Magnetic Resonance Imaging and Spectroscopy
4.1 Nuclear Magnetic Resonance Imaging
4.1.1 Principles of Nuclear Magnetic Resonance Imaging
Magnetic Resonance Imaging (MRI) is a powerful scientific measuring instrument that allows the non-invasive photography ofin-vivo anatomy and the quantitative evaluation of tissue properties in health and disease [185, 186]. The MRI technique is fundamen-tally based on principles of Nuclear Magnetic Resonance (NMR), which is a physical phenomenon that occurs when magnetically active nuclei are introduced into a static external magnetic field (B0). Elements that contain an odd number of protons or neu-trons exhibit an angular momentum or ’spin’ that aligns itself with the static magnetic field while oscillating at a specific resonant frequency. In simple terms, the frequency of oscillation, or ’Larmour frequency’ (ω), depends on the number of unpaired proton-s/neutrons within the nucleus and the strength of the static magnetic field. If a second external magnetic field is applied (B1), for example, by radiofrequency stimulation, the atom oscillates in the direction of the newly applied magnetic field, causing the nuclei to
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move out of alignment with theB0 field (Figure4.1). Once theB1field is turned off, the nuclei return to their pre-stimulated state in a process termedrelaxation. Additionally, the transverse component of the magnetization induces a voltage according to Faraday’s law that can be detected by a radio-frequency antenna or a receiver coil tuned to the Larmor frequency. This detected signal is the NMR signal, which exhibits decay as the net magnetization (M) of nuclei return to their state equilibrium in a process termed free induction decay (FID).
NMR was first described independently by Edward Purcell and Felix Bloch in 1946 and was initially used by physicists to study the magnetic properties of atomic nuclei [185].
As a magnetically reactive nucleus exhibits defined mass and spin that are dependent on the number of particles within the atomic nucleus, different isotopes exhibit different NMR properties. Examples of magnetically reactive isotopes include 1H, 13C and 31P.
Given that hydrogen is the most abundant nucleus in biological tissue, exhibiting strong and sensitive magnetic interactions, the NMR of protons (1H) is the most widely used technique to map properties of biological tissue. With the introduction of magnetic fields gradients in the 1970s, Paul Lauterbur as well as Peter Mansfield and Peter Grannel were able determine the spatial location of the induced signal, which served as a contrast for the reproduction of an image. By varying the parameters of radio-frequency pulse sequence, different contrasts could be generated mapping differences between tissues based on the relaxation properties of the hydrogen atoms.
Figure 4.1: Basic Physics of the NMR signal. (a) Nuclei with an odd number of protons and neutrons (e.g H1) exhibit a nuclear spin or angular momentum that aligns itself with an external magnetic field (B0). (B) When another magnetic field (B1) is applied, for example, by a radio-frequency pulse, the net magnetization vector is flipped at angle which produces two magnetization components (longitudinal and tranverse).
Once the radio-frequency pulse is switched off, T1 recovery and T2/T2* decay occur.
The figure was adapted from [185].
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4.1.2 NMR properties of biological tissue environments
In general, the term relaxation describes how signals change with time and return to baseline. In NMR, the deteriorating signal of the nuclei returning to the pre-stimulated state can be described in terms of two separate processes, each with its own time constant and relationship to the B0 component vector [185, 186]. The T1 relaxation time is the time constant that describes the recovery of 63% of magnetization along the longitudinal vector (i.e. along the axis of the B0 field). In other words, the T1 relaxation time — or spin-lattice relaxation time — represents the time taken to regain the ability to create an NMR signal. While the T1 relaxation time of cerebrospinal fluid is about 4000ms [196], it can be influenced by the microenvironment of biological tissue varying between
≈1800ms for gray matter and ≈1000ms for white matter at 3T [197].
On the other hand, theT2 relaxation time is responsible for the broadening of the signal and is the time constant that describes the deterioration of the transverse magnetization (i.e. perpendicular to the axis of the B0 field) to 37% [185, 186]. In tissue, T2 is usually much shorter that T1 by a factor of up to 1/10, as its mechanism involves the process of dephasing, or the oscillation of different hydrogen atoms at variable frequencies occurring as a result of the local magnetic field effects induced by neighboring atoms [185].
Nevertheless, another source of dephasing ensues as a result of local variation in theB0 field, which occurs mainly due to shielding of the main magnetic field by biological tissue structure variations (e.g. air tissue or bone tissue interfaces) and inhomogeneities of the magnetic field [185]. This source of dephasing causes the transverse magnetization to decay much faster than predicted by natural mechanisms and is usually represented by the T2* relaxation time. T2* describes the ’effective’ or ’observed’ T2, which considers the two sources of dephasing induced by local magnetic field effects from neighboring atoms and B0 non-uniformities.
4.1.3 NMR signal localization
Put simply, a magnetic resonance image is a representation of the NMR signal from hydrogen atoms in tissue. Initially, NMR signals were acquired from an individual ele-ment (pixel) or a column of eleele-ments in one dimension. The introduction of magnetic field gradients allowed excitation of a select set of elements, thus paving the way for the acquisition of NMR signals from a plane (ie. 2 dimensional) or volume of elements (ie.
3 dimensional) [185,186]. For example, for acquiring NMR data from an axial slice, a magnetic field gradient is placed perpendicular to the slice (ie. in the z-direction, head to foot), before a radio-frequency pulse (B1) with a narrow frequency range is applied to stimulate the plane (Figure 4.2). As a result, only those nuclei in the slice in which the
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range of frequencies are available would be excited, thus allowing the spatial encoding of hydrogen atoms in a specific plane where they are isolated from neighboring regions.
However, this slice selective excitation strategy provides spatial resolution in one direc-tion. Imaging a plane can be accomplished by using a second gradient field, which is turned on following theB1pulse, causing nuclei to resonate differently along the gradient, i.e. they are spatially encoded in a second dimension. To obtain the third dimension, phase encoding gradients are applied for a limited time before signal acquisition. The phase encoding gradient modifies the spin resonance frequencies of the nuclei, in which the magnetization of external elements (voxels) will precess either faster or slower com-pared to the central element. The change in the frequency of precession changes the phase of the signal relative to the signals from neighboring positions. Repeated phase encoding directions can thus be used to determine the location of the precessing spins to create a three-dimensional image.
Figure 4.2: Selective excitation of an image slice by applying a shaped RF pulse and field gradient at the same time. Adapted from [185,186].
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4.1.4 Pulse sequence design
An MRI pulse sequence is a programmed set of changing events related to magnetic field gradients, radio-frequency pulses and signal readout periods [185,186]. Careful optimiza-tion of sequence parameters and the order of events is key in emphasizing specific tissue characteristics and generating different types of tissue contrast. Signals are typically collected when the NMR signal exhibits its strongest most coherent ’echo’. The time between the application of the radiofrequency excitation pulse and peak signal induced in the coil is generally referred to as the Echo Time (TE). As radio-frequency pulses are usually applied at specific intervals to excite different elements, the time between successive radio-frequency pulses, referred to as the Repetition Time (TR), is also an important parameter in emphasizing specific tissue characteristics. For example, a long TR allows the protons in all of the tissues to relax back into alignment with theB0 field.
At short TR, on the other hand, the protons do not fully relax back into B0 alignment before the next measurement is made, thus decreasing the signal from tissue.
Two types of conventional pulse sequences that are used to generate echoes are Spin echo (SE) and Gradient Echo (GRE) (Figure 4.3) [187]. SE sequences are the most commonly used pulse sequences. After a 90◦ radio-frequency pulse is applied, precessing nuclei usually go out of phase. In SE sequences, a 180◦ refocusing pulse is applied to reverse phase shifts that occur due to static field inhomogeneities and chemical shifts.
Since the nuclei that now have a large negative phase are still oscillating at the same rate of decay, they begin to catch up with each other to go back into phase generating the peak echo signal. On the other hand, GRE sequences differ in that their flip angles are usually below 90◦and also lack a 180◦radio-frequency refocusing pulse. Utilizing low-flip angle excitation leads to more pronounced signal decay of the magnetization vector, thus allowing shorter TR/TE, shorter scan times and generation of new tissue contrasts.
4.1.5 Image reconstruction
To generate an actual image from an NMR signal, data is sampled multiple times mea-suring a large number of echoes to build the signal-to-noise ratio. The measured NMR signal is encoded in k-space which is a mathematical construct consisting of a matrix onto which frequency and phase data is mapped [185]. Typically, frequency and phase information are mapped along the x- and y-axis, respectively. To put this into per-spective, in a conventional SE sequence, one echo generates one line of data in k-space corresponding to a single phase-encoding step. Although information at the peripheral parts of the k-space matrix contain fine details with high spatial-resolution, they exhibit low-image signal. On the other hand, central elements in the matrix contain high-signal
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Figure 4.3: Conventional MRI pulse sequence diagrams(A) Spin echo and (B) Gradient Echo pulse sequence diagrams. Adapted from [187]
information, though at lower resolution. Typically, a pulse sequence is designed in a way to maximize the signal-to-noise ratio to achieve an image with fine detail and good contrast. Frequency information within k-space is then rendered into image space using Fourier transform decomposition (Figure 4.4).
Figure 4.4: MR image reconstruction from k-space. Plot of the k-space of aT1 weighted MRI image of a pineapple. The image was reconstructed from all the spatial frequences of k-space using inverse fourier transformation. Data was acquired by the
author.
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4.1.6 Encoding physio-chemical properties in images
In general,T1,T2 and hydrogen distribution (also known as Proton Density), in addition to the adjustable parameters TE and TR are all considered to ultimately achieve a particular tissue contrast (Figure 4.5) [187]. Different tissues have different T1 and T2 times and as such they will exhibit different amplitudes of free induction decay depending on the TR and TE parameters. Since white matter tissue has a shorter T1 (≈1000ms at 3T) than gray matter (≈1800ms at 3T) and cerebrospinal fluid (≈4000ms at 3T) [196, 197] it recovers its longitudinal magnetization faster after the application of the radio frequency pulse, and thus generates a stronger NMR signal [187]. A stronger longitudinal magnetization leads to a stronger transverse magnetization and stronger signal on the next pulse. Therefore, a shorter TR emphasizes the difference between tissue with different T1 relaxation times, such that tissues with short T1 (e.g. white matter) will exhibit stronger a signal and a higher intensity on the reconstructed image, whereas tissues with longT1relaxation times (e.g. cerebrospinal fluid) will exhibit smaller signals and appear darker. As grey matter has an intermediate T1, it will produce a moderate intensity thus accentuating the difference between the cortex and white matter. Images that emphasize differences based on the T1 relaxation times are designated T1-weighted images.
On the other hand, T2-weighted images are dependent on TE values [187]. Since white matter has a shorter T2 than cerebrospinal fluid and loses its transverse magnetization more rapidly, making the TE longer allows for the transverse magnetization to decay more thus emphasizing differences based on T2 relaxation times [187]. In T2-weighted images, tissues with shorter T2 times will appear darker, while tissues with longer T2 times appear brighter. If TE is short and TR is long, neitherT1 nor T2 tissue differences are emphasized. Such an imaged is labeled as a Proton Density (PD) image since it emphasizes the differences in the distribution of hydrogens within tissue. PD images provides good contrast between gray (bright) and white (darker gray) matter, with little contrast between tissue and cerebrospinal flui. Pathological processes, such as demyeli-nation or inflammation, often increase water content in tissues, which (a)decreases the T1-weighted signal such that pathological white matter appears darker;(b)increases the T2-weighted signal such that pathological white matter appears brighter making subtle changes easier to detect; and (c) increases the PD signal such that white matter also appears brighter. In general, T1,T2 and PD weighted images provide good contrast and are commonly used to segment different tissue and non-tissue classes.
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Figure 4.5: The relationship between TR/TE and the encoding of physio-chemical tissue properties as image contrasts. Adapted from [187].
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