Relaxation: T2 & T2*
Burkhard Mädler1
1Philips Precision Diagnostics, Hamburg, Germany

Synopsis

We will discuss the basic physical concepts of T2-relaxation and its distinction from T2*-relaxation, learn how to measure and quantify T2-relaxation, hear about pitfalls and challenges to access T2-relaxtion, understand what makes T2-contrast in a clinical MR-image, and brief over some fundamental clinical applications for T2-relaxation contrast (weighted T2- and T2*-contrast, quantitative relaxation time measurements).

Concept of Transverse-relaxation (T2 and T2*): Main constituent of the mammals’ body is water (about 60%-80% depending on tissue apart from cortical bone and fat). Water protons are therefore the major probe of interest in MR-imaging. MR exhibits two main relaxation principles of the macroscopic magnetization M0 after an excitation pulse: longitudinal (T1) and transverse (T2)-relaxation both mathematically described by the Bloch-equations [9]. The relaxation time T2 is the time when approximately 63% (1-1/e) of the original macroscopic magnetization M0 that has been transferred into the x-y-plane after application of an excitation pulse (Mxy) is irreversibly lost by processes due to spin-spin interaction. This process is described by an exponential decay and T2 is the time by which the actual Mxy-signal has only 1/e of its original amplitude M0. Therefore, T2 is also called spin-spin or transverse relaxation time [1,5,7]. Spin-spin interaction, in this context, refers to a process whereby the original absorbed RF-energy of protons (water) during the MR-excitation process is exchanged with other protons in the near vicinity. In contrast to T1-(longitudinal) relaxation, where energy is equilibrated between energized spins (summarized as macroscopic magnetization M0) and their surrounding lattice, transverse relaxation occurs between dynamically “active” molecules (fast or slow rotation, exchange, vibration). Originally, all (free) water protons have the same resonance frequency, depending on the strength of the main static magnetic field B0 (e.g. 42.6 MHz/Tesla). After an excitation pulse, they precess with this same frequency (Larmor frequency w0) and exhibit the same constant phase. Due to molecular interactions (in the same molecule or between different molecules) and motion of those water protons (translation, rotation, vibration, tumbling), the microscopic “snapshot” of their surrounding magnetic field will slightly vary, causing a magnetically fluctuating field and therefore a phase dispersion that leads to signal decay (lower B0 -> lower w0 -> phase moves behind, higher B0 -> higher w0 -> phase moves forward). The concept of correlation times t of such molecular motions describes in more depth the efficacy onto the T2-relaxation process [7] and is covered in the BPP-theory (Bloembergen-Purcell-Pound) [4,7,10]. It works well in pure substances but less in complex biological systems such as the human body. As time progresses, the transverse phase coherence will completely disappear while at the same time the macroscopic magnetization in the longitudinal direction (Mz) is rebuilt (T1 relaxation). The dephasing process T2 is always faster or at least equally fast compared to the T1-relaxation process: T2<T1 [1,30]. In reality, while imaging relatively large-size and complex biological objects, we have a combination of several factors that cause the loss of transverse coherence and hence transverse magnetization signal decay on even faster scale than T2. We will name this the total relaxation time T2* [1,5]. The main contribution is from the process of spin-spin interaction inside the proton-system (intrinsic process) described above. Others are non-uniformities of the magnetic field at the location of our imaging scope (extrinsic factors) such as [5]: - main field inhomogeneity over the imaging volume or field of view caused by imperfections of the magnet design or interference from surrounding material (wall studs, mounting bars and shields, large iron constructions nearby, passing trains or trucks); This effect is usually constant or with slow variation over the time of measurement. - sample-inherent inhomogeneities due to magnetic susceptibility, a physical property of almost all matter to change the penetrating magnetic field due to magnetic polarization. This behaviour also causes static magnetic field gradients on boundaries between different tissue (air-water-blood-fat-bone-interfaces); The effect is present as long as the imaging object resides in the MR-scanner (B0-field). - effect of the imaging gradients that are needed for image localization and other purposes (flow compensation, diffusion gradients, crusher and de-phaser gradients) as well as their influence on the magnet itself (eddy currents, temperature change of gradient coil and surrounding material cause a shift in B0); They are time varying and transient during the measurement. Their influence on T2 can be almost eliminated due to clever pulse programming and deliberate magnet- and gradient-manufacturing design. The combination of intrinsic and extrinsic processes leads to a more complex expression of transverse relaxation. The total, overall or effective relaxation rate R2*=1/T2* is the summation of internal (R2) and external (R2’) relaxation rates, caused by the according processes mentioned above: R2*=R2+R2’ or 1/T2*=1/T2+1/T2’ [5]. The external magnetic gradients are usually time independent or with a very slow time constant. Hence, this loss of transverse magnetization due to T2’ (external effects) can be recovered by application of an additional refocusing pulse (spin echo) applied with some delay after the excitation pulse [1-5]. The transverse phase dispersion is then revoked by a refocusing pulse, applied in such a way that it reverses the linear time dependent phase dispersion (180y-pulse) [1]. The T2-effect cannot be reverted and is therefore an intrinsic property of the material or tissue under investigation and a very important imaging contrast mechanism. With the elimination of T2’-effects by application of a spin-echo, the observed transverse relaxation time T2*becomes T2 and is an effective and important tissue property. Without the additional refocusing pulse we have the classic application of a gradient echo that will be prone to T2 and T2’-effects, hence measuring a T2* that is smaller than T2 (T2*<T2). Gradient echo sequences are applied when probing the internal magnetic field gradients or susceptibility properties of tissue become important, for example in functional neuro imaging (blood oxygenation level dependent BOLD-effect) [8a/b,34] , high resolution depiction of veins from arteries (susceptibility weighted imaging – SWI [29]), measure the B0-field, imaging with paramagnetic contrast agents, measuring iron or Gd depositions in the body, perfusion imaging and more. T2 and T2* as contrast mechanisms play an important role in conventional T2-weighted imaging (T2W) as well as in quantitative imaging (qT2), where the goal is to accurately measure those relaxation times and produce parametric relaxation maps [8c,21,22]. T2 (and T2*) in biological tissue are B0-field dependent but to a lesser extent than T1 [16,18]. Rule of thumb is that T2 decreases with increasing B0. Additionally, sometimes an orientation dependency of certain structures’ T2 (e.g. cartilage, muscle, white matter tracts) with the direction of the static B0-field can be observed and have to be taken into consideration [23]. The complex architecture of biological tissue adds another complication but also vast potential to the characterization of T2 in that sense that it is very often a combination of more than one relaxation time constant due to partial volume effects inside the imaging voxel (different tissue compartments on microscopic scale) and/or intrinsic multi-component behaviour of water due to exchange or association to different binding sites at macromolecules (e.g. myelin water in white matter, distinctly different water compartments in muscle or tumor tissue) [22,24]. This multi-exponential characteristic or subtle deviations from exponential decay hint at structural or dynamic heterogeneities in the voxel as well as ineffective exchange between different molecular environments and therefore contain important information about the tissue properties. They are in the focus of current MRI research and might lead to new useful clinical applications. In the further context of the presentation, we will describe the influence of T2 and T2* on image contrast and depict some clinical examples.

Acknowledgements

Thomas Amthor, Philips Research Hamburg,Germany (synthetic contrast video)
Hendrik Kooijman, Philips Germany (lecture material)
Christoph Katemann, Philips Germany (lecture material, clinical images)

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Internet sources and links:
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[31] Susceptibility: https://en.wikipedia.org/wiki/Magnetic_susceptibility
[32] Questions and Answers in MRI: http://mriquestions.com/t2-vs-t2.html
[33] Funny but nonetheless useful video about T2* on YouTube: Twinkle, Twinkle (song by Science Groove) - YouTube
[34] Functional MRI: https://en.wikipedia.org/wiki/Functional_magnetic_resonance_imaging

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)