Trabecular Bone Imaging Using a 3D Adiabatic Inversion Recovery Prepared Ultrashort Echo Time Cones Sequence at 3T

Abstract

Purpose:

To investigate direct imaging of trabecular bone using a three-dimensional adiabatic inversion recovery prepared ultrashort echo time Cones (3D IR-UTE-Cones) sequence.

Methods:

The proposed 3D IR-UTE-Cones sequence employed a broadband adiabatic inversion pulse together with a short TR/TI combination to suppress signals from long T₂ tissues such as muscle and marrow fat, followed by multispoke UTE acquisition to detect signal from short T₂ water components in trabecular bone. The feasibility of this technique for robust suppression of long T₂ tissues was first demonstrated through numerical simulations. Then, the proposed IR-UTE-Cones sequence was applied to a hip agarose bone phantom and to six healthy volunteers for morphological and quantitative T₂* and proton density mapping of trabecular bone.

Results:

Numerical simulation suggests that the IR technique with a short TR/TI combination provides sufficient suppression of long T₂ tissues with a wide range of T₁s. High contrast imaging of trabecular bone can be achieved ex vivo and in vivo, with fitted T₂* values of 0.3–0.45 ms and proton densities of 5–9 mol/L.

Conclusion:

The 3D IR-UTE-Cones sequence with a short TR/TI combination provides robust suppression of long T₂ tissues and allows both selective imaging and quantitative (T₂* and proton density) assessment of short T₂ water components in trabecular bone in vivo.

Introduction

Trabecular bone is highly responsive to metabolic stimuli and has a turnover rate about eight times higher than that of cortical bone (1,2), making it a prime target for detecting bone loss in early osteoporosis (OP). Areal bone mineral density (BMD) of trabecular bone in the spine and/or hip using dual energy X-ray absorptiometry (DEXA) is the most commonly used clinical diagnostic test for assessing skeletal status and fracture risk (3,4). However, a number of clinical studies have demonstrated the limitations of BMD measurements. It has been recognized that BMD can only account for about 60% of bone strength (5).

For the last two decades, quantitative magnetic resonance imaging (MRI) has been used to assess the properties of trabecular bone, including T₂* or T₂’ of bone marrow (6,7) and high resolution imaging of bone microstructure (2,4), which are helpful in predicting osteoporotic fracture risk. Quantification of T₂* or T₂’ takes advantage of the fact that local field is perturbed due to the difference in susceptibility between trabecular bone and marrow, which is affected by the density and structure of trabecular bone (6,7). High resolution imaging can directly visualize dark trabecular bone due to its low water content and short T₂ relaxation. With image postprocessing, it is possible to obtain 3D architecture and corresponding structural parameters of the trabecular bone, which are highly related to the bone strength (2,4).

Direct MR imaging of trabecular bone is technically challenging due to its fast signal decay, rendering it “invisible” with conventional clinical MRI pulse sequences (8). Recently, ultrashort echo time (UTE) sequences and their variants (e.g. water- and fat-suppressed proton projection MRI (WASPI) and zero echo time (ZTE) sequences) have been developed to directly capture the fast decaying signals of phosphorus (9–11) or proton (12–14) in trabecular bone. These techniques have been used successfully for in vivo quantitative imaging of phosphorus density and its relaxations in both cortical and trabecular bone, strong indicators for characterizing bone quality (9–11). However, the hardware for phosphorus imaging is not available in most clinical scanners, posing a limitation for further optimization of the technique and for translation to clinical practice.

Recently, researchers have also investigated direct proton imaging of trabecular bone using WASPI and fat-suppressed UTE techniques (12–14). In order to create a high contrast for trabecular bone, it is critical to suppress signals from long T₂ tissues since trabecular bone has a much lower proton density than long T₂ tissues. WASPI uses two hard pulses with narrow frequency bands to selectively excite water and fat signals. Strong gradient crushers were used following the two hard pulses to saturate water and fat signals before data acquisition (15). Alternative scans using 180° pulses have been considered to further null residual water and fat signals. Wurnig et al. employed the UTE sequence to measure T₂* of trabecular bone samples with a SPIR (spectral presaturation with inversion recovery) module to suppress marrow fat (14). These two techniques show promising results for trabecular bone imaging both qualitatively and quantitatively. However, both techniques are sensitive to B₁ and B₀ inhomogeneities, which may limit their clinical applications, especially for in vivo imaging of trabecular bone in the spine and hip.

In this study, we propose a broadband adiabatic inversion recovery prepared three-dimensional UTE Cones (3D IR-UTE-Cones) sequence for direct volumetric imaging of trabecular bone in the human spine and hip (16,17). To the best of our knowledge, this is the first proton imaging study to directly image trabecular bone in the human spine and hip on a clinical 3T scanner. The combination of a short repetition time (TR) and inversion time (TI) is chosen in order for the IR-UTE-Cones sequence to obtain robust suppression of a variety of long T₂ tissues with different T₁s. Using the adiabatic full passage (AFP) pulse with a relatively wide bandwidth (~1.6 kHz), the proposed IR preparation is insensitive to both B₁ and B₀ inhomogeneities (18). Furthermore, multispoke acquisition per IR preparation can be incorporated, allowing time-efficient volumetric imaging and T₂* quantification of trabecular bone (17,19). Proton density can also be quantified by comparing 3D IR-UTE-Cones signal of trabecular bone with that of a calibration phantom. Numerical simulations, ex vivo studies, and in vivo studies were conducted to validate the feasibility of the proposed IR-UTE-Cones sequence to directly image and quantify trabecular bone.

Theory

Figure 1 shows the features of the 3D IR-UTE-Cones pulse sequence used in this study (16,17). The adiabatic IR pulse with a specific inversion recovery time of TI is repeated every TR period (Figure 1A). Following the IR pulse are N_sp separate k-space acquisitions with an equal time interval τ for fast data acquisition. TI is defined as the time from the center of the adiabatic IR pulse to the center of the multispoke acquisition. A short rectangular pulse with a duration of 30–60 μs is used for signal excitation in each spoke (Figure 1B), followed by spiral trajectories with 3D conical view ordering (Figure 1C).

Figure 1.

The 3D IR-UTE-Cones sequence employs an adiabatic inversion pulses for long T2 suppression, followed by 3D UTE-Cones data acquisition (A). In the basic 3D UTE-Cones sequence, a short rectangular pulse is used for signal excitation followed by 3D spiral sampling with a minimal nominal TE of 32 μs (B). The spiral trajectories are arranged with conical view ordering (C). To speed up data acquisition, multiple spokes can be sampled after each long T₂ preparation (A).

The adiabatic IR pulse can effectively invert the longitudinal magnetizations of long T₂ tissues, such as marrow fat and muscle. However, the longitudinal magnetizations of short T₂ tissues such as bone are typically saturated, not inverted, by the relatively long adiabatic inversion pulse (20,21). Here, we introduce an inversion efficiency factor Q for the adiabatic IR pulse with a range of −1 (signifying full inversion) to 1 (signifying no disturbance to the z-magnetization) (21). Q is equal to zero in the condition of complete saturation.

To simplify the signal equation, a rectangular pulse was considered for excitation. At steady state, the longitudinal magnetization of the j^th spoke is expressed as follows (17,22):

$$M_z^j=A\left(j\right)M_p+B\left(j\right),$$ [1]

where

$$A\left(j\right)=E_1(e_1{f}_z{)}^{j-1},$$ [2]

$$B\left(j\right)={M_0(1-E}_1\left)\left(e_1{f}_z{)}^{j-1}+{M_0(1-e}_1\right)\right[{1-(e}_1{f}_z{)}^{j-1}]/{(1-e}_1{f}_z),$$ [3]

$$M_p=\frac{Q{[E}_2{B}_{N_{sp}}{f}_z+M_0{E}_1\left(1-E_2\right)]}{1-Q{E}_2{A}_{N_{sp}}{f}_z},$$ [4]

using the following definitions: $A_{N_{sp}}=A\left(N_{sp}\right)$, $B_{N_{sp}}=B\left(N_{sp}\right)$, E₁ = exp{−[TI – τ(N_sp − 1)/2]/T₁}, E₂ = exp{−[TR − TI – τ(N_sp − 1)/2]/T₁}, and e₁ = exp(−τ/T₁). M₀ is the signal intensity in the equilibrium state. M_p is the longitudinal magnetization after the IR pulse; its explicit derivation can be found in the Appendix section. f_z is the longitudinal magnetization mapping function that describes the response of the magnetization to the RF pulse, with $f_z\left(\alpha ,{\tau ,T}_2\right)=M_z^{+}/M_z^{-}$. $M_z^{-}$ and $M_z^{+}$ are defined as the longitudinal magnetizations before and after RF excitation. f_z is introduced to account for the signal loss during the RF excitation when tissue T₂ is close to or less than RF pulse duration. The expression of the longitudinal magnetization mapping function is shown as follows (23):

$$f_z\left(\alpha ,{d,T}_2\right)=e^{-\frac{d}{2T_2}}\left(cos\left(\sqrt{{\alpha }^2-(\frac{d}{2T_2}{)}^2}\right)+\frac{d}{2T_2}\text{sinc}\left(\sqrt{{\alpha }^2-(\frac{d}{2T_2}{)}^2}\right)\right),$$ [5]

where α is the excitation flip angle and d is the pulse duration. For the tissue with a T₂ >> d, the T₂ decaying during excitation can be neglected; thus, f_z can be simplified to the conventional cos(α).

For short T₂ tissues (e.g. T₂ < 1 ms), both Q and M_p approach 0. Therefore, Eq. [1] can be simplified to $M_z^j=B\left(j\right)$. The signal of the j^th acquisition from the short T₂ component can be expressed as follows:

$$M_{z,S}^j={M_0(1-E}_1\left)\left(e_1{f}_z{)}^{j-1}+{M_0(1-e}_1\right)\right[{1-(e}_1{f}_z{)}^{j-1}]/{(1-e}_1{f}_z).$$ [6]

Long T₂ Signal Suppression

It is difficult to completely suppress all the long T₂ tissues with different T₁s using a single IR pulse. However, when the TR is shorter, the nulling TIs for all the tissues get closer. Moreover, for long T₂ tissues with longer T₁ relaxation times, it is easier to achieve sufficient signal suppression with a broader range of TIs. More details can be found in the simulation section. When several spokes near the nulling point are acquired, the excited transverse magnetizations before the nulling point are of opposite polarity to those acquired after the nulling point. Then, long T₂ signal suppression can be achieved because these transverse magnetizations cancel each other out in the regridding process during image reconstruction.

The magnetizations of short T₂ tissues (such as trabecular bone) are not inverted, but instead largely saturated by the adiabatic IR pulse. They typically have a short T₁ (24) and quickly recover to positive longitudinal magnetizations at TI. The signal intensities of short or long T₂ tissues are both proportional to the magnetization averaging of the multispoke acquisitions:

$$M_z={\sum }_{j=1}^{N_{sp}}{M}_z^j/N_{sp}.$$ [7]

A general framework to minimize signals from long T₂ tissues for the IR-prepared sequence is expressed as follows:

$$TI=\text{arg min}\left\{\sum _{i=1}^{N_{T_1}}\left[M_z\left(TI,TR,\alpha ,\tau ,N_{sp},T_{1i}\right)\right]\right\},$$ [8]

where $N_{T_1}$ is the number of long T₂ tissues. T_1i (i = 1, 2, …, $N_{T_1}$) is the T₁ value of the i^th long T₂ tissue. When TR, α, τ, and N_sp are given, TI can be determined by Eq. [8] to achieve optimized long T₂ suppression. This framework can apply for suppressing either a single tissue component with an individual T₁ or a group of long T₂ tissues with a range of T₁s.

Methods

The 3D IR-UTE-Cones sequence (Figure 1) was implemented on a 3T clinical scanner (MR750, GE Healthcare Technologies, Milwaukee, WI). The Cones sequence sampled data along evenly spaced twisting paths in the shape of multiple cones (16). Data sampling started from the center of k-space as soon as possible after the RF excitation with a minimal nominal TE of 32 μs (17,22). The adiabatic IR pulse with a pulse shape of commonly used hyperbolic secant function, duration of 6.048 ms, bandwidth of 1.643 kHz, and maximum B₁ amplitude of 17 μT was used to invert or saturate tissues (25). The adiabatic IR pulse was centered on −220Hz in the middle of the water and fat peak at 3T.

Simulation

Numerical simulation was performed to investigate the efficiency of the IR preparation scheme in the suppression of long T₂ signals with different TRs (i.e. 50, 100, 150, 200, 250, and 1000 ms). The simulated T₁ values of the long T₂ tissues ranged from 200 to 2000 ms. α, τ and N_sp were set to 20°, 4 ms, and 5, respectively, for all simulations. The excitation pulse duration d was 60 μs, which is much shorter than typical bone T₂* (i.e. around 300 μs). Thus, the longitudinal magnetization mapping function f_z can be simplified to cos(α).

Additionally, the contrast between trabecular bone and long T₂ tissues was also investigated for the IR-UTE-Cones sequence with different TRs. The TI was determined by Eq. [8] in order to minimize the marrow fat signal since it is relatively difficult to suppress due to its relatively short T₁ and since it is a dominant component in trabecular bone. The T₁ values of marrow fat are assumed to be in the range of 320–350 ms, and the T₁ value of trabecular bone is set to 140 ms (17,24). The proton density of trabecular bone is assumed to be 12 percent of the long T₂ tissues (26).

Trabecular Bone Sample Study

Two hip bone samples (65-year-old female and 71-year-old male donors) were individually embedded in agarose gel (3 w/v %) to simulate human tissues. An 8-channel transmit/receive knee coil was used for both RF transmission and signal reception. Both clinical T₁-FSE and the proposed IR-UTE-Cones sequences were used for the hip-agarose phantom experiment; the sequence parameters are listed as follows: 1) 2D T₁-FSE: TR/TE = 550/8.1 ms, FOV = 15×15 cm², slice thickness = 5 mm, acquisition matrix = 320×256, slice number = 32, and scan time = 59 s; 2) 3D IR-UTE-Cones: TR/TI = 82/37 ms, flip angle = 20°; N_sp = 3; τ = 7 ms; FOV = 16×16×21 cm³; matrix = 160×160×42; and five separate scans with TEs = 0.032/3.3, 0.2/4.4, 0.4, 0.8, and 1.1 ms to measure T₂*, each with scan time = 4 min 20 sec.

In Vivo Trabecular Bone Study

In vivo spine imaging was performed on six healthy volunteers (24–38 years of age, 5 males and 1 female). Informed consent was obtained from all subjects in accordance with guidelines of the institutional review board. A rubber band with a T₂* around 0.3 ms was placed between the volunteer and the spine coil during scanning to serve as a reference to calibrate the proton density of trabecular bone. The proton density of trabecular bone can be calculated by the following equation (11,27):

$${\rho }_{\mathit{\text{bone}}}={\rho }_{\mathit{\text{ref}}}\frac{{\text{I}}_{\mathit{\text{bone}}}{\text{F}}_{\mathit{\text{ref}}}}{{\text{I}}_{\mathit{\text{ref}}}{\text{F}}_{\mathit{\text{bone}}}},$$ [9]

with

$$\text{F}=f_{xy}{e}^{-TE/T_2^{*}}\frac{1-e^{-TR/T_1}}{1-{\text{f}}_z{e}^{-TR/T_1}},$$ [10]

where f_xy is the mapping function that describes the response of the transverse magnetization to a constant-amplitude RF pulse. It is a function of T₂ and pulse duration (23). f_z is expressed in Eq. [5]. If the pulse duration and tissue T₂ are known, f_xy and f_z can be calculated directly. I_bone and I_ref are the signal intensities of trabecular bone and rubber band, respectively. To measure the proton density of the rubber band used in this study, an H₂O-D₂O phantom was made with 20% H₂O and 80% D₂O by volume. It was doped with MnCl₂ to achieve a T₂* of 0.34 ms and a T₁ of 6.5 ms. The T₂* and T₁ of the rubber band are 0.38 ms and 200 ms, respectively. The T₁ relaxation was measured with our previously developed 3D UTE AFI-VTR method (28). The H₂O-D₂O phantom and rubber band were put together and scanned with the proposed IR-UTE-Cones sequence with TR/TI = 150/64 ms. Together with the measured T₁ and T₂* values of the H₂O-D₂O phantom and rubber band, the proton density of the used rubber band calculated by Eq. [9] was around 19 mol/L. In addition, T₁ values of the trabecular bone was set to 140 ms (24,29).

To correct the signal intensity bias due to the coil sensitivity inhomogeneity of the spine coil, the regular 3D UTE-Cones sequence was applied twice using spine and body coils, respectively, for signal reception. Then, with the assumption that the body coil has a homogeneous reception profile, the coil sensitivity map of the spine coil was calculated by dividing UTE-Cones images acquired with the spine coil by UTE-Cones images acquired with the body coil. The final spine trabecular bone images were generated by dividing the 3D IR-UTE-Cones images by the obtained coil sensitivity map. The sequence parameters used for imaging of the spine were as follows: 1) T₂-FSE: TR/TE = 4370/103 ms, FOV = 34×34 cm², slice thickness = 3.2 mm, matrix = 360×270, slice number = 14, and scan time = 1 min 5 sec; 2) 3D IR-UTE-Cones: TR/TI = 150/64 ms, TE = 0.032 ms, flip angle = 18°, N_sp = 5, τ = 3.8 ms, FOV = 34×34×16 cm³, matrix = 160×160×32, oversampling factor = 4 (the center of k-space was oversampled by a factor of 4 to reduce artifacts), and scan time = 10 min; 3) 3D UTE-Cones: TR = 6 ms, TE = 0.032 ms, flip angle = 2°, FOV = 34×34×16 cm³, matrix = 160×160×32, oversampling factor = 4, and scan time = 1 min. T₂* measurement was used to evaluate the efficiency of long T₂ suppression in 3D IR-UTE-Cones imaging of trabecular bone. A single-component short T₂* means a sufficient suppression of pore water and fat in trabecular bone is achieved, and that only bound water in trabecular bone is detected by the 3D IR-UTE-Cones sequence. Four separate scans with TEs = 0.032/2.2, 0.2, 0.4, and 0.8 ms were employed to measure T₂* in three of the volunteer experiments.

In vivo hip imaging was performed on six healthy volunteers (24–36 years of age, three males and three females). A routine cardiac coil was used for the hip scan. The sequence parameters used for hip imaging were as follows: 1) T₂-FSE: TR/TE = 10000/92 ms, FOV = 38×38 cm², slice thickness = 3 mm, matrix = 320×320, slice number = 24, nex = 2, scan time = 3 min; 2) 3D IR-UTE-Cones: TR/TI = 150/64 ms, TE = 0.1 ms, flip angle = 18°, N_sp = 5, τ = 4.1 ms, FOV = 38×38×20 cm³, matrix = 160×160×40, oversampling factor = 3.2, and scan time = 9 min 32 sec.

Data Analysis

The trust-region-reflective algorithm was used to solve the non-linear minimization of Eq. [8] (30). A single exponential function was employed for T₂* fitting of the multiple-TE IR-UTE-Cones data. The 3D UTE-Cones images acquired with both spine and body coils were smoothed using a 3D Gaussian kernel with standard deviation of 2 before the coil sensitivity calculation. All analysis algorithms were written in Matlab (The MathWorks Inc., Natick, MA, USA) and were executed offline on the DICOM images obtained by the acquisition protocols described above.

Results

Numerical simulations of the signal variations in the IR-UTE sequence (i.e. |M_z|) for a wide range of T₁s (i.e., [200, 2000] ms) are shown in Figure 2. The TI ranges from 0 to TR for each T₁. The best signal null point for each T₁ is located in the dark blue spot. The dark blue region becomes wider when T₁ is longer, demonstrating that the signal suppression for long T₁ tissues is less sensitive to the choice of TI. Thus, sufficient signal suppression of longer T₁ tissues can be achieved with a wider range of TIs. If there are several long T₂ tissues to be suppressed, it is a good choice to set the TI at the null point of the shortest T₁ tissue. Moreover, the null points get closer for all the T₁s when the TR is shorter. Therefore, it is much easier to sufficiently suppress long T₂ tissues with a wide range of T₁s when a short TR is used in the single IR type sequences.

Figure 2.

Numerical simulation to investigate the effects of TR and TI on signal suppression of long T₂ tissues with a wide range of T₁s (i.e. [200, 2000] ms) in IR-UTE imaging. The signal intensities of the long T₂ tissues in IR-UTE imaging vary with both TI and T₁. TI ranges from 0 to TR. TRs are chosen at 50 (A), 100 (B), 150 (C), 200 (D), 250 (E), and 1000ms (F).

Figure 3 shows the simulation results of the contrast between bone and long T₂ tissues in IR-UTE imaging. The TIs are calculated by optimizing the Eq. [8] to null signal from marrow fat. Similar to the findings in Figure 2, the contrast between bone and long T₂ tissues is higher when a shorter TR is used. Even with a TR of 250 ms, we still obtain moderate bone contrast. In the case of long TR (e.g., 1000 ms), only a small range of T₁s could be well suppressed, suggesting that the signal suppression efficiency is very sensitive to the choice of TI.

Figure 3.

Investigation of the trabecular bone contrast generated by the IR-UTE sequence with different TRs. The S_ratio is defined as the signal intensity ratio between trabecular bone and long T₂ tissue. The T₁s of long T₂ tissues ranged from 200 to 2000 ms and the T₁ of trabecular bone was assumed to be 140 ms. The S_ratio curves with relatively short TRs of 50, 100, 150, 200, 250 ms are shown in A and the curve with a much longer TR of 1000 ms is shown in B. The optimal TI for each TR was determined by minimizing Eq. [8] to null marrow fat. Improved trabecular bone contrast is achieved when a shorter TR is used in the IR-UTE sequence.

Figure 4 shows representative images selected from 3D IR-UTE-Cones imaging of a hip agarose phantom. Both agarose and marrow fat are bright with the conventional T₁-FSE sequence, but almost fully suppressed with the IR-UTE-Cones sequence. Fitting of the 3D IR-UTE-Cones images with different TEs ranging from 0.032 to 4.4 ms demonstrates a short T₂* of 0.41 ± 0.02 ms for hip trabecular bone, which is similar to the T₂* of bound water in cortical bone (26). The single-component decay with R² = 0.998 and the short T₂* value suggest that marrow fat and free water of the hip sample are well suppressed by the adiabatic inversion pulse. Only water bound to the organic matrix of trabecular bone in the hip is selectively imaged with the 3D IR-UTE-Cones sequence.

Figure 4.

3D IR-UTE-Cones imaging of a hip-agarose phantom. The long T₂ agarose and marrow fat are bright in the clinical T₁-FSE image (A). In comparison, signals of agarose are almost fully suppressed in the IR-UTE-Cones images with TEs of 0.032 ms (B), 0.2 ms (C), 0.4 ms (D), 0.8 ms (E), and 4.4 ms (F). Single-component fitting is achieved for trabecular bone in the hip sample with a short T₂* of 0.41 ± 0.02 ms (G), which demonstrates that long T₂ water and marrow fat are sufficiently suppressed in the IR-UTE-Cones images.

Figure 5 shows in vivo imaging of the spine of a 36-year-old male volunteer. Similar to the hip agarose study, the 3D IR-UTE-Cones sequence shows high contrast between the vertebrae and surrounding soft tissues. These results confirm that the IR technique with a short TR allows nulling of both muscle and fat despite their large differences in T₁ relaxation times. Exponential fitting of the 3D IR-UTE-Cones images with different TEs demonstrates a short T₂* of 0.31 ± 0.01 ms for trabecular bone in the vertebrae.

Figure 5.

In vivo imaging of the spine of a 36-year-old male volunteer using the 3D IR-UTE-Cones sequence with TEs of 0.032 ms (A), 0.2 ms (B), 0.4 ms (C), 0.8 ms (D), and 2.2 ms (E). The surrounding soft tissues such as muscle and fat are well-suppressed, leading to high contrast imaging of vertebrae and ligaments in the spine. Single-component fitting is achieved for vertebrae with a short T₂* of 0.31 ± 0.01 ms, which demonstrates that long T₂ water and marrow fat are sufficiently suppressed in the IR-UTE-Cones images.

Figure 6 shows in vivo images of the hip of a 24-year-old female volunteer. In contrast to the conventional T₂-weighted FSE images, soft tissues are well-suppressed, but cortical bone is bright in the corresponding IR-UTE-Cones images. Trabecular bone of the hip shows lower proton density compared with cortical bone.

Figure 6.

In vivo imaging of the hip of a 24-year-old female volunteer with a clinical 2D T₂-weighted FSE (first column) and 3D IR-UTE-Cones (second column) sequences. The long T₂ muscle and fat are bright in the clinical T₂-FSE images. In comparison, the soft tissues are well-suppressed in the 3D IR-UTE-Cones images, demonstrating a high contrast for cortical and trabecular bone in the hip.

Figure 7 shows the bound water proton density map of vertebrae in a 31-year-old male volunteer. Since the coil sensitivity of the spine coil is quite inhomogeneous, signal intensity correction is critical for accurate quantitative proton density mapping. It can be found that images of the vertebrae are much more uniform after coil sensitivity correction. Proton densities of the vertebrae calculated by Eq. [9] range from 5 to 9 mol/L.

Figure 7.

In vivo qualitative and quantitative imaging of the spine of a 31-year-old male volunteer using the 3D IR-UTE-Cones sequence. The long T₂ muscle and fat are bright in the clinical T₂-FSE image (A). The original 3D IR-UTE-Cones image (B) show non-uniform signal intensity distribution due to the inhomogeneous coil sensitivity (C) of the spine coil. After the coil sensitivity correction, the spine bone image demonstrates a more uniform signal intensity distribution (D). The proton density map of the spine trabecular bone (E) is calculated based on the coil sensitivity corrected 3D IR-UTE-Cones image (D).

Discussion

We demonstrated in this study that the 3D IR-UTE-Cones sequence with a short TR/TI combination can suppress signals from long T₂ water and fat simultaneously, and can provide high image contrast for short T₂ trabecular bone. Our simulation study suggests that the TI should be selected close to the null point of short T₁ tissues since the long T₁ tissue suppression is less sensitive to the selection of TI. We observed that the shorter the TR of the IR-UTE sequence, the better we were able to suppress long T₂ tissues with a wide range of T₁s since their signal null points were getting closer. Our ex vivo and in vivo studies demonstrated the robustness of the 3D IR-UTE-Cones sequence in suppressing long T₂ water and fat signals in the spine and hip. Furthermore, the 3D IR-UTE-Cones sequence allowed quantitative proton density mapping and T₂* measurement of the short T₂ water component in trabecular bone.

UTE techniques can provide direct imaging of short T₂ bone, which is invisible with conventional sequences. The majority of bone studies using qualitative and quantitative UTE imaging are focused on cortical bone (31–34). However, evaluation of trabecular bone may be even more valuable since most osteoporotic fractures occur at locations that are rich in trabecular bone (35). WASPI and UTE with SPIR preparation have been proposed for trabecular bone imaging. However, these two techniques are sensitive to B₁ and B₀ inhomogeneities, making them perhaps unsuitable for in vivo spine and hip imaging. In comparison, an adiabatic IR pulse with a relatively broad spectral coverage of 1.643 kHz is used in the proposed 3D IR-UTE-Cones sequence, and the long T₂ suppression is less sensitive to B₁ and B₀ inhomogeneities (18). Together with a short TR and a short TI, the proposed IR-UTE-Cones sequence is more robust in suppressing both water and fat. In this study, a TR of 150 ms was used in 3D IR-UTE-Cones imaging of the spine and hip in vivo to balance the effectiveness of long T₂ suppression and specific absorption rate (SAR) limitation. Compared with DEXA, which is a 2D projection imaging technique that cannot distinguish between cortical and trabecular bone, the proposed 3D IR-UTE-Cones MR imaging technique can provide volumetric information of cortical and trabecular bone separately. Since the bound water proton density in cortical bone is typically much higher than that in trabecular bone (36,37), a threshold-based method can potentially be used to separate cortical and trabecular bone in 3D IR-UTE-Cones images. Therefore, the proposed 3D IR-UTE-Cones MR imaging technique may have significant advantages over the current gold standard, DEXA, which is a 2D projection imaging technique that cannot distinguish between cortical and trabecular bone.

The T₂* values measured in both ex vivo and in vivo studies were in the range of 0.3–0.45 ms, which are similar to the T₂*s of bound water in cortical bone (26,29). Thus, the proton density measured by the proposed 3D IR-UTE-Cones technique is likely collagen-bound water proton density with effective suppression of pore water components (19,24,38). The collagen bone matrix provides tensile strength and elasticity in bone (39). Thus, it would be useful to obtain information from the collagen bone matrix to evaluate bone quality. MR imaging of collagen matrix-bound water has been studied by several groups in recent years as a possible surrogate measure of collagen bone matrix (36,40,41). For example, the bound water proton density is highly correlated with collagen matrix density, with R² = 0.74, as reported in a previous study of cortical bone samples (41). A lower bound water proton density may indicate a more degenerative collagen matrix with less tensile strength/elasticity in bone. We expect that the measured volumetric proton density in this study can be used as a potential biomarker to evaluate the bone quality in early osteoporosis and osteoporotic fracture risk.

Long T₂ signal contamination is typically a major source of error in quantitative UTE imaging (26). Since the IR-UTE-Cones sequence allows for selective imaging of short T₂ tissues, it can also be used for quantitative evaluation of proton density and T₂*, as well as for T₁ relaxation times (24,26). In this study, the IR-UTE-Cones acquisition together with a reference rubber phantom provided volumetric mapping of proton density for the trabecular bone, which may be a useful biomarker to evaluate the bone quality. A relatively high data oversampling factor was used in both in vivo spine and hip imaging with the IR-UTE-Cones sequence, which can increase the image signal to noise ratio (SNR) and simultaneously reduce the motion (as a result of motion averaging) and aliasing artifacts. Respiratory gating is also an effective strategy to reduce motion artifacts due to breathing. Since the marrow fat has a relatively short T₂* between 5 and 15 ms (42), the inversion efficiency Q may not reach −1. To account for this imperfect inversion and to achieve a sufficient nulling of marrow fat, a smaller TI with 1–2 ms less than the TI calculated by the Eq. [8] was used in our study. The proposed 3D IR-UTE-Cones sequence can also be used for cortical bone imaging both morphologically and quantitatively (e.g., T₂* and proton density).

Both the rubber band and the manganese-doped water (which has an extremely short T₂) can serve as the reference to calibrate the trabecular bone proton density. The rubber band has closer T₁ and T₂* relaxations to the bound bone water than the manganese-doped water (which has a T₁ that is much shorter than that of bound bone water). Thus, the rubber band has a contrast more similar to the bound bone water. Using the rubber band as the reference may be more resistant to the error in bound bone water quantification than using the manganese-doped water within a wide range of sequence parameters. On the other hand, there is a problem with the rubber band (a polybutadiene type elastomer), which may have more than one resonance (due to chemical shift), leading to errors in bound bone water quantification. We will compare the robustness and accuracy of bound bone water quantification using the two references in our future investigations.

The IR-UTE-Cones sequence with a short TR/TI combination can be readily used for imaging of other short T₂ species, such as for direct imaging of myelin protons in the white matter of the brain. There are several groups of water protons, such as those in cerebrospinal fluid, extra- and intra-cellular water, and water trapped in the myelin bilayers, which may have different T₁s (43); therefore, efficient suppression of all kinds of water protons is essential for selective imaging of myelin protons (13,20,44). The 3D IR-UTE-Cones sequence with a short TR/TI combination can largely suppress various water groups with different T₁s as shown in Figure 2, and may thusly be used for more robust imaging of myelin where water components with various T₁s may exist in white matter of the brain (43).

This study has several limitations. First, the SNR and contrast to noise ratio (CNR) of the 3D IR-UTE-Cones sequence have not been evaluated or compared with existing trabecular bone imaging techniques such as WASPI or UTE with SPIR preparation. The current protocol for quantitation of T₂* relaxation is too long (i.e. 40 min) for clinical utility. We would expect the qualitative assessment of 3D IR-UTE-Cones images together with quantitative proton density mapping (12 min scan in total) to be the more suitable option for clinical use. Advanced fast imaging techniques, such as compressed sensing or deep learning, could be used to accelerate the scan (45–47). Third, improved long T₂ suppression can be achieved with a shorter TR for 3D IR-UTE-Cones imaging of trabecular bone. The minimal TR used in the proposed 3D IR-UTE-Cones sequence is constrained by the SAR limitation, especially for body imaging (e.g., spine imaging). A dedicated transmission RF coil with a higher transmit efficiency than that of the used body coil would be helpful to alleviate the SAR limitation. Fourth, the correlation of 3D IR-UTE-Cones measured proton density with organic matrix density in trabecular bone is of high interest and will be investigated in future studies (36,40,41). Fifth, although the 3D IR-UTE-Cones sequence is ready for in vivo study of healthy volunteers and patients, the clinical value of this technique remains to be investigated.

Conclusion

The 3D IR-UTE-Cones sequence with a short TR/TI combination provides robust suppression of long T₂ tissues such as muscle and marrow fat, thus allowing selective imaging of short T₂ trabecular bone. The 3D IR-UTE-Cones sequence also provides quantitative T₂* and proton density measurement for trabecular bone with little long T2 contamination.

Supplementary Material

Supp figS1

Supporting information Figure S1 Steady state magnetization and timing for the 3D IR-UTE-Cones sequence. The short and long arrows represent the excitation and inversion pulses respectively. Q is the inversion efficiency of the used inversion pulse. t₁ and t₂ are the duration from the center of the IR pulse to the first excitation pulse and the duration from the last excitation pulse to the center of the IR pulse, respectively. M_p, M_z,1, and M_z,2 are the longitudinal magnetizations after the IR pulse, after the last excitation pulse and before the IR pulse, respectively.

Appendix

Supporting information Figure S1 shows the element timing of the IR multispoke sequence. t₁ is the duration from the center of the IR pulse to the first excitation pulse. t₂ is the duration from the last excitation pulse to the center of the IR pulse. M_p, M_z,1 and M_z,2 are the longitudinal magnetizations after the IR pulse, after the last excitation pulse and before the IR pulse, respectively. The relations of above three magnetizations according to Bloch equations, which are expressed as follows:

$$M_{z,1}={(M}_p{A}_{N_{sp}}+B_{N_{sp}})f_z,$$ [A1]

$$M_{z,2}=M_{z,1}\text{exp}\left({-\text{t}}_2/{\text{T}}_1\right)+M_0[1-\text{exp}\left({-\text{t}}_2/{\text{T}}_1\right)],$$ [A2]

$$M_p={QM}_{z,2},$$ [A3]

where t₁ = TI – 0.5τ(N_sp − 1) and t₂ = TR − TI – 0.5τ(N_sp − 1). $A_{N_{sp}}$ and $B_{N_{sp}}$ can be found in the Theory section. M_p is determined from Eq. [A1]–[A3] and its final expression is shown in Eq. [4].