In the most common case, a single data collection period does not suffice for complete spatial encoding: the signal is not usually present long enough to fully measure its position. As a consequence, in the typical MR imaging process, these three steps must be repeated often. Many MR examinations require more than 1000 repetitions to achieve reasonable image quality. Loosely speaking, the RF excitation results in longitudinalde-magnetization of the sample. Because, as we will see below, the magnetization process is itself slow, the rate at which the process may be repeated is itself limited: the strength and character of the NMR signal change as the repetition time is decreased. Since the early days of MRI, techniques have been developed which reduce the time needed for each component of the scanning process. Before addressing speed up methods, though, we will first want to examine each of the processes in MR imaging in somewhat greater detail.
So-called "permanent magnets" are recognized by two main properties: the directive property causes two magnets (for example the earth and a small magnet in a compass) to align with each other in a preferential fashion. The second attractive property is familiar in the tendency for magnets to attract certain other materials, such as iron and some metal alloys. This attractive nature is quite different from, say, gravity, which attracts any objects regardless of chemical nature. For now, we will deal primarily with magnet's directive property. Conventionally permanent magnets are said to have two poles, labeled North and South, to correspond to the direction of the magnetic field of the earth. The North pole of one magnet will seek the South pole of a neighboring magnet. The forces between magnets are interesting in themselves, but for our purposes the most useful aspect of magnets, discovered in 1819 by Oersted, is this: the motion of electrically charged particles (that is current ) results in magnetic force. Electrons, for example, moving from one point to another result in the generation of a magnetic field orthogonal to their direction of motion. Remarkably, this force is completely reciprocal: a magnetic field which is changing in strength or direction results in an electrical force (voltage difference), such that electrons in a conductive material will move from one place to another. This behavior of electricity and magnetism is as fundamental as gravity (and at least as difficult to understand in a satisfying manner.)
Matter, as we understand it, consists of three primary constituents: electrons, protons and neutrons, which together make up atoms and molecules. Two of these, electrons and protons, are electrically charged, and all are in constant motion. The electrons, according to this model of the atom, orbit a nucleus made of protons and neutrons, and these nuclear constituents in turn exhibit the property of "spin." This attribute, spin, is detectable as angular momentum, which is utilized in the formation of MR images. As an analogy to the motion of other charged particles, we can consider the the angular velocity of the charged nuclei as resulting in the creation of a magnetic field. The new nuclei behave like tiny dipole bar magnets. That is, such nuclei have magnetic moments. Not all atomic nuclei, however, exhibit this behavior, while certain others adopt a much more complex relationship between spin and applied magnetic fields. For imaging purposes, though, we are interested primarily in the 1H (hydrogen) proton nucleus of the hydrogen atom, and we will consider the proton in this text to the exclusion of the other NMR active nuclei (including 7Li, 13C, 17O, 19F, 23Na), What of the electrons? These particles carry charge of the same magnitude (though opposite sign) of the proton, and orbit the nucleus at tremendous velocity. As a result, they too create a magnetic field which is in fact much greater than the nuclear field. Parallel to the phenomenon of nuclear magnetic resonance (NMR), there exists electron spin resonance (ESR). Although ESR is a relatively larger effect than NMR, its energy levels are too large to allow ESR to be used practically as a clinical imaging modality. Later in this paper we will address the magnetism of the electron again as it relates to "chemical shift"; our true topic, though, is nuclear magnetism.
between any two such states is related to a light frequency, 
, by Planck's constant, h:
The strength of a magnetic field is measured in units of gauss or Tesla (abbreviated, T). One Tesla is equal to 10,000 gauss. As a point of reference, the magnetic field of the earth is about 0.5 gauss, whereas small refrigerator magnets may have magnetic field strengths of several hundred, or even several thousand, gauss. When protons are placed in a 1.5 Tesla (15,000 gauss) magnetic field, the energy difference between the two allowed quantum states corresponds to a frequency difference of about 63 million cycles per second (MHz), or an energy difference of only 0.006 calories/mole. This frequency difference between high and low energy states will show up again and again in our discussion of imaging systems. Rather than derive this frequency difference from the quantum energy differences, we ordinarily use the simple formula known as the Larmor relation:
where 
L is the Larmor frequency in Hertz, 
is the Larmor constant for the nucleus of interest (e.g., protons) and B0 is the strength of the magnetic field. For protons, is equal to about 42 MHz/Tesla. This important, even central, relation shows us that the frequency difference between high and low energy states is linearly dependent on the magnetic field: double the magnetic field strength and the frequency doubles as well.
Because the energy difference between alignment with, or against, an applied magnetic field is quite small, it is reasonable to expect the number of protons in the two states to be similar. The energy differential is significant, however, and, at equilibrium and room temperature in a 1.5 Tesla magnet, the ratio between the number of nuclei in the higher and lower energy states about .99999 to 1; for every one million protons, there will be about 10 more in the lower energy, than in the higher energy state. This small excess of protons in the lower energy state gives the ensemble of protons a small net magnetization, and it is this small magnetization which is utilized to form MR images. By convention, the sample magnetization is denoted by the letter, M1. Fortunately there are a great number of protons in a small volume of tissue. One cubic centimeter of water, for example, contains about 6.7x1022 hydrogen atoms (and therefore the same number of protons). Even the very small difference in the number of high and low energy protons in our 1.5 T magnet therefore results in 6.7x1015 excess low energy protons. This number is sufficiently large, by the way, that it is seldom useful to consider the magnetization state of any individual proton.
When a patient or sample is first placed within an imaging magnet, the magnetic orientation of the protons is essentially randomly disposed between the low and high energy states. The change to the equilibrium, magnetized condition is not instantaneous, however. Collisions between protons and their environment happen randomly and, depending upon the immediate environment of the proton, may take some time to occur. Because the un-oriented state is far from equilibrium, the initial approach to that equilibrium is rapid. As an excess of low energy nuclei accumulates, however, the approach slows. Figure 1 shows the approach to magnetic equilibrium of an initially unmagnetized sample. In this graph, a value of 1.0 for M0 represents equilibrium magnetization, and the time is shown in seconds.
The rate constant with which the sample goes from an unmagnetized to a magnetized state is known as T1, and the curve shown in Figure 1 is described mathematically by the formula:
In general, the shorter the T1, the more rapidly the sample will reach its equilbrium magnetization (or will become "magnetized"). According to equation 3, when we place the sample into a magnet (i.e. when t=0), ML will be zero. As t increases, so does ML. If we wait long enough (as t approaches infinity), the magnetization ML approaches its final value, M0.
To summarize: In a field-free state, the magnetic orientations of atomic nuclei are directed randomly. Once placed into a magnetic field, these nuclei settle into their preferred orientation and the sample becomes magnetized. The transition from an unmagnetized, to a magnetized, state requires some exchange of energy, and as each nucleus flips from higher to lower energy conditions, one quantum of energy is exchanged. In general, the process of magnetization is exponential: initially it is rapid, but slows as the system nears equilibrium. The rate at which a sample becomes magnetized is controlled by a quantity known as T1.
T1 is a property of the sample and depends upon the availability of energy at the appropriate level to facilitate the flipping of individual nuclei between their two energy states. When very little energy of the correct level is available, T1 can be very long. At absolute zero (-273° Centigrade) no molecular motion takes place and T1 approaches infinity (as mentioned, about 1025 years). Remember from equation 1 that we are looking for energy corresponding to a particular frequency. In general, in biological systems, the energy exchange will be from kinetic (i.e., motional) energy, to a change of magnetic state. This motional energy comes, in turn, from random displacements of atoms and molecules in the environment of the nucleus and consists largely of rotational and translational components. Temperature is a reflection of the kinetic energy of matter. As the temperature increases, so does the motion of molecules. Furthermore, smaller molecules suffer a great deal more motion than larger ones. Water, being a very simple molecule, rotates quite rapidly, whereas large hydrocarbon molecules, such as lipids, move much more slowly and macromolecules such as large proteins are not battered around a great deal at body temperatures.
The frequencies associated with the primarily rotational motion of water are too high to effectively facilitate the magnetic energy exchange of protons in practically achievable magnetic fields. For this reason, the T1 times for water are quite long, on the order of two seconds in magnets from 0.2 to 2.0 T. On the other hand, physiological lipids move more slowly than water molecules and thus contain substantial kinetic energy in the frequency range from 10 to 100 MHz associated with these field strengths. As a consequence, the T1 times of fat are relatively short, on the order of several tens of milliseconds. Fat magnetizes far more rapidly than does water. For molecules much larger than fat, such as structural polypeptides, the motional frequencies become lower. Such large molecules too, contain very little energy in the required range, and, as a consequence T1 once again becomes long.
As T1 is the single most important limiting factor in imaging speed, it is worth a moment`s reflection. The process of magnetization takes place at the subatomic level. One might intuitively expect, therefore, that it would be extremely rapid. On the other hand, that process requires the exchange of energy resulting from random collisions and is quantized - only collisions of precisely the correct energy will enable this state transition. So infrequent are such collisions that the bulk magnetization of biological materials, such as water, takes place over the course of several seconds.
L which we have seen above.We can consider each spinning nucleus as a magnetic dipole precessing about the applied magnetic field. It is convenient to consider the dipole of these nuclei to be consist of two components, a component aligned along the applied field (the "longitudinal component") and one orthogonal to it (the "transverse component") and rotating about the applied field. The direction of the transverse component is constantly changing at the Larmor rate.
The magnetic dipole of a single proton is exceedingly small. In practice it is meaningful to deal only with systems of a large number of such dipoles and to look at their combined effects. In the absence of a magnetic field, the orientations of each of the spin dipoles will be different. When a field is applied, the longitudinal axis of the proton's magnetization, for all of the protons, will be oriented in the same direction as the applied field. The transverse component, however, will be randomly directed. For each proton pointing in one transverse direction, it is reasonable to expect another to be pointed in precisely the opposite direction. As a result, when we are dealing with the large numbers of molecules present in any macroscopic sample, such as a patient, the effects of the transverse magnetization from any individual nuclear spin is going to be effectively nulled by the effect of another spin aligned in the opposite direction. When we add up the magnetic effects of the entire ensemble, the only remaining component is along the longitudinal direction.
To move our model one step closer to reality, imagine that the applied magnetic field is not completely homogeneous, but instead, that there are small variations in its strength from one point to another. The Larmor frequency of the protons in each position will therefore vary slightly. If we once again set up initial conditions such that all of the nuclear magnets are started in the same direction, this happy condition won't last. Instead, the protons initially in phase will go out of phase as individual spins precess faster than others. The time required for this to occur depends primarily on the uniformity of the magnetic field. Since the strength of the MR signal depends upon the alignment of all of the spins, we can see that the signal, initially large, will tend to decay away as the spins lose phase coherence. Figure 2 shows a graph of the magnitude of the MR signal as it decays over time from its initial maximum.
As described above with respect to T1 relaxation, the kinetics of trasnverse relaxation are well described by a simple first order exponential equation:
The decay of the signal is initially rapid, but levels off as it approaches zero. The transverse relaxation is governed by the rate constant, T2, which, like T1 is a tissue-specific property. However, the rate of signal decay in biological samples, is influenced strongly by a variety of factors extrinsic to the tissue.
The second factor, variations in tissue magnetization, is more strongly related to the tissue sample and is thus of more clinical interest. Any object, when subjected to a magnetic field, will magnetize to a degree slightly more than (paramagnetic) or less than (diamagnetic) the applied field. The relationship between the field experienced within a sample and the applied field is known as the magnetic susceptiblity, abbreviated, 
. Susceptibility is calculated as the ratio of the internal field to the applied field. Most body tissues are slightly diamagnetic and will have internal fields a few ppm less than the applied field. Air and body tissue, for example, differ in susceptibility by as much as one or two ppm. Thus, at the interface between tissues, relatively large gradient in magnet field may exist over the distance of one millimeter or less. As a consequence, proton spins in this region will dephase very rapidly as compared to spins within homogeneous tissue.
The final factor determining transverse relaxation rates is magnetic field variation on the atomic or molecular size scale. The magnetic field experienced by a proton (and thus its resonant frequency) is influenced strongly by the presence of other diamagnetic or paramagnetic nuclei, such as other protons. Generally it is the transverse decay rate from these interactions which yields the greatest clinical information as it relates strongly to changes in intracellular structure chemical environment.
When a sample is placed in an imaging system, the apparent transverse decay rate, T2obs, results from the combined effects of macroscopic field inhomogeneity and molecular level effects. The molecular effects result in the decay time constant, T2, whereas the effects of macroscopic field variations contribute to a constant known as T2*. Not surprisingly the fastest decay process dominates and the combined effects add as their inverses:
At body temperature, water molecules tend to be in rapid rotational and translational motion. As a consequence, in a time short compared to the several tens of milliseconds needed to acquire an MR signal, these protons may move over a large distance and thus "sample" a variety of magnetic field strengths. On the average, in simple fluids, an ensemble of protons is likely to sample a sufficient variety of local magnetic fields such that the differences from one proton to the next average to zero: the T2 for simple fluids is quite long, on the order of hundreds of milliseconds. The protons on more rigid structures, such as transmembrane proteins, are strongly constrained for their motions. As a consequence there is little possibility for this spatial averaging of fields to take place. Such protons have short transverse decay times.
In part because of this strong dependence of transverse relaxation rate on averaging (or sampling) of varying magnetic fields, this rate has a strong temperature dependence. Generally at lower temperatures molecular motions are reduced and the decay times become quite short, whereas at higher temperatures, decay times become longer. Contrasting T1 and T2 effects, note that T1 is shortest at the particular temperature corresponding to motion facilitating the state transition between low and high energy states. There is therefore some temperature where T1 is at its mininum. The T2 times of most samples increase with temperature.
All of the above discussion of T2 has depended upon the idea that we can somehow cause the nuclear spins to begin to precess "in phase", but we have not yet considered how to create this condition. The process by which this is done in clinical scanners is known as nuclear induction and the experiments which first demonstrated the phenomenon were performed in 1946 by Felix Bloch (Bloch 1946; Bloch, Hansen et al. 1946). Conceptually, the process is this: taking advantage of the fact that the nuclear magnets will precess about an applied magnetic field, we simply apply a second field (the B1 field) orthogonal to the main magnetic (B0) field in such a way as to force the spins to precess simultaneously about both fields. Because, however, the nuclei are already spinning at the Larmor frequency, our B1 field must also be forced to rotate at the Larmor rate such that it is constantly oriented in the present transverse direction of the nuclear dipoles. For the typical NMR experiment, in a magnetic field, of, for example, 0.2 to 2.0 Tesla, the Larmor frequency is in the range of 10 to 100 MHz. Time varying magnetic fields of this range are known as radio frequency, or RF fields. Thus, applying a short duration, time-varying magnetic field in the imaging system is known as applying an RF pulse.
