Accurate T₁ Mapping of Short T₂ Tissues Using a Three-Dimensional Ultrashort Echo Time Cones Actual Flip Angle Imaging Variable Repetition Time (3D UTE-Cones AFI-VTR) Method

Abstract

Purpose

To develop an accurate T₁ measurement method for short T₂ tissues using a combination of a three-dimensional ultrashort echo time Cones actual flip angle imaging technique and a variable repetition time technique (3D UTE-Cones AFI-VTR) on a clinical 3T scanner.

Methods

First, the longitudinal magnetization mapping function of the excitation pulse was obtained with the 3D UTE-Cones AFI method, which provided information about excitation efficiency and B₁ inhomogeneity. Then, the derived mapping function was substituted into the VTR fitting to generate accurate T₁ maps. Numerical simulation and phantom studies were carried out to compare the AFI-VTR method with a B₁-uncorrected VTR method, a B₁-uncorrected variable flip angle (VFA) method, and a B₁-corrected VFA method. Finally, the 3D UTE-Cones AFI-VTR method was applied to bovine bone samples (n=6) and healthy volunteers (n=3) to quantify the T₁ of cortical bone.

Results

Numerical simulation and phantom studies showed that the 3D UTE-Cones AFI-VTR technique provides more accurate measurement of the T₁ of short T₂ tissues than the B₁-uncorrected VTR and VFA methods or the B₁-corrected VFA method. The proposed 3D UTE-Cones AFI-VTR method showed a mean T₁ of 240±25 ms for bovine cortical bone and 218±10 ms for the tibial midshaft of human volunteers, respectively, at 3T.

Conclusion

The 3D UTE-Cones AFI-VTR method can provide accurate T₁ measurements of short T₂ tissues such as cortical bone.

INTRODUCTION

Variable flip angle (VFA) and variable repetition time (VTR) methods based on three-dimensional spoiled gradient recalled echo (3D SPGR) sequences have been widely used for volumetric T₁ measurement (1–5). However, both the VFA and VTR methods are very sensitive to inhomogeneity in the transmitted B₁ field. As a result, the first step for accurate T₁ measurement usually requires obtaining spatial B₁ field maps (6–15). These are then used for accurate T₁ calculation (16–21).

The Actual Flip angle Imaging (AFI) technique has been proposed for fast 3D B₁ mapping (15). It utilizes interleaved acquisitions of dual-TR steady state signals that are formed by alternately changing the TR of a conventional SPGR sequence. The robustness of the AFI technique has been demonstrated for mapping the B₁ of long T₂ tissues of the human body (15, 20, 21). However, the typical AFI sequence cannot be used for mapping the B₁ of short T₂ tissues, such as cortical bone, calcified cartilage, menisci, ligaments, tendons, etc. (18, 19). This is because these tissues have short T₂ values ranging from several hundred of microseconds to a few milliseconds, and show little or no signal when imaged with conventional SPGR sequences which have TEs of several milliseconds. Ultrashort echo time (UTE) sequences with TEs less than 100 μs have been developed for imaging of short T₂ tissues, and produce detectable signals (4, 22, 23). Combination of the UTE and AFI techniques (UTE-AFI) would therefore appear to be an appropriate way to map flip angles for short T₂ tissues (18, 19).

However, there are technical challenges in accurately mapping flip angles when imaging short T₂ tissues such as cortical bone because of transverse relaxation during the radio frequency (RF) excitation pulse. This is typically ignored for long T₂ tissues, but becomes significant when imaging short T₂ tissues. Large flip angles (>40°) are typically required to make the AFI technique sensitive (15, 18). With conventional peak power limitations on the RF amplifiers of clinical scanners, the RF pulse duration must be increased in order to produce such large flip angle excitations. However, excitation efficiency is decreased when imaging short T₂ tissues with longer RF excitation pulses due to transverse relaxation during the pulse and this leads to actual flip angles that are lower than the nominal flip angles (i.e. the expected flip angles) (23–26). This causes B₁ estimation errors when the UTE-AFI method is used for imaging short T₂ tissues (as detailed in the Theory section below). It can result in inaccurate T₁ values for short T₂ tissues.

To overcome this problem, we propose a new T₁ measurement method for short T₂ tissues which combines a 3D UTE-Cones AFI technique with a 3D UTE-Cones VTR technique (3D UTE-Cones AFI-VTR). In this method, the same RF pulses and flip angles are used for signal excitation in the AFI and VTR sequences. As a result, B₁ maps are no longer required for T₁ correction. Instead, the longitudinal magnetization mapping function of the RF excitation pulse is obtained by the 3D UTE-Cones AFI method, and this is subsequently used for VTR-based T₁ fitting. Simulation, phantom, and in vivo studies were used to investigate the accuracy of the proposed method for measuring the T₁ of cortical bone, utilizing parameters appropriate for a clinical 3T scanner.

THEORY

Features of the conventional 3D UTE-Cones pulse sequence with a single TR (Figure 1A) have been described before (27–29). AFI can be achieved with the 3D dual TR UTE-Cones sequence (Figure 1B). A series of conventional 3D UTE-Cones sequences with variable TRs or variable flip angles can then be used for T₁ measurement. For both the UTE-Cones AFI and the UTE-Cones VTR/VFA sequences, a short rectangular pulse (e.g. 150 μs) was used for non-selective signal excitation (Figure 1C). This was followed by a spiral trajectory data acquisition with conical view ordering (Figure 1D).

Figure 1.

The conventional 3D UTE-Cones sequence with a single TR is used for T₁ measurement with the variable flip angle (VFA) or variable TR (VTR) method (A). The 3D UTE-Cones actual flip angle imaging (AFI) sequence employs a pair of interleaved TRs for accurate B₁ mapping (B), which together with a VFA or VTR method provides T₁ measurements. In these two UTE-Cones sequences, a short rectangular pulse is used for signal excitation followed by 3D spiral sampling with a very short TE of 32 μs (C). The spiral trajectories are arranged with conical view ordering (D).

The steady state signals acquired in TR₁ and TR₂ of the 3D UTE-Cones AFI sequence can be expressed as follows (15, 25):

$$S_1=M_0{f}_{xy}\left(\alpha ,\tau ,T_2\right)\frac{1-E_2+\left(1-E_1\right)E_2{f}_z\left(\alpha ,\tau ,T_2\right)}{1-E_1{E}_2{f}_z^2\left(\alpha ,\tau ,T_2\right)}$$ [1]

$$S_2=M_0{f}_{xy}\left(\alpha ,\tau ,T_2\right)\frac{1-E_1+\left(1-E_2\right)E_1{f}_z\left(\alpha ,\tau ,T_2\right)}{1-E_1{E}_2{f}_z^2\left(\alpha ,\tau ,T_2\right)}$$ [2]

with

$$E_1=\text{exp}\left(-T{R}_1/T_1\right)$$,

$$E_2=\text{exp}\left(-T{R}_2/T_1\right)$$.

$M_0$ is the equilibrium magnetization. $f_{xy}\left(\alpha ,\tau ,T_2\right)$ and $f_z\left(\alpha ,\tau ,T_2\right)$ are the respective transverse and longitudinal magnetization mapping functions generated by the RF pulse, with $f_{xy}\left(\alpha ,\tau ,T_2\right)=M_{xy}^{+}/M_z^{-}$ and $f_z\left(\alpha ,\tau ,T_2\right)=M_z^{+}/M_z^{-}$. $M_z^{-}$ is the longitudinal magnetization before RF excitation. $M_{xy}^{+}$ and $M_z^{+}$ are the transverse and longitudinal magnetizations after the RF excitation. $\alpha$ is the flip angle and $\tau$ is the duration of the rectangular excitation pulse. Since the RF pulse duration is much shorter than the tissue T₁, T₁ relaxation during the excitation can be neglected in the mapping functions.

For short T₂ tissues with T₂ values of the same order as the RF duration $\tau$, $f_{xy}\left(\alpha ,\tau ,T_2\right)$ and $f_z\left(\alpha ,\tau ,T_2\right)$ are determined not only by $\alpha$, but also by $\tau$ and the tissue $T_2$. Analytical expressions of these two terms can be described as follows (24):

$$f_{xy}\left(\alpha ,\tau ,T_2\right)=e^{-\frac{\tau }{2T_2}}\alpha \text{sinc}\left(\sqrt{{\alpha }^2-{(\frac{\tau }{2T_2})}^2}\right)$$ [3]

$$f_z\left(\alpha ,\tau ,T_2\right)=e^{-\frac{\tau }{2T_2}}\left(\mathit{cos}\left(\sqrt{{\alpha }^2-{(\frac{\tau }{2T_2})}^2}\right)+\frac{\tau }{2T_2}\text{sinc}\left(\sqrt{{\alpha }^2-{(\frac{\tau }{2T_2})}^2}\right)\right)$$ [4]

For long T₂ tissues with T₂s >> $\tau$, $f_{xy}\left(\alpha ,\tau ,T_2\right)$ and $f_z\left(\alpha ,\tau ,T_2\right)$ simplify to sin( $\alpha$) and cos( $\alpha$), respectively. Eqs. [1] and [2] then become identical to the conventional expression for AFI in Eq. [3] as shown in Ref. 30.

The general AFI method relies on two fundamental assumptions: (i) that complete spoiling of the transverse magnetization occurs during TR₁ and TR₂, and (ii) that TR₁s and TR₂s are short compared to T₁. Perfect spoiling during each TR is very difficult to achieve since high flip angles and relatively short TRs are used in AFI (15). Yarnykh has suggested the use of an optimized combination of RF spoiling with an extremely strong gradient crusher pair to provide additional spoiling (17). However, in this study the heavy gradient spoiler and phase cycling to provide RF spoiling may not be necessary for complete spoiling due to the fast decay of the transverse magnetization of short T₂ tissues. With TRs that are short relative to T₁, the signal ratio r of $S_1$ and $S_2$ can be simplified using a first-order approximation for the exponential terms such that (15):

$$r=S_2/S_1\approx \frac{1+n{f}_z\left(\alpha ,\tau ,T_2\right)}{n+f_z\left(\alpha ,\tau ,T_2\right)}$$ [5]

where n = TR₂/TR₁. The ratio r can then be used as a T₁-independent measure of $f_z\left(\alpha ,\tau ,T_2\right)$:

$$f_z\left(\alpha ,\tau ,T_2\right)\approx \frac{rn-1}{n-r}$$ [6]

For long T₂ tissues, $f_z\left(\alpha ,\tau ,T_2\right)$becomes cos( $\alpha$). So the actual flip angle $\alpha$ can be estimated with the following equation (15):

$$\alpha \approx \mathit{arc}\text{cos}\left(\frac{rn-1}{n-r}\right)$$ [7]

Then, the B₁ scaling factor (B_1s) is obtained by dividing the measured $\alpha$ by the nominal flip angle ${\alpha }_{\mathit{nom}}$, which is expressed as follows:

$$B_{1s}=\alpha /{\alpha }_{\mathit{nom}}$$ [8]

B_1s is used to quantify the RF inhomogeneity. B_1s = 1 corresponds to an unaltered RF field.

For short T₂ tissues, the measurement of $\alpha$ or B_1s is more complicated. With knowledge of the RF pulse duration and tissue T₂, $\alpha$ can be calculated from the analytical expression for $f_z\left(\alpha ,\tau ,T_2\right)$ or through Bloch equation simulation. However, it is very challenging to measure short T₂ values using the traditional spin echo (SE) or Carr-Purcell-Meiboom-Gill (CPMG) method due to the rapid tissue signal decay as well as the limited RF peak power and gradient strength available on clinical MR scanners. Furthermore, these methods may require extra sequences to measure short T₂ values, which subsequently suffer from errors caused by magnetization transfer (when the 2D multi-slice SE or the CPMG sequence is used to measure T₂), potential motion artifacts associated with the increased scan time and limited signal to noise ratio (SNR) when imaging short T₂ tissues. To cope with these issues, we propose a new approach which avoids the calculation of $\alpha$ required in standard approaches. The value of $f_z\left(\alpha ,\tau ,T_2\right)$ is used directly as input for T₁ calculation under the VTR method. The description of our method follows.

The 3D UTE-Cones sequence is a free induction decay (FID) sequence characterized by an ultrashort echo time (TE = 32 μs) and a 3D non-Cartesian center-out k-space encoding scheme. The detected magnetization S_spgr follows the same steady state behavior as the signal acquired with a SPGR sequence and is expressed as follows (25, 30):

$$S_{\mathit{spgr}}=M_0{f}_{xy,s}\left(\alpha ,\tau ,T_2\right)\frac{1-E}{1-E{f}_{z,s}\left(\alpha ,\tau ,T_2\right)}$$ [9]

with

$$E=exp\left(-T{R}_s/T_1\right)$$

$T{R}_s$ is the repetition time of the UTE-Cones sequence. $f_{xy,s}\left(\alpha ,\tau ,T_2\right)$ and $f_{z,s}\left(\alpha ,\tau ,T_2\right)$ are the RF pulse induced transverse and longitudinal mapping functions, respectively. Analogous to $f_{xy}\left(\alpha ,\tau ,T_2\right)$ and $f_z\left(\alpha ,\tau ,T_2\right)$ in Eqs. [1] and [2]. $f_{xy,s}\left(\alpha ,\tau ,T_2\right)$ and $f_{z,s}\left(\alpha ,\tau ,T_2\right)$ become sin( $\alpha$) and cos( $\alpha$) for long T₂ tissues.

Fitting of Eq. [9] can be used for T₁ quantification of short T₂ tissues from VTR or VFA UTE-Cones data. For long T₂ tissues, VTR and VFA data are processed with the actual flip angles, which can be calculated by applying the B₁ scaling factor B_1s to the nominal flip angles. Since it is complicated to measure B_1s for short T₂ tissues, we propose a new T₁ measurement technique which combines the UTE-AFI method and the UTE VTR method, and employs identical RF excitation pulses. As a result, $f_{z,s}\left(\alpha ,\tau ,T_2\right)$ in Eq. [9] is identical to $f_z\left(\alpha ,\tau ,T_2\right)$ in Eq. [6]. In the T₁ fitting procedure with the VTR method, the coefficients $M_0$ and $f_{xy,s}\left(\alpha ,\tau ,T_2\right)$ in Eq. [9] can be combined into a single unknown parameter (e.g., g), since $M_0$ and $f_{xy,s}\left(\alpha ,\tau ,T_2\right)$ are both not functions of TR. After the measured $f_z\left(\alpha ,\tau ,T_2\right)$ from Eq. [6] is substituted into Eq. [9], there are only two unknown parameters including g and T₁. Therefore, robust T₁ measurements can be achieved by fitting the data with variable TRs.

MATERIALS AND METHODS

In our study, the 3D UTE-Cones AFI and conventional UTE-Cones sequences (see Figure 1) were implemented on a 3T Signa TwinSpeed scanner (GE Healthcare Technologies, Milwaukee, WI). An 8-channel transmit/receive knee coil was used for both RF transmission and signal reception. The sequences used unique k-space trajectories that sampled data along evenly spaced twisted paths in the form of multiple cones (27–29). Data sampling began from the center of k-space and continued outwards. It began as soon as practical after the RF excitation with a minimal nominal delay time of 32 μs. Both RF and gradient spoiling were used to crush the remaining transverse magnetizations. In 3D UTE-Cones AFI, the areas of gradient crushers in TR₁ and TR₂ were 180 and 900 mT·ms/m respectively, and the RF phase increment was $39°$ (17). In 3D VTR or VFA UTE-Cones, the area of the gradient crushers was 180 mT·ms/m and the RF phase increment was $169°$ (17). The 3D UTE-Cones sequence allowed anisotropic resolution (e.g., high in-plane resolution and thicker slices) to provide an improved SNR and a reduced scan time relative to isotropic imaging (28, 29).

Simulation

Numerical simulation was performed to investigate the accuracy of the proposed T₁ measurement for short T₂ tissues. Identical simulated rectangular RF pulses were used for signal excitation in both the 3D UTE-Cones AFI and VTR sequences and had durations from 0.1 to 500 μs. T₂ values of simulated short T₂ tissues ranged from 0 to 1 ms. The T₁ value was set to 500 ms. The sequence parameters for the 3D UTE-Cones AFI and VTR sequences were adjusted as follows: 1) 3D UTE-Cones AFI: TR₁/TR₂ = 20/100 ms and flip angle = 45°; 2) VTR UTE-Cones: TR = 10, 50, 100, 150, and 200 ms, and flip angle = 45°. For comparison, the VFA UTE-Cones sequence was also used for T₁ measurement with the following sequence parameters: TR = 20 ms and flip angles = 7°, 14°, 22°, 30°, and 38° (31). Three simulated nominal B₁ scaling factors (B_1n) were used and set to values of 0.8, 1, and 1.2.

Phantom and Sample Study

An agarose phantom was prepared by adding 3.0 g agarose powder and 7.2 mg MnCl₂·4H₂O to 400 ml distilled water. The mixture was brought to a boil in a microwave oven and then cooled in a refrigerator, allowing the solution to gel. The T₂ value of the agarose phantom was approximately 80 ms. This was designed to simulate long T₂ tissue. Another agarose phantom was prepared by mixing 300 ml distilled water with the same concentrations of agarose and MnCl₂ as in the previous phantom. After bringing the solution to a boil, the solution was cooled to 40°, and a fresh bovine cortical bone section which had been stripped of soft tissue was suspended within it. The phantom was then allowed to cool until the agarose gelled with the suspended bone section immobilized within it. In addition, five fresh bovine cortical bone sections were stripped of soft tissue and submerged in Fomblin (perfluoropolyether) within a cylindrical container of suitable size for MR scanning. These phantoms were scanned with the 3D UTE-Cones AFI, VTR, and VFA sequences and the sequence parameters can be found in “Phantom” section in Table 1.

Table 1.

Sequence parameters of phantom, bovine cortical bone sample and in vivo tibial cortical bone studies.

	3D UTE-Cones AFI	3D UTE-Cones VTR	3D UTE-Cones VFA
Phantom	FOV = 15×15×12.8 cm3, Matrix = 128×128×32, TR1/TR2 = 20/100 ms, flip angle = 45°, bandwidth = 125 kHz, scan time = 8 min 55 sec	FOV = 15×15×12.8 cm3, Matrix = 128×128×32, TR = 20, 40, 60, 80 and 120 ms, flip angle = 45°, bandwidth = 125 kHz, total scan time = 21 min 20 sec	FOV = 15×15×12.8 cm3, Matrix = 128×128×32, TR = 24 ms, flip angle = 8°, 26° and 45°, bandwidth = 125 kHz, total scan time = 5 min 21 sec
Bovine cortical bone	3D UTE-Cones AFI	3D UTE-Cones VTR
	FOV = 15×15×6.4 cm3, Matrix = 128×128×16, TR1/TR2 = 20/100 ms, flip angle = 45°, bandwidth = 125 kHz, scan time = 4 min 40 sec	FOV = 15×15×6.4 cm3, Matrix = 128×128×16, TR = 15, 30, 50 and 80 ms, bandwidth = 125 kHz, total scan time = 6 min 41 sec
In vivo tibial cortical bone	3D UTE-Cones AFI	3D UTE-Cones VTR
	FOV = 15×15×16.8 cm3, Matrix = 128×128×24, TR1/TR2 = 20/100 ms, flip angle = 45°, bandwidth = 250 kHz, scan time = 7 min 5 sec	FOV = 15×15×16.8 cm3, Matrix = 160×160×24, TR = 15, 30, 50, and 80 ms, flip angle = 45°, bandwidth = 250 kHz, total scan time = 12 min 24 sec

A bovine cortical bone sample was used to compare the two VTR T₁ measurement techniques using two different excitation flip angles of 20° and 45° with RF pulse durations of 60 μs and 150 μs, respectively. The power of the RF pulses was near to the maximum available on the clinical scanner. The UTE-Cones AFI method was used to obtain the mapping function magnetization, $f_z\left(\alpha ,\tau ,T_2\right)$, which was subsequently used to correct T₁ measurement errors induced by both B₁ inhomogeneity and loss of magnetization during the 45° excitation pulse. The 20° pulse with a duration of 60 μs was more effective than the 45° pulse in generating transverse magnetization for materials with short T₂s since the pulse duration was much shorter than the typical T₂* value for bovine cortical bone, which is approximately 300 μs (4). The error in T₁ measurement with a 20° pulse was expected to come mainly from B₁ inhomogeneity. Other sequence parameters can be found in “Bovine cortical bone” section in Table 1.

Another bovine cortical bone sample was used to investigate the T₁ measurement accuracy of the proposed 3D UTE-Cones AFI-VTR method using three different RF pulse durations of 150 μs, 200 μs, and 300 μs with the same flip angle of 45°. Identical excitation pulses were used for the UTE-Cones AFI and VTR sequences. The AFI and VTR sequences were each scanned three times using the RF excitation pulses of different duration mentioned above. Other sequence parameters were identical to the above bovine cortical bone study.

In Vivo Study

The 3D UTE-Cones AFI-VTR method was tested in vivo on three healthy male volunteers (ages 29, 35, and 40 yr). Informed consent was obtained from all subjects in accordance with local Institutional Review Board guidelines. Sequence parameters can be found in “In vivo tibial cortical bone” section in Table 1. A higher bandwidth was used for in vivo imaging of cortical bone to minimize chemical shift artifacts from bone marrow fat, which are manifest as ring shaped artifacts with 3D UTE-Cones imaging. Other

Data Analysis

The Levenberg-Marquardt algorithm in Matlab (The MathWorks Inc., Natick, MA, USA) was used to solve the non-linear fitting of Eq. [9] for both VTR and VFA methods. The analysis algorithms written in Matlab were applied to the DICOM images obtained from the 3D UTE-Cones AFI and VTR/VFA UTE-Cones protocols described above. After each fitting calculation, B_1s scaling factor $f_z\left(\alpha ,\tau ,T_2\right)$ and T₁ maps were generated. The mean value and standard deviation of T₁ for both in vitro bovine cortical bone (n = 6) and in vivo human tibial midshaft cortical bone (n = 3) were also calculated.

RESULTS

Figure 2 shows the simulation results. The top two rows show the theoretical longitudinal ( $M_z$) and transverse ( $M_{xy}$) magnetizations generated by the rectangular RF pulses with variable durations for a variety of short T₂s. In actual scanning, $M_z$ and observed $M_{xy}$ magnetizations correspond to $f_z\left(\alpha ,\tau ,T_2\right)$ and $f_{xy}\left(\alpha ,\tau ,T_2\right)$, which were obtained using Eqs. [3] and [4]. From the color maps (Figure 2), it can be seen that longer RF pulses are less effective than shorter pulses in generating M_xy for shorter T₂ tissue components. As expected, more $M_{xy}$ is generated when the excitation pulse power is increased, i.e. when the nominal B₁ scaling factor B_1n is increased from 0.8 to 1.2. The bottom two rows in Figure 2 provide the estimated B₁ scaling factors B_1s and $f_z\left(\alpha ,\tau ,T_2\right)$ computed using the AFI method with Eqs. [8] and [6]. The measured B₁ scaling factors B_1s are more accurate when using shorter RF pulses and when imaging longer T₂ species. Otherwise, the estimated B₁ scaling factors B_1s are smaller than the nominal values. The calculated values of $f_z\left(\alpha ,\tau ,T_2\right)$ were nearly identical to the theoretical values of $f_z\left(\alpha ,\tau ,T_2\right)$ (i.e. $M_z$ shown in the first row), which demonstrates the accuracy of Eq. [6].

Figure 2.

Simulation results for short T₂ tissues (T₂s from 0 to 1 ms) with a rectangular RF pulse excitation (durations from 0.1 to 500 μs). The top two rows show color maps corresponding to the longitudinal and transverse magnetizations (i.e. $f_z\left(\alpha ,\tau ,T_2\right)$ and $f_{xy}\left(\alpha ,\tau ,T_2\right)$) calculated from Eqs. [3] and [4]. The third row shows the resulting B_1s scaling factors, and the bottom row shows the mapping function $f_z\left(\alpha ,\tau ,T_2\right)$ obtained by the AFI method. The columns represent simulation results with nominal B₁ scaling factors B_1n of 0.8, 1, and 1.2, respectively.

Figure 3 presents the simulation results of T₁ measurements using both VFA and VTR methods, with and without AFI correction. As seen in the bottom left corners of all images in the first and third rows, T₁s from B₁-uncorrected VFA and VTR methods are both subject to underestimation caused by the imperfect excitation when employing a longer RF pulse or when imaging shorter T₂ species. Additionally, the estimated T₁ values increase with larger values of the nominal B₁ scaling factor B_1n. The second row presents the VFA results using the conventional B₁ correction method (appropriate for long T₂ tissues). The calculated B_1s maps used for correction are displayed in the third row of Figure 3. Overall, the B₁-corrected VFA method is more accurate than the B₁-uncorrected VFA method. However, T₁ estimation errors still exist – especially for tissues with T₂s shorter than 0.5 ms, and the errors become larger with increased B₁ inhomogeneity. In contrast, the proposed AFI-VTR T₁ measurements presented in the last row are nearly accurate for all short T₂s, independent of the duration of the excitation pulses. Additionally, identical T₁ values are obtained with different values of the nominal B₁ scaling factor B_1n. The proposed AFI-VTR T₁ measurement method can eliminate errors induced by B₁ inhomogeneity, and is also immune to the imperfect signal excitation encountered with short T₂ species.

Figure 3.

T₁ mapping results (units of ms) generated by the VFA method without (1^st row) and with B₁ correction (2^nd row), as well as results using the VTR method without (3^rd row) and with B₁ correction (4^th row). The columns show simulation results with nominal B₁ scaling factors B_1n of 0.8, 1, and 1.2, respectively. The AFI-VTR method provides the most consistent T1 values over the range of short T₂ tissues (T₂s from 0 to 1 ms).

Figure 4 shows the phantom results obtained using the UTE-Cones AFI method. A smooth continuous spatial distribution is observed in the agarose phantom maps, corresponding to the measured B₁ inhomogeneity (calculated from Eqs. [7] and [8]) and $f_z\left(\alpha ,\tau ,T_2\right)$ distribution (calculated from Eq. [6]). High flip angles tend to appear in the central region of the knee coil. Similar results are seen in the pure agarose region of the agarose bone phantom. There are clear sharp boundaries between the bone and agarose regions in both the B_1s and $f_z\left(\alpha ,\tau ,T_2\right)$ maps. The measured B_1s values in the bone region are lower than those in the agarose region due to inefficient excitation of cortical bone with its extremely short T₂. The experimental results agree well with the simulation results presented in Figure 2. The sharp discontinuities in the B_1s map suggest that the B₁ measurement is inaccurate for cortical bone, whereas the $f_z\left(\alpha ,\tau ,T_2\right)$ values in the bone region are reasonable and are consistent.

Figure 4.

Phantom results using the 3D UTE-Cones-AFI technique and an 8-channel knee coil. The first two columns show dual-TR UTE-Cones images (left: first TR images; right: second TR images) of an agarose phantom and an agarose bone phantom, who’s B_1s and $f_z$ maps are shown in right two columns, respectively. As can be seen from the results of agarose phantom, higher B_1s is observed in the center area of the knee coil. However, the bone region in the agarose bone B_1s map shows a much reduced B_1s values due to inefficient excitation of the short T₂ tissue.

Figure 5 demonstrates the effect of short tissue T₂s on the T₁ map calculation. Panels 5A and 5B are regions of interest (ROIs) extracted from Figures 4E and 4F which show the spatial distribution of B_1s and $f_z\left(\alpha ,\tau ,T_2\right)$. B₁ inhomogeneity and excitation inefficiency lead to complicated distributions in the bone region of the agarose-suspended bone phantom. The VFA T₁ map in the bone region still suffers from signal inhomogeneity even with B₁ correction. The bone T₁ map measured with the proposed UTE-Cones AFI-VTR method is far more uniform than the T₁ map measured with the B₁-corrected VFA method or the B₁-uncorrected VTR method. For the long T₂ agarose phantom, the T₁ map obtained with the UTE-Cones AFI-VTR method was much more uniform than the T₁ map measured with the B₁-uncorrected VTR method. These results demonstrate that the proposed UTE-Cones AFI-VTR method can obtain consistent T₁ measurements for both short and long T₂ tissues.

Figure 5.

Phantom T₁ related maps using 3D UTE-Cones VFA and VTR based methods. Cropped B_1s and $f_z$ maps from the bone region of the agarose bone phantom are shown in Panels A and B (these agarose bone phantom maps are also shown in Figs. 4G and 4H with different scaling). Panels C through F are bone T₁ maps (units of ms) obtained using VFA without B₁ correction (C), VFA with B₁ correction (D), VTR without B₁ correction (E) and the proposed AFI-VTR method (F). The bottom row shows the T₁ maps of the agarose phantom corresponding to B_1s and $f_z$ maps of the agarose phantom shown in Figs. 4A-D, without B₁ correction (G), and with B₁ correction (H). The maps are most uniform in (F) and (H) when the AFI-VTR method is used.

Figure 6 shows the effect of RF pulse duration on bovine cortical bone T₁ measurement using the regular VTR and AFI-VTR methods. The bovine cortical bone T₁ measurements were obtained from the UTE-Cones VTR method with an excitation pulse of 45° and duration of 150 μs (6E and 6F), and with an excitation pulse of 20° and duration of 60 μs (6G) (5). As shown in Figures 6E and 6G, the T₁ map measured with the conventional B₁-uncorrected VTR method shows a higher average T₁ value when using a shorter excitation pulse (60 μs vs 150 μs) because of its higher excitation efficiency. Figure 6F is the same T₁ measurement as Figure 6E, but displayed with a narrower color bar range for better comparison with Figure 6G. The same color distribution can be found in Figures 6F and 6G, which suggests that they were subject to the same B₁ inhomogeneity modulation. These results demonstrate that T₁ measurements using a longer RF pulse with a lower excitation efficiency underestimate T₁ values without affecting the B₁ inhomogeneity modulation. Figure 6H shows the T₁ map measured with the proposed UTE-Cones AFI-VTR method, which is more uniform than that shown in Figure 6G, demonstrating that the proposed UTE-Cones AFI-VTR T₁ measurement method can correct for the effect of both B₁ inhomogeneity and excitation inefficiency.

Figure 6.

The effect of RF pulse duration on bovine cortical bone T₁ measurement using the VTR method. A longer rectangular RF pulse duration of 150 μs with a flip angle of 45° was used in panels A to F. Panels A and B are cropped sections from the 3D UTE-Cones AFI images with a TR of 20 ms (A) and a TR of 100 ms (B). The B_1s map (C) and the $f_z$ map (D) were calculated from these dual TR images. Panels E and F show the T₁ maps obtained using the regular VTR method. The panels display a different color range. Panel G shows the T₁ map generated with the regular VTR method using a shorter RF pulse of 60 μs and flip angle of 20°. This shows increased T₁ values relative to E but a similar T₁ spatial distribution similar to F. Panel H is the T₁ map obtained by the 3D UTE-Cones AFI-VTR method. This shows a much more homogeneous T₁ distribution.

Figure 7 further demonstrates the robustness of the proposed UTE-Cones AFI-VTR method for T₁ measurement of bovine cortical bone using rectangular RF excitation pulses with three different durations of 150, 200 and 300 μs. The mapping $f_z\left(\alpha ,\tau ,T_2\right)$ values increases with longer RF duration, which is consistent with the simulation results in Figure 2. However, the measured T₁ maps are almost identical showing that the UTE-Cones AFI-VTR method can provide accurate T₁ measurement of short T₂ tissues with different excitation pulse durations.

Figure 7.

Effect of RF pulse durations ( $\tau$ = 150, 200 and 300 μs) with the same flip angle of 45° on bovine cortical bone T₁ maps using the proposed 3D UTE-Cones AFI-VTR method. The first row shows $f_z$ maps generated with the 3D UTE-Cones AFI method. The second row shows the 3D UTE-Cones AFI-VTR T₁ maps. These maps are uniform and consistent across each of the three RF pulse durations.

Figure 8 shows in vivo T₁ mapping of the tibial midshaft in a healthy volunteer. The VTR T₁ map without correction shows lower T₁ values and more B₁ spatial modulation than the T₁ map generated with the proposed UTE-Cones AFI-VTR method, consistent with the simulation and phantom results.

Figure 8.

In vivo tibial cortical bone results. Panels A and B show the B_1s and $f_z$ maps calculated from 3D UTE-Cones dual-TR images, respectively. Panels C and D show the T₁ maps generated using the uncorrected VTR method (C) and using the proposed UTE-Cones AFI-VTR method (D), respectively. The T₁ map appears more uniform in (D).

Table 2 summarizes T₁ measurements for the bovine cortical bone samples (n = 6) and tibial midshaft cortical bone in the healthy volunteers (n = 3). The mean T₁ value and standard deviation obtained with the proposed 3D UTE-Cones AFI-VTR method for the six bovine cortical bone samples and the three in vivo human volunteer tibial cortical bones were 240±25 ms and 218±10 ms, respectively.

Table 2.

T₁ values and the fitting standard error (units of ms) obtained by the proposed 3D UTE-Cones AFI-VTR method for in vitro bovine cortical bone samples (n = 6) and in vivo human tibial midshaft cortical bone in healthy volunteers (n = 3).

	#1	#2	#3	#4	#5	#6
In vitro bovine cortical bone sample	257±7	251±6	211±5	206±8	256±6	259±7
In vivo human tibial cortical bone	#1		#2		#3
	229±12		215±11		209±9

DICUSSION

We have demonstrated that the proposed 3D UTE-Cones AFI-VTR method can quantify the T₁s of short T₂ tissues more accurately by dealing with the problems created by RF excitation inefficiency and B₁ inhomogeneity. Numerical simulations show that T₁ measurements using the B₁-uncorrected VTR and VFA methods are subject to errors from both B₁ inhomogeneity and excitation inefficiency. The B₁ maps obtained from Eqs. [7] and [8] are no longer accurate due to the complex relationship between the flip angle and the mapping functions shown in Eqs. [3] and [4] when imaging short T₂ species, due to the significant transverse magnetization loss during the relatively long RF excitation process. Simulation shows that the proposed 3D UTE-Cones AFI-VTR method provides accurate T₁ measurements for tissues with a wide range of T₂ values. The technique is relatively insensitive to the duration of the excitation pulse. Phantom and sample studies demonstrate that the 3D UTE-Cones AFI-VTR method generates uniform T₁ maps for both short (i.e. bovine cortical bone) and long (i.e. agarose phantom) T₂ tissues. In addition, the bovine cortical bone T₁ maps are nearly identical with the three different RF durations (see Figure 7), demonstrating the robustness of the proposed method. Finally, uniform T₁ maps were obtained using the proposed method to provide in vivo tibial cortical bone measurements in healthy volunteers.

Many T₁ measurement techniques have been proposed including inversion recovery (IR), saturation recovery (SR), and SPGR-based VFA and VTR methods (32–34). The IR method is generally regarded as the gold standard for T₁ mapping of long T₂ tissues (32). However, this IR method is not useful for T₁ measurement of short T₂ tissues because the typical inversion pulse available on clinical scanners is too long to provide complete inversion of the short T₂ magnetization. The SR method provides accurate and precise T₁ measurements for short T₂ tissues (34); however, this technique is often too slow to be used clinically. SPGR-based VFA or VTR methods can provide fast volumetric T₁ mapping (4, 5, 19), but they suffer from high sensitivity to B₁ inhomogeneity (16–21). Obtaining an accurate B₁ map is crucial with VFA and VTR T₁ measurement approaches. AFI is a fast 3D B₁ mapping technique which fits very well with VFA and VTR based T₁ corrections. It has been used for volumetric B₁ mapping of brain, body, and MSK tissues (15, 20, 21, 35). Uniform T₁ maps can be derived using the B₁ correction. Kobayashi proposed a B₁ mapping method for short T₂s based on an implementation of the AFI technique using a 3D radial sequence called Concurrent Dephasing and Excitation (CODE) on a 9.4T 31-cm bore MRI system (18). The sequence shows potential for in vivo imaging on clinical scanners. Han et al. proposed a 3D radial-UTE based AFI approach for B₁ mapping of cortical bone (19). However, this group did not consider the B₁ measurement errors induced by the imperfect excitation resulting from the use of a 200 μs rectangular pulse which could produce discontinuities in the B₁ maps at the bone-marrow boundary (19).

In contrast to these studies our method does not require B₁ maps for T₁ correction. Instead, the longitudinal magnetization mapping function $f_z\left(\alpha ,\tau ,T_2\right)$ of the excitation pulse is obtained by the 3D UTE-Cones AFI method which effectively reduces the impact of B₁ inhomogeneity. When identical RF pulses and flip angles are used with both the UTE-Cones AFI and UTE-Cones VTR sequences, the derived $f_z\left(\alpha ,\tau ,T_2\right)$ can be substituted in the VTR function directly for T₁ fitting. This method avoids the complex B₁ estimation from Eq. [4] and corrects for both B₁ inhomogeneity and excitation inefficiency simultaneously.

As shown in the original VFA images of the agarose bone phantom (Supporting Figure S1), ringing artifacts were present in the bone regions due to the relatively low image resolution used and high signal intensity difference between bone and agarose. The ringing artifacts then transferred to the calculated VFA T₁ maps (Figures 5C and 5D). The VFA T₁ map with B_1s correction has a higher average T₁ value than the uncorrected VFA T₁ map. However, the spatial B_1s variation (Figure 5A) still existed in the corrected VFA T₁ map (Figure 5D) due to the inaccurate B_1s map which was used, and the complicated relationships between the excitation flip angles in the VFA sequences and mapping functions (Eqs. [3] and [4]). Therefore, the VFA T₁ maps did not show much improvement after B₁ correction, which was similar to the simulation results in Figure 3.

The proposed UTE-Cones AFI-VTR method could be used to measure T₁ in a variety of short T₂ tissues, including ligaments, menisci, the deep layers of articular cartilage and myelin. In the case of myelin, the proposed 3D UTE-Cones AFI-VTR method may be used to accurately measure myelin T₁ with an extra IR pulse to suppress signals from the long T₂ water components (36). Accurate T₁ measurements may also be crucial as input for other quantitative MRI techniques such as quantitative MT modeling and UTE-Cones $T_{1\rho }$ imaging. These produce tissue characterizing parameters such as macromolecular proton fraction and low frequency exchange information in short T₂ tissues (37, 38).

There are several limitations of this study. First, the total data acquisition time is relatively long, in part due to the selected parameters for high accuracy, high image resolution and broad spatial coverage. A number of strategies can be employed to reduce the total scan time, including decreasing the total number of TRs, using lower resolution for $f_z$ mapping and advanced techniques for image reconstruction. For instance, other authors have found that T₁ can be calculated from VTR data using only two different TRs (39, 40), suggesting that the total scan time of the UTE-Cones VTR sequences can be reduced (four TRs were used in the in vivo portion of our study). In addition, the scan time of UTE-Cones AFI sequence can be reduced by decreasing the image resolution for $f_z$ measurement, and acquiring fewer slices. Furthermore, the scan time may be reduced by employing advanced parallel imaging and compressed sensing reconstruction (41). With a combination of the above strategies to greatly reduce the total scan time, our proposed 3D UTE-Cones AFI-VTR method should be acceptable in clinical applications. Second, fat and chemical shift artifacts (which produce ring artifacts in 3D UTE-Cones imaging) may lead to errors in T₁ estimation, necessitating some form of fat-water signal separation to improve accuracy (42). Third, the clinical application of the 3D UTE-Cones AFI-VTR method remains to be investigated. However, considering the importance of accurate T₁ measurement, the new technique is expected to be useful in the diagnosis and treatment monitoring of many diseases such as osteoporosis, osteoarthritis and multiple sclerosis where short T₂ tissues or tissue components are involved in the disease process.

CONCLUSION

The 3D UTE-Cones AFI-VTR method provides a robust technique for the measurement of T₁ of short T₂ tissues such as cortical bone in acceptable scan times using a clinical 3T scanner.

Supplementary Material

Supp Figures

Supporting Figure S1 The original VFA images with flip angle α = 8° (left), 26° (middle) and 45° (right) in the agarose bone phantom study. There are ringing artifacts inside the bone region.