### 2-T1 Longitidinal Relaxation Time

```T1: Longitudinal
Relaxation Time
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
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  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   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() 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
 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
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