T1: Longitudinal Relaxation Time Mohammad Reza Nazem-Zadeh Milad Seyfi Physical basis of T1: A hydrogen atom placed inside a static magnetic field B Nucleus spins assume two different states: parallel & antiparallel Vector M has two components longitudinal component (parallel to B) transverse component (perpendicular to B) Under equilibrium conditions, M is parallel to B transverse component is zero longitudinal component assumes equilibrium value M0 RF Excitation By a radiofrequency (RF) pulse with protons’ Larmor frequency, energy is absorbed A certain number of spins assume energetically higher state, leaving equilibrium conditions. A rotation of M by a certain angle in classical view M has a non-zero transverse component which rotates around B with Larmor frequency producing a signal Longitudinal component of M is reduced and assumes a value between −M0 and +M0. Relaxation phenomenon Consists of two simultaneous processes, transverse and longitudinal relaxation. transverse process causes an exponential decay of transverse magnetization longitudinal process causes a change of longitudinal magnetization towards equilibrium value M0 Bloch equations : time constant T1: longitudinal relaxation time exponential change of Mz towards equilibrium value M0 Physical basis of T1: A special case: Inversion recovery curve: describes time course of Mz after a full spin inversion so Mz(0) = –M0 (5.3) inversion time TI: time interval between spin inversion and measurement. As an example, Figure 5.1 shows an inversion recovery curve for a T1 of 1 s. Biological basis of T1: T1 relaxation time depends on physical properties and microstructural composition of underlying tissue, related to (a) the free water content (prolongs T1) Cerebrospinal fluid (CSF) has a longer T1 than cerebral WM and GM due to high water content. (b) concentration and types of macromolecules such as myelin (reduce T1) T1 in WM is shorter than in GM, mainly due to larger proportion of myelin thus smaller water fraction in WM (c) iron content (reduce T1) Biological basis of T1: Comparing T1 values across different MR systems may be biased by (variable with) several parameters such as hardware used or subject age. How to measure T1: Gold standard: The inversion recovery technique T1 quantification via inversion recovery (IR) technique several measurements performed, each of which comprises spin inversion, a subsequent delay TI, spin excitation and signal readout By varying TI, IR curve as given in Equation 5.3 is sampled, so T1 can be obtained via exponential data fitting The problem: equilibrium conditions have to be attained before each single experiment, requiring a full spin relaxation before each spin inversion Full T1 measurement is time-consuming How to measure T1: How to measure T1: IR-based gold standard techniques for measuring T1 usually employ spin echo (SE) imaging with integrated spin inversion Typical durations are 13 min for a single-slice measurement In-plane resolution = 2mm Slice Thickness = 5mm Alternatively, spectroscopic signal acquisition shown in Figure 5.2 can be converted into an imaging experiment via replacing it by an echo-planar imaging (EPI) module A single-slice measurement has a total duration of about 5:30 min an isotropic resolution of 3 mm 15 different TI values ranging from 100 ms to 5000 ms relaxation delay of 20 s before each inversion These relatively long durations stress the need for fast T1 mapping techniques. The Look-Locker technique: Originally designed for use in MRS The idea: to measure T1 during one single T1 relaxation process after inverting magnetization, a series of excitation pulses with a small tip angle 𝛼 and an intermediate repetition time TR is sent. Each pulse tilts the magnetization, creating a transverse magnetization and thus a signal that is proportional to current value of longitudinal magnetization Mz The Look-Locker technique: The signal series samples relaxation curve Mz(t) with a temporal resolution of TR, so T1 can be obtained via exponential fitting Problem: Excitation pulses distort free relaxation curve. effective relaxation curve (black) differs from unperturbed case (red) and has a nonexponential behavior. The Look-Locker technique: Mz approaches a saturation value M0* < M0 with a modified relaxation time T1* < T1, where T1* and M0* are given by the following : Exponential fitting of sampled curve yields T1* T1 can be obtained via Equation 5.4b, provided 𝛼 is known. The Look-Locker technique: Look-Locker (LL) concept is applied by acquiring a series of spoiled GE images after spin inversion. Each GE image acquisition irradiation of a series of excitation pulses with TR and 𝛼 acquisition of a GE for each excitation Acquisition time must be shorter than T1,* so relaxation curve can be sampled with sufficient temporal resolution. TR is relatively short and number of phase encoding (PE) steps is limited unless more advanced techniques are used The Look-Locker technique: The TAPIR sequence (Shah et al., 2001) Based on LL concept Allows multislice T1 mapping with high spatial and temporal resolutions Short acquisition time due to use of a banded k-space data collection scheme, acquiring three gradient echoes with different PE per excitation pulse A duration of 6:44 min has been reported for the acquisition of a T1 map comprising 32 slices with an in-plane resolution of 1 mm and a slice thickness of 2 mm, sampling the relaxation curve at 20 time points (Mollenhoff 2016). The variable flip angle technique: This technique is again based on acquisition of GE data sets. In contrast to LL technique, acquisition times are considerably longer than T1* due to use of long TR and a large number of PE steps, for example by acquiring 3D data sets with a high spatial resolution Mz corresponds to steady-state value (M0*) during major part of data acquisition, so data are acquired under steady-state conditions. Underlying idea: to acquire several data sets with different excitation angles α and to evaluate the signal dependence S(𝛼) for each pixel. The variable flip angle technique: An Example The variable flip angle technique: Signal is given by longitudinal magnetization Mz directly before RF excitation, multiplied with sine of excitation angle Since in variable flip angle (VFA) data, Mz corresponds to M0* as defined in Equation 5.5, the signal amplitude follows from The variable flip angle technique: For each pixel, different signal amplitudes Si are determined for different excitation angles αi yi = Si/sin(αi) and xi = Si/tan(αi) are calculated. A plot of yi versus xi shows a linear dependence with the slope m = exp(−TR/T1), From which T1 can be derived The advantage of the VFA method Speed A full T1 map can be derived from only two spoiled GE data sets acquired with different excitation angles. High spatial resolution, in particular for 3D data. The variable flip angle technique: The variable flip angle technique: In case of a 2-point measurement, 2 optimum excitation angles: for the TR chosen and the approximate target T1 value, a parameter tE is derived: The optimum angles α1 and α2 are then given by: A duration of about 10 min has been reported for acquisition of a T1 map with whole brain coverage and an isotropic resolution of 1 mm. VFA requires correction for non-uniformities of RF transmit profile an additional 1 min for B1 mapping Pitfalls in T1 measurements: General: B1 inhomogeneities: Both the LL and VFA techniques require knowledge of excitation angle for T1 evaluation. Amplitude B1 of RF field sent by transmit coil usually is not uniform. Local excitation angle can deviate from nominal value. Example Pitfalls in T1 measurements: Pitfalls: The IR technique: The analysis of IR data via Equation 5.3 is only warranted if: A complete spin inversion via a perfect 180° RF pulse. A sufficiently long delay after each measurement, allowing full spin relaxation to take place before next inversion. If the delay between measurements is too short for full spin relaxation, a modified equation can be used for fitting Pitfalls in T1 measurements: Pitfalls: The LL technique: Problem 1: The LL technique requires knowledge of the actual excitation angle difficult to determine in presence of B1 inhomogeneities. For 2D sequences with slice-selective RF pulses, excitation angle varies across slice in correspondence with respective slice profile. Fortunately, LL data may be analyzed without knowledge of the excitation angle. Since TR << T1 usually holds, the term exp(−TR/T1) can be approximated as 1−TR/T1. A similar approximation holds for exp(−TR/T1*). Inserting Equation 5.4a in Equation 5.5 and using this approximation yields A three-parameter analysis of relaxation curve as sampled with LL technique (Figure 5.4, blue curve) yields the start value (−M0), asymptotic end value (M0*) and time constant (T1*), so T1 can be calculated from these values via Equation 5.9. Pitfalls in T1 measurements: Pitfalls: The LL technique: Problem 2: Acquisition time per image must be similar to T * or shorter to sample relaxation curve with sufficient temporal resolution 1 Restricts number of PE steps and spatial resolution. The TAPIR sequence avoids this problem by repeating measurement several times, covering different portions of k-space each time. Several gradient echoes with different PE are sampled per excitation. Permits a more detailed sampling of relaxation curve Pitfalls in T1 measurements: Pitfalls: The VFA technique: Problem 1: If B1 inhomogeneities are not accounted, analysis yields an apparent value T1app given by: 5% deviation of B1 would yield a 10% error in T1. VFA requires additional B1 mapping calculation of the actual excitation angle α for each pixel usage of this angle in Equation 5.7 B1 profile can be inferred from VFA data, if it varies smoothly across space A method dubbed UNICORT treats reciprocal maps of T1app as anatomical data sets that are affected by a smooth bias given by 1/ B^2 Pitfalls in T1 measurements: Pitfalls: The VFA technique: Problem 2: For correct T1 evaluation via VFA technique, exact local excitation angles have to be known. 3D sequences with non-selective excitation pulses: B1 mapping is required. 2D sequences with slice-selective excitation pulses: excitation angle shows a variation across the slice corresponding to RF excitation profile. This requires a further correction factor, in addition to the B1 correction. Pitfalls in T1 measurements: Pitfalls: The VFA technique: Problem 3: The VFA theory assumes that in GE imaging, residual transverse magnetization is spoiled after each echo acquisition. Stimulated echoes may yield considerable deviations of the actual steady-state magnetization from the theoretical value. A technique dubbed RF spoiling: employs RF pulses with different pulse phases , so residual transverse magnetization components will point in different directions and cancel each other, provided phase list is chosen appropriately. Pitfalls in T1 measurements: Pitfalls: The VFA technique: Problem 3: In the original publication on RF spoiling: ‘phase increment’ Δϕ = 117° For most values of Δϕ: deviations from theoretical value given by Equation 5.5 (shown as a horizontal line). Deviations yield erroneous T1 values, requiring suitable corrections. Alternative: apply very strong crusher gradients after each echo acquisition: faster decay of residual transverse magnetization components due to diffusion effects Pitfalls in T1 measurements: Precision, reproducibility and quality assessment: Precision of Look-Locker method: (Deichmann 2005) A sampling relaxation curve at 8 time points with whole brain coverage, inplane resolution of 1 mm, 30 contiguous slices with a thickness of 4 mm and 9:38 min acquisition time Measurement was repeated 6 times on a healthy subject at a field strength of 1.5 Tesla. Standard deviation across measurements was 19 ms in WM and 33 ms in GM, corresponding to a precision of 3.5% and 3.2%, respectively Precision, reproducibility and quality assessment: Precision of VFA method: (Nöth et al., 2015). Acquisition of 2 GE data sets with different excitation angles, whole brain coverage with an isotropic resolution of 1 mm and 10 min acquisition time T1 standard deviation due to background noise has been reported to be 26 ms in WM and 51 ms in GM at a field strength of 3 Tesla Precision of the measured T1 value for a single pixel. Precision, reproducibility and quality assessment: Reproducibility of T1 values in a multi-centre study: (Weiskopf et al., 2013). In a study comparing T1 data acquired with the VFA method on 5 healthy subjects and at 3 different sites operating 3 Tesla MR systems A high intra-site and inter-site reproducibility of the resulting T1 maps was reported, with a coefficient of variance of about 5% . Anatomical data sets that were derived from the T1 maps showed a better intra-site and inter-site reproducibility than conventional T1weighted data sets. The authors stressed requirement for accurate B1 mapping and subsequent data correction to avoid any hardware and thus sitedependent bias on results. Precision, reproducibility and quality assessment: Comparison of T1 mapping methods and quality assessment: (Stikov et al., 2015), A study comparing 3 methods (IR, LL, VFA) for T1 mapping all methods similar T1 values for a phantom considerable discrepancies in vivo, with deviations of more than 30% in WM. LL and VFA yield shorter and longer T1 values, compared to IR respectively. These method-dependent deviations were due to B1 inhomogeneity particularly, and effects of insufficient spoiling of transverse magnetization. Recommended suitable quality assessment procedures, comparing results obtained with a certain T1 mapping protocol with data derived from an IR-based gold standard experiment. In particular, quality assessment should be performed both for a T1 phantom and under in vivo conditions Clinical applications of T1 quantification : Multiple sclerosis Movement disorders Brain tumours