Feasibility of a UTE Stack-of-Spirals Sequence for ${\mathrm{T}}_{1\rho }$ Mapping of Achilles Tendinopathy

Abstract

We analyzed the feasibility of using a UTE stack-of-spirals Turbo-FLASH (STFL) sequence to measure ${\mathrm{T}}_{1\rho }$ relaxation in the Achilles tendon. Six HS (25–31yrs) and five AT patients (32–47yrs) participated. The study evaluates the clinical utility of the STFL sequence to generate ${\mathrm{T}}_{1\rho }$ maps using mono-exponential (ME) and bi-exponential (BE) fitting models. In a phantom experiment, $\text{ME}-{\mathrm{T}}_{1\rho }$ values and SNR estimated from the STFL sequence are compared with those of the Cartesian Turbo-FLASH (CTFL) sequence. In human subjects, we evaluate differences in estimated ME ($\text{ME}-{\mathrm{T}}_{1\rho }$) and BE parameters (short ${\mathrm{T}}_{1\rho }$, long ${\mathrm{T}}_{1\rho }$, and short fraction) between AT and HS groups along with repeatability of STFL. The agarose phantom demonstrates biases of 2.89% (3% agarose), −1.88% (5%), and −0.92% (7%) between $\text{ME}-{\mathrm{T}}_{1\rho }$ values from STFL and CTFL. In the bovine Achilles tendon, STFL shows a large bias of −58.6%, with a lower median $\text{ME}-{\mathrm{T}}_{1\rho }$ (2.9ms) than CTFL (4.6ms). SNR is higher in STFL (77.05–80.72 for 3%–7% agarose; 24.43 for bovine tendon) than CTFL (66.73–58.97 for agarose; 3.21 for bovine tendon). ME and BE parameters were averaged over the entire Achilles tendon, and none showed significant group differences (p>0.05; effect size=0.05–0.22). Sub-regional analysis showed that in the mid-Achilles tendon, short and long $\text{BE}-{\mathrm{T}}_{1\rho }$ components were 26% and 37% lower in AT than HS, though not statistically significant. The LDA-combined BE parameter showed significant group separation in the mid-tendon region (p=0.016; effect size=1.53). In HS, the long $\text{BE}-{\mathrm{T}}_{1\rho }$ component showed subregional variation (p=0.006), increasing 58% from calcaneal to mid-tendon, then decreasing 23% toward the intramuscular region. ME and BE fitting showed high repeatability with scan-rescan variations of 2.64% (${\mathrm{T}}_{1\rho }$), 3.38% (short ${\mathrm{T}}_{1\rho }$), 3.0% (long ${\mathrm{T}}_{1\rho }$), and 0.21% (short fraction). We demonstrated the feasibility of using STFL for ${\mathrm{T}}_{1\rho }$ quantification in the Achilles tendon.

1. Introduction

The Achilles tendon is the largest in the human body, connecting the calf muscle to the calcaneal bone. The Achilles tendon absorbs and stores energy, which is essential for efficient locomotion, jumping, and running (1,2). Reduced Achilles tendon stiffness requires greater excitation (3) and potentially, a higher metabolic cost for walking (4).

The biochemical composition and structure of the Achilles tendon play an important role in the mechanical functioning of the Achilles tendon. It is composed mainly of water (70%), highly organized collagen fibers (CFs), and proteoglycans (5). Highly organized CFs form the extracellular matrix (ECM) and maintain the structural integrity of the tendon. Proteoglycans support viscoelastic properties, helping with much-needed flexibility to the Achilles tendon and also modulating collagen fibrogenesis (6). The small leucine-rich proteoglycans (SLRP) help in maintaining the ECM of the tendon by binding collagen fibrils to form collagen fibers (7). The large proteoglycans play an important role in modulating the reorganization of the ECM after injuries to the tendon.

Damage, rupture, and other conditions in the Achilles tendon can debilitate an individual's quality of life (8). One such condition is tendinopathy, characterized by pain and swelling in the tendons. Tendinopathy in the Achilles tendon is caused by several factors, including overuse, aging, weak muscles, obesity (9), reduced tendon vascularization (10), reduced fascicle sliding (11), and metabolic dysfunction (12). The tendinopathy is induced by repeated stress on the tendon and results in the disruption of collagen fiber structures. Stress is marked by an increase in glycosaminoglycan (GAG) content and proteoglycans (aggrecan and biglycan), as shown in (13). An increase in proteoglycan content in the tendon is an early sign of tendinopathy. Repeated stress leads to the disruption of the ECM structure. The tendon tries to heal the damage by remodeling the ECM, which is marked by increased proliferation of type III collagen fibers, fibronectin, and tenascin C (5). There is an overall increase in vascularization for AT (6). The disruption to the healing process can lead to chronic Achilles tendinopathy(14,15).

Quantitative MRI (QMRI) provides a useful tool to measure these biochemical changes in the composition of the Achilles tendon. QMRI has been used extensively to analyze the intrinsic biochemical composition of the musculoskeletal system (16-18), and can help to track both the mechanism of injury and its healing process (19). The CFs are organized, rigid, and compact; hence, it has a very short T₂ relaxation time. To acquire the signal associated with CF in the Achilles tendon, we need to use ultra-short echo times (UTE) (20). Unfortunately, Cartesian acquisitions present longer echo times due to their side-to-side linear trajectories, long enough to critically attenuate the signal from CF. On the other hand, spiral-out acquisitions start collecting k-space data from the center, enabling the use of UTE and measuring these fast-relaxing signals. Several other center-out k-space trajectories, such as radial, stack-of-spirals (21), and 3D cones (22), have been used for UTE.

In the QMRI literature, T₁ (23), bound water fraction (24), T₂* (25-27), Diffusion Tensor Imaging (DTI) (28) , and ${\mathrm{T}}_{1\rho }$ (29-31) have been proposed as quantitative approaches sensitive to biochemical changes in the Achilles tendon ${\mathrm{T}}_{1\rho }$ relaxometry method enables us to probe molecular processes that occur at an applied spin-lock frequency (i.e, low-frequency molecular processes). ${\mathrm{T}}_{1\rho }$ is sensitive to water and molecular interaction at a low correlation times (32), which are characteristic of soft tissues in the musculoskeletal system, like cartilage and tendons. ${\mathrm{T}}_{1\rho }$ is particularly known to be sensitive to proteoglycan (33). T₁ relaxation and bound water fraction are sensitive to hydration, but not to proteoglycans, disruption of collagen fibers, or inflammation. T₂* is influenced by the interaction of bound water within collagen fibers, as well as local magnetic field inhomogeneities caused by disruptions in the collagen fiber structure (27). DTI directly measures the collagen fiber orientation and organization. ${\mathrm{T}}_{1\rho }$ was shown to be more sensitive to proteoglycan content than T₂ (34) , although not specific to proteoglycan content. As the early stages of tendinopathy are marked by an increase in proteoglycan content (35); therefore, changes in ${\mathrm{T}}_{1\rho }$ values can potentially serve as a biomarker for early-stage tendinopathy.

The standard approach in much of the musculoskeletal imaging literature, including studies focused on tendons, is to fit the ${\mathrm{T}}_{1\rho }$ relaxation to a mono-exponential model. This model assumes tissue homogeneity, a single pool, and can be obtained from a few acquisitions with different spin-locking times (TSL). Since ${\mathrm{T}}_{1\rho }$ relaxation in the tendons is influenced by interactions of water molecules and PG and of water molecules and collagen fibers (36), the relaxation behavior can be different within these two water compartments, and their contributions can change with the spin-lock frequency and orientation of the tendon (37). Given this complexity, a bi-exponential fitting model may be more appropriate for modeling ${\mathrm{T}}_{1\rho }$ in anisotropic tissues like tendons. Bi-exponential models are computationally more intensive to fit and require a larger number of spin-lock times (TSLs) to achieve reliable estimation when compared to mono-exponential models.

In this study, we use the UTE stack of spirals ${\mathrm{T}}_{1\rho }$-prepared sequence proposed in (21) to analyze the differences in ${\mathrm{T}}_{1\rho }$ in the Achilles tendon associated with tendinopathy using both mono- and bi-exponential models. We compared the signal-to-noise ratio (SNR) and the parametric maps accuracy of the sequence against a Cartesian sequence in a model phantom. Furthermore, we demonstrate the feasibility of the sequence on human subjects by assessing repeatability and its utility in detecting changes due to Achilles tendinopathy.

2. Materials and Methods

This study was approved by the Institutional Review Board (IRB) and was compliant with the Health Insurance Portability and Accountability Act (HIPAA). All human subjects provided written informed consent before MRI scanning. All MRI data in this study were acquired on a 3T scanner (MAGNETOM Prisma, Siemens Healthineers AG, Forchheim, Germany). A vendor-supplied 16-channel Foot/Ankle coil was used to acquire raw data from model phantoms, healthy volunteers, and tendinopathy patients. The built-in body coil serves as the transmitter, while the 16-channel Foot/Ankle array serves as the receiver.

2.1. $\mathrm{T}1\rho$-Prepared Cartesian and Acquisition-Weighted Stack-of-Spirals Sequences

The stack-of-spirals Turbo-FLASH (STFL) sequence (21) consists of a magnetization recovery delay, a Spectrally Attenuated Inversion Recovery (SPAIR) module for fat suppression, a magnetization-preparation module, and a GRE train with stack-of-spirals readout and an Optimized variable flip angles (OVFA) (38) strategy, as illustrated in Figure 1a. At the beginning of each acquisition, 6 dummy shots are played to achieve a steady state. Spiral interleaves are acquired at a minimum echo time (TE) of 0.03ms and repetition time (TR) of 5.09ms.

Figure 1.

(a)The STFL (Spiral) sequence incorporates a SPAIR pulse for fat suppression, followed by a continuous wave ${\mathrm{T}}_{1\rho }$ preparation module. Data acquisition is performed using a 3D stack-of-spirals trajectory. (b)The CTFL (Cartesian) sequence applies a water excitation (WE) pulse at each repetition for fat suppression, maintaining a constant flip angle across repetitions. K-space sampling is conducted using a 3D Cartesian trajectory.

${\mathrm{T}}_{1\rho }$-weighting was achieved using a self-balanced spin-locking module with spin-lock times (TSL) of 0, 0.2, 2.6, 5,10, and 20ms; and spin-lock frequency (FSL) of 500Hz. Spin-locking frequencies above 500Hz increase Specific Absorption Rate (SAR), exceeding the clinical safety thresholds for 3T- MRI systems due to the body transmit coil.

The Cartesian Turbo-Flash (CTFL) sequence is a generic Siemens turbo flash sequence modified to include the spin-lock preparation module and was used as a reference in phantom experiments. The CTFL sequence uses a water-excitation pulse instead of SPAIR, with a TE of 5.12ms and TR of 8.7ms. The CTFL sequence diagram is illustrated in Figure 1b.

We also acquire proton density (PD) images using the vendor-provided (Siemens Healthcare, Forchheim, Germany) Sampling Perfection with Application optimized Contrast using variable flip angle Evolution (SPACE) sequence. The resolution, size, and positioning of the FOV were matched with STFL sequence acquisition. The raw data was acquired with an acceleration factor of 2 in 4minutes and 13seconds. The images were reconstructed by the scanner using vendor-provided software. This sequence was used to make clinical evaluations and to segment the subregions of the Achilles tendon. All the pulse sequence parameters are illustrated in Table 1.

Table 1.

Summary of ${\mathrm{T}}_{1\rho }$-prepared CTFL, ${\mathrm{T}}_{1\rho }$-prepared STFL, and SPACE-PD sequence parameters used on a 3T scanner.

	${\mathrm{T}}_{1\rho }$		SPACE-PD
Trajectory	Spiral	Cartesian	Cartesian
Imaging Plane	Sagittal	Sagittal	Sagittal
FOV (mm)	200	200	200
TR(ms)	5.09	8.7	1690
TE(ms)	0.03	5.15	26
TSL(ms)	0, 0.2, 2.6, 5, 10, 20	0, 0.2, 2.6, 5, 10, 20	-
SL frequency (Hz)	500 Hz	500 Hz	-
Flip Angle	9°(first FA)	8°	160°(first FA)
Slice Thickness (mm)	0.8	1.25	0.8
Number of Slices	128	36	128
Matrix Size	256x256	256x256	256x256
Number of Interleaves	126	-	-
Spiral Duration	1840 μs
Variable Flip Angle	✓	x	✓
Acceleration Factor	1	1	2
Acquisition time (minutes:Seconds)	2:40/TSL	3:10/TSL	4:13
Phantom Scans	✓	✓	x
Human Scans	✓	x	✓

CTFL: Cartesian Fast Low Angle Shot; STFL: Stack-of-Spirals Fast Angle Low Angle Shot; SPACE: Sampling Perfection with Application optimized Contrast using different flip angle Evolution; PD: Proton Density; FOV: Field of View; TR: Repetition Time; TE: Echo Time; TSL: Spin-Lock Time

2.2. Image Reconstruction

The 3D images were reconstructed from the STFL sequence offline. A 1D inverse Fast Fourier Transform was applied to 3D k-space data in the stack direction to reconstruct independent 2D k-space slices. All subsequent operations are applied independently on each slice. To correct system imperfections, the acquired 2D k-space trajectories were adjusted using the Gradient Impulse Response Function (GIRF). The coil sensitivity maps were calculated from an autocalibration area using power iteration over simultaneous patches, interpolation, ellipsoidal kernels, and FFT-based convolution (PISCO) (39). The 2D images were reconstructed iteratively using a SENSE-like approach (40) incorporating a non-uniform FFT operator. This reconstruction method is applied to all slices to reconstruct the 3D STFL images. The complex-valued images for CTFL were reconstructed by a 1D inverse Fast Fourier transform in the readout direction to separate the 3D k-space data into independent 2D k-space slices. The sensitivity maps for each 2D slice were calculated using the efficient iterative self-consistent parallel imaging reconstruction (ESPIRIT) (41). The 2D images are reconstructed from the 2D k-space slices using the corresponding sensitive maps and an iterative SENSE-like algorithm. The reconstruction method is applied to all slices to reconstruct the 3D CTFL images. We implemented reconstruction algorithms for CTFL and STFL sequences using MATLAB R2023b.

2.3. Model Phantoms Preparation and Imaging

The model phantom comprises 4 tubes of rubber eraser, 3%, 5%, and 7% agar gel, as shown in Figure 2. The agar gel phantoms were prepared by mixing the agar with gadolinium trichloride (GdCl₃)-doped water and heating the mixture in 30s bursts in a microwave oven until all the agar dissolved. All 3 tubes were cooled in the refrigerator overnight. The GdCl₃ lowered the T₁ values to range between 850 and 1000ms, whereas T₂ values were within the range of 23 and 50ms.

Figure 2.

(a) ${\mathrm{T}}_{1\rho }$-weighted images of the phantom acquired using Spiral Turbo-FLASH (STFL) and Cartesian Turbo-FLASH (CTFL) sequences at TSLs of 0, 0.2, 2.6, 5, 10, and 20ms. The phantom contains vials of rubber eraser, 3%, 5%, and 7% agar gel, and a bovine Achilles tendon specimen illustrated in (b). (c) illustrates Corresponding ${\mathrm{T}}_{1\rho }$ maps and SNR maps for each vial and the bovine tendon, obtained using STFL and CTFL. Imaging was performed with a 16-channel foot-ankle coil. No B₁ correction was used to correct the ${\mathrm{T}}_{1\rho }$ weighted images.

The bovine Achilles tendon and adjacent tissue regions were sourced from a local butcher shop. Specific sections of the tendon were dissected and stored in a freezer until use. On the day of imaging, a sample was thawed at room temperature for approximately 4 hours before MRI acquisition.

The model agar-gel phantoms and ex vivo bovine tendon specimen were imaged together (Figure 2) using the STFL and CTFL sequences. The FOV size used in the phantom imaging was 200mm x 200mm x 102mm at a resolution of 0.8mm x 0.8mm x 0.8mm for STFL sequence; 200mm x 200mm x 100mm at a resolution of 0.8mm x 0.8mm x 1.25mm for CTFL sequence. The axial plane was used as the imaging plane for the phantom experiment.

2.4. In-vivo Achilles Tendon Imaging

We scanned five individuals with AT and six healthy subjects (HS) after obtaining informed consent. The average age of AT patients was 37.4 ± 5.68years. The average age of healthy subjects was 27.7 ± 2.43years. Both groups were approximately well-balanced in terms of gender, comprising approximately 50% females in both groups.

The inclusion criteria for the AT group were: 1) Age between 18-70years, 2) Unilateral tendon pain while jumping, running, and hopping for at least 12 weeks, 3) Involved in recreational running once a week. The exclusion criteria for the AT group were: 1) History of surgical repair or a rupture of the Achilles tendon, 2) Individuals who have been prescribed/ administered quinolone antibiotics within the last 3 months (42), 3) History or symptoms of soft tissue or joint pain below the knee in the last 3 months, 4) History of rheumatological disease, such as rheumatoid arthritis (43) , 5) History of neurological disorders, such as multiple sclerosis (44) , and 6) History of a chronic pain condition such as fibromyalgia (45). The patient selection followed the methodology described in (46). The HS participants were included if they had no history of Achilles tendon injury or current tendon pain.

The volunteers were positioned supine with feet entering the bore first. The ankle was in a neutral position. Padding was used to minimize motion and ensure comfort. The Achilles tendon was aligned approximately parallel to the bore of the MRI scanner. The images with FOV of 200mm x 200mm x 102mm at a resolution of 0.8mm x 0.8mm x 0.8mm were acquired using both STFL and SPACE sequences. The imaging plane was oriented in the sagittal plane.

2.5. Clinical Assessment

For five AT patients, the pain and physical function of the Achilles tendon were assessed using the Victorian Institute of Sport Assessment-Achilles Tendinopathy (VISA-A) questionnaire (47). VISA-A index helps us determine the clinical severity of Achilles tendinopathy. The VISA-A score ranges from 0 to 100. Where 100 refers to volunteers which shows no clinical markers of Achilles tendinopathy. Jump height (JH) performance was quantified using 3D marker-based motion capture with a 16-camera system (Qualysis, Sweden) and two force plates (Kistler, Winterthur, Switzerland) at the Arthur J. Nelson Human Performance lab at NYU’s Department of Physical Therapy. The maximum jump height achieved from the ground was recorded during this process. The process of jump height calculation was reported in (46).

2.6. Data Analysis, Segmentation, and Statistical Tests

We perform voxel-wise fitting of six ${\mathrm{T}}_{1\rho }$-weighted images with varying TSLs (i.e. 0,0.2,2.6,5,10,20ms) BE and ME fitting models. The parameters estimated using these fitting models help us assess the relaxation properties of ${\mathrm{T}}_{1\rho }$ relaxation. The ME model is described as:

$$x(t,n)=c(n)e^{\left(-\frac{t}{\tau (n)}\right)},$$ (1)

where $x(t,n)$ refers to the complex signal value corresponding to the voxel index $n$ and spin-lock time $t$. The $c(n)$ is the estimated amplitude in the mono-exponential fitting model, and $\tau (n)$ is the relaxation constant associated with $\text{ME}-{\mathrm{T}}_{1\rho }$ at the voxel index $n$. Parameters are estimated using the trust-region conjugate gradient descent. The $c(n)$ and $\tau (n)$ values were limited within the range [0, 1e300] and [0.1,400.0]ms, respectively.

The BE model (48) on the other hand, assumes that the ${\mathrm{T}}_{1\rho }$ relaxation consists of a short and a long component. The BE model is expressed as:

$$x(t,n)=c(n)\left(f_s(n)e^{\left(-\frac{t}{{\tau }_s}\right)}+(1-f_s(n))e^{\left(-\frac{t}{{\tau }_l}\right)}\right),$$ (2)

where $f_s(n)$ corresponds to the fraction of the short component in the relaxation model. ${\tau }_s(n)$ and ${\tau }_l(n)$ corresponds to the short and long components of the ${\mathrm{T}}_{1\rho }$ relaxation time. BE model parameters such as $c(n)$, short fraction ($f_s(n)$), short ${\mathrm{T}}_{1\rho }({\tau }_s(n))$ and long ${\mathrm{T}}_{1\rho }({\tau }_l(n))$ were estimated using the trust-region conjugate gradient descent algorithm. The algorithm was run over the range [0, 1e300], [0.05,0.95], [0.1,10]ms, and [11,400]ms to limit the estimated $c(n)$, $f_s(n)$, ${\tau }_s(n)$, and ${\tau }_l(n)$ values, respectively. The initial start-point during ME model fitting was 25ms for $\text{ME}-{\mathrm{T}}_{1\rho }$. The initial start-point for BE model fitting was .5, 6ms, and 50ms for short fraction, short ${\mathrm{T}}_{1\rho }$, and Long ${\mathrm{T}}_{1\rho }$, respectively. Figure 3 illustrates the block diagram for the ME and BE fitting. The ME and BE fitting algorithm is implemented on MATLAB R2023b.

Figure 3.

The figure illustrates the block diagram for the generation of parametric ${\mathrm{T}}_{1\rho }$ maps using mono-exponential (ME) and bi-exponential (BE) fitting. (a) multiple ${\mathrm{T}}_{1\rho }$-weighted images, (b) relaxation fitting model in one voxel of tendon, (c) BE model with short and long ${\mathrm{T}}_{1\rho }$ maps with short fraction in Achilles tendon, and (d) ME model with ${\mathrm{T}}_{1\rho }$ map in Achilles tendon.

On phantom data, we compare the parametric maps generated from the STFL images with the parametric maps generated from the CTFL images. We generate the ${\mathrm{T}}_{1\rho }$ map of the agarose gel phantom, rubber, and bovine Achilles tendon using ME fitting on both sequences. We calculate the median, inter-quartile range (IQR) of $\text{ME}-{\mathrm{T}}_{1\rho }$ estimated on bovine Achilles tendon, rubber eraser, and 3%, 5%, and 7% agarose gels using both STFL and CTFL sequences. We compare these values between STFL and CTFL sequences using percentage bias and coefficient of variation (CV). Additionally, we compare the signal-to-noise ratio (SNR) of the STFL and CTFL sequences. The SNR is estimated using the Marchenko–Pastur Principal Component Analysis (MP-PCA) method (49,50). Using the neighborhood windows, signal evolution across TSLs, and MP-PCA, we estimate noise maps for each voxel. The absolute value of the signal from the first TSL is divided by the absolute value of the noise map to obtain the SNR maps of each acquisition. We measure the average SNR for bovine Achilles tendon, rubber eraser, and 3%, 5%, and 7% agarose gels.

We acquired several ${\mathrm{T}}_{1\rho }$-weighted images with varying TSLs, there is a high chance that the Achilles tendon region across ${\mathrm{T}}_{1\rho }$-weighted images is misaligned. To co-register and match STFL images across different TSLs, we utilize the multi-resolution rigid registration approach (with Euler transform and Mattes mutual information metric as a registration cost function). The ME and BE fitting is performed on the STFL images after registering all the STFL images to a common image.

The Achilles tendon was divided longitudinally into 2 insertional regions, i.e., intramuscular and calcaneal tendons, and one mid-tendon section. The segmentation of the Achilles tendon into its subregions is illustrated in Figure 4a. The Achilles tendon and its subregions are manually segmented using SPACE PD. The multi-resolution rigid registration approach (same properties as the one used to co-register between STFL images) is employed to generate transforms to align the SPACE PD image with the STFL images. The ROI from the SPACE PD images is transformed and overlaid on STFL images. The resampling of ROI is performed using the B-spline transformation. The ROIs are corrected using STFL images, as they provide better contrast than the SPACE PD images. The STFL images cannot differentiate between the fat pad and the Achilles tendon. The segmentation of the Achilles tendon and its subregions is performed manually using the volumeSegmenter toolbox in MATLAB R2023b. All image registration processes are performed using the Elastix toolbox (51).

Figure 4.

(a) Illustrates the subregions of Achilles tendon (CT: Calcaneal tendon, MT: Mid-tendon, and IMT: Intramuscular tendon). (b) Illustrates the image reconstructed from the raw data acquired from a set of STFL sequences with varying TSL.

To analyze the intra-rater repeatability of the segmentation, the segmentation was performed again within a 2-month interval. Mono-exponential and bi-exponential parameters estimated from the regions-of-interest (ROI) in the repeated segmentation were then compared to those obtained from the initial segmentation. The two-way random intra-class correlation (ICC) is used to analyze the consistency of the segmentation between the repetitions.

The ${\mathrm{T}}_{1\rho }$-weighted STFL images corresponding to the human subject are illustrated in Figure 4b. The image also illustrates the signal decay in the subregion of the Achilles tendon as we increase the TSL in the STFL image. We estimate the BE and ME parametric maps from the STFL images on all human subjects. The fitting error is calculated between the fitting models (BE and ME) vs the measured signal intensity using root mean square error. The fitting errors for the BE and ME models are compared in the results section.

The median for ME and BE parametric maps were calculated on the Whole Achilles tendon and its subregions (Calcaneal, Mid, and Intramuscular Tendon). We compare these median values between the AT and HS groups using the Wilcoxon Rank-Sum test (significance of separation of AT and HS groups) and the Cohen’s d Effect Size (Es; degree of separation) (52,53). The formula for Es is illustrated in Equation 3, where M₁ and M₂ refer to the means of AT and HS groups; SD refers to the standard deviation for either AT or HS group.

$$Es=\frac{M_1-M_2}{SD},$$ (3)

We calculate the partial correlation between the parametric map values and the grouping labels (AT:1 and HS:0) while controlling confounding factors like age and BMI. We performed this test to gauge the effect of age and BMI on the degree of separation between AT and HS.

The BE fitting model consists of three parameters (short ${\mathrm{T}}_{1\rho }$, long ${\mathrm{T}}_{1\rho }$, and short fractions), which can be linearly combined into a single parameter. Using the in vivo data, we estimate the weights corresponding to these three parameters. These weights are determined using Linear Discriminant Analysis (LDA), which projects the three parameters onto a 1D axis to maximize the separation between the AT and HS groups. The resulting LDA projection serves as a potential marker for Achilles tendinopathy. The significance of separability and the degree of separation between the AT and HS groups in the LDA projection are assessed using the Wilcoxon rank-sum test and Es, respectively. Similar to individual parametric map values, partial correlation between the LDA projection values and groups is performed.

In the AT group, we tracked the severity of AT using clinical metrics such as VISA-A and JH. We calculate the Pearson correlation between parametric maps (BE and ME) and clinical metrics (VISA-A and JH). We note all the relationships between parametric maps and clinical metrics that are moderately and strongly correlated. We also test for the significance of correlation (i.e., p-value<0.05).

There is a large gap with respect to age between the AT and HS groups. Other clinical markers, like BMI, can act as confounding factors in our analysis as well. We combine AT and HS groups and calculate the Pearson correlation between BE and ME parametric maps with BMI and age. We note the relationship where the correlation values are significant (i.e., p-value < 0.05). This correlation would help us establish which BE and ME parameters are sensitive to AT without being affected by other confounding factors.

We use all 11 subjects in the AT and HS group to analyze the variation in parametric maps across the subregions (i.e., calcaneal tendon, mid-tendon, and intramuscular tendon) of the Achilles tendon. The significance of the variation is tested using the Kruskal-Wallis test.

We use data from 3 volunteers from the HS group to test repeatability. The spatial transform between repeated acquisitions was estimated using multi-resolution rigid registration (Euler transform with Mattes mutual information as the cost function) using the ${\mathrm{T}}_{1\rho }$ weighted image at TSL=2.6ms. The TSL = 2.6ms image demonstrated adequate SNR and provided a sharp contrast between the Achilles tendon and surrounding tissue, making it a suitable candidate for performing registration between two repeat acquisitions. Additionally, the TSL = 2.6ms acquisition lies near the midpoint of the TSL sequence (0, 0.2, 2.6, 5, 10ms), offering greater robustness to motion between spin-lock times. The ROI masks identified in the first scan were then transferred to the second scan using this transformation. The BE and ME parametric map values are calculated in the subregions of the Achilles tendon for both repetitions. We measured the bias and coefficient of variation (CV) of the parametric maps between two repetitions of the sequence, showing them as percentages. We analyzed the variation between repetitions within the subregions of the Achilles tendon. The Bland-Altman plot illustrates the bias between repetition visually, along with the standard deviation of the bias.

3. Results

Table 2 presents the median ${\mathrm{T}}_{1\rho }$ values (estimated using ME fitting) and interquartile ranges for 3%, 5%, and 7% agar gel, bovine Achilles tendon, and a rubber eraser acquired using both STFL and CTFL sequences. The table also reports the percentage bias and CV between the two sequences. Notably, the 5% and 7% agar gels and the bovine tendon show higher ${\mathrm{T}}_{1\rho }$ values with the CTFL sequence compared to STFL. However, CTFL consistently exhibits lower SNR than STFL across all samples. On average, SNR in agar gel tubes is 27% higher with STFL than CTFL, while for the bovine tendon, STFL shows a dramatic 661% increase in SNR. This result suggests that the increase in SNR from STFL is due to the UTE nature of the sequence, and to a more SNR-efficient trajectory. The average ${\mathrm{T}}_{1\rho }$ in the rubber eraser was estimated at 0.11ms using the STFL sequence, while the CTFL sequence was unable to detect signals from the rubber eraser, as indicated by the measured SNRs.

Table 2.

The table summarizes the median and interquartile range (Q1–Q3) of ${\mathrm{T}}_{1\rho }$ values (ms) obtained from ME fitting of image series acquired using the STFL and CTFL sequences. Data were collected from agarose gel phantom tubes with concentrations of 3%, 5%, and 7%; Bovine Tendon and Rubber Eraser. Differences between the STFL- and CTFL-derived estimates are reported in terms of bias and coefficient of variation (CV), both expressed as percentages. Additionally, the table includes signal-to-noise ratio (SNR) measurements across the phantom tubes for both sequences.

Model		STFL Median [Q1-Q3]	CTFL Median [Q1-Q3]	Bias (%)	CV (%)
ME-T1ρ (ms)	3% Agar	48.4 [47.4- 49.1]	47 [45.9- 48.2]	2.89	2.08
	5% Agar	26.6 [26.4- 26.8]	27.1 [26.6- 27.7]	−1.88	1.32
	7% Agar	21.8 [21.6- 22]	22 [21.4- 22.5]	−0.92	0.65
	Bovine Tendon	2.9 [2.3- 4.3]	4.6 [2.3- 7.9]	−58.62	32.06
	Rubber Eraser	0.11 [0.1-0.13]	(cannot be measured)	N/A	N/A
SNR	3% Agar	77.05	66.73
	5% Agar	84	65.23
	7% Agar	80.72	58.97
	Bovine Tendon	24.43	3.21
	Rubber Eraser	13.56	(cannot be measured)

ME: Mono-Exponential; SNR: Signal to Noise Ratio; CTFL: Cartesian Fast Low Angle Shot; STFL: Stack-of-Spirals Fast Angle Low Angle Shot.

In the in vivo experiments, the average SNR for the proposed STFL sequence in healthy subjects’ Achilles tendons is 19.35. The SNR increases from 13.80 to 25.72 as we move from the intramuscular subsection of the Achilles tendon to the calcaneal subsection of the Achilles tendon. The intra-rater repeatability of the segmentation resulted in an ICC of 0.99-1 with p-value <0.001 for BE and ME parametric maps.

Figure 5 illustrates the fitting residue maps for both models across the Achilles tendon. The root mean square error (RMSE) in the intramuscular tendon is 0.49 for the BE model and 0.66 for the ME model. In the mid-tendon, the RMSE is 0.73 (BE) and 0.87 (ME), while in the calcaneal tendon, it is 0.47 (BE) and 0.55 (ME). Overall, the BE model demonstrates a better goodness of fit than the ME model. Fitting errors are more pronounced in the mid-tendon as compared to other regions of the tendon.

Figure 5.

(a) The image illustrates the root mean square error (RMSE) residuals for both mono-exponential (ME) and bi-exponential (BE) fitting models. It highlights the differences between the measured ${\mathrm{T}}_{1\rho }$ signal decay and the corresponding fitted curves from each model, providing a visual comparison of how well each model captures the signal behavior. (b), (c) and (d) illustrate the decay curve of an average of 3x3x3 voxels and its corresponding fitting models (BE and ME) in Intramuscular, mid, and calcaneal Achilles tendons, respectively.

Table 3 presents the median and interquartile range (1st - 3rd quartile) for ME fitting parameter (${\mathrm{T}}_{1\rho }$) and BE fitting parameters (short ${\mathrm{T}}_{1\rho }$, long ${\mathrm{T}}_{1\rho }$, and short fraction) across subregions and the entire Achilles tendon. No significant group differences were found for any parameter. Figure 6 illustrates that there is a significant overlap in $\text{ME}-{\mathrm{T}}_{1\rho }$ between healthy subjects and AT patients across all analyzed regions. Similarly, Figure 7 (a, b, and c) shows BE fitting parameters do not exhibit significant separability between groups. In the mid-tendon, the BE long ${\mathrm{T}}_{1\rho }$ demonstrates the highest degree of difference between AT and HS groups (p-value = 0.095, effect size = −1.03). The BE long ${\mathrm{T}}_{1\rho }$ shows moderate partial correlation (p-value = 0.092; Pearson correlation = −0.62) with the group labels while controlling for age and BMI. When BE parameters were combined using LDA, the differences between AT and HS groups increased, particularly in the mid-tendon. Figure 7d displays a 3D scatter plot where the x, y, and z axes correspond to BE fitting parameters (short ${\mathrm{T}}_{1\rho }$, long ${\mathrm{T}}_{1\rho }$, and short fraction) for the entire Achilles tendon and its subregions, along with the LDA hyperplane separating the groups. BE parameters are combined and projected onto a line maximizing the separation between the AT and HS groups. Figure 7e illustrates the LDA projections across the Achilles tendon and its subregions for AT and HS groups. The LDA projection achieves significant separability between the groups in the mid-tendon (p-value=0.016; effect size = −1.53), and near-significant separability in the intramuscular subregion (p-value=0.056; effect size = −1.20). The LDA projects show significant and strongly negative partial correlation with group labels (AT vs HS) while controlling age and BMI for mid-tendon (p-value = 0.01; Pearson-correlation = −0.81) and intramuscular tendon (p-value = 0.009; Pearson-correlation = −0.84). Figure 8 illustrates the ${\mathrm{T}}_{1\rho }$-weighted images, ME, and BE maps for an AT patient and a healthy subject.

Table 3.

The table illustrates the median and 25%-75% range for mono-exponential (ME) fitting parameters and bi-exponential (BE) parameters estimated on images acquired using the STFL sequence across the subregions (calcaneal, mid, and intramuscular tendon).

Model		Group	Mid-tendon	Intramuscular tendon	Calcaneal tendon	Achilles tendon
ME	${\mathrm{T}}_{1\rho }$ (ms)	Achilles tendinopathy	8.99 [5.4-10.13]	10.22 [7.08-12.53]	10.23 [6.25-10.84]	8.5 [7.14-10.85]
		Healthy subject	10.23 [9.83-12.65]	5.92 [5.35-11.26]	10.18 [8.3-10.24]	9.28 [9.24-10.71]
BE	Short ${\mathrm{T}}_{1\rho }$ (ms)	Achilles tendinopathy	0.82 [0.67-1.07]	0.85 [0.83-0.98]	1.12 [0.64-1.18]	0.92 [0.89-1.09]
		Healthy subject	1.03 [1-1.16]	0.53 [0.41-1.19]	0.97 [0.92-1.11]	0.95 [0.86-1.1]
	Long ${\mathrm{T}}_{1\rho }$ (ms)	Achilles tendinopathy	24.05 [24-27]	26.56 [23.8-29]	21.7 [21.5-23.3]	24.61 [24-25]
		Healthy subject	33.45 [26.9-33.5]	24.92 [24.5-26.8]	19.14 [18.9-23.7]	23.32 [22.9-27.8]
	Short Fraction	Achilles tendinopathy	0.48 [0.46-0.52]	0.46 [0.42-0.54]	0.46 [0.37-0.52]	0.43 [0.42-0.52]
		Healthy subject	0.47 [0.43-0.5]	0.58 [0.47-0.62]	0.41 [0.39-0.43]	0.45 [0.42-0.47]

Figure 6.

Illustrates the scatter plot of mono-exponential parameter (${\mathrm{T}}_{1\rho }$) between subjects with Achilles Tendinopathy (AT) and healthy subjects (HS) for subregions of the Achilles tendon (CT: Calcaneal, IMT: Intramuscular tendon, MT: Mid-tendon) and the entire Achilles tendon (Global).

Figure 7.

(a), (b), and (c) display the distributions of bi-exponential (BE) parameters (short $\mathrm{T}1\rho$, long $\mathrm{T}1\rho$, and short fraction) for Achilles tendinopathy (AT) and healthy subjects (HS) in the Calcaneal Tendon (CT) intramuscular tendon (IMT), mid-tendon (MT), and whole Achilles tendon (Global). Linear Discriminant Analysis (LDA) combines these BE parameters using the weights that optimize the separation between AT and HS groups. The 3D scatter plot in (d) illustrates the distribution of subjects in BE parameter space, along with the LDA decision boundary (hyperplane) that best separates the two groups. The LDA projection refers to the one-dimensional projection of each subject onto the LDA axis, which maximizes group separability; the distribution of these projections in each tendon subregion and whole Achilles tendon is shown in (e). Wilcoxon test p-values and effect sizes (Es) are provided in (a), (b), (c), and (e) to quantify statistical significance and the degree of group differences.

Figure 8.

(a) Illustrates the ${\mathrm{T}}_{1\rho }$ weighted images with varying spin-lock times (TSLs) of Achilles tendinopathy (AT) patient. (b) Illustrates the mono-exponential (ME) and bi-exponential (BE) fitting maps for an AT patient. (c) Illustrates the ${\mathrm{T}}_{1\rho }$ weighted images with varying TSLs of a healthy subject. (d) Illustrates the ME and BE fitting maps for a healthy subject.

The correlations between demographic data and fitting parameters are illustrated in Table 4. For the intramuscular tendon, short ${\mathrm{T}}_{1\rho }$ (BE) demonstrated a significantly strong positive correlation with BMI (r = 0.62, p < 0.05), while long ${\mathrm{T}}_{1\rho }$ (BE) showed a significant correlation with age (r = 0.62, p < 0.05). In the calcaneal tendon, long ${\mathrm{T}}_{1\rho }$ (BE) showed non-significant moderate positive correlations with both age (r = 0.41) and BMI (r = 0.35). Other regional correlations, such as those in the mid-tendon and global tendon, exhibited weak to moderate trends, although none reached statistical significance. Notably, short fraction (BE) was negatively correlated with BMI in both the intramuscular (r = −0.56) and global tendon (r = −0.40) regions, suggesting a possible inverse association between BMI and the relative contribution of the short component.

Table 4:

Pearson correlation coefficients between ${\mathrm{T}}_{1\rho }$ decay parameters (ME and BE) and subject characteristics (age and BMI) across different regions of the Achilles tendon: Calcaneal Tendon, Intramuscular Tendon, Mid Tendon, and whole Achilles tendon (Global). Positive correlations are shown in green shades and negative correlations in red shades. Significant correlations (p < 0.05) are marked with an asterisk. This analysis includes data from both healthy subjects and Achilles tendinopathy patients.

Calcaneal Tendon
Model		Age	BMI
ME	${\mathrm{T}}_{1\rho }$	−0.28	−0.04
BE	Short ${\mathrm{T}}_{1\rho }$	−0.16	−0.25
	Long ${\mathrm{T}}_{1\rho }$	0.41	0.35
	Short Fraction	0.32	0.29
Mid Tendon
Model		Age	BMI
ME	${\mathrm{T}}_{1\rho }$	−0.17	0.27
BE	Short ${\mathrm{T}}_{1\rho }$	−0.2	0.32
	Long ${\mathrm{T}}_{1\rho }$	−0.34	−0.24
	Short Fraction	−0.03	−0.48
Intramuscular Tendon
Model		Age	BMI
ME	${\mathrm{T}}_{1\rho }$	0.05	0.46
BE	Short ${\mathrm{T}}_{1\rho }$	0.2	0.62*
	Long ${\mathrm{T}}_{1\rho }$	0.62*	0.19
	Short Fraction	−0.15	−0.56
Global
Model		Age	BMI
ME	${\mathrm{T}}_{1\rho }$	−0.14	0.21
BE	Short ${\mathrm{T}}_{1\rho }$	0.12	0.09
	Long ${\mathrm{T}}_{1\rho }$	0.06	−0.4
	Short Fraction	−0.15	0.33

The VISA-A score shows an average of 68.17 ± 10.98 for all AT cohort. The average jump height (JH) for the AT cohort is 0.11 ± 0.03meters. The Pearson correlation between VISA-A and parametric maps (BE and ME) is shown in Table 5. The VISA-A score shows strong positive correlation with short fraction (BE) parameters and strong negative correlation with ${\mathrm{T}}_{1\rho }$ (ME) in the calcaneal tendon. Short ${\mathrm{T}}_{1\rho }$ (BE) shows weak correlation (positive or negative) with VISA-A in the Achilles tendon and its subregions. Long ${\mathrm{T}}_{1\rho }$ (BE) shows weak positive correlation in the intramuscular tendon and moderate positive correlation in the calcaneal tendon.

Table 5:

Pearson correlation between the BE and ME fitting parameters vs clinical metrics VISA-A and jump height for subregions of the Achilles tendon (MT, IMT, and CT), as well as the entire Achilles tendon (Global). * indicates p-value < 0.05

Model		VISA-A vs. MT	VISA-A vs. IMT	VISA-A vs. Global	VISA-A vs. CT
ME	${\mathrm{T}}_{1\rho }$	0.01	−0.08	−0.12	−0.78
BE	short Fraction	−0.06	−0.07	0.13	0.95
	Short ${\mathrm{T}}_{1\rho }$	0.24	0.46	0.28	−0.22
	Long ${\mathrm{T}}_{1\rho }$	0.02	0.47	0.35	0.54
		JH vs.MT	JH vs. MT	JH vs. Global	JH vs. CT
ME	${\mathrm{T}}_{1\rho }$	0.95*	0.88	0.89	0.21
BE	short Fraction	−0.98*	−0.96*	−0.91	0.52
	Short ${\mathrm{T}}_{1\rho }$	1.00*	0.94	0.81	−0.79
	Long ${\mathrm{T}}_{1\rho }$	0.54	−0.4	0.17	0.31

^*p-value < 0.05

The correlation values between JH versus BE and ME parametric maps are shown in Table 5. Short fraction (BE) shows strong negative correlations with JH in the mid and intramuscular tendons. It shows a moderately positive correlation with JH for the calcaneal tendon. Short ${\mathrm{T}}_{1\rho }$ shows strong positive correlation in the mid and intramuscular tendons and strong negative correlation in the calcaneal tendon with JH. Long ${\mathrm{T}}_{1\rho }$ shows moderate correlation in the mid-tendon with the JH metric. ${\mathrm{T}}_{1\rho }$ (ME) shows strong positive correlations for mid and intramuscular tendons with JH.

Figure 9 presents Bland-Altman plots illustrating the scan-rescan repeatability for ME and BE fitting parameters, while Table 6 summarizes the results across the Achilles tendon and its subregions. For ${\mathrm{T}}_{1\rho }$ estimated using ME fitting, the intramuscular tendon exhibits the highest bias (−6%) and CV (4.6%) between repeated acquisitions, while the entire Achilles tendon shows a bias of −4.2% and a CV of 2.6%.

Figure 9.

(a) illustrates the Bland-Altman repeatability plot for the mono-exponential fitting parameter (${\mathrm{T}}_{1\rho }$). (b), (c) and (d) illustrate the Bland-Altman repeatability plot for bi-exponential fitting parameters (short ${\mathrm{T}}_{1\rho }$, long ${\mathrm{T}}_{1\rho }$, and short fraction).

Table 6.

The table illustrates the coefficient of variance (CV) and bias between repeated measurements of ME parameters (${\mathrm{T}}_{1\rho }$) and BE parameters (short ${\mathrm{T}}_{1\rho }$, long ${\mathrm{T}}_{1\rho }$, and short fraction).

Model		ROI	CV (%)	Bias (%)
ME	${\mathrm{T}}_{1\rho }$ (ms)	Intramuscular tendon	4.61	−5.95
		Mid-tendon	2.15	−2.91
		Calcaneal tendon	2.53	−3.40
		Achilles tendon	2.64	−4.2
BE	Short ${\mathrm{T}}_{1\rho }$ (ms)	Intramuscular tendon	0.30	−0.02
		Mid-tendon	1.47	2.10
		Calcaneal tendon	5.70	8.93
		Achilles tendon	3.38	3.64
	Long ${\mathrm{T}}_{1\rho }$ (ms)	Intramuscular tendon	2.38	−3.21
		Mid-tendon	4.82	−6.20
		Calcaneal tendon	2.73	−3.65
		Achilles tendon	3.00	−5
	Short Fraction (a.u)	Intramuscular Tendon	1.01	1.46
		Mid-tendon	0.77	−1.08
		Calcaneal tendon	1.36	−1.84
		Achilles tendon	0.21	−0.46

ME: Mono-Exponential; BE: Bi-Exponential; CV: Coefficient of Variation

Among BE parameters, short ${\mathrm{T}}_{1\rho }$ has the highest bias (8.9%) and CV (5.7%) in the calcaneal tendon, whereas for the entire Achilles tendon, bias and CV are 3.6% and 3.4%, respectively. Long ${\mathrm{T}}_{1\rho }$ shows the highest bias (−6.2%) and CV (4.8%) in the mid-tendon, while the values for the entire Achilles tendon are −5% and 3%, respectively. The short fraction parameter exhibits the highest bias (−1.8%) and CV (1.4%) in the calcaneal tendon, while for the entire Achilles tendon, bias and CV are −0.5% and 0.2%, respectively.

In the subregional analysis, we observe that long ${\mathrm{T}}_{1\rho }$ maps exhibit the most significant variation across subregions of the Achilles tendon, particularly in healthy subjects (p-value < 0.05). On average, there is a 33% increase in long ${\mathrm{T}}_{1\rho }$ between the calcaneal tendon and mid-tendon, followed by a 3.6% decrease between the mid-tendon and intramuscular tendon. In healthy subjects, the increase in long ${\mathrm{T}}_{1\rho }$ between the calcaneal tendon and mid-tendon is more pronounced at 58%, while a 23% decrease is observed between the mid-tendon and intramuscular tendon. In contrast, variation in long ${\mathrm{T}}_{1\rho }$ values across the Achilles tendon subregions is insignificant in AT patients. Figure 10 illustrates the variation of ME and BE fitting parameters across subregions of the Achilles tendon.

Figure 10.

The image illustrates the variation in mono-exponential (ME) and bi-exponential (BE) fitting parameter values across the subregions (calcaneal tendon, intramuscular tendon, and mid-tendon) of the Achilles tendon using a box plot. (a) correspond to the variation in ${\mathrm{T}}_{1\rho }$ values estimated from ME fitting across subregions of the Achilles tendon. (b), (c), and (d) illustrate the similar variation for short ${\mathrm{T}}_{1\rho }$, long ${\mathrm{T}}_{1\rho }$, and short fraction across the subregions. The subregional variation is plotted for both Achilles tendinopathy patients (AT) and healthy subjects (HS).

In summary, the STFL sequence achieves a better SNR than the CTFL sequence in the phantom experiment. In in-vivo experiments, ME fitting shows limited differences between AT patients and healthy subjects. The Combined BE parameters improve group differences discrimination between AT patients and healthy subjects, particularly in the mid-tendon. The repeatability experiment illustrates that the ME and BE fitting maps are stable with CV ranging from 0.2% to 5.7%. The short fraction parameters show the best stability with an average CV of 1.4%. The subregional experiments illustrate that long ${\mathrm{T}}_{1\rho }$ values in the Achilles tendon for healthy subjects vary significantly between subregions. No such subregional variation is observed for AT patients.

4. Discussion

This study investigates the feasibility of using a UTE sequence for both mono-exponential and bi-exponential ${\mathrm{T}}_{1\rho }$ fitting in the Achilles tendon. This study focuses on both healthy subjects and patients with Achilles tendinopathy.

Phantom experiments reveal that non-UTE sequences are relatively insensitive to materials such as rubber eraser and bovine Achilles tendon structure, while UTE sequences can effectively capture their properties. Since the Achilles tendon is highly organized and rigid with a very fast T₂* relaxation, the UTE-based sequences are well-suited for its imaging and characterization.

In healthy subjects, the ME ${\mathrm{T}}_{1\rho }$ value measured using UTE at a spin-lock frequency of 500Hz is approximately 8.5ms, compared to 9.28ms in subjects with Achilles tendinopathy. These values are elevated compared to those reported in (54), where 2D-UTE imaging at spin-lock times of 0.2, 1, 4, and 12ms yielded a ${\mathrm{T}}_{1\rho }$ of 3.45ms for healthy tendons at 500Hz. These differences in reported values may arise from several factors, such as partial volume effects from differences in slice thickness [3mm in (54)], differences in spin-locking methods, and the fitting model. Additionally, (54) shows that ${\mathrm{T}}_{1\rho }$ values in cadaveric Achilles tendons increase from 2.06ms to 7.8ms as spin-lock frequency increases from 250 to 1000Hz. In (31), 3D ${\mathrm{T}}_{1\rho }$ imaging is performed using a UTE sequence with a cone trajectory on a cadaveric human Achilles tendon. The Continuous Wave-${\mathrm{T}}_{1\rho }$ values range from 7.0ms at 0° (magic angle) to 42.6ms at 55°. In reference (30), the authors, using a similar age-matched cohort, report significant differences in adiabatic ${\mathrm{T}}_{1\rho }$ values between psoriatic arthritis (PsA) patients and healthy controls, with elevated values observed in both the enthesis (11.4 ± 2.6ms vs. 10.4 ± 2.4ms) and the Achilles tendon near the calcaneal bone (9.8 ± 2.8ms vs. 7.7 ± 1.7ms). In contrast, our study using ME fitting–based ${\mathrm{T}}_{1\rho }$ analysis shows comparable values between AT patients and healthy subjects in the region near the calcaneal bone (10.23ms vs. 10.18ms, respectively).

Our results indicate that $\text{ME}-{\mathrm{T}}_{1\rho }$ values alone do not provide sufficient contrast to differentiate healthy tendons from those affected by tendinopathy. However, the most pronounced between-group differences emerged from BE fitting parameters, particularly in the mid-portion of the Achilles tendon. Specifically, the long ${\mathrm{T}}_{1\rho }$ component in the mid-tendon decreases from 33.45ms in healthy subjects to 24.05ms in AT patients (28% reduction). The long ${\mathrm{T}}_{1\rho }$ component corresponds to water loosely bound to proteoglycans. Shortening of the long ${\mathrm{T}}_{1\rho }$ component corresponds to decreased flexibility and more stiffness in the tendon. In the intramuscular region of the Achilles tendon, patients with AT exhibit substantially elevated mean ME ${\mathrm{T}}_{1\rho }$ by approximately 72%, and the BE short ${\mathrm{T}}_{1\rho }$ by around 60%. However, both parameters show considerable intra-group variability, and their distributions exhibit substantial overlap between the AT and HS groups. Despite the large differences in mean values, the effect sizes are low, indicating that high within-group variance diminishes the potential discriminatory power of these parameters. A small decrease in ${\mathrm{T}}_{1\rho }$ value is also noticed in the calcaneal tendon for AT patients compared to healthy subjects, but it is hard to determine if it is because of measurement limitations or due to biochemical processes happening in the Achilles tendon due to the smaller sample size.

When the BE parameters (short ${\mathrm{T}}_{1\rho }$, long ${\mathrm{T}}_{1\rho }$, and short fraction) are combined using learned weights, the composite metric in the mid-tendon demonstrates even greater between-group differences when comparing healthy subjects and AT patients. These metrics are robust to the confounding factors introduced by age and BMI. In this study, all subjects show symptoms aligned with mid-portion Achilles tendinopathy. The management strategies of Achilles tendinopathy also vary based on the affected subregions (55). In literature, tendinopathy most commonly occurs in the mid-portion, especially in athletes and the general population (12). Insertional tendinopathy is more common with diabetes (56,57) and older adults (58).

When comparing ${\mathrm{T}}_{1\rho }$ values across different tendons, the Achilles tendon consistently shows lower values than both the patellar and quadriceps tendons. The ME fitting yields a value of 9.23ms for the Achilles tendon, in contrast to 12.7ms and 12.6ms for the patellar and quadriceps tendons as reported in (21). Additionally, an ex vivo study reported a ME ${\mathrm{T}}_{1\rho }$ value of 8.6ms for the patellar tendon (59). In (21), the author illustrates that in cases of tendon injury, the long ${\mathrm{T}}_{1\rho }$ component calculated BE fitting provides the greatest discrimination between healthy and damaged patellar tendons. These findings are consistent with the results observed in this study.

The BE and ME parameters show either weak or no correlation with BMI and age in the mid-tendon. The BE parameter long and short ${\mathrm{T}}_{1\rho }$ in intramuscular tendons show moderate but significant correlation with age and BMI, respectively. Short fraction intramuscular tendon is also moderately correlated with BMI. BE and ME parameters in the calcaneal tendon show weak correlation. The clinical score VISA-A, which tests the severity of AT, shows a strong correlation with BE and ME parameters in the calcaneal tendon. In other regions, BE and ME parameters show weak or no correlation with VISA-A. On the other hand, the JH shows strong correlation with BE and ME parameters in almost all subregions of the Achilles tendon. The dataset for these correlations is limited, hence the correlation values are not particularly significant, but they help us understand the effects of confounding factors as well as draw linkages between other clinical scores of AT.

4.1. Limitations

This study has several key limitations. The sample size is relatively small (i.e., 6 healthy subjects and 5 tendinopathy patients), which limits the statistical power of the results of the study. A large cohort could enhance the statistical power and robustness of our findings. In this study, we wanted to test the feasibility of the STFL sequence. In future studies, we plan to collect larger patient and control data to make more statistically significant conclusions.

All imaging and analysis in the study are limited to one scanner and one center. The robustness and reproducibility of the proposed method across scanners and institutions have not been analyzed, thereby limiting the generalizability of the results. In future studies, we plan to test for reproducibility and robustness across scanners and centers.

Based on our analysis, we find certain limitations in the sequence as well. The UTE-based sequence with continuous wave spin-lock preparation pulse used in this study was susceptible to the magic angle effect, which may contribute to the variability of ${\mathrm{T}}_{1\rho }$ fitting parameters. In recent literature (31), it has been shown that there was reduced variability in the magic angle effect due to the use of an adiabatic spin-lock preparation pulse. In future experiments, we plan to incorporate the adiabatic spin-lock pulses to measure ${\mathrm{T}}_{1\rho }$ values in the Achilles tendon.

The phantom experiment demonstrated that the STFL sequence is more sensitive to fat compared to the CTFL sequence. This increased fat sensitivity arises because the STFL sequence uses a single SPAIR fat suppression pulse at the beginning of each shot, allowing fat signal recovery by the end of the shot. In contrast, the CTFL sequence employs a longer RF pulse, enabling the use of water-selective excitation before each repetition. This allows multiple water excitation pulses to be applied within a single shot, improving fat suppression performance. As a result, fat-related bias is likely to be more pronounced in the STFL sequence than in CTFL. Further investigation is needed to explore methods for reducing fat sensitivity in the STFL sequence.

The Achilles tendon is the largest in the human body, long, and surrounded by high-contrast tissues such as bone and muscle. To improve the accuracy of the ${\mathrm{T}}_{1\rho }$ fitting process in human subjects, which may be affected by motion, we apply both rigid and non-rigid registration between TSLs in the preprocessing steps. To reduce the influence of outliers, we used the median of the BE and ME parametric map values rather than the mean. The median is more robust to outliers in estimating the central tendency of the distribution, whereas the mean is less robust and may be affected by these outliers. In this study, we did not compare the UTE ${\mathrm{T}}_{1\rho }$ with corresponding T₂*, DTI, or bound water fraction metrics. In future work, we plan to incorporate these comparisons to gain a more comprehensive understanding of the biochemical processes underlying Achilles tendinopathy.

4.2. Conclusion

In this paper, we demonstrate the feasibility of measuring the ${\mathrm{T}}_{1\rho }$ relaxation properties of the Achilles tendon using a UTE-based sequence with a spiral trajectory and continuous wave ${\mathrm{T}}_{1\rho }$ preparation pulse. Our preliminary results suggest that the ${\mathrm{T}}_{1\rho }$ measurements can discriminate between Achilles tendinopathy patients and healthy subjects, particularly in the subregions of the Achilles tendon (i.e., mid-section of the Achilles tendon). However, due to the small sample size, it remains difficult to draw definitive conclusions at this stage.

List of Abbreviations and Acronyms

AWSOS

Acquisition-Weighted Stack-of-Spirals

LDA

Linear Discriminant Analysis

SPAIR

Spectrally Attenuated Inversion Recovery

SPACE

Sampling Perfection with Application Optimized Contrast using variable flip angle Evolution

CTFL

Cartesian Turbo Fast Low Angle Shot

ESPIRiT

Efficient Iterative Self-Consistent Parallel Imaging Reconstruction

FA

Flip-Angle

FFT

Fast Fourier Transform

FOV

Field-of-View

GIRF

Gradient Impulse Response Function

GRAPPA

Generalized Autocalibrating Partial Parallel Acquisition

HIPAA

Health Insurance Portability and Accountability Act

IQR

Interquartile Range

IRB

Institutional Review Board

MP

Magnetization Preparation

MP-PCA

Marchenko-Pastur principal component analysis

NLS

Nonlinear Least Squares

NUFFT

Non-Uniform Fast Fourier Transform

PGs

Proteoglycans

AT

Achilles Tendon

RF

Radio Frequency

SENSE

Sensitivity Encoding

SNR

Signal-to-Noise Ratio

STFL

Stack-of-spirals Turbo Fast Low Angle Shot

TE/TR

Echo Time/Repetition Time

TFL

Turbo Fast Low Angle Shot

TSL

Spin-Locking Time

UTE

Ultra-Short Echo Time

JH

Jump Height

VISA-A

Victorian Institute of Sport Assessment-Achilles Tendinopathy

Data Availability Statement.

The data that support the findings of this study are not openly available due to privacy or ethical restrictions but are available from the corresponding author with permission from the Center for Biomedical Imaging at New York University Grossman School of Medicine.