are very prominent comparedto those measured at 3 T. On top of that, the contrast obtained by MTRasym is clearly strongerat 7 T. The conclusion of these measurements is that CEST largely benefits from higher staticfield 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 peaksincreases 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 totransfer into the water pool

Due to these reasons, it is highly desirable to perform CEST experiments at higher fieldstrengths. However, this transition is accompanied by a different set of challenges. Both B0 andB1 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 thespecific contrast of healthy as well as pathogenic tissue should be continued. In order to verifythe 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 availabilityin the following years will remain low compared to 3 T scanners. The following approachesmight further improve CEST imaging at lower field strengths:

• The usage of adiabatic pulses could lead to a more effective selective saturation of CESTpools and thus enhance the overall effect. Several measurements were already performedduring this work, but the acquired data was still compromised by oscillation artifacts nearthe water resonance

• CEST involves the acquisition of the same slice for a relatively large number of differentoffsets. A faster image acquisition with EPI or a radial sequence paired with imagereconstruction result in the overall reduction of the acquisition time. The time advantagecould be used to increase the SNR by averaging. However, this time gain would be rathersmall because saturation is the dominant factor when it comes to acquisition time.

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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.

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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. Thefollowing results were found:

• No significant differences in form of an asymmetry in the z-spectrum were found for varyingschemes. This supports the findings of numerical simulations and phantom experiments[10]. However, lower segmentation schemes are generally more desirable due to the timeadvantage caused by a Duty cycle 6= 100%.

• The flip angle could sucessfully be optimized and the trend resembles the behaviour of theFLASH signal equation with a shift to smaller optimal values. This also verifies findingsof the numerical simulation [10].

• Higher static field strengths lead to an increase of CEST effects and greatly enhance thedesired specific contrast. However, due to the higher availability of 3 T scanners, thesearch for better methods at lower field strengths needs to be continued.

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Bibliography

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[2] F. Bloch. Nuclear induction. Phys. Rev., 70:460–474, Oct 1946.

[3] E. L. Hahn. Spin echoes. Phys. Rev., 80:580–594, Nov 1950.

[4] E. M. Purcell, H. C. Torrey, and R. V. Pound. Resonance absorption by nuclear magneticmoments in a solid. Phys. Rev., 69:37–38, Jan 1946.

[5] P. C. Lauterbur. Image formation by induced local interactions: Examples employingnuclear magnetic resonance. Nature., 242(5394):190–191, mar 1973.

[6] Craig K. Jones, Michael J. Schlosser, Peter C.M. van Zijl, Martin G. Pomper, Xavier Golay,and Jinyuan Zhou. Amide proton transfer imaging of human brain tumors at 3t. MagneticResonance in Medicine, 56(3):585–592, 2006.

[7] Craig K. Jones, Alan Huang, Jiadi Xu, Richard A.E. Edden, Michael Schr, Jun Hua,Nikita Oskolkov, Domenico Zac, Jinyuan Zhou, Michael T. McMahon, Jay J. Pillai, andPeter C.M. van Zijl. Nuclear overhauser enhancement (noe) imaging in the human brainat 7 t. NeuroImage, 77:114 – 124, 2013.

[8] Jinyuan Zhou, Bachchu Lal, David A. Wilson, John Laterra, and Peter C.M. van Zijl.Amide proton transfer (apt) contrast for imaging of brain tumors. Magnetic Resonance inMedicine, 50(6):1120–1126, 2003.

[9] Moritz Zaiss and Peter Bachert. Chemical exchange saturation transfer (cest) and mr z -spectroscopy in vivo : a review of theoretical approaches and methods. Physics in Medicineand Biology, 58(22):R221, 2013.

[10] Christian David. Studie einer Magnetisierungstransfer-MR-Sequenz mit kombinierter Saet-tigung und Bildgebung. Master’s thesis, Ruprecht-Karls-Universitt Heidelberg, 2015.

[11] E. Mark Haacke, Robert W. Brown, Michael R. Thompson, and Ramesh Venkatesan.Magnetic resonance imaging. Wiley-Liss, New York [u.a.], 1999. Includes bibliographicalreferences and index.

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[14] Harden M. McConnell. Reaction rates by nuclear magnetic resonance. The Journal ofChemical Physics, 28(3):430–431, 1958.

[15] Patrick Schunke. Quantitative Multi-Pool-Analyse von Glukose-CEST in vitro. Master’sthesis, Ruprecht-Karls-Universitt Heidelberg, 2013.

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[17] Moritz Zaiss, Patrick Kunz, Steffen Goerke, Alexander Radbruch, and Peter Bachert. Mrimaging of protein folding in vitro employing nuclear-overhauser-mediated saturation trans-fer. NMR in Biomedicine, 26(12):1815–1822, 2013.

[18] Jan Eric Meißner. Neue Methoden fr die Multi-Pool CEST Bildgebung in vivo. Master’sthesis, Ruprecht-Karls-Universitt Heidelberg, 2013.

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List of Figures

2.1 Schematics of a gradient echo readout . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Pool model in-vivo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 CEST data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Z-spectrum of the human brain at 7 T . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1 The 3D Gradient Echo Timing Diagram . . . . . . . . . . . . . . . . . . . . . . . 154.2 The interleaved CEST sequence scheme . . . . . . . . . . . . . . . . . . . . . . . 164.3 3 T scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.4 7 T scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.5 The 2/1 and 4/2 segmentation schemes in comparison . . . . . . . . . . . . . . . 20

5.1 Z-spectrum and contrast @ -3.6 ppm . . . . . . . . . . . . . . . . . . . . . . . . . 225.2 MTR′asym as a function of the segmentation (slice 6) . . . . . . . . . . . . . . . . 235.3 MTR∗aysm as a function of the segmentation . . . . . . . . . . . . . . . . . . . . . 245.4 MTR∗aysm as a function of the segmentation scheme (slice 8) . . . . . . . . . . . . 245.5 MTR∗aysm as a function of the flip angle . . . . . . . . . . . . . . . . . . . . . . . 255.6 Simulated unnormalized Asymmetry @ 3.5 ppm as a function of the flip angle . . 265.7 SNR of the M0 measurement as a function of the flip angle . . . . . . . . . . . . 265.8 Z-contrast obtained at flip angles 8 and 10 @ -3.8 ppm . . . . . . . . . . . . . 275.9 MTR∗aysm as a function of B1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.10 The simulated MTRaysm @ 3.5 ppm plotted as a function of B1 . . . . . . . . . . 285.11 Comparison of 3 T and 7 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

39

List of Tables

5.1 Experimental parameters for the optimization of the segmentation scheme . . . . 225.2 experimental parameters for the optimization of the flip angle . . . . . . . . . . . 255.3 Parameters for the simulation of the unnormalized asymmetry as a function of

the flip angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.4 Parameters for the simulation of MTRasym (3.5 ppm) as a function of B1 . . . . 275.5 Experimental parameters for measurements with varying B1 . . . . . . . . . . . . 27

6.1 The simulated acquisition time for different segmentation schemes assuming theacquisition of 16 slices with 2 different offsets . . . . . . . . . . . . . . . . . . . . 32

41

Erklarung

Ich versichere, dass ich diese Arbeit selbststandig verfasst und keine anderen als die angegebe-nen Quellen und Hilfsmittel benutzt habe.

Heidelberg, den 21.03.2016.

43

Danksagung

An dieser Stelle mochte ich allen danken, die mir das Verfassen dieser Arbeit ermoglicht haben.

• Herrn Prof. Dr. Bachert danke ich fur die Moglichkeit, in dieser Arbeitsgruppe selb-ststandig geforscht haben zu durfen.

• Herrn Prof. Dr. Schlegel danke ich fur die Zweitbeurteilung meiner Arbeit.

• Ein ganz besonderes Dankeschon geht an Moritz. Seine einzigartige Leidenschaft fur dieForschung hat mich jeden Tag motiviert. Außerdem ist er halt einfach ein cooler Typ mitdem man immer lachen kann. (Mal abgesehen davon, dass er ein ziemlich genialer Kopfist)

• Das gleiche gilt fr Jan: Ich hoffe er hat nicht zu viele Stunden mit der Korrektur verbracht.

• Dankeschon an die Probandinnen und Probanden Pascal, Nico, Leo (er hat wahrend dergesamten 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 Prasentationen gezeigt hat, dass ichnoch langst nicht alles kapiert habe, was mit MR Bildgebung zu tun hat.)

• Mein Dank richtet sich auch an meine Mathe- und Physiklehrer Herrn Schatzle und HerrnPiffer, die mich fur die Naturwissenschaft begeistert haben. (Und das, obwohl ich docheigentlich Journalist werden wollte)

• Danke an die 21-E-Street. Fur die bisher geilste Zeit meines Lebens.

• Naturlich danke ich an letzter Stelle meiner Familie: Meiner Mutter, meinem Vater undmeinem Bruder, die nicht nur wahrend meines Studiums, sondern in allen Lebenslagen zumir gehalten haben.

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