Fine-tuning Deep Learning Model for Quantitative Knee Joint Mapping with MR Fingerprinting and Its Comparison to Dictionary Matching Method

Abstract

Magnetic resonance fingerprinting (MRF), as an emerging versatile and noninvasive imaging technique, provides simultaneous quantification of multiple quantitative MRI parameters, which have been used to detect changes in cartilage composition and structure in osteoarthritis. Deep learning (DL)-based methods for quantification mapping in MRF overcome the memory constraints and offer faster processing compared to the conventional dictionary matching (DM) method. However, limited attention has been given to the fine-tuning of neural networks (NNs) in DL and fair comparison with DM. In this study, we investigate the impact of training parameter choices on NN performance and compare the fine-tuned NN with DM for multiparametric mapping in MRF. Our approach includes optimizing NN hyperparameters, analyzing the singular value decomposition (SVD) components of MRF data, and optimization of the DM method. We conducted experiments on synthetic data, the NIST/ISMRM MRI system phantom with ground truth, and in vivo knee data from 14 healthy volunteers. The results demonstrate the critical importance of selecting appropriate training parameters, as these significantly affect NN performance. The findings also show that NNs improve the accuracy and robustness of T₁, T₂, and T_1ρ mappings compared to DM in synthetic datasets. For in vivo knee data, the NN achieved comparable results for T₁, with slightly lower T₂ and slightly higher T_1ρ measurements compared to DM. In conclusion, the fine-tuned NN can be used to increase accuracy and robustness for multiparametric quantitative mapping from MRF of the knee joint.

1. INTRODUCTION

Osteoarthritis (OA), as one of the most common and debilitating chronic joint diseases, is primarily characterized by the progressive degeneration of articular cartilage and other joint structures¹. Quantitative MRI techniques, including spin-lattice relaxation time (T₁), spin-spin relaxation time (T₂), and spin-lattice relaxation time in the rotating frame (T_1ρ), have been used to detect changes in cartilage composition and structure during the early stages of the disease before the onset of morphologic cartilage loss². Cartilage T₂ and T_1ρ measurements, which have been shown to reliably distinguish between subjects with and without knee OA^3,4, are commonly performed together in OA research studies for evaluation of cartilage composition and structure⁵.

Magnetic resonance fingerprinting (MRF) is a new versatile and noninvasive imaging technique, allowing for simultaneous quantification of multiple quantitative MRI parameters, which can reduce the MRI examination times in research studies⁶. In MRF, pulse sequence parameters such as flip-angles (FAs) and repetition times (TRs) are modulated in such a way that results in a unique signal evolution (SE), also called MR fingerprint, for a particular type of tissue, depending on the T₁, T₂, and T_1ρ values. The measured voxel-wise MR fingerprints are then matched to a precomputed dictionary of simulated signals for different combinations of parameters using the scalar product, usually adopted as a similarity measure. This approach is referred to as dictionary matching (DM), and it is a brute-force grid search. This approach is simple but has known practical challenges, such as discretization errors and the so-called curse of dimensionality⁷, which essentially corresponds to the exponential increase of memory, and computation time requirements with the linear increase in the number of biophysical parameters^8,9. Part of the computational burden of DM can be alleviated by singular value decomposition (SVD) techniques.^9–14 Nonetheless, these improvements do not overcome the curse of dimensionality, and the computational burden is prohibitive for models with many parameters¹⁵. In contrast, dictionary-free regression methods^16,17, as well as deep learning (DL) methods can overcome this issue. As a result, these methods are very fast once the network has been trained.

Although the feasibility of neural network (NN) approaches for quantitative mapping from MRF has been investigated in previous works^15,18–23, little consideration has been given to the fine-tuning of NN for quantitative mapping from MRF. Previously, different sampling strategies were considered, Virtue et al.²³ constructed the training dataset by sampling the MR parameter space using a random uniform distribution, while Hoppe et al.²¹, Cohen et al.¹⁹, and Golbabee et al.¹⁸ used a grid sampling of the MR parameter space. Different strategies have been studied regarding using noise during the training phase, mainly the use of additive Gaussian noise with zero mean and 1% standard deviation ^15,19 or using no noise at all^21,23. The choice of the compressed dimension that should be used, the noise level during training, and the learning rate can largely affect the accuracy, and robustness of the NN, however, few works have investigated those aspects, and no work has been done to compare the noise robustness between NN and DM.

In this sense, this study has two main goals: 1) to investigate how the performance of the NNs is affected by these training choices, and 2) to compare the performance of the fine-tuned NN against DM in multiparametric mapping from MRF. To have a fair comparison, the DM is also optimized. To achieve these aims, we first explored the fine-tuning of NN in different aspects, including the SVD components of MRF, training hyperparameters, and the optimization of DM, including the SVD components and dictionary size, and tested them in synthetic data, and NIST/ISMRM MRI system phantom data with ground truth. We then studied the noise robustness of the fine-tuned NN and optimized DM by adding different noise levels to a test dataset with sampled T₁, T₂, and T_1ρ covering the range in the knee joint. Finally, we compared the results of both approaches for T₁, T₂, and T_1ρ mapping in 14 healthy subjects.

2. METHODS

2.1. Pulse sequences

A 3D-golden-angle radial stack-of-stars sequence, which quantifies four parameters: T₁, T₂, T_1ρ, and B₁⁺, was used for the MRF acquisition^24,25. This 3D-MRF sequence consists of an inversion recovery preparation followed by two FISP segments, two FLASH segments, each with 250 flip-angles, and 4 T_1ρ-prepared FLASH segments, each with 125 flip-angles, resulting in a total of 1500 radial spokes for each shot. A slab-selective excitation was used to allow the imaging with less than full coverage of the knee joint. A detailed description of the sequence parameters can be found in Table 1.

Table 1.

Imaging parameters of the 3D-MRF sequence.

Parameters	MRF
Sequence	3D-T1ρMRF
Scan plane	Sagital
FOV(mm2)	140x140
TR(ms)	7.5
TE(ms)	3.4
TI(ms)	15
TSL/T2 preparation (ms)	0.5,3.8,9.8,21.8
FA(°)	0–60
Slice Thickness(mm)	3
Number of slices	18
Matrix size	192×192
Receiver bandwidth(Hz/px)	490
TA(min:s)	4:30/shot

Abbreviations: FOV, field of view; TR, repetition time; TE, echo time; TI, inversion time; TSL, spin-lock pulse duration; FA, flip angle; TA, acquisition time.

2.2. MRF dictionary construction

Dictionaries of simulated MR fingerprints based on extended phase graphs (EPG)²⁶ were created with a T₁ range of 50–2000 ms, T₂ range of 2–200 ms, and T_1ρ range of 2–200 ms and flip-angle ranges of 30° to 90° in steps of 15°. For the DM method, cartilage T₁, T₂, and T_1ρ maps were created using an iterative pattern-matching algorithm utilizing maximum correlation. In order to find the balance between computation burden and performance, dictionaries were simulated with different step sizes by varying the scaling factors (SF) in the parameter range. The larger the SF is, the smaller the number of points sampled from the value range of the parameter, leading to a smaller dictionary size and vice versa. The details of the simulated dictionaries are displayed in Figure 1(a).

Figure 1:

(a) Details of the simulated dictionaries with different scaling factors (SF) in the 3 segments of the sampling range of T₁, T₂, and T_1ρ. (b) Details of the architecture of the modified fully connected network (MFCN) used in this study. The 2D complex-valued coefficients of each voxel are concatenated and fed into the MFCN. The network outputs the tissue parameters of T₁, T₂, and T_1ρ.

The measured MR fingerprints, and the simulated dictionary were compressed using SVD to speed up the offline dictionary matching^15,27. The number of components is decided by the cumulative percentage of variance (CPV) ²⁸ which is defined as:

$$CPV=\frac{\sum _{i=1}^D{S}_i}{{\sum }_{i=1}^M{S}_i}\times 100\%,$$ (1)

Where $M_{\left\{S_i\right\}}^{i=1}$ is the set of singular value components, indexed by $i$ and ordered from the largest, i.e. $S_1$, to the smallest, i.e. $S_M$. D is the number of components used in the compressed representation (that are also the first and largest components) and M is the total number of components.

2.3. Test dataset simulation

We built a test dataset using parameter ranges that cover the ranges in the knee joint, which are T₁ ranging from 400 ms to 1400 ms with a stepsize of 50 ms, T_2, and T1ρ ranging from 10 ms to 140 ms with a stepsize of 5 ms, resulting in a total of 309582 entries of fingerprints. We refer to this as “test dataset”. This dataset is used for the optimization of DM and the noise robustness comparison between NN and DM.

2.4. Network training and fine-tuning

In this study, we used a modified fully connected network (MFCN) that was used in a previously reported MRF study¹⁵. It consists of 14 fully connected layers with rectifier linear units activation functions, group normalization, and 4 skip connections were used to avoid the vanishing gradient during training^29–31. Figure 1(b) shows the details of the MFCN structure. During training, the weights of the network were initialized randomly using the ADAM optimizer with a batch size of 512. The network was trained for 400 epochs. Mean relative absolute error (MRAE) was used as a loss function during the training. We used the simulated dictionary with SF=0.15 described in Section 2.2 as our training dataset. We chose the largest dictionary to reduce the overfitting possibility. During training, 75% of the data were used for training and 25% were used for validation. To optimize the performance of the network for the specified task of estimating T₁, T_2, and T_1ρ from MRF data in the knee joint, we systematically tuned the network for the learning rate, noise level, and SVD compression dimension.

Learning rates (LR) tuning:

The learning rate was initially set to a specified value and decayed by half every 20 epochs with a minimum limit of 0.00005. In our study, we searched initial LR values from 0.0001 to 0.1.

Noise level tuning:

To increase the noise robustness of the trained network, we added noise to the training data. While random perturbations in MRF signals may be difficult to accurately model, we noticed that the use of Gaussian statistics seems good enough. In this sense, we added Gaussian noise, supported by the Central Limit Theorem⁴¹ and by some recent studies⁴² that followed the same direction. The noise level is defined as the standard deviation (SD) of the zero-mean Gaussian distribution. In our study, we searched noise levels ranging from 0.0001 to 0.1.

Training data SVD dimension (D) tuning:

As shown in equation (1), the variance explained by the SVD compression is determined by the number of components used, denominated as D. In our study, we explored CPV ranging from 82% to 99.9999% percent, which changed D from 10 to 100.

Sequential search strategy:

A joint optimization in the entire space is not practical, so we sequentially tuned the three parameters. For this reason, we called the procedure “fine-tuned”, instead of optimized. In our approach, in order to find a good starting point for fine-tuning, we roughly tuned the parameters in a very large range with coarse step sizes. In our sequential fine-tunning approach, we first fine-tunned the parameter of LR, and we fixed D components at 30 as it showed good convergence in the rough tunning step, and we found noise level at 0.003 as it gave good performance on the validation dataset in the rough tunning step. Then D was tuned next, by fixing LR at the previous optimized value of 0.005 and noise level at 0.003. Finally, the noise level was tuned, with LR at the optimized value of 0.005 and the noise level at the optimized value of 0.002. After the network was tuned, the same trained network was used for estimation in the noise robustness analysis, NIST/ISMRM MRI system phantom study, and in-vivo knee joint study.

2.5. Dictionary matching optimization

We optimized the SF and the number of SVD components (D) for the DM method on the test dataset, and on the NIST/ISMRM MRI system phantom data as well. The computation burden for a high-dimensional dictionary is known, therefore, in addition to the accuracy, we also need to consider the computation demand for practical use. To give a clear idea of the fitting time used for each SF, we computed the fitting time for a volume with matrix $192\times 192\times 18$ based on the averaged fitting time for each fingerprint for each SF. After the DM was optimized, the same dictionary size and SVD components were used for estimation in the noise robustness analysis, NIST/ISMRM MRI system phantom study, and in-vivo knee joint study.

2.6. Noise robustness analysis

After the network was tuned, and the DM method was optimized, we analyzed the noise robustness of both methods on the test dataset. Four different levels of noise, which were 0.001, 0.003, 0.007, and 0.01, were added to the test dataset. We have 10 different realizations for each noise level, which results in 40 realizations of each fingerprint. The mean and standard deviation of MRAE were calculated.

2.7. NIST/ISMRM MRI system phantom study

We used a model system phantom developed by the NIST in collaboration with the ISMRM Ad-Hoc Committee on Standards for Quantitative Magnetic Resonance ^32–34. The phantom compartments contain solutions with a broad range of T₁ and T₂ values that have been well characterized by NIST^33,34. We scanned this phantom on a 3.0T MRI scanner (MAGNETOM Prisma, Siemens Healthcare, Germany) using a 20-channel receive-only birdcage head coil (Siemens Healthcare), due to its size, with the 3D-MRF sequence, and we scanned this phantom at room temperature by setting the phantom in the scanner room for several hours to allow the temperature to stabilize. It takes about 20 minutes to acquire 36 slices on the phantom. The T₁ and T₂ reference values in the phantom profiled were used as ground truth. As the dictionaries were simulated with the T₁, T₂, and T_1ρ ranges covering the knee joint, we only analyzed the spheres in the phantom that cover the same ranges.

2.8. In-vivo knee joint study

Fourteen healthy volunteers (35.4±9.3 years, age range 19–62 years; eight males) with no current or prior history of knee pain, trauma, surgery, OA, or inflammatory or crystalline-induced arthritis were recruited. This study was performed in compliance with the Health Insurance Portability and Accountability Act (HIPAA) regulations and with approval from our Institutional Review Board. All subjects provided written informed consent prior to their participation in the study. The scans were acquired on the same 3T MRI scanner used for the phantom study (MAGNETOM Prisma) using a 15-channel Tx/Rx knee coil (Quality Electrodynamics, Mayville, OH, USA) with the 3D-MR. It takes less than 10 minutes to acquire 18 slices with 192×192 matrix size on the knee joint. Five cartilage regions of interest (ROI) were manually drawn, including medial femoral condyle (MFC) and lateral femoral condyle (LFC), medial tibial condyle (MTC) and lateral tibial condyle (LTC), and patellar cartilage (PC). All MRF parameter comparisons were conducted in those ROIs.

3. Results

Figure 2 shows the details of the fine-tuning of the network. From 2(a) and 2(b), we can see that LR plays a critical role in the converged value of the loss. Based on the results, we used 0.005 as the LR for the network. Figures 2(c) and 2(d) show the validation loss for a different number of components in the SVD compression, and the CPV explained by the corresponding D components. From 2(c) and 2(d), we observed the MRAE decreased first and then increased while SVD components got larger, which is due to the information of the signal and noise contained in the components. As the D increases, the effects of excessive compression are reduced and the validation loss is reduced. However, the validation loss started to increase again when D>30. This indicates that D=30 is a good choice for the SVD compression. Also, our choice of D=30 corresponds to CPV=99.5% for the compression.

Figure 2:

Validation loss (MRAE) during training for different learning rates (a), SVD dimensions (c), and noise levels (e) for the neural network using a dictionary with SF=0.15. (b) shows the zoom-in of the red box in (a). (d) displays the converged loss and CPV of the D components in the SVD compression, and the y-axis of the converged validation loss has the same range as in (c). (f) demonstrates the loss (mean±std) when mixed noise levels were added to the testing data for each model trained with a fixed noise level as shown in (e). LR: learning rate; Noise level: standard deviation of the Gaussian distributed noise; D: Dimension in the SVD-compression.

Figure 2(e) shows the validation loss for different noise levels added during training and Figure 2(f) shows the mean and standard deviation of the error on the test dataset with the model trained in Figure 2(e). In Figure 2(e), each model was trained with a fixed noise level. In Figure 2(f), 10 different noise levels were added to the test dataset to test the robustness and generability of the trained model, and for each noise level, 40 realizations were used. Figure 2(e) shows that training noise level=0.001 has the smallest converged error, however, training noise level=0.002 has better performance on the test dataset when subject to different testing noise levels. Therefore, we chose noise level=0.002 for training as it has an overall smaller error for a broader noise range. By choosing the noise level that has the best performance for a wider noise range, the trained network is more robust to different noise levels in estimation. Supporting Information Figure S2 shows the performance for specific noise levels added to the testing data and more details in Figure 2(f). Supporting Information Figure S3 demonstrates a wider range of noise levels (0.0001 to 0.1) with a large step size. From the rough training, it is shown that when the noise level added in the training is too large or too small, the prediction performance of the network will degrade when using testing data. This indicates that the best choice for added training noise with fine-tuning should be in the range between 0.001 and 0.01, which echoes the noise level choice presented in the literature¹⁵, as seen in Figure 2.

Table 2 shows the detailed results of the DM optimization on the simulated test dataset with 4 different added noise levels. To show the fitting time clearly, we display the average time for fitting a volume data with 192×192 matrix size and 18 slices. As shown in the table, the fitting time for SF=0.15 and 0.25 is too long to be used in practice, while the MRAE is not reduced on a large scale. For SF=1 and 2, the MRAE is too large which shows a large bias and large standard deviation. For SF=0.5, it takes about 7.5 hours to perform the fitting tasks on a volume of 18 slices using MATLAB with a good performance in T₁ and T₂ with an acceptable error for T_1ρ. CPV=0.95 with 28 SVD components reaches an overall good performance compared to higher CPV. Therefore, based on those results, we should choose SF=0.5 with D=28 as a compromise for fitting time and fitting accuracy for the DM method.

Table 2.

Optimization results on the test dataset for dictionary matching method. The estimation error (MRAE) is too large for SF=1 and 2 while the time for fitting is too long for SF=0.15 and 0.25. SF=0.5 is a good balance between fitting time and accuracy.

SF		CPV	Time(hour/Vol) (192*192*18)	MRAE (%, mean±std)
				T1	T2	T1ρ
0.15		0.82	22.85	6.79 ± 5.32	8.19 ± 10.61	46.45 ± 51.67
		0.90		5.91 ± 4.32	4.01 ± 3.58	32.51 ± 34.37
		0.95		4.20 ± 3.15	3.41 ± 3.01	17.96 ± 14.77
		0.99		4.23 ± 3.63	3.50 ± 3.25	18.21 ± 15.46
		0.9999		4.25 ± 3.71	3.62 ± 3.19	18.27 ± 15.69
0.25		0.82	14.51	6.80 ± 5.35	8.20 ± 10.68	46.10 ± 51.44
		0.90		5.93 ± 4.51	4.05 ± 4.40	36.80 ± 38.66
		0.95		4.25 ± 3.45	3.56 ± 3.81	18.26 ± 15.53
		0.99		4.29 ± 3.55	3.54 ± 3.75	18.81 ± 16.04
		0.9999		4.27 ± 3.43	3.71 ± 3.64	18.57 ± 16.11
0.5		0.82	7.46	7.04 ± 5.68	10.14 ± 10.20	45.85 ± 49.40
		0.90		5.91 ± 4.69	7.40 ± 5.74	36.42 ± 36.71
		0.95		4.12 ± 3.57	7.30 ± 5.73	19.93 ± 16.71
		0.99		4.19 ± 3.64	7.27 ± 5.74	20.22 ± 17.48
		0.9999		4.19 ± 3.64	7.27 ± 5.74	20.18 ± 17.46
1		0.82	3.69	8.72 ± 7.10	12.45 ± 11.32	44.11 ± 49.75
		0.90		7.53 ± 5.86	10.41 ± 7.62	76.35 ± 155.14
		0.95		5.81 ± 5.24	10.28 ± 7.48	71.14 ± 148.32
		0.99		5.85 ± 5.27	10.26 ± 7.46	69.75 ± 145.69
		0.9999		5.85 ± 5.27	10.26 ± 7.46	69.72 ± 145.76
2		0.82	0.35	9.51 ± 7.63	22.26 ± 24.62	40.52 ± 47.21
		0.90		8.24 ± 6.64	20.55 ± 21.04	42.09 ± 55.36
		0.95		6.98 ± 5.92	20.50 ± 20.93	39.32 ± 42.13
		0.99		7.03 ± 5.95	20.48 ± 20.91	38.75 ± 39.24
		0.9999		7.03 ± 5.95	20.48 ± 20.91	38.73 ± 39.27

Figure 3 shows the mean of the normalized absolute error (MNAE) for different dictionary sizes on the NIST/ISMRM MRI system phantom for T₁ and T₂. As shown in the figure, the dictionary size affects T₂ to a large degree while having less impact on T₁ for the step size used. With SF=0.15 and 0.25, the error decreased around 2–3% in bias. Ideally, the finer dictionary for T₂ measurement is preferred, however, this will increase the computation requirement substantially as shown in Figure 1 and Table 2. Therefore, as a compromise of performance and computation burden based on Table 2 and Figure 3, we chose SF=0.5 for building the dictionary for DM in this study.

Figure 3:

Mean of the normalized absolute error (MNAE) of measurements from dictionary matching and neural network for different dictionary sizes on the NIST/ISMRM MRI system phantom with ground truth provided by the phantom profile.

Figure 3 also shows the comparison of NN and DM for different SFs. The NN method always has a superior performance in T₂, which shows 5% less bias with a much smaller variance, and comparable performance in T₁ compared to DM. This demonstrates that NN has a better performance in T₂ while preserving the same performance in T₁ measurements on the NIST/ISMRM MRI system phantom. For both methods, T2 has larger variations than T1, this is due to the fact that T₂ is shorter than T₁, so T₂ is intrinsically more challenging to estimate.

Figure 4 displays the noise robustness analysis results on the simulated test dataset. We observed a slightly smaller bias (deviation of the measured diagonal red line from the ideal black line) and variance (vertical red dispersion bars) in T₂, a considerably smaller bias and variance in T_1ρ especially when T_1ρ >50ms, and a slightly smaller bias in T₁ for the range covering the knee joint with four different noise levels. We also observed that the bias of T₁ increases as the value of T₁ increases in DM, while this trend is not obvious in the NN method. Those findings show that the fine-tunned network is more robust to the noise in estimating knee joint parameters, especially for T_1ρ and the large value range of T₁.

Figure 4:

DM and NN measurements mean±STD for T1, T2, and T1ρ on the simulated test dataset with 4 different noise levels. As shown from the simulated dataset, NN has better performance for all three parameters shown as smaller bias and standard deviation and higher slope in regression, especially for T_1ρ, for which the DM shows a large standard deviation when T_1ρ >50ms.

Table 3 shows the MRAE of T₁, T₂, and T_1ρ estimation from the fine-tuned NN and the optimized DM on the simulated dataset. With four different noise levels added to the test dataset, NN shows smaller bias and variance than DM for all three parameters, especially for T_1ρ and T₂ with an overall 11.18% and 4.72% reduction in mean MRAE, and a 7.19% and 2.47% reduction in variance.

Table 3.

Mean relative absolute error (MRAE) of T₁, T₂, and T_1ρ estimation from the fine-tuned NN and the optimized DM on the simulated test dataset with 4 different noise levels added.

	DM	NN
T1 (%)	4.40±3.77	2.89±3.29
T2 (%)	7.35±5.80	2.63±3.33
T1ρ (%)	21.18±18.34	10.00±11.15

Figure 5 shows the measurements and errors on the NIST/ISMRM MRI system phantom using the DM and NN methods. From the error and absolute error, we observe that NN has a slightly higher mean error and standard variance for T₁, especially high error for large values. For T₂, NN has the smallest error and shows better performance in estimating small values of T₂ while DM shows degraded performance in estimating small T₂ values.

Figure 5:

Representative slice of T₁ and T₂ maps on the NIST/ISMRM MRI system phantom. DM: dictionary matching; GT: ground truth; NN: neural network. As shown in the figure, both methods have a comparable estimation for T₁ and slightly better performance of NN for T₂.

Figure 6 shows a representative cartilage PD, T₁, T₂, and T_1ρ for different ROI using the fine-tuned NN and DM. As shown in the figure, T₁ and T₂ have very good correspondence with a slight difference in the ROI for both methods, while NN shows higher T_1ρ compared to DM. This aligns with the results from the simulated dataset as shown in Figure 4 that DM and NN have good correspondence for T₁ and T₂, while discrepancy in T_1ρ.

Figure 6:

Representative cartilage T₁, T₂, and T_1ρ maps for a subject using DM, and NN methods. For most regions, DM and NN have good correspondence.

Figure 7 shows the mean and standard deviation of the relaxation values for different ROI of the knee cartilage. In this example, NN shows consistently slightly smaller values in T₁ and T₂ measurements, while slightly higher values in T_1ρ. Overall, NN shows a smaller variance in parameter estimations, which is consistent with the result from the noise robustness analysis. Supporting Information Figure S1 shows the same measurements, however using SF=0.15 for both, DM and NN. As expected, increasing the dictionary size to SF=0.15 does not show much difference when compared to SF=0.5, which aligns with the results in Figure 3.

Figure 7:

Mean and standard deviation of measurements of T₁, T₂, and T_1ρ, for all subjects, using the DM and NN methods. Compared to DM, the NN shows comparable estimation in T₁, reduced estimation in T_2, and slightly higher estimation in T_1ρ.

4. DISCUSSION

This study has investigated the effects of dictionary size, SVD compression components for the DM method, and explored different aspects of training NN in parameter estimation with data acquired with a 3D-MRF sequence. This study shows that T₁ is less sensitive to the dictionary size while T_1ρ is the most sensitive in the DM method. In the NN approach, the hyperparameters affected the convergence of the network, especially the compression and the noise level, which should be carefully chosen. In the SVD compression, the number of components should be chosen to provide enough signal-rich components while excluding noise components. We also demonstrated that NN is more robust to noise than DM, especially for T_1ρ estimation. In the DM method, the bias increased the T₁ values. This trend is not obvious in the NNs. Overall, NN has a superior performance than DM in T₂ and T_1ρ while preserving a comparable performance in T₁. We conducted a paired-t test, and no significance was found between the two methods.

In the NN fine-tuning, we ended up using a sequential strategy after a rough tunning in a large range instead of a global search in the parameter space because of the large number of combinations, making global optimization not practical, this may result in a local good solution in the parameter space, hence the denomination fine-tuning. We tested tunning the network with different orders, and the convergence of the parameters is similar, though not equal, to the one we reported. However, each local good solution we tested has superior performance compared to the DM, without the expensive search of local or global minima.

In the NN fitting, we chose to use the largest dictionary (SF=0.15) to reduce the chance of overfitting, though the training time may be longer, it is an offline procedure. Once the network has been trained, the estimation for any input fingerprints will be very fast, which is less than 1 minute for a knee joint volume while it takes more than 18 hours using DM on the same hardware.

In the in vivo data, the discrepancy between the T2 and T1ρ does not align with the results in the synthetic experiment between the two methods. One possibility is that this could be due to the magnetization transfer (MT) effects^35–39, which we did not consider in the sequence since we inspected and excluded motion errors or outliers. In a previously reported study, Hilbert et al showed that the MT has effects in quantification of T1 and T2 using MRF³⁵. For in vivo experiments, longer T1 (~1060 ms vs. ~860 ms) and T2 values (~47 ms vs. ~35 ms) have been observed in white matter if MT is accounted for. They concluded that a better match between simulations and acquired MR signals can be obtained using an MT model. The MT effects, in particular, are strong determinants of observed signals in human tissue, Gloor et al. showed that on-resonance MT effects are expected to change the signal from balanced steady-state free-precision (SSFP) sequences in the brain by approximately 30% and muscle by 50%³⁸. Considering the MT effects in signal modeling^15,35, such as the classic two-pool model⁴⁰, or implementing off-resonance preparation pulses in the sequence³⁵, can help to mitigate the MT effects in parameter quantifications. Another possibility could be the mismatch between using a Gaussian distribution to represent the noise ( as in the synthetic data) and the actual noise distribution of in-vivo data.

We acknowledge that this study has few limitations. The NN has to be retrained for different MRF pulse sequences. Our study only investigated the fine-tuning of the fully connected network, while other networks are also used in literature, such as a network using spatial information besides time evolution²². Moreover, the conclusion on the test dataset was made with 5ms for T₂ and T_1ρ while 50ms for T₁ as T₁ has a much larger value range. Furthermore, we only investigated the proposed methodology in healthy subjects and further studies are needed to assess its robustness in OA patients. This sequence takes about 10 minutes, which reduces the acquisition time tremendously compared to the traditional methods for T₁, T₂, and T_1ρ measurement separately^25,44, but a 10-minute scan may still be long for patients. In this work, we only included in-vivo data on healthy subjects and will test this method on knee OA patients in further work.

The variance for T_1ρ measurements was higher than for T₁ and T₂. We suspect this is related to a lower encoding capacity for T_1ρ in the sequence used and not an intrinsic problem of T_1ρ, as other sequences show similar variances for T₂ and T_1ρ⁴³. The T_1ρ prepared segments²⁵ are shorter than the other segments, in total representing about one-third of the sequence, and use a maximum flip angle of 20°. Additionally, the variance for T_1ρ measurements increases dramatically for values over 50ms, which could mean that the sequence needs longer T_1ρ preparations to retain the lower variance. Future work should investigate this hypothesis.

5. CONCLUSION

In this study, we demonstrated that the fine-tuned NN has superior performance in T₂ and T_1ρ measurements when compared to DM. NN is also more robust to noise in parameter estimation of the knee cartilage using a 3D-MRF sequence. This study shows that fine-tuning the NN training and properly selecting dictionary size for the DM is an essential task in parameter mapping with knee joint MRF data.

List of Abbreviations and Acronyms:

MRF

Magnetic resonance fingerprinting

DM

Dictionary matching

DL

Deep learning

OA

Osteoarthritis

SF

Scaling factor

SVD

Singular value decomposition

NN

Neural network

FA

Flip angle

SE

Signal evolution

TR

Repetition time

EPG

Extended phase graphs

MFCN

Fully connected network

CPV

Cumulative percentage of variance

MRAE

Mean relative absolute error

LR

Learning rate

ROI

Regions of interest

MFC

Medial femoral condyle

LFC

Lateral femoral condyle

MTC

Medial tibial condyle

LTC

Lateral tibial condyle

PC

Patellar cartilage

MT

Magnetization transfer

SSFP

Steady-state free-precisi

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.