Fast quantitative three-dimensional ultrashort echo time (UTE) magnetic resonance imaging of cortical bone using extended cones sampling

Abstract

Purpose:

To investigate the effect of stretching sampling window on quantitative 3D UTE imaging of cortical bone at 3T.

Methods:

Ten bovine cortical bone and seventeen human tibial midshaft samples were imaged with a 3T clinical MRI scanner using an eight-channel knee coil. Quantitative 3D UTE imaging biomarkers including T₁, T₂*, magnetization transfer ratio (MTR) and MT modeling were performed using radial or spiral Cones sampling trajectories with various durations. Errors in UTE-MRI biomarkers as a function of sampling time were evaluated using radial sampling as a reference standard.

Results:

For both bovine and human cortical bone samples, no significant differences were observed for all UTE biomarkers (single-component T₂*, bi-component T₂*s and relative fractions, T₁, MTR, MT modeling of macromolecular fraction) for spiral sampling windows of 992 to 1600 μs compared with a radial sampling window of 688 μs.

Conclusion:

The total scan time can be reduced by 76% with quantification errors less than 5%. Quantitative UTE-MRI techniques can be greatly accelerated using longer sampling windows without significant quantification errors.

1. Introduction

Cortical bone accounts for approximately 80% of the skeleton mass (1). Cortical bone microstructure plays a critical role in determining the risk of fracture and is altered by diseases such as osteoporosis, hyperparathyroidism, renal disease and diabetes that often have diffuse effects on bone metabolism and remodeling (2–5). With the rapidly growing prevalence of osteoporosis, fragility fractures have become a major public health concern, motivating the urgent need to develop noninvasive clinical biomarkers of cortical bone strength, elasticity and toughness (6) (7).

Cortical bone is comprised of approximately 40% mineral, 35% collagen and 25% water by volume (8). Previous NMR spectroscopy studies have demonstrated that the cortical bone MR signal has multiple components that differ by transverse relaxation times (T₂ values) (9). The short T₂ signals (T₂ values vary from 12–400 μs) originate from collagen backbone and side-chain protons, as well as from collagen-bound water, whereas longer T₂ signals (T₂ values on the order of milliseconds or longer) are mainly from pore water and lipid methylene protons. The short T₂ components predominately result in a mean T₂ value of approximately 0.42–0.50 ms (10); therefore, conventional MRI sequences with TEs of several milliseconds or longer detect little or no signal from cortical bone.

Ultrashort echo time (UTE) MRI sequences with TEs on the order of microseconds allow for direct imaging and quantitative assessment of cortical bone (1). A series of techniques including dual echo UTE acquisition with echo subtraction, long T₂ saturation UTE imaging, UTE with off-resonance saturation as well as single and dual adiabatic inversion recovery UTE techniques have been developed for high contrast imaging of cortical bone (11–14). Notably, the short T₂ component detected by UTE is predominantly from bound water: collagen backbone protons give no signal on UTE sequences (15), but can be indirectly measured by magnetization transfer (MT) methods (16).

A series of quantitative UTE MRI techniques have been developed to evaluate cortical bone (1). These biomarkers include T₁ (17), single-component apparent transverse relaxation time (T₂*) (18), bi-component analysis of bound and pore water T₂*s and relative fractions (19), magnetization transfer ratio (MTR) (20) and MT modeling of water and macromolecular fractions with their exchange rates (21). These biomarkers have been shown to be related to key biomechanical properties of cortical bone. For instance, bound water was found to be positively associated with bone strength and toughness, while free water was inversely related to modulus of elasticity (22,23). MTR has shown significant correlations with bone porosity and bone mechanics (24). Recently, MT modeling was found to be capable of detecting ex vivo bone stress injuries (25). However, UTE biomarkers have not been widely used in the clinical setting, with one major limitation being the long scan time.

For short T₂ species, the signals may decay significantly during the process of RF excitation and data acquisition (10,26). To minimize TE, UTE sequences begin data acquisition at the center of k-space and use non-Cartesian sampling. The decay of the signal along the sampling trajectory to outer k-space can result in blurring of short T₂ components. Radial sampling (PR) is often used in UTE sequences to minimize short T₂ blurring, but has a long scan time because fully sampling outer k-space is inefficient (27). The total scan time can be reduced by employing more efficient sampling patterns such as those using twisted radial or spiral trajectories (28,29). Both Rahmer et al. (26) and Du et al. (27) found that the reduction of scan time using these trajectories is limited by short T₂ blurring as the sampling window is lengthened. A number of UTE biomarkers including T₁, T₂*, MTR and MT modeling of water and macromolecular proton fractions have been developed for quantitative assessment of cortical bone (1,14). To the best of our knowledge, the effect of extending the sampling window on those quantitative UTE biomarkers has not been systematically investigated.

The purpose of this study was to quantitatively analyze the errors associated with extending the sampling duration on 3D quantitative UTE-MRI of midshaft tibia cortical bone (which represents a low spatial resolution short T2 object). These results were used to develop an optimized protocol for quantitative imaging of cortical bone that represents a balance between speed and quantification errors, thus facilitating the clinical use of quantitative UTE-MRI.

2. Methods

2.1. Sample preparation

Cortical bone specimens were harvested from ten fresh bovine samples and seventeen fresh-frozen human tibial midshafts from 15 donors (67 ± 24 years old, 7 females and 8 males). The human bone specimens were provided by a nonprofit whole-body donation company (United Tissue Network, Phoenix, AZ), while the bovine bone samples were obtained from a local slaughter house. All bone specimens were cut to 3 cm in length using a Delta ShopMaster band saw (Delta Machinery, Tennessee, USA). The bone marrow and other soft tissues were removed with a scalpel (to get higher signal to noise ratio (SNR), as tissue noise from surrounding muscle and marrow fat is greatly reduced). The bone specimens were equilibrated for at least two hours in phosphate buffered saline (to minimize trapped gas), then put in a plastic container filled with Fomblin (to minimize dehydration and susceptibility) before scanning. All scans were performed at room temperature.

2.2. UTE-MR imaging

All imaging was performed on a 3T clinical MRI scanner (MR750, GE Healthcare Technologies, Milwaukee, WI, USA) using an eight-channel knee coil. The maximum gradient amplitude, slew rate and ramp time are 50 mT/m, 200 T/m/s and 250 μs, respectively. The maximum gradient amplitude used in this experiment was 45 mT/m for PR and all Cones acquisitions; the maximum slew rate was 182 T/m/s for PR and 128 T/m/s for all cones acquisitions. All 3D UTE sequences used a short rectangular excitation pulse followed by 3D radial or spiral sampling with various data acquisition window lengths (Figure 1a, 1b).

Figure 1.

UTE pulse sequence diagram and trajectories. (a) For 3D UTE sequences, a short rectangular hard pulse excitation is followed by 3D radial or spiral sampling. 3D dual echo UTE was used for acquisition with the first short TE of 32 μs. (b) 2D representation of example trajectories: radial trajectory (green line), spiral trajectory with short sampling window (blue line), spiral trajectory with longer sampling window (pink line). As the sampling window is increased, the spiral trajectories have greater curvature and more k-space coverage with each spoke. Note that radial sampling has the shortest sampling window length, but that all trajectories oversample central k-space. (c) Conventional 3-dimensional ultrashort echo time cones (3D UTE-Cones) sequence with a single Cones actual flip angle imaging (AFI) sequences uses a pair of interleaved TRs for accurate B₁ mapping, which together with VTR method provides T₁ measurement. (d) A Fermi pulse was used for MT preparation followed by multiple spoke (Nsp) excitation. Scan time can be reduced by a factor of N_sp.

3D re-gridding with a Kaiser-Bessel kernel was used for reconstruction. After re-gridding, a Fermi filter was applied to the k-space data to reduce Gibbs ringing. Then, a fast Fourier transform was applied to the filtered data to generate the multichannel images. Finally, a commonly used sum of squares method was used for multi-channel image combination.

Three quantitative imaging protocols were performed: 1) a dual-echo 3D-UTE sequence (TR = 100 ms; five dual TE = 0.032/2.2, 0.2/4.4, 0.4/6.6, 0.6/8.8, and 0.8/11 ms; flip angle (FA) = 10°) for single and bi-component T₂* analysis (Figure 1a) (30); 2) a 3D UTE actual flip angle-variable TR (UTE-AFI-VTR) method for accurate T₁ mapping (AFI: TR = 20/100 ms, FA = 45°; VTR: TR = 20, 30, 50, and 100 ms; FA = 45°) (Figure 1c) (31,32); and 3) a 3D UTE-MT sequence (MT saturation power = 500°, 1000°, and 1500°; frequency offset = 2, 5, 10, 20, and 50 kHz; TR = 100 ms; FA = 10°; 11 spokes per MT preparation to accelerate the scan) (Figure 1d) to measure the MTR in addition to two-pool MT modeling of water and macromolecular proton fractions and exchange rates. Other imaging parameters included: field of view (FOV) = 6 × 6 × 4 cm³, acquisition matrix = 128×128×20, and readout bandwidth = 62.5 kHz. The Nyquist requirement was fulfilled for all data acquisitions. The designed k-space (i.e. ellipsoid) was used for the raw data filling with a lower resolution in the slice direction. All kz data were used for re-gridding reconstruction (In ellipsoid sampling, kz gradient was scaled down to achieve the prescribed slice thickness. The number of cones was reduced so that only 20 slices were acquired and reconstructed during re-gridding reconstruction).

To investigate the effect of extended sampling window on quantitative UTE imaging, each of the above sequences was repeated using several sampling trajectories: radial (PR) and several Cones trajectories (spiral trajectories with conical view ordering) with different stretch factors (Figure 1b). Ramp sampling was used for all acquisitions in both PR and Cones sequences. Gradient delay was measured to correct the radial and spiral trajectories (33). For both bovine and human bone samples, the PR trajectory had a sampling time of 688 μs. The Cones sampling times were 992 (Cones with a stretching factor of 1.0, or Cones1.0), 1200 (Cones1.2), 1392 (Cones1.4) and 1600 μs (Cones1.6), corresponding to acceleration factors of 2.6, 3.5, 4.1 and 5.0 over PR sampling, respectively. The stretching factor was defined as the ratio of sampling window using the stretched spiral sampling over sampling window using the PR trajectory, while the acceleration factor was defined as the ratio of total scan time of PR sequence to each Cones sequence. For example, the scan times for dual-echo 3D-UTE imaging with radial trajectory and the above mentioned spiral trajectories were 9.75, 3.67, 2.80, 2.32 and 1.95 min, respectively. There are 5327, 4813, 3639, 2943 and 2473 projections for PR and Cones with a stretch factor of 1, 1.2, 1.4 and 1.6, respectively.

2.3. Data analysis

The analysis algorithm was written in Matlab (The MathWorks Inc. Natick, MA, USA) using the Levenberg-Marquardt method for non-linear least-squares curve fitting and was executed offline on DICOM images obtained by the protocols described above. Regions of interest (ROIs) were manually drawn on the first UTE image of each series, then copied to each of the subsequent images. The mean intensities within each of the ROIs were used for curve fitting. Single-component (S(TE) ∝ exp(−TE/T2*) + constant) and bi-component $\left(S\left(TE\right)\propto F_S\times \text{exp}\left(-TE/T{2}_S^{*}\right)+F_L\times \text{exp}\left(-TE/T{2}_L^{*}\right)+\mathit{\text{constant}}\right)$ fitting models were utilized for T₂* decay analyses acquired from the dual-echo 3D-UTE-Cones sequence. Bi-component analysis estimates the T₂*s and relative fractions of a short T₂* component and a long T₂* component, presumably the bound and pore water pools, respectively [30]. T₁ was analyzed from the 3D UTE-AFI and UTE-VTR sequences using single-component fitting [29]. The UTE-MT data set was analyzed for MTR (34) and with a two-pool model (21) to estimate the macromolecular fraction. ROIs were carefully drawn on the outer 2/3 band of cortical bone to avoid signal contamination from residual bone marrow fat near the endosteal surface.

2.4. Statistical analysis

After all data analyses, error percentages in UTE-MRI biomarkers from spiral trajectories were determined for each measured parameter using results from radial sampling as a reference standard. Statistical analyses were performed using SPSS software (SPSS, BIM 24) and the R statistical computing environment (v3.5.1). One-way ANOVA with two-sided Dunnett’s test was used for the significance of the mean differences of all the biomarker compared to radial sampling. The null hypothesis of the omnibus ANOVA test was that the mean was the same for all evaluated trajectories. Bland-Altman analysis was used for agreement assessment of the spiral sampling windows compared with radial sampling. P-values less than 0.05 were considered statistically significant.

3. Results

Figure 2 shows UTE images of a representative bovine cortical bone sample with gradually increasing sampling windows from radial (688 μs) to Cones with a stretching factor of 5.0 (1600 μs). Blurring was more visually apparent with increasing stretching factor. Similarly, Figure 3 shows UTE images of a representative human cortical bone sample with gradually increasing sampling windows from radial (688 μs) to Cones1.6 (1600 μs). The images looked more blurred with increasing stretching factor due to short T₂ decay of cortical bone. With longer sampling duration, off-resonance ringing artifacts from residual endosteal fat also became more prominent. The qualitative effects of extended sampling windows were observed to be similar.

Figure 2.

Representative T₁ (a-e), T₂ (f-j) and MT (k-o) magnitude images of the same bovine bone sample with different sampling windows: radial (a,f,k), cones1.0 (b,g,l), cones1.2 (c,h,m), cones1.4 (d,i,n) and cones1.6 (e,j,o).

Figure 3.

Representative T1 (a-e), T2 (f-j) and MT (k-o) magnitude images of the same human tibial bone specimen with different sampling windows: radial (a,f,k), cones1.0 (b,g,l), cones1.2 (c,h,m), cones1.4 (d,i,n) and cones1.6 (e,j,o).

Figure 4 shows the signal intensity curves of two representative ROIs of bovine and human cortical bone samples with different sampling windows. The signal intensity of T₁, T₂* and MT images in both bovine and human bones have a decreasing trend from PR to longer Cones sampling windows, indicating that extending the sampling window leads to signal loss. The most obvious signal intensity losses were observed from PR to Cones 1.0, while the changes were relatively small among different Cones sampling windows.

Figure 4.

Signal intensity variation of T₁ (TR=200, FA=45°, TE=32 μs), T₂* (TR=100, FA=10°, TE=32 μs) and MT (FA=500°, offset=2000, TE=32 μs) images with different sampling windows (PR: 688 μs, Cones 1.0: 992 μs, Cones 1.2: 1200μs, Cones 1.4: 1392 μs, Cones 1.6: 1600 μs) of two representative ROIs for bovine (a,b) and human (f,g) bone samples. The corresponding signal intensity variation curves of T_1, T₂* and MT were shown in c, d and e, respectively, for bovine bone and shown in h, i and j for human bone, and were normalized to the PR signal intensities.

Table 1 shows the mean and standard deviation of all biomarkers of 10 bovine bone samples, along with percent error and p-values from one-way ANOVA with Dunnett’s test using the PR results as the reference standard. There were no significant differences (all p values >0.05) for any biomarker when the sampling window length was 1600 μs or lower. For T₁, errors were all within 2%, while errors of macromolecular fraction were all within 3% when the sampling window was 1600 μs, which has an acceleration factor of 5.0 over radial sampling. Increased errors in MTR were observed with longer sampling windows, with errors less than 2% with an acceleration factor of 5.0. With longer sampling windows, increased errors were also observed in both the single component and bi-component T₂* analyses, including single component T₂*, long T₂* and short T₂* fraction, with errors of single component T₂*, short T₂* and long T₂* within 3% when the sampling window was 1392 μs and within 5% for all the T₂* biomarkers when the sampling window was 1600 μs. Although errors of T₂* biomarkers were all less than 5% with an acceleration factor of 5.0, the error ranges were relatively large, especially single component T₂*, when compared to T₁, MTR and macromolecular fraction.

Table 1.

Mean and standard deviation of MR properties in bovine bone samples. Errors (%) and p-values from Dunnett’s test compare the results of each UTE Cones trajectory with PR results.

Mean ± SD (Error %)		PR	Cones1.0	Cones1.2	Cones1.4	Cones1.6
T2* single component (ms)		0.45±0.06	0.46±0.06 (1.79%)	0.46±0.06 (2.19%)	0.47±0.06 (2.98%)	0.47±0.05 (4.76%)
		P value	0.99	0.99	0.94	0.80
T2* bi-component	T2*S (ms)	0.27±0.01	0.27±0.01 (−1.67%)	0.26±0.01 (−2.57%)	0.26±0.01 (−2.55%)	0.26±0.01 (−2.69%)
		P value	0.93	0.42	0.22	0.22
	T2*L(ms)	2.45±0.68	2.42±0.68 (−1.15%)	2.40±0.67 (−2.07%)	2.38±0.64 (−2.90%)	2.37±0.63 (−3.40%)
		P value	1.00	1.00	1.00	1.00
	Fraction Short (%)	75.5±6.3	74.3±6.2 (−1.54%)	73.7±5.9 (−2.37%)	73.1±5.8 (−3.13%)	72.3±5.6 (−4.28%)
		P value	0.98	0.91	0.79	0.57
T1 (ms)		234.4±10.9	231.9±10.4 (−1.03%)	231.1±10.4 (−1.37%)	232.8±9.9 (−0.68%)	231.9±10.0 (−1.05%)
		P value	0.96	0.89	0.99	0.96
MTR (%) (1500°, 2kHz)		0.54±0.10	0.54±0.09 (0.67%)	0.54±0.09 (0.74%)	0.54±0.09 (0.89%)	0.55±0.10 (1.66%)
		P value	1.00	1.00	1.00	1.00
Macromolecular fraction (%)		62.3±9.3	63.8±9.3 (2.42%)	64.0±9.4 (2.74%)	62.4±9.3 (0.16%)	63.9±10.0 (2.43%)
		P value	0.99	0.98	1.00	0.99
Sampling window (μs)		688	992	1200	1392	1600
Acceleration factor		1	2.6	3.5	4.1	5.0

Table 2 shows the mean and standard deviation of all biomarkers of 17 human bone samples, along with percent error and p-values from one-way ANOVA with Dunnett’s test using the PR results as the reference standard. No significant differences (all p values >0.05) were observed for any biomarker when the sampling window was 1600 μs or lower. As for T₁, macromolecular fraction, the errors were almost within 1% when sampling windows were lower than 1600 μs, other than macromolecular fraction with a 1.13% error when sampling window was 1200 μs. Errors of single component T₂* and long T₂* were all within 2%, while relatively larger errors were observed for short T₂* and short T₂* fraction. Increased errors were observed with longer sampling window in short T₂* and short T₂* fraction as well as MTR; however, errors were typically less than 5% with an acceleration factor of 4.1.

Table 2.

Mean and standard deviation of MR properties in human bone specimens. Errors (%) and p-values from Dunnett’s test compare the results of each UTE Cones trajectory with PR results.

Mean ± SD (Error %)		PR	Cones1.0	Cones1.2	Cones1.4	Cones1.6
T2* single component (ms)		0.45±0.13	0.46±0.15 (1.47%)	0.46±0.15 (0.82%)	0.46±0.15 (0.95%)	0.46±0.16 (1.52%)
		P value	1.00	1.00	1.00	1.00
T2* bi-component	T2*S (ms)	0.29±0.03	0.29±0.02 (−1.30%)	0.28±0.02 (−2.81%)	0.28±0.02 (−4.61%)	0.27±0.02 (−6.11%)
		P value	0.96	0.73	0.23	0.05
	T2*L(ms)	7.24±1.76	7.30±1.70 (0.75%)	7.36±1.65 (1.59%)	7.35±1.60 (1.47%)	7.31±1.62 (0.89%)
		P value	1.00	0.99	0.99	1.00
	Fraction Short (%)	75.2±4.4	73.9±4.8 (−1.70%)	73.7±4.9 (−2.00%)	73.2±5.2 (−2.68%)	72.5±5.5 (−3.51%)
		P value	0.87	0.79	0.58	0.35
T1 (ms)		222.7±26.4	223.9±27.1 (0.58%)	224.0±28.4 (0.62%)	224.6±28.1 (0.89%)	224.6±28.4 (0.84%)
		P value	1.00	1.00	0.99	0.99
MTR (%) (1500°, 2kHz)		0.37±0.06	0.36±0.06 (−3.63%)	0.36±0.06 (−3.72%)	0.35±0.06 (−4.14%)	0.35±0.06 (−4.31%)
		P value	0.93	0.92	0.88	0.87
Macromolecular fraction (%)		56.6±12.4	56.3±11.6 (−0.46%)	56.0±13.8 (−1.13%)	56.2±13.2 (−0.68%)	56.5±11.9 (−0.25%)
		P value	0.99	1.00	1.00	1.00
Sampling window (μs)		688	992	1200	1392	1600
Acceleration factor		1	2.6	3.5	4.1	5.0

Figure 5 shows the Bland-Altman plots of all the biomarkers (T₁, macromolecular fraction, MTR, T₂*, short T₂*, long T₂* and short T₂* fraction) for bovine cortical bone samples. The difference between Cones and radial sampling trajectories and the average of each measurement comprise the axes. The 95% limits of agreement between biomarkers obtained from various Cones trajectories and radial trajectory were −9.88 and 5.05 for T₁, −2.35 and 4.76 for MT modeling of macromolecular fraction, −0.020 and 0.031 for MTR, −0.023 and 0.050 for single component T₂*, −0.019 and 0.007 for short T₂*, −0.36 and 0.24 for long T₂* and −6.55 and 2.28 for short T₂* fraction. There were no significant trends in the distribution of errors as Cones stretch factor was increased.

Figure 5.

Bland-Altman plots of biomarkers T₁ (a), macromolecular fraction (b), MTR (c), T₂* (d), short T₂* (e), long T₂* (f) and short T₂* fraction (g) for bovine cortical bone samples comparing various Cones sampling trajectories with radial trajectory. The two dash black lines are showing the 95% upper and lower limits of agreement (LoA) respectively, while the black line is showing the level of average difference.

Figure 6 shows the Bland-Altman plots of all the biomarkers (T₁, macromolecular fraction, MTR, T₂*, short T₂*, long T₂* and short T₂* fraction) for human cortical bone samples. The 95% limits of agreement between biomarkers obtained from various Cones trajectories and radial trajectory were −5.13 and 8.38 for T₁, −5.46 and 4.75 for MT modeling of macromolecular fraction, −0.029 and −0.003 for MTR, −0.048 and 0.058 for single component T₂*, −0.051 and 0.028 for short T₂*, −0.74 and 0.91 for long T₂* and −4.91 and 1.19 for short T₂* fraction. There were no significant differences in the distribution of errors as Cones stretch factor was increased, though there was a slight trend towards decreased short T₂* fraction as stretch factor increased.

Figure 6.

Bland-Altman plots of biomarkers T₁ (a), macromolecular fraction (b), MTR (c), T₂* (d), short T₂* (e), long T₂* (f) and short T₂* fraction (g) for human cortical bone samples comparing various Cones sampling trajectories with radial trajectory. The two dash black lines indicate the 95% upper and lower limits of agreement (LoA), respectively, while the black line shows the level of average difference.

4. Discussion:

Quantitative biomarkers derived using 3D Cones UTE MRI techniques have many potential clinical applications in musculoskeletal system imaging, but the relatively long scan time is a significant barrier for widespread clinical adoption. This study investigated the effects of sampling window on several quantitative 3D Cones UTE MRI techniques aiming to reduce the total scan time while retaining the measurement accuracy within an acceptable range. The results are likely to help in developing translational quantitative 3D Cones UTE imaging of cortical bone and other musculoskeletal tissues.

The 3D spiral trajectories require no phase encoding at the beginning of readout and begin at the center of k-space, making them suitable for UTE acquisitions. The spiral trajectory has significantly higher efficiency in filling k-space than the radial trajectory (35). Stretching the spiral trajectory results in a further increased readout time (sampling window length) and a much decreased number of readouts because outer k-space is more efficiently sampled. This leads to a much shorter scan time as well as to a more uniform sampling density, which improves SNR efficiency (36). Potential disadvantages of the increased readout time are increased flow effects and off-resonance blurring, as well as greater sensitivity to T₂* decay (36).

Few studies have focused on the optimization of the sampling window length. Rahmer et al. (26) investigated an optimal acquisition time for 3D radial UTE imaging, and 0.81 times the T₂ value was suggested for maximal SNR. However, Rahmer’s study did not consider the effect of ramp sampling, which might play a major role in optimizing SNR and spatial resolution. Furthermore, the spatial resolution might be rather low and suboptimal for many MSK imaging applications when such a short sampling window is used. Du et al. (27) investigated the effect of different spiral sampling durations on short T₂ spatial blurring in 2D UTE imaging and demonstrated that increased sampling window resulted in more blurring (or spatial resolution reduction), but higher SNR. A spiral sampling window of two to four times the T₂* value was suggested for in vivo imaging of short T₂ tissues to obtain a balance between spatial resolution and SNR.

The current study is the first study to investigate the effects of sampling window length on UTE-based quantitative biomarkers, using ex vivo analysis of bovine and human cortical bone samples. No significant differences were observed for the calculated UTE biomarkers (T1, macromolecular fraction and MTR, single-component T2*, bi-component T2*s) between the radial sampling trajectory (688 μs) and spiral sampling trajectories with a duration of 992 to 1600 μs. One possible explanation would be that quantitative imaging of a low spatial frequency object relies more on central k-space and may be less sensitive to short T2 blurring than morphological imaging.

The results of this study indicate that quantitative UTE-MRI of low spatial frequency objects can be greatly accelerated with longer spiral sampling windows (i.e., 992 to 1600 μs) without substantial measurement errors (Table 1 and 2). Errors were all within 3% in T₁, macromolecular fraction and MTR for bovine bone samples, while errors were within 5% for human bone samples when the sampling window was 1600 μs or shorter. Errors in T₂* biomarkers were all within 5% when the sampling window was 1392 μs or shorter for both bovine and human bone specimens. Thus, a recommended sampling window time could be ~1392 μs, which can decrease the total scan time by 76% with respect to radial sampling. Furthermore, the UTE biomarkers obtained in the current study were largely consistent with values reported in previous studies (16,37,38).

Both single-component and bi-component T₂* analyses were more sensitive to the effect of extended sampling windows compared with T₁, macromolecular fraction and MTR. There are multiple factors contributing to the increased errors, including the high sensitivity of T2* to B₀ field inhomogeneity and local susceptibility, as well as the very different response of short and long T2* components to extended sampling windows (39). Thus, the robustness of T₁ and MT modeling analysis is slightly higher than T₂* analysis. Eddy currents may affect the quantification accuracy for all UTE biomarkers, as radial and spiral samplings are sensitive to eddy current-related gradient distortions.

There are several limitations in our study. First, the choice of spiral sampling windows was arbitrary, with four windows chosen to compare a wide range of sampling window lengths. More sampling windows could be tested within the range of 992 μs and 1600 μs to further optimize scan time. Increased artifacts were observed when the sampling window was longer than 1600 μs, likely due to increased eddy currents and off-resonance effects. Second, we imaged cortical bone of the tibial midshaft, which has a cylindrical shape with mainly low frequency components that do not require high spatial resolution for morphological imaging, and placed ROIs on the outer 2/3rds band to minimize influences from fat. Therefore, the results have only been shown to hold for low spatial frequency objects. Third, this study was done ex vivo, with soft tissues surrounding the bone removed, a situation which may differ from the physiological situation. We removed the surrounding tissues to avoid the chemical shift artifacts of fat so that it is clear that the assessed artifacts are from the stretching sampling windows. Our results suggest that 3D UTE-Cones with an extended sampling window can be used to quantitatively image thick segments of cortical bone without significant errors and with a greatly reduced scan time. Extending these results to thinner cortical bone or cortical bone near the endosteum—which may be contaminated by chemical shift artifacts from bone marrow fat—will require further studies using advanced fat-suppression methods with minimal effect on water excitation as well as confirmation of these results with intact ex vivo joints and in vivo human studies. Fourth, this study was focused only on cortical bone. The effects of the extended sampling window on other musculoskeletal tissues, such as articular cartilage, menisci, tendons and ligaments should be investigated; however, these tissues have longer T₂ values than cortical bone and should experience less T₂* decay during longer sampling windows. Finally, the radial trajectory was used as the reference standard, but it is also subject to measurement error and bias.

5. Conclusion

Compared with radial sampling, quantitative UTE-MRI techniques using spiral trajectories with extended sampling windows were able to reduce scan time without major effects on quantification accuracy of T₁, single component T₂*, bi-component short and long T₂*s and relative fractions, MTR and macromolecular fraction in low spatial frequency objects, such as cortical bone of the tibial midshaft. Our recommended sampling window for human cortical bone was around 1392 μs, resulting in an acceleration factor of 4.1 and measurement errors typically less than 5% in all UTE biomarkers.

This study suggests that quantitative UTE-MRI techniques can be greatly accelerated with longer sampling windows without significant quantification errors in low spatial frequency objects such as midshaft tibia. These results are expected to facilitate clinical imaging of cortical bone using accelerated quantitative 3D UTE-Cones techniques.