Fast T₁ Measurement of Cortical Bone using 3D UTE Actual Flip Angle Imaging and Single Repetition Time Acquisition (3D UTE-AFI-STR)

Abstract

Purpose:

To describe a new method for accurate T₁ measurement of cortical bone which fits the datasets of both 3D UTE Actual Flip Angle Imaging (UTE-AFI) and UTE with a Single TR (UTE-STR) simultaneously (UTE-AFI-STR).

Theory and Methods:

To make both the constant values and longitudinal mapping functions in the signal equations for UTE-AFI and UTE-STR identical, the same RF pulses and flip angles were used. Therefore, there were three unknowns in the three equations. This was sufficient to fit the data. Numerical simulation as well as ex vivo and in vivo cortical bone studies were performed to validate the T₁ measurement accuracy with the UTE-AFI-STR method. The original UTE-AFI-VTR (i.e. combined UTE-AFI and UTE with Variable TR (UTE-VTR)) and simultaneous fitting (sf) of UTE-AFI and UTE-VTR (sf-UTE-AFI-VTR) methods were performed for comparison.

Results:

The numerical simulation study showed that the UTE-AFI-STR method provided accurate value of T₁ when the SNR of the UTE-STR image was higher than 40. The ex vivo study showed that the UTE-AFI-STR method measured the T₁ of cortical bone accurately, with difference ratios ranging from −5.0% to 0.4%. In vivo study showed a mean T₁ of 246 ms with the UTE-AFI-STR method, and mean difference ratios of 2.4% and 5.0% respectively compared with the other two methods.

Conclusion:

The 3D UTE-AFI-STR method provides accurate mapping of the T₁ of cortical bone with improved time efficiency compared with the UTE-AFI-VTR/sf-UTE-AFI-VTR methods.

INTRODUCTION

Cortical bone is MR invisible with conventional clinical MRI sequences, such as gradient recalled echo and fast spin echo, which typically have TEs of several milliseconds or more. This is because the T₂* of cortical bone water is very short (less than 1ms) and the signal decays to a low or zero level by the time of the data acquisition (1). UTE sequences with nominal TEs of less than 100 μs have been used for cortical bone water imaging and quantification in order to acquire useful MR signals (2). Researchers have found that measurement of the T₁ of cortical bone is useful to assess cortical bone porosity and age related deterioration (3). T₁ is also a sensitive biomarker for monitoring temperature change in cortical bone (4). In addition, accurate T₁ measurement is an essential input for other quantitative MRI methods of assessing cortical bone such as quantitative magnetization transfer modeling (5,6). As a result, several UTE-based methods for measurement of the T₁ of cortical bone have been developed. These include adiabatic Inversion Recovery prepared UTE (IR-UTE) (7,8), Saturation Recovery prepared UTE (SR-UTE) (9), UTE with Variable Flip Angle (UTE-VFA) (4,10) and UTE with Variable TR (UTE-VTR) (11,12). Because the transverse magnetization of cortical bone matrix water decays very rapidly during the relatively long inversion pulses used on clinical systems, its longitudinal magnetizations cannot be effectively inverted (2). As a result, conventional IR-based T₁ measurement techniques are not suitable for measurement of cortical bone T₁s. In addition, with both the IR and SR techniques, multiple acquisitions are required for T₁ modeling (multiple inversion times with the IR method, and multiple saturation recovery times with the SR method). This makes the acquisition times of these techniques too long for routine clinical use.

UTE-VFA and UTE-VTR are more time efficient methods for T₁ measurement than IR-UTE and SR-UTE based methods. However, both UTE-VFA and UTE-VTR are very sensitive to B₁ inhomogeneity. Actual flip angle imaging (AFI) can be used for fast B₁ mapping to correct B₁ inhomogeneity and so improve T₁ quantification. This fits well with UTE-VFA and UTE-VTR methods, especially for 3D sequences (13). Typically, a relatively large flip angle (FA) (> 40°) is required with the AFI or UTE-AFI technique to achieve high sensitivity for accurate B₁ measurement (12,13). This large FA requires a relatively long RF excitation pulse due to the peak power limitations of the RF amplifiers used on clinical MRI scanners (12). As a result, the excitation of cortical bone water with its ultrashort T₂ is not efficient during the RF excitation pulse and so the actual FA achieved is less than the expected FA (12,14). Consequently, the B₁ map obtained with the AFI technique is inaccurate and this leads to errors in VFA and VTR based T₁ measurements (12).

To overcome the excitation inefficiency problem with ultrashort T₂ tissue imaging using the UTE-AFI sequence, we recently implemented a 3D UTE-AFI-VTR method and used this to obtain accurate T₁ measurements of cortical bone (12). Instead of calculating a B₁ inhomogeneity map with the usual AFI method, a longitudinal magnetization mapping function containing information about both B₁ inhomogeneity and excitation efficiency was obtained using the UTE-AFI-VTR method. With the longitudinal magnetization mapping function as input, several UTE-VTR acquisitions with the same FA as the UTE-AFI sequence (to maintain the same excitation efficiency) were used for T₁ fitting. As a result, the UTE-AFI-VTR method achieved accurate measurement of the T₁ of cortical bone without degradation from the inefficient RF excitation of clinical scanners. However, the scan time of the 3D UTE-AFI-VTR sequence was relatively long for clinical practice because multiple TRs were required.

To address this problem and improve time efficiency for accurate T₁ measurement we combined the UTE-AFI method and the UTE with a single TR (UTE-STR) method as UTE-AFI-STR. A generalized optimization framework was utilized to simultaneously fit the UTE-AFI and UTE-STR data sets to estimate T₁. Numerical simulations, ex vivo human cortical bone studies, as well as in vivo human tibial cortical bone studies were conducted to assess the feasibility and accuracy of the proposed UTE-AFI-STR method for measurement of the T₁ of cortical bone water using a clinical 3T scanner.

THEORY

The features of the 3D UTE-AFI and UTE-VTR sequences are shown in Supporting Information Figure S1 (12). A short rectangular RF pulse (duration 150 μs) is used for signal excitation and this is followed by a spiral trajectory data acquisition with 3D conical view ordering in these two sequences.

For ultrashort T₂ tissue excitation, the steady-state signals in TR₁ and TR₂ of the 3D UTE-AFI sequence conform to the following signal models (12,13):

$$S_{AFI,1}=M_0{F}_{xy}\left(\alpha ,\tau ,T_2\right)\frac{1-E_{AFI,2}+\left(1-E_{AFI,1}\right)E_{AFI,2}{F}_Z\left(\alpha ,\tau ,T_2\right)}{1-E_{AFI,1}{E}_{AFI,2}{F}_Z^2\left(\alpha ,\tau ,T_2\right)}$$ [1]

$$S_{AFI,2}=M_0{F}_{xy}\left(\alpha ,\tau ,T_2\right)\frac{1-E_{AFI,1}+\left(1-E_{AFI,2}\right)E_{AFI,1}{F}_Z\left(\alpha ,\tau ,T_2\right)}{1-E_{AFI,1}{E}_{AFI,2}{F}_Z^2\left(\alpha ,\tau ,T_2\right)}$$ [2]

where E_AFI,1 = exp(−TR₁/T₁) and E_AFI,2 = exp(−TR₂/T₁). M₀ is the equilibrium magnetization. F_xy (α, τ, T₂) $\left(F_{xy}\left(\alpha ,\tau ,T_2\right)=M_{xy}^{+}/M_z^{-}\right)$ and F_z (α, τ, T₂) $\left(F_Z\left(\alpha ,\tau ,T_2\right)=M_Z^{+}/M_Z^{-}\right)$ are respectively the transverse and longitudinal magnetization mapping functions generated by the RF pulse (12). $M_{xy}^{+}$ and $M_Z^{+}$ are respectively the transverse and longitudinal magnetizations after RF excitation, and $M_z^{-}$ is the longitudinal magnetization before RF excitation. For a tissue with a T₂ of the same order as the RF pulse duration τ, F_xy (α, τ, T₂) and F_z (α, τ, T₂) are functions of τ, FA α, and tissue T₂ (14). T₁ relaxation during the excitation is neglected in the mapping function since the RF pulse duration is much shorter than the T₁ of the tissue.

As reported with the UTE-AFI-VTR method, when TR₁ and TR₂ are much shorter than T₁, F_z (α, τ, T₂) can be calculated as follows (12):

$$F_Z\left(\alpha ,\tau ,T_2\right)\approx \frac{rn-1}{n-r}$$ [3]

where r = S_AFI,2/S_AFI,1, and n = TR₂/TR₁. The value obtained for F_z (α, τ, T₂) is subsequently utilized in the VTR signal model for T₁ calculation.

The signal detected by the 3D UTE sequence is described by the following equation (12):

$$S_{VTR}=M_0{F}_{xy,VTR}\left(\alpha ,\tau ,T_2\right)\frac{1-E_{VTR}}{1-E_{VTR}{F}_{Z,VTR}\left(\alpha ,\tau ,T_2\right)}$$ [4]

with E_VTR = exp(−TR_VTR/T₁). TR_VTR is the TR used in the 3D UTE sequence. Analogous to F_xy (α, τ, T₂) and F_z (α, τ, T₂) in Eqs. [1] and [2], F_xy,VTR (α, τ, T₂) and F_z,VTR (α, τ, T₂) in Eq. [4] are the respective transverse and longitudinal magnetization mapping functions produced by the RF pulse. When the RF pulse and FA used in the AFI and VTR sequences are identical, F_xy,VTR (α, τ, T₂) and F_z,VTR (α, τ, T₂) in Eq. [4] are equal to F_xy (α, τ, T₂) and F_z (α, τ, T₂) in Eqs. [1] and [2]. Thus, F_z (α, τ, T₂) calculated from Eq. [3] can be substituted into Eq. [4]. In addition, since M₀ and F_xy,VTR (α, τ, T₂) are independent of TR, they can be combined into a single unknown parameter (e.g., κ) for fitting. As a result, in the original UTE-AFI-VTR method, there are two unknown parameters (κ and T₁) in Eq. [4] to fit.

Eq. [3] of the AFI method is valid when two fundamental requirements are met. These are: (i) TR₁ and TR₂ must be much shorter than T₁; (ii) the transverse magnetizations must be completely spoiled at the end of both TR₁ and TR₂ (13). Since the transverse magnetization of ultrashort T₂ tissues decays rapidly during TR₁ and TR₂, the second requirement is easily achieved. In some conditions when the T₁ of a tissue is very short (e.g. from exposure to high concentrations of either a paramagnetic contrast agent or organic iron) and is close to, or less than the TRs used in AFI (7), the first condition may not be met (15). To generalize the AFI technique for accurate F_z measurements for both short and long T₁ tissues, we used the optimization framework below to simultaneously fit (sf) UTE-AFI and UTE-VTR (sf-UTE-AFI-VTR) data without requiring compliance with the first requirement above using:

$$\left[\mathrm{\kappa }{T}_1{F}_Z\right]=\text{arg}\underset{\mathrm{\kappa },T_1,F_Z}{\text{min}}\left\{\sum _{i=1}^2{\left[I_{AFI,i}-S_{AFI,i}\right]}^2+\sum _{j=1}^N{\left[I_{VTR,j}-S_{VTR,j}\right]}^2\right\}$$ [5]

where arg min_x(y(x)) means finding a x value which can make y(x) attain its minimum value. I_AFI,i (i = 1 and 2) and I_VTR,j (j = 1, 2, …, N) are the sampled signal intensities from the UTE-AFI and UTE-VTR sequences respectively. N is the total number of TRs. When identical RF pulses and FAs are used with both the AFI and VTR sequences, κ = M₀F_xy (α, τ, T₂) = M₀F_xy,VTR (α, τ, T₂). This framework simultaneously yields a solution for the three unknown parameters: κ, T₁, and F_z.

Since there are only three unknown parameters in Eq. [5], a single regular UTE acquisition together with the other two UTE-AFI acquisitions is sufficient to estimate them using the optimization framework. To save scan time, we therefore propose a UTE-AFI-STR method (i.e. a combination of the UTE-AFI and UTE-STR methods) to provide accurate measurement of T₁.

METHODS

All sequences were implemented on a clinical 3T MRI scanner (MR750, GE Healthcare Technology, Milwaukee, WI) with a maximum gradient amplitude of 50 mT/m and a maximum slew rate of 200 T/m/s. An eight-channel transmit/receive knee coil was used for RF transmission and signal reception. With the 3D UTE-AFI sequence, the areas of the gradient crushers used during TR₁ and TR₂ were 450 and 2250 mT ms/m respectively, and the RF phase increment was 39° (16). With the 3D UTE-VTR sequence, the gradient crusher was 450 mT/ms/m and the RF phase increment was 169° (16). With both the UTE-AFI and UTE-VTR sequences, a TR of 20 ms was the shortest value achievable on the scanner due to the need for a strong gradient crusher. Both the RF pulse duration (i.e. τ = 150 μs) and FA (i.e. 45°) were kept identical in the UTE-AFI and UTE-VTR sequences in all the studies.

To assess the accuracy of T₁ measurement of cortical bone and provide a comparison with the UTE-AFI-STR method, T₁ maps were also calculated using two other fitting methods: namely the original UTE-AFI-VTR method described by Eqs. [3] and [4] and the sf-UTE-AFI-VTR method described by Eq. [5]. In the original UTE-AFI-VTR method, at least four TRs were usually employed for UTE-VTR fitting (11,12). All the UTE-AFI and UTE-VTR data were used in the sf-UTE-AFI-VTR fitting.

Numerical Simulation

Numerical simulations were performed to generate UTE-AFI and UTE-VTR images with different signal to noise ratios (SNRs) for T₁ mapping using the three fitting methods (i.e. UTE-AFI-VTR, sf-UTE-AFI-VTR and UTE-AFI-STR). The UTE-AFI and UTE-VTR images were generated using Eqs. [1] to [3] with sequence parameters matching those listed in Table 1 for the in vivo experiments:(i) 3D UTE-AFI: TR₁/TR₂ = 20/100 ms, FA = 45°, τ = 150 μs; (ii) 3D UTE-VTR: TR = 20, 30, 40, and 80 ms, FA = 45°, τ = 150 μs. T₁ and T₂ were set to 220 ms and 0.4 ms respectively (2,12). The B₁ inhomogeneity scale factor (defined as the ratio between actual FA and the expected FA) was linearly distributed from 0.8 to 1.2 in the left-to-right direction of the image. A UTE-STR acquisition with the minimum TR of 20 ms was used for UTE-AFI-STR fitting.

Table 1.

Sequence parameters of ex vivo and in vivo human cortical bone studies.

	UTE-AFI	UTE-VTR
Ex Vivo	FOV = 140 × 140 ×100 mm3, matrix = 256 × 256 × 100, TE = 32 μs, TR1/TR2 = 20/100 ms, FA = 45°, bandwidth = 166.6 kHz, total scan time = 36 min 6 sec.	FOV = 140 × 140 ×100 mm3, matrix = 256 × 256 × 50, TE = 32 μs, TR = 20, 30, 50 and 100 ms, FA = 45°, bandwidth = 166.6 kHz, total scan time = 60 min 14 sec, scan time of TR = 20 ms sequence was 6 min.
In Vivo	FOV = 130 × 130 ×144 mm3, matrix = 140 × 140 × 48, TE = 32 μs, TR1/TR2 = 20/100 ms, FA = 45°, bandwidth = 250 kHz, total scan time = 14 min 4 sec.	FOV = 130 × 130 ×144 mm3, matrix = 140 × 140 × 24, TE = 32 μs, TR = 20, 30, 40 and 80 ms, FA = 45°, bandwidth = 250 kHz, total scan time = 19 min 40 sec, scan time of TR = 20 ms sequence was 2 min 41sec.

Complex-valued noise with independent real and imaginary parts was added to the simulated UTE-AFI and UTE-VTR data. Both the real and imaginary noise followed a normal distribution with a mean value of zero and a standard deviation of 1 (17). The magnitude of the complex valued images was used for SNR and T₁ measurements. The SNRs of the UTE-STR acquisitions were set to five different values (SNR = 160, 80, 40, 20, and 10). At each SNR level, both the T₁ and the corresponding error ratio maps for the three methods described above were calculated. The error ratio map is defined as the ratio of the difference between the measured and the standard T₁ maps (i.e. T₁ of 220 ms) divided by the standard T₁ map. In addition, a T₁ map was calculated using the regular UTE-VTR method without B₁ correction with a SNR of 160 to investigate the effect of B₁ inhomogeneity on T₁ measurement.

Ex Vivo Study

Nine human cortical bone samples (donors aged from 38 to 95 years, 5 females) were scanned. The human cortical bone specimens were provided by a nonprofit whole body donation company (United Tissue Network, Phoenix, AZ). The bone marrow and other soft tissues were removed manually and the bone specimens were then immersed in phosphate-buffered saline for 2–4 hours to minimize gas trapping. The bone specimens were next immobilized in plastic containers filled with Fomblin (MRI invisible) to minimize the effects of dehydration, and susceptibility artifacts during scanning. The sizes of the nine human bone samples are summarized here: diameters ranged from 2.5 to 4.0 cm, thicknesses ranged from 0.3 to 1.4 cm, and lengths ranged from 2.4 to 3.2 cm. More details about how these measurements were made can be found in Supporting Information Figure S2.

The parameters of both 3D UTE-AFI and UTE-VTR sequences for this cortical bone sample study and following in vivo study are shown in Table 1. The total scan time of UTE-AFI-STR method was about 54 minutes less than the UTE-AFI-VTR/sf-UTE-AFI-VTR methods.

In Vivo Study

Both 3D UTE-AFI and UTE-VTR sequences were used in four healthy volunteers (35 ± 16 years old, 3 males) to measure the T₁ of tibial cortical bone. Informed consent was obtained from each subject in accordance with the guidelines of the Institutional Review Board. The total scan time of the UTE-AFI-STR method was about 17 minutes less than that of the UTE-AFI-VTR/sf-UTE-AFI-VTR methods (see Table 1).

Data Analysis

All data analyses were conducted offline with Matlab (MathsWork Inc, Natick, MA, USA). The Levenberg-Marquardt algorithm was used to solve the nonlinear minimization of Eq. [5]. Before data fitting, both the UTE-AFI and UTE-VTR images were smoothed with a gaussian filter of kernel size 4×4 and standard deviation 0.9. For the sample study, the regions of interests were drawn in relatively central sections to avoid errors in T₁ measurement due to partial volume effects at cortical bone boundaries. The difference ratios were defined as the ratios of the mean T₁ differences between the UTE-AFI-STR and UTE-AFI-VTR/sf-UTE-AFI-VTR methods divided by the mean T₁ obtained from the UTE-AFI-VTR/sf-UTE-AFI-VTR sequences. The SNR of cortical bone on the UTE-STR image was calculated by dividing the mean signal intensity of the cortical bone region by the standard deviation of background noise on the corresponding image. Before any other data processing for the in vivo studies, 3D motion registration was performed with elastix software on images obtained with both the UTE-AFI and UTE-VTR methods. This was to correct the subject inter-scan motion (18).

RESULTS

Figure 1 shows simulations of two UTE-AFI (with TR = 20 ms (a) and with TR = 100 ms (b)) images, and a UTE-VTR (i.e. UTE-STR) (with TR = 20 ms) image (c), a B₁ map (d), as well as the T₁ map calculated using the regular VTR method without B₁ correction with a SNR of 160 (e). The T₁ map generated using the VTR method shows obvious B₁ inhomogeneity (e). Thus, B₁ correction is essential for this VTR based method.

Figure 1.

Simulations of two UTE-AFI (with TR of 20 ms (a) and with TR of 100 ms (b)) images, and a UTE-VTR (TR = 20 ms) (i.e. UTE-STR) image (c), B₁ map (d), and T₁ map generated with the regular VTR method without B₁ correction (e). The T₁ map in (e) was calculated using the VTR method with four UTE acquisitions with TRs of 20, 30, 40, and 80 ms.

Figure 2 shows T₁ maps calculated using the three methods (i.e. UTE-AFI-VTR, sf-UTE-AFI-VTR and UTE-AFI-STR) with simulated UTE-AFI and UTE-VTR images at five different SNRs. The corresponding error ratio maps are shown as well. The B₁ inhomogeneity was effectively corrected using all three methods. Greater fluctuation is present on the T₁ maps generated with the lower SNR images than with the higher SNR images, and the errors increase accordingly. When the SNR of the UTE-STR image was higher than 40, the error ratios ranged from −5% to 5%, which shows that the T₁ values derived from these three methods are close to the standard T₁ value (i.e. 220 ms). When the SNR of the UTE-STR image was lower than 40, the T₁ maps fluctuated widely and the corresponding error ratio values exceeded 5%. These observations show that the fast UTE-AFI-STR method is accurate for T₁ measurement when the SNR of the UTE-STR image is higher than 40.

Figure 2.

Simulation results for T₁ measurement using the UTE-AFI-VTR (first row), sf-UTE-AFI-VTR (second row) and UTE-AFI-STR (third row) methods at five different SNRs (i.e. SNR = 160 in the first column, 80 in the second column, 40 in the third column, 20 in the fourth column and 10 in the last column). The error ratio maps between the T₁ maps generated by the UTE-AFI-STR method and the standard T₁ value (i.e. 220 ms) at each SNR level are shown in the fourth row. Degradation of the error ratio is seen in this row when the SNR is decreased.

Figure 3 shows representative cortical bone T₁ maps of an ex vivo human cortical bone sample and four in vivo healthy volunteers. The T₁ maps of both ex vivo and in vivo cortical bones obtained with these three methods looked similar. This consistency is also seen in Table 2 where the difference ratios range between −5.0% and 0.4%, and −5.0% to 7.6% for ex vivo and in vivo measurements, respectively. This observation is not surprising since all the UTE-STR data have a SNR higher than 40 (see Table 2). Both the ex vivo and in vivo studies demonstrate the accuracy and good agreement of the T₁ measurement of the UTE-AFI-STR method compared with the other two methods which require much more scan time. The average cortical bone T₁ for the four volunteers calculated using the UTE-AFI-STR method was 246 ms, which is similar to previously reported values (9,11,13).

Figure 3.

Representative ex vivo human cortical bone sample (first row) and in vivo tibial cortical bone T₁ maps of four healthy volunteers (second to fifth row) generated using the UTE-AFI-VTR (first column), the sf-UTE-AFI-VTR (second column) and the UTE-AFI-STR (third column) methods. Similar appearances on the T₁ maps are seen with each of the three methods.

Table 2.

Mean and standard deviation of the T₁s (ms) of ex vivo and in vivo human cortical bone samples calculated with the UTE-AFI-VTR, sf-UTE-AFI-VTR and UTE-AFI-STR methods, corresponding difference ratios (%), as well as SNRs of the UTE-STR data with a TR of 20 ms.

Human Cortical Bone		T1 (ms)			SNR
		UTE-AFI-VTR	sf-UTE-AFI-VTR	UTE-AFI-STR
Ex Vivo	#1	235±17 (−3.8%)	231±19 (−2.2%)	226±23	55
	#2	219±18 (−5.0%)	216±21 (−3.7%)	208±27	68
	#3	226±22 (−4.0%)	222±23 (−2.3%)	217±29	63
	#4	225±16 (−4.4%)	220±20 (−2.3%)	215±23	42
	#5	222±17 (−5.0%)	216±20 (−2.3%)	211±24	50
	#6	221±14 (−3.6%)	218±17 (−2.3%)	213±20	43
	#7	231±25 (−1.7%)	226±26 (0.4%)	227±36	43
	#8	207±21 (−4.3%)	203±22 (−2.5%)	198±25	59
	#9	220±16 (−4.1%)	217±20 (−2.8%)	211±24	45
	meana	223±8 (4.0%)	219±8 (2.3%)	214±9
In Vivo	#1	226±21 (−1.3%)	219±19 (1.8%)	223±27	59
	#2	230±44 (4.8%)	228±36 (5.7%)	241±32	64
	#3	250±36 (2.0%)	237±37 (7.6%)	255±49	54
	#4	269±28 (−1.5%)	279±30 (−5.0%)	265±41	50
	meanb	244±20 (2.4%)	240±27 (5.0%)	246±18

^aMean T₁ values and mean absolute difference ratios of the nine ex vivo human cortical bone samples.

^bMean T₁ values and mean absolute difference ratios of the four in vivo human tibial cortical bones.

DISCUSSION

In this study we demonstrated the use of a new UTE-AFI-STR method with simultaneous fitting of UTE-AFI and UTE-STR datasets to obtain accurate T₁ mapping of cortical bone water. This was validated by numerical simulations as well as ex vivo and in vivo cortical bone studies. Numerical simulations demonstrated that the UTE-AFI-STR method provides reliable measurement of T₁ when the bone SNR in UTE-STR images (TR = 20 ms) is higher than 40. In both the ex vivo and in vivo cortical bone studies, the T₁ maps estimated using the UTE-AFI-STR method with its much shorter scan time were almost identical to maps derived from the original UTE-AFI-VTR and sf-UTE-AFI-VTR methods which have much longer scan times. The proposed 3D UTE-AFI-STR method is time efficient and has considerable potential for accurate mapping of the T₁ of cortical bone in clinical practice.

The mean cortical bone T₁ values for the four volunteers measured with UTE-VTR, UTE-AFI-VTR, sf-UTE-AFI-VTR and UTE-AFI-STR methods were 179, 244, 240, and 246 ms, respectively. The UTE-VTR method without correction of both B₁ inhomogeneity and excitation inefficiency underestimated the T₁ value, which is consistent with the findings in our previous work (12).

Theoretically, UTE-VTR data with different TR setups for T₁ measurement by the UTE-AFI-VTR/sf-UTE-AFI-VTR methods are not expected to make a significant difference to the estimation of T₁s. A systematic validation study with variable sequence setups for the same sample would be of interest in a future study.

The UTE-AFI-STR method is time efficient. In the original UTE-VTR and UTE-AFI-VTR methods, a series of UTE acquisitions with different TRs were needed to ensure accuracy of the T₁ measurement (11,12). However, with the framework used by the UTE-AFI-STR method, a single UTE acquisition with a short TR is sufficient to achieve accurate T₁ measurement (in addition to the AFI dataset). This significantly reduces scan time compared with the UTE-AFI-VTR/sf-UTE-AFI-VTR methods. In theory, more accurate T₁ estimation by UTE-AFI-VTR method can be achieved from UTE-VTR data with more TRs of different values, including ones in particular with long TRs (i.e., high image SNRs and dynamic range). In this study, it is beneficial to validate the T₁ measurement accuracy of our proposed UTE-AFI-STR method by comparing it with reliable T₁ estimates obtained by the UTE-AFI-VTR method. Thus, referring to the previous UTE-VTR T₁ measurement papers, UTE-VTR data with four different TRs were employed for UTE-AFI-VTR T₁ measurement in this study (9,11,12). In comparison, T₁ values measured with the three shortest TRs of 20, 30, and 40 ms (to reduce the scan time) for volunteers #1 through # 4 were respectively 318 ms, 390 ms, 274 ms, and 216 ms. The corresponding difference ratios were 40.7%, 69.6%, 9.6%, and −19.7% as compared with T₁ values calculated with four TRs. This demonstrated that UTE-VTR data with more TRs, especially for the long TRs, can be essential for accurate cortical bone T₁ measurement for the UTE-AFI-VTR method.

In this study, the minimum TR used in the UTE-STR acquisition was 20 ms, which was determined by the need to employ gradient Crusher pulses and avoid overheating the gradient system. A dedicated gradient system with a smaller bore, or a more efficient water chiller system would be helpful in allowing reduction of TR, and thus reduction of the scan time. In addition to UTE-STR data with a TR of 20 ms, UTE-VTR data with a TR of 100 ms was used to investigate the accuracy of the T₁ measurement of UTE-AFI-STR method in the ex vivo study. The mean T₁ value of the nine human cortical bone samples using the data with a TR of 100 ms was 219 ms, which was very similar to the result obtained using the data with a TR of 20 ms (i.e. mean T₁ value = 214 ms) for the UTE-AFI-STR T₁ measurement. More systematic investigation using various combinations of TR₁/TR₂ in UTE-AFI and TR of UTE-STR, especially shorter TR₁s, TR₂s and TRs (corresponding to shorter total scan times), would be of interest and will be the subject of a future study.

Another limitation in this study is that the total scan time of the UTE-AFI-STR method for the in vivo study was about 17 min, which is still too long for wide usage in the clinical domain. The matrix sizes of UTE-AFI acquisitions can potentially be reduced to improve the scan efficiency of the UTE-AFI-STR method. Together with our recently developed combined parallel imaging and compressed sensing reconstruction for fast 3D UTE imaging (19), it is potentially possible to generate a cortical bone T₁ measurement protocol with a clinically acceptable scan time of around 5 min. We will work on this protocol and report the results in a future study.

CONCLUSION

The proposed 3D UTE-AFI-STR method provides accurate T₁ mapping of cortical bone with improved time efficiency compared with the UTE-AFI-VTR/sf-UTE-AFI-VTR methods using a clinical 3T scanner.

Supplementary Material

Sup Fig S1-S2

Supporting Information Figure S1. 3D UTE-based AFI and VTR sequences. The conventional 3D UTE sequence is used for multiple-TR data acquisition (a). The 3D UTE-AFI sequence acquires data with two interleaved TRs (TR₁ and TR₂) to generate B₁ or F_z maps (b). Diagram of a single UTE unit in (a) and (b) shown in (c). In (c), a short rectangular RF pulse with a nominal TE of 32 μs is used for signal excitation and is followed by 3D spiral sampling. The spiral trajectories are arranged with 3D conical view ordering (d). RF = radiofrequency; DAW = data acquisition window.

Supporting Information Figure S2. Human cortical bone sample size measurement. (b) is a sagittal slice along the white dashed line in coronal plane (a). The red, green, blue, yellow [in (a)] and orange [in (b)] arrows show the longest and shortest diameters, the greatest and least thicknesses, as well as the length of each sample, respectively. Data from the nine thickxest bones was used.