FUNDAMENTALS OF MRI:
FUNDAMENTALS OF MRI:
Author: William G. Bradley, MD, PhD, FACR
Objectives: Upon the completion of this CME article, the reader will be able to:
- Explain how different tissues have different T1 relaxation times and how this affects the overall image that is created.
- Define the meaning of TR (repetition time) and TE (echo delay time).
- Discuss the differences between T1-weighted images, proton density-weighted images, and T2-weighted images.
Physical Basis for TI and T2
T1 is the longitudinal relaxation time. It indicates the time required for a substance to become magnetized (as shown in
figure 1) after first being placed in a magnetic field or, alternatively, the time required to regain longitudinal magnetization following an RF pulse. T1 is determined by thermal interactions between the resonating protons and other protons and other magnetic nuclei in the magnetic environment or "lattice". These interactions allow the energy absorbed by the protons during resonance to be dispersed to other nuclei in the lattice.
All molecules have natural motions due to vibration, rotation, and translation. Smaller molecules like water generally move more rapidly, thus they have higher natural frequencies. Larger molecules like proteins move more slowly. When water is held in hydration layers around a protein by hydrophilic side groups, its rapid motion slows considerably (as illustrated in
The T1 relaxation time reflects the relationship between the frequency of these molecular motions and the resonance (Larmor) frequency – which depends on the main magnetic field of the MR scanner. When the two are similar, T1 is short and recovery of magnetization is rapid; when they are different, T1 is long. The water molecule is small and moves too rapidly for efficient T1 relaxation, whereas large proteins move too slowly. Both have natural frequencies significantly different from the Larmor frequency and thus have long T1 relaxation times. Cholesterol, a medium-sized molecule, has natural frequencies close to those used for MR imaging and has a short T1 when it is in the liquid state (as illustrated in
figure 3). Thus the liquid cholesterol in craniopharyngiomas appears bright on T1-weighted images.
Water in the bulk phase (for example, CSF) has a long T1 relaxation time because the frequency of its natural motions is much higher than the range of Larmor frequencies used clinically. However, when this same CSF is forced out into the periventricular white matter (as interstitial edema due to ventricular obstruction) its T1 relaxation time is much shorter
(figure 4). The T1-shortening reflects the fact that water is now in hydration layers around the myelin protein rather than in the bulk phase
(figure2). Proteinaceous solutions (such as abscesses and necrotic tumors) have a higher percentage of water in the hydration layer environment and thus have a shorter T1 when compared to "pure" aqueous solutions like CSF.
Subacute hemorrhage has a shorter T1 than brain tissue. This reflects the paramagnetic characteristics of the iron in methemoglobin. T1-shortening is produced by a dipole-dipole interaction between unpaired electrons on the paramagnetic iron and water protons in the solution. The short T1 allows subacute hemorrhage to recover longitudinal magnetization very quickly relative to brain. Thus, subacute hemorrhage will generally appear brighter than brain (as illustrated in
figure 5). The same dipole-dipole mechanism accounts for T1-shortening that is seen with the MRI contrast agent, gadolinium
T2 is the "transverse" relaxation time. It is a measure of how long transverse magnetization would last in a perfectly uniform external magnetic field
(figure7). Alternatively, it is a measure of how long the resonating protons remain coherent or precess (rotate) "in phase" following a 90°
RF pulse. T2 decay is due to magnetic interactions that occur between spinning protons. Unlike T1 interactions, T2 interactions do not involve a transfer of energy but only a change in phase, which leads to a loss of coherence.
T2 relaxation depends on the presence of static internal fields in the substance. These are generally due to protons on larger molecules. These stationary or slowly fluctuating magnetic fields create local regions of increased or decreased magnetic fields, depending on whether the protons align with or against the main magnetic field (as discussed in Fundamentals of MRI – Part I). Local field non-uniformities cause the protons to precess (rotate) at slightly different frequencies. Thus following the 90°
pulse, the protons lose coherence and transverse magnetization is lost. This results in both T2* and T2 relaxation.
When paramagnetic substances are compartmentalized, they cause rapid loss of coherence and have a short T2* and T2. For example,
figure 8 illustrates that the magnetization induced inside a deoxygenated red blood cell is greater than in the plasma outside the red cell because the intracellular deoxyhemoglobin is paramagnetic. This compartmentalization of substances with different degrees of induced magnetization leads to magnetic non-uniformity with shortened T2*, causing the free induction decay (FID) to decay more rapidly. Since gradient echo images are essentially rephased FID images, this also leads to signal loss on gradient echo images. Thus acute and early subacute hemorrhage (containing deoxy and intracellular methemoglobin, respectively) appear dark on T2-weighted gradient echo images. The different magnetic field inside and outside red cells results in rapid dephasing of water protons diffusing across the red cell membrane in an acute hematoma with secondary T2-shortening and loss of signal (as seen in
As the natural motional frequency of the protons increases, T2 relaxation becomes less and less efficient and T2 prolongs. Rapidly fluctuating motions (such as in liquids) average out so there are no significant internal fields and there is a more uniform internal magnetic environment. The hydration-layer water in brain edema has a shorter T1 than bulk phase water like CSF, yet the motion of the protons in brain edema is not so slow that T2 relaxation is efficient, so T2 remains long. This accounts for the intense appearance of the vasogenic edema associated with brain tumors on T2-weighted MR images
An MR pulsing sequence involves acquisition of multiple spin echo signals. For a 256 x 192 image (pixels in the frequency direction x pixels in the phase direction) with two excitations, 384 separate spin echoes are acquired. During the time between acquisitions, the longitudinal magnetization recovers or "relaxes" along the z-axis. Longitudinal recovery is identical to the process of initial magnetization when the body was first placed in the magnet. When the body is in the magnet, the "equilibrium state" is that of full magnetization. Therefore, longitudinal relaxation represents the recovery of magnetization along the z-axis, which occurs between spin echo acquisitions.
In the first step of a spin echo pulsing sequence, a 90°
RF pulse flips the existing longitudinal magnetization from the z-axis 90°
into the transverse xy-plane. Whenever transverse magnetization is present, it rotates at the Larmor frequency and induces an oscillating MR signal in a receiver coil (as discussed in Fundamentals of MRI – Part I). The magnitude of the transverse magnetization after the 90°
pulse is essentially equal to the magnitude of the longitudinal magnetization which had recovered during the interval between 900 pulses. This interval is called the "repetition time" (TR) and is one of the programmable sequence parameters.
In the process of flipping the longitudinal magnetization 90°
into the transverse orientation, the longitudinal component of magnetization is totally lost and must be allowed to recover before another signal can be generated. The amount of longitudinal magnetization that is recovered depends on the rate of recovery (T1) and the time allowed for recovery to occur, which is the TR
The magnitude of the signal detected depends not only on longitudinal recovery between repetitions but also on how well the signal persists, or alternatively, on how slowly the transverse magnetization decays from its initial maximum value
(figure 12). This decay depends on the T2 of the substance. The amount of time allowed for decay to occur (the time between the initial 90°
RF pulse and the detection of the spin echo) is called the echo delay time (TE) and is another programmable sequence parameter.
Mathematically the intensity (I) of the spin echo signal can be approximated:
I = N(H)f(v)(1 - e-TR/T1)e-TE/T2
where N(H) is the NMR-visible, mobile proton density and f(v) is an unspecified function of flow. This equation indicates that the intensity of the MR signal increases as hydrogen density and T2 increase and as T1 decreases. It should also be noted that T1 and T2 influences are both subject to TR and TE, the programmable sequence parameters. Thus, the effect of the T1 and T2 relaxation times of the substance on signal intensity is subject to the specific values of TR and TE selected before the image is acquired. Only mobile protons, that is, those associated with liquids, return an NMR signal. Solids have very short T2s and thus have no significant NMR signal.
When considered in the most simplistic terms, the spin echo is a two-step process. The first step (longitudinal recovery) determines the starting intensity for the second step (transverse decay). The starting intensity reflects the relationship between T1 and TR and is ultimately limited by the proton density. The subsequent decay from this starting intensity reflects the relationship between T2 and TE. Consider the differentiation of brain tissue and CSF shown in
figure 13. At TR = 0.5 seconds, the CSF signal starts to decay from a markedly decreased initial value. Despite the longer T2 of CSF, the intensity remains less than that of brain over the range of echo delay times shown. If the repetition time TR is lengthened to 2.0 seconds, the CSF signal starts to decay from a greater initial intensity and still decays more slowly than the signal from brain. Thus the two signals will become isointense at a TE of approximately 50 msec. With a longer TE, the CSF is more intense than brain.
The difference in T1 values between brain parenchyma (shorter T1) and CSF (longer T1) can be used to enhance contrast between the two. This is important when seeking abnormalities at the brain-CSF interface. A short TR time allows a shorter T1 substance (such as brain) to recover signal between repetitions to a much greater extent than a longer T1 substance (such as CSF). The contrast in short TR/short TE sequences is based primarily on differences in T1 and are called "T1-weighted" images. Note that substances with low values of T1 have the highest signal intensity on T1-weighted images.
As the TR is prolonged, all substances eventually recover full longitudinal magnetization between repetitions and the pixel intensity becomes dependent only upon proton density and is independent of T1. With short TE’s, the effect of T2 decay is minimized and one is left with an image that depends primarily on differences in proton density, that is, a "proton density-weighted" image.
Substances with longer T2 times will generate stronger signals than substances with shorter T2 times, if both are acquired at the same TE and if proton density and T1 are comparable (as illustrated in
figure 12). When multiple spin echoes are acquired, the signal strength generally decreases as TE is lengthened due to increasing T2 decay (as discussed in Fundamentals of MRI – Part I). Increasing the echo delay time (TE) increases the differences in the T2 decay curves between substances, increasing the T2-weighting. Images obtained with a sufficiently long TR and TE such that the CSF is more intense than brain tissue are regarded as T2-weighted images.
A typical edematous or cystic lesion has a longer T1 and longer T2 than brain. On T1-weighted images, these lesions will appear dark (i.e. will have negative contrast). On T2-weighted images they appear bright and will thus have positive contrast. If a short TR/long TE sequence is inadvertently chosen, the tendencies towards positive and negative lesion contrast will cancel and the lesion may not be detected. In general, the strongest signal is detected from those substances with the highest proton densities (high water content), shortest T1 times (rapid recovery) and longest T2 times (slowest decay). The high signal from short T1 substances, such as liquid cholesterol
(figure 3), fat, subacute hemorrhage
(figure 5), and gadolinium enhanced brain tumor
(figure 6) is enhanced on short TR/short TE images. The high signal from long T2 substances such as mucus, late subacute hemorrhage
(figure 14), and CSF is enhanced on long TR/long TE spin echo images. The weakest MR signals come from tissues with low proton density, long T1 values (slow recovery), short T2 values (rapid decay), and rapidly flowing blood. Air, dense calcification, and cortical bone have low mobile hydrogen density. Short T2 substances such as acute hemorrhage and early subacute hemorrhage have low signal on long TR/long TE images.
To summarize: the spin echo MR signal is greatest when the T1 is short and the T2 and proton density are high; it is decreased if the T1 is long and the T2 and proton density are low. The differentiation of lesions from normal tissues can be enhanced if one is aware of the differences in the relaxation times and selects the TR and TE times accordingly.
- T1 recovery occurs exponentially with first order time constant T1 (longitudinal relaxation time), plateauing at the proton density.
- Boundary Layer Water. Water bound to protein in hydration (boundary) layers has molecular motions between the very rapid motion of pure water and the very slow motion of the protein, and thus is close to the MRI frequency (i.e. T1 is shortened).
- Liquid cholesterol in a craniopharyngioma appears bright on a T1-weighted image due to a short T1.
- Interstitial edema. When CSF is forced through the ependyma into the periventricular white matter, it is adsorbed to myelin protein in hydration layers, shortening its T1 and increasing its signal intensity.
- Subacute hemorrhage appears bright in these subdural hematomas due to the short T1 of paramagnetic
- Enhancing metastasis appears bright on a T1-weighted image due to a short T1 of paramagnetic gadolinium (the MR contrast agent).
- When a magnetized sample is exposed to a radiowave at a specific (Larmor) frequency, the sample "rings" or "resonates", send out radiowaves of the same frequency. The more magnetically homogeneous the environment of the sample, the longer the sample rings (i.e. the longer the T2).
- Magnetic susceptibility effects in hemorrhage. While the red cells are intact, the presence of paramagnetic substances inside causes T2 shortening. Oxyhemoglobin (hyperacute hemorrhage) is not paramagnetic and does not have a short T2. Deoxyhemoglobin (acute hemorrhage) has four unpaired electrons which makes it less paramagnetic than Methemoglobin (subacute hemorrhage) with five.
- Acute hemorrhage appears dark on a T2-weighted image due to its short T2 relaxation time.
- Long T2 vasogenic edema appears bright on a T2-weighted image such as FLAIR.
- T1 recovery vs. repetition time TR. The shorter the T1 or the longer the TR, the greater the signal intensity.
- T2 Decay. Substances with long T2s decay more slowly than those with short T2s. The differences between the two are enhanced at long echo delay times (TE) on a T2-weighted image.
- Differentiation of Brain and CSF. During T1 recovery, brain recovers signal more rapidly than CSF due to its shorter T1 relaxation time. If this recovery is stopped at TR=0.5sec (T1-weighted image), brain starts to decay from a relatively greater signal than CSF, whereas if 2 seconds are allowed for T1 recovery (TR), CSF almost catches up with brain and the two start to decay from similar intensities. During T2 decay, brain decays more rapidly than CSF due to its shorter T2. With a
short TR of 0.5 sec, brain will remain brighter than CSF up to TE 75 msec, however, at a TR of 2.0 sec, CSF becomes brighter than brain at about TE 50
- Late subacute hemorrhage has the greatest signal of any naturally occurring substance due to its short T1 and long T2.
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- Bradley WG, Crooks LE, Newton TH. Physical principles of NMR. In Newton TH, Potts DG, eds. Advanced Imaging Techniques, Vol II. (Clavadel Press: San Francisco 1983), 1562.
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Dr. William Bradley currently is the director of the Magnetic Resonance Imaging Center at Long Beach Memorial Medical Center, in Long Beach, California. He is also a Professor of Radiology at the University of California, Irvine. He actively teaches Magnetic Resonance Imaging to medical students, Radiology residents and fellows in Radiology.
Dr. Bradley has over 100 publications in peer-review journals and is actively involved in research in the filed of Magnetic Resonance Imaging. He has presented his research and has given lectures on MRI topics at major conferences around the country as well as internationally, including Europe, Japan, and India.