1.5 Outline
2.1.2 Magnetic Resonance Imaging
Fundamentals. MRI is an imaging modality that makes use of magnetic fields and radio waves to visualize the human body. The underlying physical principle of MRI is called nuclear magnetic resonance (NMR), which is based on the interaction of atomic nuclei with a magnetic moment [187]. Nuclei with an odd number of protons and neutrons exhibit a non-zero spinQswhich is associated with a magnetic dipole moment that is given by
µd =γgQs (2.3)
whereγg is the nucleus-specific gyromagnetic ratio. Typical nuclei for MR applica-tions include hydrogen1H, carbon13C, sodium23Na and Phosphor31P. For MRI, the most important nucleus is hydrogen, which is very common in the human body, for example, in water and also larger molecules such as proteins and lipids. In addition, hydrogen’s gyromagnetic ratio of of26.752 rad/Tsis large compared to other nuclei.
Without any external magnetic field, hydrogen’s spins are isotropically distributed.
Once an external magnetic field is applied, the spins precess into two different orienta-tions along the direction of the magnetic field, which are associated with different energy levels (Zeeman effect) [71]. For hydrogen, the two spin orientations can be parallel and antiparallel and their respective occupation numbersnpandnap, for a steady-state, can be described with a Boltzmann distribution as
np
nap = exp(−2|µd||B0|
kBTB ) (2.4)
wherekBis the Boltzmann constant,TBthe temperature, andB0describes the external magnetic field [452]. As the occupation numbers for both orientations are different, the vector sum of the nuclei’s magnetic dipole moments results in a magnetizationM, which is in parallel to the external fieldB0. A stronger external field leads to a larger difference in occupation numbers and, thus, a larger, measurable magnetizationM, which is why clinical MRI devices typically rely on powerful magnetic fields with1.5 Tto3.0 T.
The parallel spin orientation is referred to as the fundamental state with a lower energy level, and the antiparallel spin orientation is called the excited state with a higher energy level. The difference in energy levels is given by
∆El =γhp
2π|B0| (2.5)
wherehp is the Planck constant. Nuclear magnetic resonance occurs if the energy
∆El is added to the system. An excitation pulse with energy Erad = hp
2πω0 (2.6)
leads to the transition from the fundamental state into the excited state. The excitation pulse is an alternating magnetic field, and its frequency ω0 is chosen such that the resonance condition
ω0 =γ|B0| (2.7)
2.1 Image Data Representations
is met. The excitation pulse deflects the measurable magnetization vectorM by an angleθE. Typical scenarios include a deflection by90◦with anα-Pulse and180◦ with a β-Pulse. After deflection, the spins start to fall back into the initial steady-state, which is referred to as relaxation. In addition, the spins start to precess along the external magnetic field’s orientation. The spins rotating in phase start to dephase, which leads to a second transversal relaxation process. The measurable magnetization along the external magnetic field’s orientationMz is referred to as the longitudinal magnetization.
The measurable magnetization perpendicular to the external magnetic field’s orientation Mxy is referred to as the transversal magnetization.
The longitudinal and transversal relaxation processes show different behavior in different tissue types, which allows for differentiation in the final MR images. Based on the superposition principle, the two processes’ superposition is undisturbed. Longitudinal relaxation, which is also calledT1-relaxation, refers to the process ofMz returning to its original steady state. During the process, energy is emitted, which is equivalent to the difference in the energy levels between the excited and the steady-state. For anα-Pulse, the longitudinal magnetization is defined as
Mz(t) =M∞(1−exp(− t
T1)) (2.8)
whereM∞ = M(∞)is the magnetization in steady-state and T1 is the relaxation time. The timeT1 describes the time that is required forMz to reach63 %ofM∞. An example of two longitudinal relaxation processes is shown in Figure 2.8. The relaxation processes also illustrate how the intensity and contrast of MR images with different sampling time points can differ. When sampling atts = 100 ms, the first process shows a higher measurable magnetization. When sampling atts = 500 ms, the second process shows a higher magnetization and the difference between the processes is smaller.
The transversal relaxation process is also calledT2-relaxation, which is the process of the rotating spin’s dephasing after excitation with a pulse. In contrast to longitudinal relaxation, no energy is emitted during the process. After excitation with anα-Pulse, the spins rotate along the axis of the external magnetic field with the resonance frequency ω0. Due to the interaction of the spin’s local magnetic field, the spins start dephasing in thexy-plane, which is perpendicular to the external magnetic field’s orientation. Finally, the spins are isotropically distributed in thexy-plane with a measurable magnetization ofMxy = 0. This process is described by
Mxy =M0exp(− t
T2) (2.9)
whereM0 =Mxy(0)andT2represents the transversal relaxation time.M0 is equal to the magnetizationMz at the time of excitation. ExampleT2-relaxation processes are shown in Figure 2.9. Again, the intensity which is derived from magnetization is very different for different sampling time points. In biological tissue,T2 times are generally shorter thanT1times as the dephasing processes are much faster than the recovery of the longitudinal magnetizationMz.
In addition,T2-relaxation processes are often the sum of multiple exponential pro-cesses in biological tissue. This can be observed in fat tissue or at tissue borders if
0 100 200 300 400 500 600 700 800 0
200 400 600 800 1,000 1,200 1,400
t in ms Mz
Minf = 1000 T1 = 60ms Minf = 1100 T1 = 120ms
Fig. 2.8: Two examples of longitudinal relaxation processes are shown. Vertical lines represent sampling time points. Marks represent the sampling points.
0 50 100 150 200 250 300 350 400 450 500 0
200 400 600 800 1,000 1,200 1,400
t in ms Mxy
M0 = 1200 T2 = 80 ms M0 = 600 T2 = 2000 ms
Fig. 2.9: Two examples of transversal relaxation processes are shown. Vertical lines represent sampling time points. Marks represent the sampling points.
2.1 Image Data Representations
multiple tissue types are present in a single voxel. This is also referred to as the partial volume effect. This type of process is defined as
Mxy =
ksup
X
i=1
M0iexp(− t
T2i) (2.10)
whereksupis the number of superimposed processes.
Imaging Modalities. Based on the physical properties of relaxation processes, differ-ent modalities with differdiffer-ent weighting can be produced. For this purpose, relaxation processes are induced inside the tissue, and the magnetization is measured at predefined echo timesTE.
When using spin echo sequences,T2-relaxation processes are triggered. With a short TE time, proton density-weighted images are created whose intensity is largely governed by the proton density in the current volume element. With a longerTE time, measured signals are more affected byT2-relaxation characteristics, thus, the obtained images are calledT2-weighted images.
Images governed by T1-relaxation processes can be obtained by using inversion recovery or saturation recovery sequences which induce an excitation angle ofθE = 180◦ orθE = 90◦, respectively. Sampling with a shortTE leads toT1-weighted MR images.
For some applications, a gadolinium-based contrast agent is used to enhance, for example, active tumor borders of a glioblastoma.
To visualize and distinguish different tissue types in MR images, relaxometry is employed where tissue-specific parameters such asT1- andT2-relaxation times are determined. Afterward, by choosing a specificTE time and repetition timeTR, certain tissue types can be enhanced or suppressed. The repetition timeTRis the period to wait between excitation pulses. For example, fluid-attenuated inversion recovery (FLAIR) is aT1-weighted method where fluids such as cerebrospinal fluid are suppressed by choosing suitable timesTE andTR.
2D and 3D Spatial Data.The following description is based on Sprawls et al. [462].
For image acquisition, target regions need to be specifically excited and spatially resolved.
MRI acquisition is typically performed in a slice-wise manner. As a first step, a slice is selected in the human body using selective excitation. Here, gradient coils are used to target a specific slice. The gradient coils are an additional component in the MRI scanner that creates a gradient vector, which results in a change of the magnetic field along its orientation. Thus, along with the gradient vector’s orientation, the magnetic field strength changes, and therefore, the resonance frequency ω0 of the tissue inside the magnetic field changes as well. As a result, differentω0 encode different spatial locations and can be specifically targeted by adjusting the excitation pulse frequency accordingly. Given a resonance frequencyω0, associated with the main magnetic field B0, the location-dependent resonance frequency is given by
ω(x, y, z) = ω0+γ(Gxx+Gyy+Gzz) (2.11) whereGis the magnetic field strength of the gradient coils in each direction. Assuming slice selection along thez-axis, an excitation frequencyωi shifts the slice position by
ωi−ω
γGz . Accordingly, slice thickness is determined by the excitation pulse’s bandwidth with
M
Fig. 2.10: A single MR imaging cycle is depicted. The three events happen in succes-sion. For each imaging cycle, a different phase-encoding gradient is applied.
M refers to magnetic field strength. Different colors imply magnetic field gradients along different spatial dimensions.
∆z = γG∆ω
z. By adjusting the gradient vector’s orientation, arbitrary slice orientations can be achieved.
After slice selection, the other gradient directions are used to resolve the slice spatially.
For this purpose, phase and frequency encoding are used. After a selected slice is excited, a phase-encoding gradient is applied, which causes the magnetic spin along a spatial dimension to have different phases. Thus, the received signal will have components with different phases that can be associated with a spatial location. After phase encoding, the slice’s second spatial dimension is encoded by frequency. Similar to the slice selection process, a gradient is applied along an additional direction. The change in the magnetic field leads to different resonance frequencies that can be associated with a spatial location. All steps of the acquisition process are shown in Figure 2.10. First, slice selection is performed by turning on a gradient for a short time. Now the spins are in an excited state. Then, the phase-encoding gradient is turned on for a short time period. Last, when the excited tissue emits the signal that is measured by the receiving coil, the frequency-encoding gradient is turned on. This imaging cycle produces a single row for the final 2D image. Thus, for a 2D image withNcol columns, the imaging cycle has to be repeatedNcol times. For each repetition, the phase-encoding gradient is set differently to capture a different spatial location.
A full 3D volume is obtained by acquiring multiple slices. The process can be sped up by a technique called multi-slice imaging. Here, the next slice is already excited while the previous slice is still undergoing phase- and frequency-encoding. Another method for 3D volume acquisition is called 3D imaging. Instead of exciting a selected slice, the entire volume is excited without applying a selection gradient. Then, phase-encoding is used for slice selection. In this process, all three gradient directions are used instead of two for slice-wise acquisition with selective excitation. While 3D imaging requires longer acquisition times, phase-encoding-based slicing allows for thinner slices.
After acquisition, the MR image is encoded in a spatial frequency domain, also referred to ask-space. The final Cartesian image can be reconstructed with a 2D Fourier transform. Example 2D and 3D MR images are shown in Figure 2.11.
3D and 4D Short-Term Spatio-Temporal Data. An important drawback of MRI is its long acquisition time. Still, some imaging techniques allow for capturing short-term temporal processes. A typical method is cardiac cine MRI, which is used for imaging of
2.1 Image Data Representations
Fig. 2.11: An MRI scan of the human brain is shown. Left, a 2D slice is shown. Right, a 3D rendered volume is shown.
Fig. 2.12: An example of 3D spatio-temporal cardiac cine MRI data. From left to right, different phases of the cardiac cycle are imaged. Four images from a whole sequence of 20 images are shown.
the cardiac cycle in order to assess function and diagnose heart diseases. To enable faster acquisition, specialized gradient-echo techniques such as TrueFISP [75] are employed, which are characterized by very shortTE andTR values. Still, the acquisition of a full slice during a phase of the cardiac cycle is infeasible as the imaging cycle needs to be repeated several times, see Figure 2.10. Therefore, electrocardiography (ECG) is used for retrospective gating. Both the MRI and ECG signal are acquired simultaneously over several cardiac cycles. After the acquisition, the MRI signals can be assigned to the respective cardiac phase using the ECG signal. The entire procedure can be completed within a breath-hold of the patient [23]. Often, this procedure is used to acquire a single slice over time, which results in 3D spatio-temporal data. If the entire heart needs to be imaged, the procedure needs to be repeated several times, which results in 4D spatio-temporal data. An example of 3D spatio-temporal cardiac cine MRI data is shown in Figure 2.12.
The same acquisition technique can be used for phase-contrast cine MRI which allows for imaging of blood flow in the human body [322]. The method relies on the fact that changes in the MRI signal phase along a magnetic gradient are proportional to blood flow velocity. When extending the method to 3D spatial data ("4D flow MRI"),
Fig. 2.13: An example of longitudinal 3D spatio-temporal MRI data of the human brain.
From left to right, scans taken several months apart are shown.
Tab. 2.2: Overview of the different MRI data representations.
Acquisition Type Dimensionality Typical Application 2D/3D Imaging 2D Spatial
Tissue Imaging 3D Spatial
Cine MRI 3D Spatio-Temporal
Cardiac Imaging/Blood Flow 4D Spatio-Temporal
Longitudinal
2.5D Spatio-Temporal
Disease Tracking 3D Spatio-Temporal
3.5D Spatio-Temporal 4D Spatio-Temporal
acquisition becomes more difficult. Often, radialk-space acquisition is used, and due to long acquisition times, respiratory gating is additionally required [322].
3.5D and 4D Longitudinal Spatio-Temporal Data. Besides short-term temporal analysis, MRI is employed for long-term longitudinal analysis. A typical application is tracking disease progression for multiple sclerosis [60]. Here, individual MRI scans are acquired several months or years apart. In terms of the acquisition, there are no specific challenges, however, the individual time points can differ a lot due to different acquisition parameters, different scanners, or other major changes between the long time intervals. Often, only two volumes from two time points are compared to which we refer as longitudinal 3.5D spatio-temporal data. If more than two time points are part of the analysis, we refer to the data as longitudinal 4D spatio-temporal. If 2D slices instead of 3D volumes are used for longitudinal analysis, the data is referred to as 2.5D and 3D, respectively. An example for longitudinal 3D spatio-temporal data is shown in Figure 2.13.
Summary. MRI is an imaging technique with a lot of different medical applications, which are also often associated with different data representations. Typically, 2D slices are acquired, which can be combined to form 3D image volumes. Similar to OCT, spatio-temporal data is also a common occurrence. However, both short-term and longitudinal spatio-temporal data are used. While both are similar in structure, the meaning of the temporal dimension is very different, which might affect deep learning-based processing methods. An overview of the presented data representations is shown in Table 2.2.