Development and application of efficient strategies for parallel magnetic resonance imaging [Elektronische Ressource] / vorgelegt von Felix Breuer

Sujets

• Physik

Informations

• Publié par: julius-maximilians-universitat_wurzburg
• Publié le: 01 janvier 2006
• Nombre de lectures: 24
• Langue: English
• Poids de l'ouvrage: 7 Mo

Extrait

Development and
Application of Efficient
Strategies for Parallel
MagneticResonanceImaging
Dissertation zur Erlangung des
naturwissenschaftlichen Doktorgrades
der Bayerischen Julius-Maximilians-Universität Würzburg
vorgelegt von
Felix Breuer
aus Würzburg
Würzburg 2006Eingereicht am:
bei der Fakultät für Physik und Astronomie
1. Gutachter: Prof . Dr. rer. nat. P. M. Jakob
2. Gutachter: Prof . Dr. rer. nat. A. Haase
der Dissertation.
1.Prüfer:Prof.Dr.rer.nat.P.M.Jakob
2. Prüfer:
im Promotionskolloquium.
Tag des Promotionskolloquiums:
Doktorurkunde ausgehändigt am:Contents
1BasicsofMRI 5
1.1 NuclearMagneticResonance ............................ 5
1.2 Relaxation....................................... 6
1.3 SpatialEncoding................................... 6
1.3.1 SelectiveExcitation ............................. 6
1.3.2 k-SpaceFormalism.............................. 7
1.3.3 FrequencyEncoding............................. 8
1.3.4 PhaseEncoding................................ 8
1.4 Sampling k-Space...................................10
1.4.1 InfiniteSampling...............................10
1.4.2 FiniteSampling................................1
1.4.3 TheFourierShiftTheorem .........................13
1.4.4 Aliasing....................................15
1.5 ImagingSpedandSNR...............................15
2 Basics of Parallel Imaging 19
2.1 Introduction......................................19
2.2 HistoricalOverview..................................20
2.3 BasicConcepts....................................21
2.4 TechnicalOverview .................................23
2.4.1 SENSE ....................................23
2.4.2 SMASH....................................25
2.4.3 AUTO-SMASHandVD-AUTO-SMASH..................26
2.4.4 GRAPPA...................................27
2.5 SensitivityAssessment................................30
2.6 Auto-Calibration...................................30
2.7 CoilArangementConsiderations .........................31
2.8 OpenIsues......................................31
34 CONTENTS
3 TGRAPPA for dynamic imaging 33
3.1 Introduction......................................3
3.2 Methods........................................34
3.3 Results.........................................36
3.4 Discussion.......................................40
3.5 Summary.......................................43
4 MS CAIPIRINHA 45
4.1 Introduction......................................45
4.2 Theory.........................................46
4.3 MaterialandMethods................................53
4.4 Results.........................................54
4.5 Discusion.......................................58
4.6 Summary.......................................59
5 2D CAIPIRINHA 61
5.1 Introduction......................................61
5.2 Theory.........................................62
5.3 Methods........................................71
5.4 Results.........................................72
5.5 Discussion.......................................80
5.6 Conclusion.......................................81
6 3D CAIPIRINHA 83
6.1 Introduction......................................83
6.2 Zig-zagSamplinginParallelMRI..........................84
6.3 3DChemicalShiftImaging.............................87
6.4 DiscusionandConclusion..............................92
7 Conclusions and Perspectives 93
Bibliography 97Chapter 1
Basics of MRI
1.1 Nuclear Magnetic Resonance
The phenomenon of Nuclear Magnetic Resonance (NMR) was first described by Bloch [1]
and Purcell [2] in 1946. Simultaneously, but idependently they investigated the interaction
between the non-zero magnetic moment of atomic nuclei and an external magnetic field. They
found that whenever a nucleus with non-zero spin angular momentum is placed in a magnetic
field, the energy level is forced to split into multiple levels. For spin 1/2-systems,suchas
1 13 19H, C or F the spin will seek to align itself either parallel or anti-parallel to the external
field in accordance with the quantization of angular momentum, thereby creating two distinct
energy levels. Spins precess around the main field with the so called Larmor frequency, which
is given by:
ω = γB (1.1)
0 0
B is the field strength of the magnetic field, which in accordance to convention is applied
0
in the z-direction, and the parameter γ is known as the gyromagnetic ratio, which has a
characteristic value for each atomic nucleus. For protons the gyromagnetic ratio has value
γ/2π =42.57MHz/T which corresponds to a resonance frequency of ν = ω /2π =63.86MHz
0
at 1.5T. Because the spins parallel to the magnetic field have a slightly lower energy than
those anti-parallel to the field, there will be slightly more parallel spins than anti-parallel.
This difference in energy population leads to a net macroscopic magnetization. In order to
achieve a detectable signal, the magnetization vector must be tipped from the static magnetic
field direction, resulting in a changing flux in a nearby receiver coil. This can be accomplished
by rotating the magnetization away from its alignment by applying an oscillating magnetic
field B perpendicular to the static magnetic field for a short time τ. This radio frequency
1
(rf) pulse is produced by a transmit coil tuned to the Larmor frequency in order to match
the resonance condition. The angle by which the magnetization is rotated away from the6 1.2. RELAXATION
z-direction by the rf-pulse is referred to as excitation angle or flip angle.
τ
α = γ |B (t)| dt (1.2)
1
0
1.2 Relaxation
After the rf excitation pulse has been applied, part of the magnetization has been moved from
the longitudinal axis to the transversal plane and therefore is no longer in thermal equilibrium.
The time needed for the longitudinal magnetization to return to equilibrium is characterized
by the relxation time constant T . This phenomenon is known as spin-lattice relaxation,
1
because energy is transferred between the spin and the lattice to achieve equilibrium. Simul-
taneously, a second relaxation mechanism occurs. The transversal part of the magnetization
decreases in time to zero, characterized by the relaxation time constant T.Thereasonfor
2
this phenomenon is that spins transfer energy among each other. Due to these interactions
the phase coherence between the spins decreases in time resulting in a steady reduction of the
net transversal magnetization. This relaxation process is known as transversal or spin-spin
relaxation. In addition to the spin-spin interactions, further dephasing may occur due mag-
∗netic field inhomogeneties in the sample (T relaxation). The relaxation times T and T are
1 2
2
characteristic for different tissues. Thus, signal from different tissues relax differently after rf
excitation and in between subsequent rf excitations allowing one to influence image contrast.
1.3 Spatial Encoding
The precession frequency given in Eq. 1.1 can be modified by applying additional magnetic
field gradients, thereby forcing the Larmor frequency to be spatially dependent. An addition-
1 ally applied magnetic field gradient G =∇B≈∇B yields the following spatially dependentz
precession frequency ω:

ω(r,t)=γ B + G(t)· r (1.3)
0
Thus, by exploiting magnetic field gradients in all three spatial dimensions, one is able to
fully spatially encode the object under investigation. This procedure is known as Magnetic
Resonance Imaging (MRI) and is described in more detail below.
1.3.1 Selective Excitation
At the beginning of every conventional 2D MRI experiment the slice to be imaged must be
selected, normally in the z-direction. To this end, a selective rf excitation pulse is required,
1

B and B can be neglected because |B || B(r)|
x y 0CHAPTER 1. BASICS OF MRI 7
which excites only spins in a well defined frequency range. Such rf pulses have a well defined
shape such as Gaussian or sinc with a finite frequency bandwidth Δω around the centerrf
frequency ω . For small flip angles, the actual excitation profile of such pulses can roughly berf
approximated by a simple Fourier transformation of the temporal modulation function of the rf
pulse (small tip angle approximation [3]). In this case, a sinc-type excitation pulse corresponds
to a box-car-shaped excitation profile, a Gaussian rf pulse to a Gaussian excitation profile. By
applying a frequency-selective rf pulse with frequency bandwidth Δω in combination withrf
∂B
za constant magnetic field gradient B = only spins within a distinct slice with thicknessz ∂z
Δz are excited.
Δωrf
Δz = (1.4)
γ· Gz
The slice position z is adjusted by the carrier frequency ω of the pulse, which can be chosen
0 rf
slightly off-resonant from the Larmor frequency given in Eq. 1.1. Exploiting again Eq. 1.3,
the frequency offset corresponds to an offset in the slice position.
ω − ωrf 0
z = (1.5)
0
γ· Gz
To compensate for spin dephasing caused by the slice gradient, an inverted gradient must be
applied after slice-selection.
1.3.2 k-Space Formalism
According to Eq. 1.3 magnetic field gradients G(t) result in a spatially dependent Larmor
frequency. In the presence of such at, the signal S(t) picked up by the receiver is
composed of t