Fast quantitative three-dimensional ultrashort echo time (UTE) magnetic resonance imaging of major tissues in the knee joint using extended cones sampling

Abstract

The purpose of this study is to investigate the effect of extending the spiral sampling window on quantitative 3D UTE Cones imaging of major knee joint tissues including articular cartilage, menisci, tendons, and ligaments at 3T. Nine cadaveric human whole knee specimens were imaged on a 3T clinical MRI scanner. A series of quantitative 3D UTE Cones imaging biomarkers including T₂*, T₁, Adiabatic T_1ρ, magnetization transfer ratio (MTR), and macromolecular fraction (MMF) were estimated using spiral sampling trajectories with various durations. Errors in UTE MRI biomarkers as a function of sampling time were evaluated using a non-stretched spiral trajectory as reference standard. No significant differences were observed by increasing the spiral sampling window from 1116 μs to 2232 μs in the calculated T₂*, T₁, Adiabatic T_1ρ, MTR, and MMF, as all p-values were over 0.05 as assessed by ANOVA with two-sided Dunnett’s test. Although extending the sampling window results in signal loss for short T₂ components, there was limited effect on the calculated quantitative biomarkers, with error percentages typically smaller than 5% in all evaluated tissues. The total scan time can be reduced by up to 54% with quantification errors less than 5% in any evaluated major tissue in the knee joint, suggesting that the 3D UTE Cones MRI techniques can be greatly accelerated by using a longer spiral sampling window without causing additional quantitative bias.

1. Introduction

Articular cartilage, menisci, tendons, and ligaments are major tissues of the human knee joint, all of which are vital to its health^1–3. Osteoarthritis (OA) usually involves all of these major tissues, although degeneration of articular cartilage has been investigated most extensively^4–7. Noninvasive magnetic resonance imaging (MRI) can detect biochemical changes in these major tissues, facilitating diagnosis of OA at the early stage^8,9. In order to detect multi-tissue lesions within knee joints, high resolution MR imaging of the whole knee is necessary, though this may result in a relatively long scan time. Patient motion may occur during the long scan time leading to impaired quantitative MR accuracy.

Many knee joint tissues, including the deep cartilage, menisci, tendons, and ligaments, contain a majority of short T₂ components (< 10 milliseconds)⁵. In such tissues, the signal decays so quickly that little or no signal can be detected with conventional clinical MR sequences, which typically have echo times (TEs) of several milliseconds or longer. Ultrashort echo time (UTE) MRI sequences, including their variants such as water- and fat-suppressed proton projection MRI (WASPI), zero echo time (ZTE), and pointwise encoding time reduction with radial acquisition (PETRA) sequences^10–13, have TEs on the order of several to tens of microseconds, allowing for direct imaging and quantitative assessment of cartilage, menisci, tendons, and ligaments in human knee joints.

In recent years, 3D Cones UTE MRI techniques have become available for high resolution imaging of short T₂ tissues^14–17. Compared with WASPI, ZTE, PETRA and radial UTE techniques, the 3D Cones sequence divides the k-space into multiple cones with twisted radial trajectories along each cone, which is highly time-efficient for volumetric morphological imaging^10–17. For comprehensive assessment of knee joint tissues, a series of quantitative UTE MRI techniques have been developed based on 3D Cones, including T₂*, T₁, Adiabatic T_1ρ, magnetization transfer ratio (MTR), and magnetization transfer (MT) modeling of macromolecular fraction (MMF)^18–21. However, the clinical use of these biomarkers has been impeded by their relatively long scan time.

By using extended spiral sampling trajectories, the total scan time for these techniques can be shortened considerably compared with conventional radial sampling in UTE sequences^22,23. The concept of stretching the spiral trajectory in 3D UTE Cones imaging, which means decreasing the pitch of a spiral readout, thereby increasing the duration of the readout to reach the same |k_max|, results in increased readout time (sampling window), but reduced number of readouts. Specifically, stretching the spiral trajectory leads to more efficiently sampled outer k-space, shorter scan time, and more uniform sampling density, which improves signal to noise ratio (SNR) efficiency^14,22,23. However, the signal of short T₂ components may decay significantly during the process of RF excitation and data acquisition^5,24. The signal decay along the sampling trajectory to outer k-space can also result in spatial blurring of short T₂ components²⁵, potentially exerting influence on the accuracy of quantitative MR biomarkers. The effect of extended sampling window on quantitative 3D UTE Cones biomarkers has not yet been systematically investigated for various knee joint tissues including articular cartilage, menisci, tendons, and ligaments.

The purpose of this study was to evaluate the quantitative errors associated with extended sampling windows on 3D UTE Cones MRI biomarkers including T₂*, T₁, Adiabatic T_1ρ, MTR and MMF in major knee joint tissues. These results may be used to develop an optimized protocol for quantitative imaging that balances between speed and error considerations, facilitating the use of quantitative whole knee UTE MRI in a clinical setting.

2. Methods

2.1. Specimens

High resolution MR imaging was performed on nine whole knee joint specimens from eight donors (65 ± 26 years old, seven males and one female), which were provided by a nonprofit whole-body donation company (United Tissue Network, Phoenix, AZ). The ethical approval was waived by the Institutional Review Board. All joints experienced one freeze-thaw cycle. The specimens were freezed at −80℃ and thawed at room temperature for twelve hours before being scanned. 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) with the maximum gradient amplitude, slew rate, and ramp time being 50 mT/m, 200 T/m/s, and 250 μs, respectively. An eight-channel transmit/receive knee coil was used for RF excitation and signal receive. All 3D UTE Cones sequences used a short rectangular excitation pulse followed by 3D spiral sampling trajectory with an initial short TE of 32 μs (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 spiral sampling trajectory. 3D dual echo UTE is used for acquisition with an initial short TE of 32 μs. (b) 2D representation of example trajectories: spiral trajectory with a short sampling window (blue line), spiral trajectory with a longer sampling window (pink line). As the sampling window increases, the longer spiral trajectories have greater curvature and more k-space coverage with each spoke. (c) The 3D UTE-Cones sequence with a single TR was used for T₁ measurement with the variable flip angle (VFA) method. The 3D UTE actual flip angle imaging (UTE-AFI) sequence with a pair of interleaved TRs was used for B₁ mapping. The combination of 3D UTE-VFA and UTE-VFI methods provides accurate T₁ measurement. (d) The 3D UTE Cones Adiabatic T_1ρ sequence employs a train of AFP pulses to generate T_1ρ contrast. (e) A Fermi pulse is used for MT preparation followed by multi- spoke (Nsp) excitation. Scan time can be reduced by a factor of N_sp.

To investigate the effect of increasing stretch factor on T₂* measurement, the six-echo Cones T₂* sequence with an echo spacing of 8.8 ms and a series of stretch factors including Cones 1.0 (non-stretched), 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, and 3.0 (plots of the k-space trajectories for each stretch factor were shown in Supporting Figure S1), was performed on a cadaveric human knee joint specimen. Four different regions of interest (ROIs) were manually drawn in articular cartilage (the central region of both medial and lateral side of femoral and tibial cartilage) and two different ROIs were manually drawn in quadriceps and patellar tendons, respectively. The average T₂*s and quantification errors were calculated. Then three stretch factors of 1.0, 1.5 and 2.0 were chosen for the following three quantitative imaging protocols (only three stretch factors were investigated for T₁, Adiabatic T_1ρ, MTR, and MMF as these protocols were time-consuming and MR scanner time was limited): 1) a UTE actual flip angle imaging (UTE-AFI) method (TR₁/TR₂ = 20/100 ms and flip angle = 45°) for B₁ correction, followed by a 3D UTE variable flip angle method (UTE-VFA) (FAs = 5°, 10°, 20°, 30°; TR = 20 ms) method for accurate T₁ mapping (Figure 1c); 2) an adiabatic full passage pulse train-prepared UTE (spin lock time=0, 12, 24, 36, 48, 72, 96 ms; TR = 500; FA = 10°) for Adiabatic T_1ρ mapping (Figure 1d). The maximum RF power was 17uT and the readout number per preparation was 21; 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 1e) for two-pool MT modeling and MTR measurement. The readout number for MT sequence was 9. Other imaging parameters included: field of view (FOV) = 15×15×8 cm³, matrix = 256×256×40, and readout bandwidth = ±83.33 kHz.

The above described sequences including UTE-VFA T₁, Adiabatic T_1ρ, and MT were repeated using Cones trajectories (spiral trajectories with conical view ordering) with three different stretch factors (Figure 1b) to investigate the effect of extended sampling window on quantitative 3D UTE MRI biomarkers. Ramp sampling was used for data acquisition and gradient delays for all three physical gradients were measured to correct the sampling trajectories. Cones sampling windows were: 1116 μs (Cones with a stretching factor of 1.0, or Cones 1.0), 1668 μs (Cones 1.5) and 2232 μs (Cones 2.0), corresponding to acceleration factors of 1.60 and 2.23 over Cones 1.0, respectively, due to reduced number of readouts. The acceleration factor was defined as the ratio of the scan time of non-stretched Cones sequence to each stretched Cones sequences, while the stretching factor was defined as the ratio of the sampling window of stretched trajectories to the non-stretched trajectory. For example, the scan times for T₁ imaging with the abovementioned trajectories were 4.65, 2.87, and 2.08 minutes, respectively; the scan times for each Adiabatic T_1ρ imaging with the above mentioned spiral trajectories were 5.58, 3.48, and 2.55 minutes, respectively; and the scan times for each MT imaging were 2.7, 1.68, and 1.25 minutes, 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. ROIs were manually drawn on the first UTE image of each series, then copied to each of the subsequent images. The mean intensities within the selected ROIs were used for curve fitting. A single-component (S(TE) ∝ exp(−TE/T2*) + constant) fitting model was used for T₂* decay analyses acquired from the six-echo 3D-UTE-Cones sequence. T₁ was analyzed from the 3D UTE-VFA sequences using single-component exponential fitting $\text{S}=M_{0}sin\left(\alpha \right)\frac{1-E}{1-E\text{cos}\left(\alpha \right)}$ with E = exp(−TR_s/T₁)^19,26. Quantitative Adiabatic T_1ρ was analyzed from the 3D UTE Cones Adiabatic T_1ρ data set with a series of spin-lock time (TSLs)²⁰. The UTE-MT data set was analyzed for MTR calculations^21,27,28 and for estimation of the MMF using a two-pool model²¹. ROIs were manually drawn in articular cartilage (the central region of both medial and lateral side of femoral and tibial cartilage), menisci (anterior and posterior horns of both medial and lateral side), quadriceps tendons, patellar tendons, as well as anterior cruciate ligament (ACL) and posterior cruciate ligament (PCL).

2.4. Statistical analysis

After all data analyses, error percentages in the UTE MRI biomarkers were calculated for results from Cones 1.5 and Cones 2.0 versus results from Cones 1.0, with the latter used as reference standard. Afterwards, all statistical analyses were performed using SPSS software (SPSS, BIM 24). One-way ANOVA with two-sided Dunnett’s test was used to determine the significance of the mean differences of all biomarkers compared with Cones 1.0 trajectory. Bland-Altman analysis was used for the agreement assessment of sampling windows from Cones 1.5 and Cones 2.0 compared to Cones 1.0. A p-value less than 0.05 was considered a significant difference.

3. Results

Excellent single-component T₂* fitting curves were achieved for articular cartilage (Supplemental Figure S2) with various stretch factors ranging from 1.0 to 3.0, and with a step size of 0.25. The error percentages compared to the results of Cones 1.0, which were used as reference standard, are presented in Figure 2. The quantitative percentage errors of T₂* values increased with stretch factor. Significantly higher percentage errors were observed for stretch factor higher than 2.0. Similar results were also observed for the patellar tendon (Supplemental Figures 3 and 4).

Figure 2.

T₂* values and error percentages vs stretch factor for cartilage, with fixed echo spacing (a, b). All stretch factors from Cones 1.0 to 3.0 (step size of 0.25) are included. Error percentages were calculated by using Cones 1.0 results as reference standard. Four different ROIs are included in analysis, with dots representing the mean values and with error bars representing the standard deviation of the measurements in a, while the dots in b represent the average error percentages of results measured from four ROIs.

Figure 3 shows two representative slices of 3D UTE T₁, Adiabatic T_1ρ, and MT images of the same whole knee specimen (male, 31 years old) with gradually increasing sampling windows from Cones 1.0 (1116 μs readout) to Cones 2.0 (2232 μs readout). As expected, the fast signal decay of short T₂ components and the extended sampling window resulted in signal loss and blurring of short T₂ components.

Figure 3.

Two representative slices of 3D UTE Cones AFI-VFA T₁ (a-c), 3D UTE Cones Adiabatic T_1ρ (d-f) and 3D UTE Cones MT (g-i) images of a whole knee specimen with different sampling windows of Cones1.0 (a, d, g), Cones1.5 (b, e, h), Cones2.0 (c, f, i), with the red arrows indicating the deep cartilage and the yellow arrow indicating the PCL.

Figure 4 shows the mean values and standard deviations of T₁, Adiabatic T_1ρ, MTR, and MMF with different sampling windows (Cones 1.0, Cones 1.5, and Cones 2.0) for cartilage, menisci, tendons, and ligaments of nine knee joint specimens.

Figure 4.

The representative ROIs are shown in a. The mean values and standard deviations of T₁, Adiabatic T_1ρ, MTR, and MMF in cartilage, menisci, tendons, and ligaments with different sampling windows (Cones 1.0: 1116 μs; Cones 1.5: 1668μs; Cones 2.0: 2232 μs) are shown in b, c, d, and e, respectively, with dots representing the mean value and with error bars representing the standard deviation of biomarkers of nine knee joint specimens.

Table 1 presents the mean and standard deviation of MR properties for cartilage, menisci, tendons, and ligaments of nine knee joint specimens, along with error percentages measured via comparisons with the Cones 1.0 results as reference standard. Errors in the measured T₁ increased with longer sampling windows for articular cartilage, tendons, and ligaments. The error percentages were all within 5% for all evaluated tissues, except for ligaments with a sampling window of 2232 μs (an error percentage of 8.06% was observed). There were no significant differences (p>0.05) in the measured T₁ of any knee joint tissue. Errors in the estimated Adiabatic T_1ρ and MTR also increased with a longer sampling windows, but the error percentages were all within 5% for all evaluated tissues. The error percentages in estimated MMF did not have any clear trend but remained within the 5% range for all evaluated tissues. Overall, an extended sampling window had limited effect on quantitative UTE MRI biomarkers.

Table 1.

Mean and standard deviation of MR properties in the major tissues of knee joint, including cartilage, menisci, tendons and ligaments. Errors compare the results of Cones 1.5 and Cones 2.0 with Cones 1.0, which considered reference standard.

Mean ± SD (Error %)	Tissues	Cones1.0	Cones 1.5	Cones 2.0
T1 (ms)	Cartilage	756.71±67	752.17±75	744.74±70
		Error% (p)	−0.60 (0.99)	−1.58 (0.91)
	Menisci	645.17±68	655.75±71	654.58±71
		Error% (p)	1.64 (0.93)	1.46 (0.94)
	Tendons	616.40±111	620.86±110	622.63±110
		Error % (p)	0.72 (0.99)	1.01 (0.99)
	Ligaments	787.40±87	759.80±92	723.95±85
		Error % (p)	−3.51 (0.74)	−8.06 (0.24)
Adiabatic T1ρ (ms)	Cartilage	45.43±4.5	45.10±4.6	43.78±3.8
		Error % (p)	−0.74 (0.98)	−3.65 (0.63)
	Menisci	28.00±3.6	27.93±4.4	27.51±4.2
		Error % (p)	−0.27 (0.99)	−1.75 (0.95)
	Tendons	28.43±8.3	27.86±8.2	27.37±7.1
		Error % (p)	−2.01 (0.98)	−3.73 (0.94)
	Ligaments	43.04±5.8	42.17±5.0	40.92±5.5
		Error % (p)	−2.03 (0.92)	−4.94 (0.62)
MMF (%)	Cartilage	13.26±1.4	13.55±1.4	13.15±1.2
		Error % (p)	2.21 (0.85)	−0.80 (0.98)
	Menisci	20.31±2.2	20.51±1.7	19.77±1.9
		Error % (p)	0.98 (0.97)	−2.68 (0.78)
	Tendons	16.81±1.9	17.39±1.9	16.52±2.5
		Error % (p)	3.45 (0.78)	−1.74 (0.94)
	Ligaments	13.38±1.5	13.74±1.5	13.58±1.9
		Error % (p)	2.67 (0.85)	1.49 (0.95)
MTR (%) (1500°, 2kHz)	Cartilage	0.43±0.06	0.43±0.06	0.44±0.06
		Error % (p)	1.09 (0.97)	2.42 (0.91)
	Menisci	0.54±0.05	0.54±0.05	0.53±0.05
		Error % (p)	0.43 (0.99)	−0.77 (0.98)
	Tendons	0.41±0.07	0.42±0.09	0.43±0.08
		Error % (p)	2.56 (0.94)	4.36 (0.85)
	Ligaments	0.44±0.05	0.44±0.05	0.44±0.06
		Error % (p)	−0.45 (0.99)	−2.07 (0.91)
Sampling window (μs)		1116	1668	2232
Acceleration factor		1.00	1.60	2.23

Figure 5 shows the Bland-Altman plots of all four biomarkers of cartilage for each of the nine cadaveric human knee joint specimens (averaged over two slices per specimen and two ROIs per slice), with the results from the Cones 1.0 sampling trajectory considered as baseline. The differences between baseline and longer Cones trajectories (i.e., Cones 1.5 and 2.0) are depicted on the vertical axis and their averages on the horizontal axis. For T₁, Adiabatic T_1ρ, MTR, and MMF, the range for 95% of the differences was −39 ms to +23 ms, −4.6 ms to +2.6 ms, −1.0 ms to +1.2 ms, and −0.00 ms to +0.02 ms, respectively. Most of the errors were within the 95% CI without definite trends in distribution.

Figure 5.

Bland-Altman plots of biomarkers T₁ (a), Adiabatic T_1ρ (b), MTR (c), and MMF (d) in articular cartilage comparing Cones 1.5 and 2.0 sampling trajectories with Cones 1.0 trajectory. The two dash black lines show the upper and lower limits of agreement (LOAs) respectively, while the black line shows the level of average difference.

Supporting Figures S2 and S3 show the typical T₂* fitting curves for articular cartilage and tendons with different stretching factors of 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75 and 3.0, respectively. Supporting Figure S4 shows the T₂* values and their corresponding error percentages for tendons with different stretch factors. Supporting Figures S5–7 show the Bland-Altman plots of 3D UTE Cones based biomarkers including T₁, Adiabatic T_1ρ, MTR, and MMF in menisci, tendons, and ligaments, respectively. Similar to cartilage, most of the errors were within the threshold of the 95% CI.

4. Discussion

This is the first study to investigate the effects of sampling window length on 3D UTE Cones based quantitative biomarkers including T₂*, T₁, Adiabatic T_1ρ, MTR, and MMF in the major knee joint tissues. Understanding such impacts can help to reduce the total scan time while maintaining the accuracy of UTE MRI measurement within an acceptable range. Quantitative UTE biomarkers obtained using 3D Cones UTE MRI techniques may have promising clinical applications in musculoskeletal imaging, but the relatively long scan time is a major barrier for widespread clinical applications.

The preliminary study of T₂* measurement suggests that stretch factors higher than 2.0 may result in significantly increased error percentages in articular cartilage and tendons. We only used Cones 1.0, 1.5, and 2.0 for further study, as the total scan time would be much longer if Cones 1.25 and 1.75 were included. Furthermore, radial trajectory was not included in this study due to the much increased scan time. Our prior study of cortical bone specimens showed very similar results (<3% difference) for T₁, T₂*, MTR and MMF derived from 3D UTE Cones imaging with radial and Cones 1.0 trajectories, respectively²³. The differences are expected to be even smaller for knee joint tissues as they have longer T₂*s than that of cortical bone.

In nine studied human knee joint specimens, no significant differences were observed in calculated 3D UTE Cones biomarkers (T₁, Adiabatic T_1ρ, MTR, and MMF) when increasing the spiral sampling window from 1116 μs to 2232 μs. Extending sampling window resulted in signal loss, particularly for the short T₂ components. However, extending the sampling window has a limited effect on the quantitative biomarkers, with error percentages typically smaller than 5% in all evaluated tissues when the sampling window was equal or less than 2232 μs. The results are likely to help facilitate the clinical translation of quantitative 3D UTE Cones imaging of articular cartilage, menisci, tendons, and ligaments in the knee joint.

Several other studies have attempted to optimize the sampling window for speed and accuracy of 3D UTE biomarkers. Notably, a study by Rahmer et al.²⁴ determined that 0.81 times the T₂ value of the tissue provided the maximal SNR for 3D radial UTE imaging. However, using a short sampling window with radial acquisitions may be suboptimal when high resolution quantitative imaging is required, such as in the knee joint. An earlier study by our group using 2D spiral UTE imaging suggested that higher SNR efficiency can be achieved by using a longer sampling window acquisition method²⁵. In addition, the scan time for 2D spiral UTE imaging of short T₂ tissues including myelin in white matter of the brain, calcified cartilage, menisci, and cortical bone, can be efficiently shortened by more than 50% compared with the scan time using 2D radial UTE acquisitions²⁵. Our previous work primarily investigated qualitative assessment of morphologic images and the reduction of total scan time, whereas the accuracy of quantification had not yet been systematically studied. In contrast, our current study directly investigated the sampling window length on estimation accuracy using 3D UTE Cones imaging of a range of knee joint tissues, some of which require high spatial resolution.

The quantitative 3D UTE techniques in this study can be applied to other body parts and MR scanners, as all the major MR vendors have UTE techniques or variants available on their systems. These techniques can also be applied to small animal imaging systems with more than 10 times stronger gradient strength, slew rate and RF power. In fact, quantitative UTE measurements on such high performance systems should be more appropriate as the reference standard due to more accurate excitation (stronger RF power, shorter RF pulse duration, thus more accurate excitation of short T₂ species) and reduced blurring. Quantitative UTE techniques have also been investigated at higher field strengths such as 7T^12,29. However, more research is needed to investigate the effect of sampling window on quantification accuracy, especially considering the increased short T₂* blurring at a higher field strength.3D spiral trajectories are suitable for UTE acquisitions because they begin at the center of k-space (minimizing TE), efficiently fill k-space compared to radial trajectories, and are entirely frequency encoded without the need for phase encoding^30,31. An extended sampling window has the advantage of more efficient k-space sampling, which allows rapid scanning time, but with the disadvantage of greater sensitivity to T₂* decay and increased susceptibility to flow effects and off-resonance blurring¹⁴. While flow effects are negligible ex vivo, blurring due to short T₂* decay was observed in some tissues, as expected. However, measurement errors typically remained within 5%. One potential bias is that the ROIs were drawn in the Cones 1.0 images with the least T₂* blurring, and it is possible that inappropriately large ROIs that may have been drawn in the Cones 2.0 images would result in lower accuracy. Moreover, in contrast to morphological analysis, quantitative methods typically fit a series of signal intensities in a fixed ROI, and may therefore be less sensitive to signal decay in outer k-space.

It is important to clarify that a formal power analysis was not done for this exploratory study. The number of samples was determined largely by feasibility. Published results for a similar situation were not available to guide our choice of an effect size for the power analysis. In part, the intent of this work was to obtain effect sizes to guide future studies. This study was also not powered to test for differences of a certain magnitude. There are not many papers reporting T₁ values for normal and degenerated cartilage. Rautiainen J, et al., reported a T₁ of 1390 ± 87 ms for early OA (OARSI < 1.5), and 1566 ± 21 ms for advanced OA (OARSI>1.5)³². The T₁ values were measured at 9.4 T, therefore longer than the T₁ values measured at 3T in this study. However, the same trend of longer T₁ for more degenerated cartilage is expected. In our study, T₁ was 756.71 ± 67 ms for Cones 1.0, 752.17 ± 75 ms for Cones 1.5, and 744.74 ± 70 ms for Cones 2.0. T₁ variations due to extended sampling are much smaller than those due to degeneration, as reported by the Rautiainen study³². Therefore, the use of a longer spiral sampling window is expected to greatly accelerate quantitative 3D UTE Cones measurements without significant impact on reliable separation of normal from degenerated cartilage.

Our study had several limitations. First, the choice of spiral sampling windows was arbitrary, with three windows chosen to compare a wide range of sampling window durations. More sampling windows could be tested within the range of 1116 μs and 2232 μs. Second, this study was performed ex vivo and the conclusions remain to be confirmed for in vivo human studies. We will include healthy volunteers in a future study. Third, the sample size of our study was relatively small, which may affect the statistical power. Fourth, B₀ field inhomogeneity, gradient error and eddy current effects were not considered in this study. Those effects may significantly affect T₂* quantification based on multi-echo acquisitions, especially for later echoes²⁵. However, other measurements including T₁, Adiabatic T_1ρ, MTR and MMF are more robust to those effects as they are based on preparation pulses with echo times fixed to 32 μs. Finally, the spiral Cones 1.0 trajectory was used as reference standard, but it was itself subject to measurement error and bias. That said, systematic error due to the use of Cones trajectories was likely to be similar between the Cones 1.0, 1.5, and 2.0 trajectories.

5. Conclusion

Quantitative UTE MRI techniques using spiral trajectories with an extended sampling window were able to reduce total scan time without major effects on quantitative accuracy of T₁, Adiabatic T_1ρ, MTR, and MMF measurements. The variations of UTE biomarkers were typically under 5% for all analyzed tissues in knee joints (articular cartilage, menisci, tendons, and ligaments).

This study suggests that quantitative 3D UTE Cones MRI techniques can be greatly accelerated with a longer spiral sampling window without additional bias. The total scan time can be reduced by 38% with a stretch factor of 1.5, and 54% with a stretch factor of 2.0, while keeping relatively small errors less than 5%. These results are expected to facilitate clinical use of accelerated quantitative 3D UTE Cones MRI techniques for whole knee imaging.

Supplementary Material

Supporting figures

Supporting Figure S1. Plots of the k-space trajectories for stretch factors of 1.0 (a), 1.25 (b), 1.5 (c), 1.75 (d), 2.0 (e), 2.25 (f), 2.5 (g), 2.75 (h), and 3.0 (i), respectively.

Supporting Figure S2. The typical T₂* fitting curves for cartilage, with a fixed echo spacing. All stretch factors from Cones 1.0 to 3.0 (a-j) (step size of 0.25) are included. The fitting errors of T₂* measurements are small regardless of stretch factor.

Supporting Figure S3. The typical T₂* fitting curves for tendons, with fixed echo spacing. All stretch factors from Cone 1.0 to 3.0 (a-j) (step size of 0.25) are included.

Supporting Figure S4. T₂* values (a) and error percentages (b) vs stretch factor for tendons, with fixed echo spacing. All stretch factors from Cone 1.0 to 3.0 (step size of 0.25) are included. Error percentages were calculated by regarding Cones 1.0 results as reference standard.

Supporting Figure S5. Bland-Altman plots of biomarkers T₁ (a), Adiabatic T_1ρ (b), MTR(c), and MMF (d) in menisci comparing Cones 1.5 and 2.0 sampling trajectories with Cones 1.0 trajectory. The two dash black lines show the upper and lower LOAs, respectively, while the black line shows the level of average difference.

Supporting Figure S6. Bland-Altman plots of biomarkers T₁ (a), Adiabatic T_1ρ (b), MTR (c), and MMF (d) in tendons comparing Cones 1.5 and 2.0 sampling trajectories with Cones 1.0 trajectory. The two dash black lines show the upper and lower LOAs, respectively, while the black line shows the level of average difference.

Supporting Figure S7. Bland-Altman plots of biomarkers T₁ (a), Adiabatic T_1ρ (b), MTR (c), and MMF (d) in ligaments comparing Cones 1.5 and 2.0 sampling trajectories with Cones 1.0 trajectory. The two dash black lines show the upper and lower LOAs, respectively, while the black line shows the level of average difference.

Abbreviations used:

UTE

ultrashort echo time

OA

osteoarthritis

MTR

magnetization transfer ratio

MMF

macromolecular fraction

MT

magnetization transfer

SNR

signal to noise ratio

VFA

variable flip angle

FOV

field of view

ROI

regions of interest

TSL

spin lock time

ACL

anterior cruciate ligament

PCL

posterior cruciate ligament

LOA

limit of agreement