T ₁ relaxation is the process that is responsible for recovery of longitudinal magnetization after excitation by an rf pulse. Since longitudinal magnetization is defined by the difference of spins in parallel and antiparellel orientation, it is related to the energy of the spin system and the corresponding relaxation is the recovery from an excited state back to thermal equilibrium through loss of energy. This is an exponential process (see Fig. 3) that is characterized by the time constant T ₁ (see Note 5). The full range of relaxation occurs after an inversion pulse with a zero passage at (inversion-recovery experiment). Almost complete recovery after maximum signal generation by a 90° pulse that leaves no longitudinal magnetization (the so-called saturation-recovery experiment) is achieved after ca. 3T ₁.

Exchange of energy occurs with the neighbouring nuclei and molecules that are sometimes summarized in the generalized term “lattice” (see Note 6). T ₁ relaxation is therefore also called spin–lattice relaxation. The source of the relaxation process is the fluctuating fields caused by the sum of the fields attributed to surrounding electrons and nuclei. The detected nuclei experience an oscillating field due to molecular tumbling. If the spectrum of the fluctuations caused by the surrounding molecules contains components at the NMR resonance frequency ω (ca. 50–500 MHz) or 2ω it can absorb energy from the detected spin system and therefore drive the system back into its thermodynamic equilibrium. Components contributing at 2ω are actually weighted four times as much as components at ω (2). T ₁ relaxation increases as the molecular mobility decreases but becomes very slow again for extreme conditions such as those in solids. Therefore, areas with less restriction in molecular tumbling (such as the cerebrospinal fluid) are characterized by long T ₁ values whereas tissue rich in microstructure (e.g. muscle) exhibit fast T ₁ relaxation. Some examples are given in Table 1.

Most standard MR-imaging sequences require a repetitive excitation of the magnetization because the spatial encoding is not done in a single shot (5). The raw data space from which the image is finally computed is filled up in a line-by-line scheme, thus introducing a dependence of each line’s signal intensity on the previous acquisition step. Sufficient spatial resolution often requires the acquisition of tens to hundreds of lines in raw data space and the desired acquisition time ranges from the sub-second regime to the order of several minutes or even hours. This combination yields repetition times (TR) that are on the order of T ₁ relaxation and therefore automatically allows using this effect for generation of contrast by adjusting TR properly.

A fast repetition of the pulse sequence can “saturate” the spin system (see Note 7) and therefore impair the subsequent generation of transverse magnetization to encode the image information. In contrast, very slow repetition will eliminate the relaxation influence and the differences in T ₁ between various tissues fade out, thus yielding a method to eliminate this contribution to emphasize other types of contrast.

The fact that relaxation depends on the fluctuating magnetic fields experienced by the nuclear spins introduces the opportunity to enhance natural T ₁ relaxation by introducing additional magnetic moments that influence the detected protons in water (and fat) molecules. Such magnetic moments are provided by unpaired electrons, e.g. in Fe³⁺, Mn²⁺ or Gd³⁺ ions (6). The paramagnetic effect from electron-rich systems like lanthanide complexes is especially efficient since the magnetic moment of each electron is ca. 600 times larger than that of protons. Gadolinium, e.g. has seven unpaired electrons that alter the relaxation of adjacent protons very efficiently. The element itself is toxic and has to be made harmless by complex formation, e.g. with hydrophilic poly(aminocarboxylate) ligands. One or two coordination sites are occupied by water molecules (7) that are temporarily bound to the Gd ion and therefore experience efficient dipolar interactions with the electron spins. Such interactions fall off rapidly with increasing distance but water molecules in the inner hydration shell of these complexes are also affected to some extent by relaxation effects.

Such complexes influence both T ₁ and T ₂ relaxation but the dominant effect is shortening the slower longitudinal relaxation. Gd chelates therefore cause bright signal contributions in T ₁-weighted MR images (so-called positive contrast). This can be used to increase contrast between two types of tissue or allow retaining contrast while speeding up the acquisition by using shorter repetition times. The effect can be amplified even more by “adjusting” the correlation time of such molecules: macromolecular contrast agents have a higher relaxivity due to their reduced tumbling rate and can therefore be detected at lower concentrations (see Note 8). In any case, this type of contrast agents only affects areas where it is directly accessible since the water needs to get close to the paramagnetic centre.

Since there is no way to reduce the number of fluctuating magnetic moments in tissue, a reduction of T ₁ relaxation can only be achieved by reducing the matching frequency components in the above-mentioned range of fluctuations. By increasing the field strength B ₀ of the scanner system, the resonance frequency of the detected water molecules is shifted against the fixed spectrum of field fluctuations due to molecular motion. Resonant contributions are less pronounced and T ₁ relaxation times increase when switching from standard clinical field strengths of 1.5–3 T to modern high-field scanners of  7 T or more (8).

Several experimental setups require a certain temporal resolution for consecutive imaging or are subject to other constraints that determine an upper limit for the total acquisition time. Since longitudinal relaxation is a property of the tissue that can be manipulated by contrast agents only to some extent, choice of the suitable imaging sequence can depend on the speed of the encoding scheme. The total acquisition time is given by the product of the repetition time (TR), the number of phase encoding steps (N _ph) and the number of acquisitions (N _aq; see Note 9):

For some applications, it is therefore necessary to use sequences that achieve the desired contrast even for relatively short TR, i.e. acquisition schemes that minimize the disturbance of the longitudinal magnetization.

It should be mentioned at this point that T ₁ relaxation of protons is relatively favourable for most in vivo applications (see Table 1). Other nuclei such as ³¹P have longer relaxation times (9) (see Note 10). Given the fact that the relative sensitivity for such nuclei is much smaller (see Note 11), small flip angle excitations often yield insufficient signal and the required 90° excitation is then related to very long TR or substantial saturation effects. This aggravates the problem for many nuclei other than ¹H to collect MRI datasets in a reasonable amount of time.

The signal strength induced by the precessing transverse magnetization depends on the phase coherence among the different spin packages. Loss of this coherence is called transverse relaxation. The amplitude of the vector sum of all magnetizations is decreasing exponentially with a time constant T ₂ (Fig. 4a, b). The process is also called spin–spin relaxation and is not related to loss of energy (like T ₁ relaxation). Compared to longitudinal relaxation, this process occurs more rapidly because additional mechanisms contribute. Microscopic processes such as interactions with the local magnetic fields of neighbouring nuclei are governed by the molecular tumbling rate and the spectral density of different tumbling modes. Transverse relaxation is influenced by spectral components at ω, 2ω (less weighted than the previous one) and low-frequency components (intermediate weight) (2). Rapid motion causes averaging of spin–spin interactions over time and makes such processes less efficient, thereby slowing down T ₂ relaxation. Relaxation times for free water molecules are therefore relatively long (ca. 3 s and are mostly independent of the magnetic field strength) whereas T ₂ values for macromolecules bound to cell membranes are on the order of a few microseconds only. In the latter case, relaxation is more efficient because of the longer “contact time” between molecules. Skeletal muscle tissue is an example for tissue with relative short T ₂ values (see Table 1).

Very rapid T ₁ relaxation usually does not impose a problem (in fact, it is sometimes desired and generated with suitable contrast agents); however, extensive T ₂ relaxation can impede acquisition of sufficient signal intensity even for short echo times. The scanner hardware is limited in terms of arbitrarily fast pulse sequences due to minimum times for switching the rf and gradient pulses on and off. Hence, some nuclei with very short T ₂ (e.g. sodium or even protons in case they are in a macromolecular environment) are hard to detect and give only small signal contributions.

Loss of phase coherence between the different magnetizations within a sample happens not only as an intrinsic process in terms of spin–spin interactions, it is also a consequence of local field inhomogeneities ΔB that cause small differences in precession frequencies of different spin packages. This process therefore enhances transverse relaxation. It is called T ₂* relaxation and happens on a timescale faster than pure T ₂ processes. T ₂ and T ₂* relaxation rates, i.e. the inverse of the relaxation times, are linked through the following equation:

Since we deal with the sum of the rates, the differences between T ₂ and T ₂* are less pronounced for fast-relaxing tissue for a given field inhomogeneity. In general, imperfections of the magnetic field increase with the distance from the centre of the magnet (the so-called iso-centre or sweet spot; see Note 12). Inhomogeneities can also be caused by exogenous para- or ferromagnetic material (see Note 13).