To measure T₁ of short T₂ species Using an Inversion Recovery Prepared Three-Dimensional Ultrashort Echo Time (3D IR-UTE) Method: A Phantom Study

Abstract

Purpose

To demonstrate the feasibility of a new method for measuring T₁ of short T₂ species based on an adiabatic inversion recovery-prepared three-dimensional ultrashort echo time Cones (3D IR-UTE-Cones) sequence.

Methods

T₁ values for short T₂ species were quantified using 3D IR-UTE-Cones data acquired with different repetition times (TRs) and inversion times (TIs). An inversion efficiency factor Q was introduced into the fitting model to accurately calculate T₁ values for short T₂ species. Experiments were performed on twelve MnCl₂ aqueous solution phantoms with a wide range of T₁ values and T₂* values on a 3T clinical MR system to verify the efficacy of the proposed method. For comparison, a variable flip angle UTE (VFA-UTE) sequence, a variable TR UTE (VTR-UTE) sequence, and a conventional 2D IR fast spin echo (IR-FSE) sequence were also used to quantify T₁ values of those phantoms. T₁ values were compared between all performed sequences.

Results

The proposed 3D IR-UTE-Cones method provided higher contrast images of short T₂ phantoms and measured much shorter T₁ values than the 2D IR-FSE, VFA-UTE, and VTR-UTE methods. T₁ values as short as 2.95 ms could be measured by the 3D IR-UTE-Cones sequence. The 3D IR-UTE-Cones methods with different TRs were applied to different ranges of T₁ measurement, and the scan time was significantly decreased by using 5 TIs along the recovery curves to perform fitting with comparable accuracy.

Conclusion

The 3D IR-UTE-Cones sequence could accurately measure short T₁ values while providing high contrast images of short T₂ species.

Graphical Abstract

INTRODUCTION

Spin-lattice relaxation time (T₁) is an intrinsic MR tissue property. T₁ is also an important biomarker for many diseases, thus playing a key role in MR signal intensity and imaging contrast. For example, T₁ mapping of the brain can be used for the assessment of multiple sclerosis (MS) and Parkinson’s disease [1–4]. Osteoarthritis (OA) can be detected at an early stage with T₁ mapping in delayed gadolinium-enhanced MRI of cartilage (dGEMRIC) [5, 6]. In nanoparticle-based hyperthermia, T₁ can be used as a biomarker to evaluate the concentration of iron-oxide nanoparticles (IONPs) [7–10]. In MRI-guided thermal ablation procedures, such as radiofrequency, laser, or focused ultrasound, T₁ mapping can be used to monitor the temperature [11–13].

A variety of T₁ measurement techniques have been reported, including inversion recovery (IR), Look-Looker (LL), variable flip angles (VFA), and variable repetition time (VTR)-based methods [14–18]. IR is the gold standard for T₁ measurement. The combinations of these methods with conventional spin echo (SE), fast spin echo (FSE), or gradient recalled echo (GRE) sequences have been used to measure T₁ values of primarily long T₂ species [1, 19–23], such as gray matter (GM), white matter (WM), cerebrospinal fluid (CSF), muscle, the superficial layers of articular cartilage, etc. However, for species with short T₂s, such as the deep layers of articular cartilage, menisci, tendons, ligaments, bone, and iron overload, their longitudinal magnetizations cannot be accurately rotated as their T₂s are around or shorter than the duration of the preparation (e.g., inversion or saturation) pulses [22]. The transverse magnetizations may decay significantly during the preparation pulses. Furthermore, conventional sequences may have too long echo times (TEs) to detect short T₂ signals. As a result, accurate T₁ mapping cannot be achieved for short T₂ species using conventional T₁ measurement methods.

Ultrashort echo time (UTE) based-methods are promising alternatives to overcome this problem. For example, the combination of variable flip angle (VFA) and UTE (VFA-UTE), variable TR and UTE (VTR-UTE), and adiabatic inversion recovery and UTE (IR-UTE) methods have been reported to provide accurate measurement of T₁ values of short T₂ species in the musculoskeletal (MSK) system [22,24–27]. VFA-UTE and VTR-UTE could provide volumetric T₁ mapping of short T₂ species, but they suffer from high sensitivity to B₁ inhomogeneity, with poor image contrast for short T₂ species. Adiabatic IR-UTE pulse sequences have been used for high contrast imaging of short T₂ species by suppressing signals from long T₂ species [27, 28]. The adiabatic IR-UTE method is able to provide not only high contrast morphological imaging but also quantitative evaluation, such as proton density (PD) and T₂* and T₁ mapping of short T₂ species [24, 25]. This is especially important since species with short T₂* values typically have short T₁ values, which are difficult or impossible to evaluate with conventional clinical sequences.

In this study, we aimed to develop a novel 3D IR-UTE based method to quantitatively measure T₁ values of short T₂* species. Data were acquired using an adiabatic inversion recovery prepared 3D UTE Cones (3D IR-UTE-Cones) sequence with a series of repetition times (TRs) and inversion times (TIs). An inversion efficiency factor Q was introduced to account for partial inversion of the longitudinal magnetization, and further incorporated into the fitting model for accurate T₁ mapping. Experiments were performed on twelve MnCl₂ aqueous solution phantoms with a wide range of T₁ values and T₂* values on a 3T clinical MR system to verify the efficacy of the proposed method.

THEORY and METHOD

Phantom Preparation

As reported in [29], the T₂* values of the MnCl₂ aqueous solutions had a linear relationship with their concentrations. Based on the linear relationship between concentrations and T₂* values, a wide range of concentrations of MnCl₂ aqueous solutions were made to explore the shortest T₁ values the proposed method could measure.

Twelve 5-mL polypropylene tubes filled with MnCl₂ aqueous solutions with concentrations ranging from 0 to 89.16 mM (details in Table 1) were placed inside a cylindrical container (8.5 cm in diameter, 9.5 cm in height) filled with agarose gel (1% by weight). During the scan, the tubes were aligned parallel to the B₀ field to minimize susceptibility artifact.

Table 1.

T₂* and T₁ results of different imaging protocols

Tube Numbers	Concentration (mM)	T2* (ms)	Estimated T1 values (ms)
			3D IR-UTE (TR = 400 ms)	3D IR-UTE (TR = 50 ms)	VFA-UTE	VTR-UTE	IR-FSE
1	0	-	3133.23±794.74	-	2418.00±148.26	1433.08±487.12	2953.34±16.86
2	0.08	-	2639.91±304.17	-	1710.69±98.14	1337.63±334.19	2092.08±3.51
3	0.24	-	863.31±20.15	-	662.89±32.35	695.72±25.30	782.66±1.08
4	1.43	10.61±0.42	158.43±0.48	231.34±39.83	143.56±71.32	159.93±4.03	166.52±0.49
5	2.86	4.99±0.16	76.53±0.14	90.09±6.84	71.32±14.65	82.55±2.42	73.13±14.65
6	4.29	3.44±0.11	51.86±0.15	58.29±2.43	53.29±3.36	60.23±1.97	59.33±2.34
7	6.20	2.34±0.05	36.08±0.09	37.56±0.64	41.23±3.01	46.26±1.96	-
8	11.92	1.16±0.03	19.09±0.07	18.88±0.03	29.27±3.95	32.33±3.07	-
9	23.84	0.55±0.02	9.55±0.58	9.39±0.01	-	-	-
10	35.76	0.35±0.02	6.33±0.13	6.31±0.01	-	-	-
11	77.72	0.16±0.02	-	3.17±0.04	-	-	-
12	89.16	0.14±0.03	-	2.95±0.07	-	-	-

Pulse sequence and fitting model

The diagram of the 3D IR-UTE-Cones pulse sequence is illustrated in Figure 1 [30–32]. An adiabatic inversion recovery preparation pulse with a specific TI is followed by N number of spokes (Ns) separated with an equal time interval τ for fast data acquisition (Figure 1a). In this situation, TI is defined as the time from the center of the adiabatic inversion pulse to the center of the spoke cluster. A short rectangular pulse (duration of 26–52 μs) is used for non-selective signal excitation in each spoke (Figure 1b) followed by 3D spiral trajectories with conical view ordering (Figure 1c).

Figure 1.

3D IR-UTE-Cones sequence diagram for T₁ measurement. (a) The pulse sequence scheme showing an adiabatic inversion preparation pulse followed by a 3D UTE-Cones data acquisition. (b) In the basic 3D UTE-Cones sequence, a rectangular pulse is used for signal excitation followed by 3D spiral sampling with TE of 32 μs. (c) Conical view ordering of the spiral trajectories. (d) Longitudinal magnetization scheme of three representative tissues (yellow, tissues with ultrashort T₂* saturated during the IR pulse; blue, tissues with short T₂* partially inverted during the IR pulse; purple, tissues with long T₂* fully inverted during the IR pulse) during the course of inversion recovery.

Adiabatic inversion pulses can effectively invert the longitudinal magnetizations of long T₂ species, while the longitudinal magnetizations of short T₂ species can only be partially inverted because of their fast decay during the relatively long adiabatic inversion process. To accurately describe the inversion status of species with different T₂s, we introduced an inversion efficiency factor Q with a range of −1 (full inversion, for species with long T₂s, e.g., T₂ > 100 ms) to 1 (no disturbance to the longitudinal magnetization, for species with extremely short T₂s, e.g., T₂ < 1 μs), and Q is 0 when the magnetization is completely saturated (for tissues with ultrashort T₂s, e.g., T₂ ~ 0.1 ms), as shown in Figure 1d.

Within a steady-state, the longitudinal magnetization of the $N_s^{th}$ spoke is as follows:

$$S_z^{N_s}=K_{N_s}{S}_p+L_{N_s},$$ (1)

Where

$$K_{N_s}=C_2{\left[c_1\cos (\theta )\right]}^{N_s},$$ (2)

$$L_{N_s}=S_0\left(1-C_2\right){\left[c_1\cos (\theta )\right]}^{\left(N_s-1\right)}+S_0\left(1-c_1\right)\frac{1-{\left[c_1\cos (\theta )\right]}^{N_s-1}}{1-c_1\cos (\theta )},$$ (3)

And

$$S_p=\frac{Q{C}_3{L}_{N_s}\cos (\theta )+S_{0}Q\left(1-C_3\right)}{1-Q{C}_3{K}_{N_s}\cos (\theta )}.$$ (4)

In Equations (2)–(4), c₁ = exp(−τ/T₁), which is related to the longitudinal T₁ relaxation during each spoke τ in the multi-spoke IR-UTE data acquisition; $C_2=\exp \left[{\tau }^{\left(N_s-1\right)}/2T_1\right]$, which is related to the longitudinal T₁ relaxation during the whole multi-spokes (Ns-1) τ; and C₃ = exp {– [TR – TI – τ(N_s – 1)/2]/T₁}, which is related to the longitudinal T₁ relaxation during the interval between the last spoke and next adiabatic IR pulse [TR – TI – τ(N_s – 1)/2]. S₀ is the steady-state magnetization, τ is the time interval between two spokes, and θ is the flip angle. S_p is the longitudinal magnetization after the adiabatic IR pulse. The explicit derivation of S_p can be found in appendix I.

As the UTE-Cones sequence can achieve echo time (TE) as short as 32 μs, which is much shorter than the T₂ of most species. Theoretically, the 3D IR-UTE-Cones sequence can detect signals from short T₂ species before they decay to near zero. According to Equations (1)–(4), when TR is kept constant and TIs are set incrementally along the recovery curve of the longitudinal magnetization, T₁ can be calculated by nonlinear fitting of equations (1)–(4).

Imaging Parameters

All sequences were implemented on a 3T clinical MRI scanner (MR750, GE Healthcare Technology, Milwaukee, WI) with maximum gradient amplitude of 50 mT/m and 200 T/m/s slew rate. An eight-channel transmit/receive knee coil was used for RF transmission and signal reception.

The 3D IR-UTE-Cones sequence used an adiabatic inversion pulse (Silver-Hoult with a pulse duration of 6.048 ms, a bandwidth of 1.643 kHz, and a maximum B₁ amplitude of 17 μT) for robust inversion. The duration of the hard RF pulse is 30 μs. As T₁ values of the phantoms distributed on a wide range, two TRs of 50 ms and 400 ms were used to compare the effects of different TRs. For each TR, we used a series of TR/TI combinations (for TR = 50 ms, TI = 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 28, 32, 36, 40 ms; for TR = 400 ms, TI = 13, 15, 18, 25, 30, 40, 50, 70, 100, 130, 160, 200, 240, 280, 320, 360 ms). Other parameters were the same: TE = 32 μs; flip angle (FA) = 10°; field of view (FOV) = 120 × 120 × 128 mm³; acquisition matrix size = 160 × 160 × 32; readout bandwidth = ± 125 kHz. Total scan times were about 145 min and 362 min, respectively.

For the purpose of comparison, the commonly used 2D IR-FSE sequence and two previously reported T₁ measurement methods (18, 21), UTE Cones-based variable flip angle (VFA-UTE) sequence and variable repetition time (VTR-UTE) sequence, were performed as well. To minimize the signal loss caused by fast T₂* decay, the shortest TE achievable for each sequence was selected. The parameters for 2D IR-FSE were: TE/TR = 6.52/4000 ms; FOV = 120 × 120 mm²; slice thickness = 5 mm; matrix size = 192 × 192; readout bandwidth = ± 62.5 kHz; 13 TIs (TI = 50, 75, 100, 200, 300, 400, 600, 900, 1500, 2000, 2500, 3000, 3500 ms) were utilized for single slice imaging. The total scan time was about 30 min. Since both VFA-UTE and VTR-UTE are sensitive to the inhomogeneity of the transmitted B₁ field, the 3D dual TR UTE-Cones sequence was employed for actual flip angle imaging (AFI) and therefore B₁ field mapping. Parameters for AFI were: TE = 32 μs; TR = 20/100 ms; FOV = 120 × 120 × 128 mm³; matrix size = 160 × 160 × 32; FA = 45°; bandwidth = ± 125 kHz; scan time was about 20 min. Parameters for VFA were: TE = 32 μs; TR = 20 ms; FOV = 120 × 120 × 128 mm³; matrix size = 160 × 160 × 32; FA = 4°, 8°, 12°, 16°, 20°, 24°, 28°, 32°, 36°; bandwidth = ± 125 kHz; scan time was about 31 min. VTR-UTE used similar parameters except for the following changes: TR = 20, 40, 60, 80 ms; FA = 45°; scan time was about 34 min.

Furthermore, in order to estimate the range of T₂* values of phantoms, conventional 3D UTE-Cones acquisitions with 15 different TEs were executed. Parameters for T₂* measurement were: TE = 0.032, 0.2, 0.4, 0.8, 1.4, 2.2, 4.4, 6.6, 8.8, 11, 22, 33, 44, 66, 88 ms; TR = 100 ms; FOV = 120 × 120 × 128 mm³; matrix size = 160 × 160 × 32; FA = 20°; bandwidth = ± 125 kHz; scan time was about 86 min.

Data Analysis

The data analysis algorithm was written in MATLAB (MathWorks, Natick, MA). Levenberg-Marquard method was used for nonlinear least-squares curve fitting and executed offline on DICOM images obtained by the protocols described above. Regions of interest (ROIs) were placed in the center of each tube to avoid susceptibility artifacts near the interface. ROIs were then copied automatically to the corresponding site for all the images performed with different TIs at each TR. T₁ was calculated by nonlinear fitting of equations (1)–(4). The mean and standard deviation of T₁ were calculated for each tube. Linear regression analysis was performed between T₁ and MnCl₂ concentration for each method. The total scan time for the 3D IR-UTE-Cones method can be reduced by using a smaller number of TIs for each TR. We investigated the accuracy in T₁ estimation by using a smaller number of TIs, e.g., 5 vs. 16 or 17 TIs. Percent errors were calculated for each phantom by dividing the difference between the two T₁ values and the T₁ with more TIs, which was considered the reference standard.

RESULTS

Figure 2 displays representative images acquired with the 3D IR-UTE-Cones and 2D IR-FSE sequences with different TR/TI combinations. Tubes with higher MnCl₂ concentrations are “visible” with the 3D IR-UTE-Cones sequence but “invisible” with the 2D IR-FSE sequence with most TIs and TRs. In contrast, tubes with lower MnCl₂ concentrations (e.g., <= 0.24 mM) are more “visible” with the 2D IR-FSE sequence, and less “visible” with the 3D IR-UTE-Cones sequence, especially when a shorter TR of 50 ms is used. Tubes 7–12 were dark for all TIs with the 2D IR-FSE sequence, largely because of the high MnCl₂ concentrations and thus very short T₂* values (i.e., T₂*s were shorter than the TE of the 2D IR-FSE sequence). The 3D IR-UTE-Cones sequence captured signals of tubes with short T₂*s (tubes 7–12), which were undetectable (dark at any TI) with the 2D IR-FSE sequence. As a result, T₁ values of those tubes cannot be measured with the conventional 2D IR-FSE sequence but can be measured with the 3D IR-UTE-Cones sequence. Meanwhile, T₁ values of tubes with very low concentrations of MnCl₂ (e.g., tubes 1–3) can be measured with the 2D IR-FSE sequence but cannot be reliably measured with the 3D IR-UTE-Cones sequence, especially when a short TR (e.g., 50 ms) is used. The adiabatic IR pulse together with a short TR leads to efficient long T₂ suppression (27), precluding accurate quantification of T1s for phantoms with low concentrations of MnCl₂.

Figure 2.

Images acquired with 3D IR-UTE-Cones and 2D IR-FSE sequences. The first and middle row are representative images acquired with the 3D IR-UTE protocol at different TR/TI combinations: TR/TI = 50/8, 16, 24, and 36 ms (first row), TR/TI = 400/13, 50, 200, and 360 ms (middle row). The bottom row shows the images acquired with the 2D IR-FSE protocol at TR/TI = 4000/50, 300, 1500, and 3500 ms. The numbers of the tubes are labeled on the first image of the middle row.

The averaged T₁ and T₂* values, as well as standard deviations of each tube calculated from different protocols, are listed in table 1. The dashes in table 1 indicate data using those specific settings were not suitable for fitting (too big fitting errors due to inappropriate imaging parameters, for example, too narrow range of TIs/TEs to measure long T₁ values/T₂* values). The 3D IR-UTE-Cones method could measure T₁ values as short as 2.95 ms, with corresponding T₂* values as short as 0.14 ms, which was unachievable with the other three methods.

Figure 3 shows the fitting curves of each tube with the 3D IR-UTE-Cones method. Two different TRs of 50 ms and 400 ms were investigated. Excellent fitting was achieved for tubes 4–12 with a TR of 50 ms, and tubes 1–10 with a TR of 400 ms. Less accurate fittings were achieved for tubes with lower MnCl₂ concentrations, and thus longer T₂* values, when a shorter TR of 50 ms and a narrower range of TIs of 8–40 ms were used. On the other hand, increased fitting errors were observed for tubes with high MnCl₂ concentrations when a longer TR of 400 ms and a broader range of TIs of 13–360 ms were used. A shorter TR and narrower range of TIs are required for a more accurate estimation of extremely short T₁ values.

Figure 3.

The fitting curves of each tube under the 3D IR-UTE-Cones method. (a) The fitting curves of the TR = 50 ms set. (b) The fitting curves of the TR = 400 ms set.

Figure 4 presents the linear fittings between the MnCl₂ concentration and the relaxivity rate R₁ (1/T₁) calculated by the 3D IR-UTE-Cones method. The R₁ values show strong correlations (R equaled to 0.99904 and 0.99995 for TR of 50 ms and 400 ms respectively) with the MnCl₂ concentrations, suggesting that the 3D IR-UTE-Cones method could reliably measure T₁ values, especially short T₁ values for phantoms with high MnCl₂ concentrations and thus short T₂* values.

Figure 4.

The correlations between the R₁ values calculated using the 3D IR-UTE-Cones method and MnCl₂ solution concentrations. (a) The correlation between R₁ values from TR = 50 ms set (tube 4–12) and concentrations. (b) The correlation between R₁ values from TR = 400 ms set (tube 1–10) and concentrations.

Figure 5 shows nearly perfect correlations between MnCl₂ concentrations and R₁ values calculated from different methods, and correlations between the 3D IR-UTE-Cones and other methods (i.e., VTR-UTE, VFA-UTE, and IR-FSE) in terms of T₁ values. Those results demonstrate that the 3D IR-UTE-Cones method could accurately measure a broader range of T₁ values than the other three methods.

Figure 5.

Correlations between R₁s obtained from different methods and MnCl₂ solution concentrations and the correlations between the 3D IR-UTE-Cones method and other methods. (a) The correlations between R₁s obtained from 3D IR-UTE-Cones, VTR-UTE, VFA-UTE, and IR-FSE and MnCl₂ solution concentrations. (b) The enlargement of the region marked with a yellow dashed line in (a). (c) The correlations between T₁ values calculated by 3D IR-UTE-Cones and VTR-UTE, VFA-UTE, and 2D IR-FSE.

Table 2 shows the mean value and standard deviation of T₁ values calculated by fitting with 5 TIs at both TRs, and the T₁ percent errors between T₁ values calculated with 5 TIs and 16 TIs (when TR was 400 ms) or 17 TIs (when TR was 50 ms). Most of the percent errors were less than 5%, except for tubes 1 and 2 when TR was 400 ms (TR was too short to accurately calculate long T₁ values), tube 10 when TR was 400 ms (TR was too long to accurately calculate short T₁ values), and tubes 1–4 when TR was 50 ms (TR was too short to accurately calculate long T₁ values). The results demonstrated that five TIs were enough to calculate T₁ values accurately with the 3D IRUTE-Cones method when the parameters were appropriately set.

Table 2.

T₁ values calculated by fitting with five TIs under 3D IR-UTE-Cones method.

Tube Numbers	TR = 400 ms		TR = 50 ms
	T1_5 (ms)a	Percent Error (%)b	T1_5 (ms)a	Percent Error (%)b
1	5252.08±1423.90	67.63%	-	-
2	3173±628.66	20.20%	-	-
3	847.94±57.16	1.78%	-	-
4	159.07±2.23	0.40%	181.22±1.74	21.67%
5	76.59±0.31	0.08%	87.6±3.19	2.76%
6	51.87±0.33	0.02%	55.53±0.22	4.73%
7	37.03±0.05	2.63%	37.21±0.88	0.93%
8	19.10±2.87	0.05%	18.98±0.03	0.53%
9	9.68±0.55	1.36%	9.41±0.01	0.21%
10	6.86±2.26	8.37%	6.32±0.01	0.16%
11	-	-	3.16±0.10	0.32%
12	-	-	2.99±0.24	1.36%

^aT₁_5 represents the T₁ values calculated with five TIs at both TRs (TR/TI = 50 / 8, 12, 16, 24, 40 ms; TR/TI = 400 / 13, 40, 130, 240, 360 ms ).

^bPercent Error represents the T₁_5 value errors compared with T₁ values calculated with 16 TIs when TR = 400 ms and 17 TIs when TR = 50 ms, respectively. The percent error of each tube is the difference between the T₁_5 and the corresponding T₁ in Table 1 divided by T₁ values in Table 1.

DISCUSSION

This phantom study demonstrated that the 3D IR-UTE-Cones method can be used as a valid method for T₁ measurement, especially for species with short T₂* values and short T₁ values. For phantoms with relatively long T₂* values and T₁ values, all four methods, including 2D IR-FSE, 3D VFA-UTE, 3D VTR-UTE, and 3D IR-UTE-Cones methods, provided similar results where excellent linear correlations were observed between T₁ relaxation rates (R₁s) and MnCl₂ concentrations. For phantoms with short T₂* values and short T₁ values, the 2D IR-FSE method was incapable of either imaging or T₁ quantification. Compared with 3D VFA-UTE and VTR-UTE methods, the 3D IR-UTE-Cones method produced a more accurate measurement of shorter T₁ values (phantoms with higher concentrations of MnCl₂). For the 3D IR-UTE-Cones method, the scan time was shortened by fitting with fewer TIs at an acceptable error (i.e., less than 5% error). However, the 3D IR-UTE-Cones method was not suitable for measuring long T₁ values, unless a very long TR was used at the cost of scan time. The method worked best for measuring short or extremely short T₁ values of short T₂ species.

Benefitting from the combination of the inversion recovery method and the 3D UTE-Cones acquisition scheme, the proposed 3D IR-UTE-Cones method provided both excellent imaging contrast and accurate measurement of T₁ values for phantoms with short T₂* values. This was a significant advantage over the clinical 2D IR-FSE method, as well as the new 3D VFA-UTE and VTR-UTE methods. The echo time of the 3D UTE-Cones sequence is as short as 32 μs, which was short enough to capture signals from short T₂* phantoms (e.g., T₂* of 0.14 ms for tube 12), as shown in Table 1. On the other hand, for the clinical 2D IR-FSE sequence, the shortest echo time was 6.52 ms, during which the signals from tubes 6 to 12 had completely decayed. Previously reported 3D UTE-Cones-based VFA and VTR methods have drawbacks, such as high sensitivity to the B₁ field inhomogeneity [26] and poor image contrast for short T₂ species. Both VFA and VTR methods need to be combined with AFI to do B₁ correction, but one of the fundamental assumptions which general AFI relies on is that the two TRs (a shorter TR1 and a longer TR2) are much shorter than the T₁ [33]. TRs for the AFI-VFA-UTE-Cones and AFI-VTR-UTE-Cones protocols could not satisfy the condition TR << T₁ values when the T₁ values were very short. Consequently, the ultrashort T₁ values of tube 9 to 11 were unable to be measured with these two methods. Furthermore, the fitting model of the proposed 3D IR-UTE-Cones method introduced an inversion recovery efficiency factor Q, which describes the inversion status of tissues with different T₂* values more precisely than conventional SE- and GRE-based IR methods, making the measured short T₁ values of short T₂* species more accurate.

The 3D IR-UTE-Cones method also provided high contrast images for short T₂ species, another significant advantage over the other three methods. In 3D IR-UTE-Cones imaging, long T₂ and long T₁ species were excellently suppressed, especially when a shorter TR was used, providing excellent contrast for short T₂ species. The short T₂ species appear with much reduced image contrast with both VFA-UTE and VTR-UTE due to the high signals from species with longer T₁ and T₂ values. The advantage of the 3D IR-UTE-Cones method in terms of high contrast imaging is even more obvious for short T₂ species, such as cortical bone, as these species are nearly “invisible” to both VFA-UTE and VTR-UTE imaging due to their low proton density and short T₂*, resulting in much lower signal than the surrounding species which have higher proton densities and longer T₂s, such as muscle and marrow fat.

As shown in Table 1 and Figure 3, TR plays an important role in the accurate quantification of T₁ relaxation when using the 3D IR-UTE-Cones method. The general rule is that a longer TR is preferred for more accurate quantification of longer T₁s, while a shorter TR is preferred for more accurate quantification of shorter T₁s. When the T₁ is much longer than the TR, the fitting is unreasonable and the resulting T₁ value is deemed unacceptable due to the considerable fitting error. The nulling points of the fitting curves of tubes 1–3 should be greater than the curves of tubes 4–12 in Figure 3(a) and the nulling point of the fitting curve of tube 1 should be greater than tubes 2–12 in Figure 3(b), indicating that the TRs of 50 ms and 400 ms were inappropriate for T₁ measurements of tubes 1–3 and tube 1, respectively. When the T₁ is much shorter than the TR, measurement with a relatively long TR would be inaccurate, as well. As shown in Figure 3(b), the data sample points of tubes 11–12 deviated significantly from the fitting curves, which resulted in large fitting errors and unreasonable fitting results, illustrating that the data acquired with a long TR of 400 ms were not suitable for short T₁ calculations. In IR-UTE imaging, long T₂ signals will be suppressed more efficiently by using a shorter TR (e.g., 50 ms in this study) (27). Tubes 4–5 have relatively long T₂*s of 10.61 and 4.99 ms, respectively, as shown in Table 1. The IR pulse will partially invert their longitudinal magnetizations as the duration of the adiabatic IR pulse is on the order of their T₂*s [27, 34]. When a short TR (e.g., 50 ms) is used, tubes 4–5 show as low signal in 3D IR-UTE-Cones imaging, leading to increased errors in T₁ quantification. A longer TR (e.g., 400 ms) is expected to provide more accurate T₁ quantification for tubes 4–5, consistent with results shown in Tables 1 and 2. A longer T₁ means much increased scan time with the 3D IR-UTE-Cones method. Furthermore, tissues with longer T₁s may also be imaged and quantified with conventional clinical sequences. And thus the 3D IR-UTE-Cones method is of less importance. On the other hand, tissues with very short T₁s, such as iron overload in the liver or spine [35, 36], or hemosiderin in the hemophilia joint [37], cannot be imaged and quantified with conventional clinical sequences. The 3D IR-UTE-Cones sequence with a longer TR (e.g, 400 ms) may not work well when the iron concentration is too high and T₂* too short (e.g., T₂* < 0.3 ms). In such cases, a shorter TR (e.g., 50 ms) is expected to work better, providing more accurate quantification of T₁ relaxation. Consequently, the 3D IR-UTE-Cones method based on short TRs is extremely suitable for short T₁ measurements of short T₂ species. However, the shortest TR is limited by the acceptable specific absorption ratio (SAR).

With the advantage of being able to measure short T₁ values of short T₂ species, the proposed 3D IR-UTE-Cones method could be promising in a variety of applications. For instance, as the accumulation of iron shortens both T₁ and T₂* values of local tissue, T₁ could be used as a biomarker of iron overload, both spatially (location) and quantitatively (concentration). In several pathologies, accumulation of iron occurs after frequent blood transfusions or in the case of excess iron absorption [38, 39]. Recently, quantitative susceptibility mapping (QSM) was supposed to quantify the liver iron concentration (LIC), but the QSM and LIC only showed correlation at low LIC levels [35, 40]. The 3D IR-UTE-Cones method can be used to quantify LIC with T1 mapping at high LIC levels. Similarly, the presence of hemorrhage modulates T₁ and T₂ values. T₂ values have previously been used to identify hemorrhage [41]; analogously, T₁ mapping could be used as a probe for hemorrhage detection. The proposed 3D IR-UTE-Cones T₁ mapping might therefore be a useful method. In the iron oxide nanoparticles (IONPs)-based hyperthermia therapy and stem cell therapy, the 3D IR-UTE-Cones method could be utilized to visualize the locations and concentrations of the IONPs or labeled stem cells with T₁ mapping [10, 42]. One of our recent studies showed that the iron accumulation in the cartilage of hemophilic populations decreased T₂* values of cartilage [37], presenting another potential application of the proposed 3D IR-UTE-Cones T₁ measurement method.

This study has several limitations. First, we have only demonstrated the technical feasibility of the 3D IR-UTE-Cones method in measuring short T₁ values of short T₂* species by studying MnCl₂ aqueous solution phantoms. No ex vivo or in vivo experiments were completed in this study. Second, the efficiency and accuracy of the 3D IR-UTE-Cones protocol in terms of signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were not assessed or compared with the other three T₁ measurement methods mentioned above. However, it is quite obvious that the 3D IR-UTE-Cones method provides improved CNR for phantoms with high MnCl₂ concentrations over 2D IR-FSE, VFA-UTE, and VTR-UTE methods. Third, Nss were set to 1 for both TRs, and the number of TIs along each inversion recovery curve for a TR of 50 ms and 400 ms were set to 17 and 16, respectively. These were the main reason for the long total scan time. Multi-spoke acquisitions (e..g, Ns of more than 30) and fewer TIs could be used in future study to reduce the scan time. Fourth, as there are many potential clinical applications, such as iron quantification in diseases like hemophilia, thalassemia, liver diseases, etc., and T₁ mapping for cortical bone, ligaments, tendons, etc., clinical evaluation of this novel technique remains to be done.

CONCLUSION

In this study, we demonstrated the feasibility of using the inversion recovery-prepared 3D ultrashort echo time Cones sequence to accurately measure short T₁ values while providing high contrast images of short T₂ species.

• Capable of quantifying the T1 of short T2 species;

• Can measure T1 as short as 2.95 ms;

• Introduce an inversion efficiency factor Q to accurately measure a wide range of T1.