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Jointly Reconstructed Undersampled Multiparameter MRI for Imaging Intratumoral Subpopulations
Shraddha Pandey1,2, Arthur David Snider1, Wilfrido Moreno1, Harshan Ravi2, Ali Bilgin3, and Natarajan Raghunand2,4
1Electrical Engineering, University of South Florida, Tampa, FL, United States, 2Cancer Physiology, Moffitt Cancer Center, Tampa, FL, United States, 3Departments of Medical Imaging, Biomedical Engineering, and Electrical & Computer Engineering, University of Arizona, Tucson, AZ, United States, 4Department of Oncologic Sciences, University of South Florida, Tampa, FL, United States

Synopsis

A joint reconstruction framework is proposed to reconstruct a series of T1-weighted, T2-weighted, and T2*-weighted images and corresponding parameter maps simultaneously from undersampled cartesian k-space data. Joint Total Variation (JTV) and model-based constraints were employed to resolve the ambiguity introduced due to undersampling. T1 and T2 maps were used to identify fluid, adipose, muscle and tumor tissue types. T2*w images reconstructed from undersampled data were analyzed to produce maps of Proton Density Fat Fraction (PDFF), Proton Density Water Fraction (PDwF), and the relaxation rates of water ($$$R^*_{2w}$$$) and fat ($$$R^*_{2f}$$$) in each tissue type [1].

Purpose

MRI offers excellent soft-tissue contrast, and the option of varying the contrast observed between tissues, by varying the type of acquisition, e.g., T1, T2 and T2* weighted, even without the use of exogenously administered contrast agents. To make quantitative image information comparable across patients and scan dates it is often preferable to acquire parameter maps (e.g., T1, T2, T2*, and proton density maps). Co-registered multiparametric MRI (mpMRI) images and parameter maps are amenable to multispectral analysis to objectively identify various tissue types to assist differential diagnosis, identify tumors and their evolution in response to therapies, and to predict patient outcomes [2-6]. However, the sequential acquisition of mpMRI images and parameter maps is potentially time-consuming, and techniques to accelerate this process are desirable. Least-squares based approaches along with regularizers such as Total Variation (TV), low rank approximation, model-based priors, and sparsity-based priors have been employed to accelerate the reconstruction of multicontrast images and generate the corresponding parametric maps from undersampled k-space data [7-10]. Our hypotheses are, that co-registered T1, T2 and T2* weighted images share significant amounts of structural information, and, each series must follow either a longitudinal or transverse relaxation model. Using these two hypotheses as regularizers, in addition to a least-squares data consistency term, we have simultaneously estimated a series of T1, T2 and T2* weighted images, and the corresponding parameter maps of T1, T2 and T2*, from undersampled k-space date. Reconstructed images and parameter maps were used to compute tissue type maps and maps of PDFF and PDwF, $$$R^*_{2w}$$$ and $$$R^*_{2f}$$$ compared against ground truth.

Method

K-space data for six tumor-bearing mice corresponding to T1-weighted (variable TR), T2-weighted (multi-echo spin-echo), and T2*-weighted (multi-echo gradient-echo) sequences were acquired at 7T. It is proposed to reconstruct T1w images $$$u$$$ of size $$$N1 \times N2 \times M$$$ , the corresponding proton density map $$$ A^{T1}$$$ and T1 map of size $$$N1 \times N2$$$ simultaneously. Corresponding to this, an objective function comprising of a data consistency least-squares term, joint total variation term, and magnetization relaxation model based on the longitudinal/transverse relaxation spin, is formulated as in equation 1.
$$\underset{u^m \in\mathbb{C}^{N1 \times N2},\mathcal{A^{T1}},T_1 \in \mathbb{R}^{N1 \times N2}}{min}\sum_{m=1}^{M}\frac{||SFu^{(m)}- k^{(m)}||_2^2}{2} + \alpha_1 ||[\mathcal{D}u]^{(m)}||^1_1 \\ + \alpha_2 |||u^{(m)}| -\mathcal{A^{T1}}(1-exp(-t_m/T_1)||_2^2 \hspace{1cm} where [\mathcal{D}u]^{(m)} = \frac{\eta |\nabla u^{(m)}|}{\sqrt{|\nabla v^{(m)}|^2+\eta^2}} ....(1)$$
The first term is the data consistency term. Here $$$S$$$ is the sampling mask and $$$F$$$ represents the 2D FFT function. The next constraint is the Joint Total Variation (JTV) term. Here, $$$v$$$ is the 1st echo of the T2w images which is used to improve the confidence of the edge location in the JTV algorithm[11] and $$$\eta$$$ is a weighting parameter . Finally, a model-based prior based on the longitudinal relaxation of spins is used. Here $$$t_m$$$ is the repetition time and $$$ \alpha_{1} , \alpha_{2}$$$ Lagrangian coefficients. This formulation is solved iteratively using the ADMM algorithm[12]. The proposed algorithm is repeated to reconstruct a series of T2w/T2*w images and the corresponding T2/T2* map with prior based on the transverse relaxation of spin. Finally, validation of T1w and T2w reconstructions is carried out using tissue type segmentation as shown in Figure 1 to objectively identify fluid, adipose, muscle and tumor. Validation of T2*w images was carried out by fitting them according to [1] and calculating the mean PDFF, PDwF, $$$R^*_{2w}$$$ and $$$R^*_{2f}$$$ in each tissue type. Results from undersampled reconstructions are compared against ground truth results from fully-sampled data.

Results and Discussion

Figures 2 & 3 show the reconstructed images and Mutual Information(MI) for T1w &T2w images respectively. MI values are found to increase as k-space data increases, up to a point. Higher MI values are obtained for longer TR and shorter TE times, which may be due to higher signal-to-noise ratio (SNR) in these images. Figures 4a and 4b show example reconstructed T1 and T2 maps, respectively. Despite some loss of fidelity vis-à-vis the ground truth T1 and T2 maps, tissue type maps computed from undersampled T1 and T2 maps show excellent agreement with tissue type maps computed from fully-sampled T1 and T2 maps (Figure 4c).The mean and standard deviation (SD) of T1 & T2 values in each tissue type and the Dice coefficient are shown in Figure 4d, 4e and 4f respectively. Here, SD represents the true heterogeneity of T1 and T2 values within a given tissue type. Expectedly, Dice coefficients are found to increase as amount of k-space data used increases. Figure 5a and 5b shows the estimated PDFF, PDwF, $$$R^*_{2w}$$$ and $$$R^*_{2f}$$$ for two different mouse slices. Some loss of fidelity may be observed in their estimates, however key features are preserved. The mean and SD values of the estimated parameters in different tissue types are shown in Figure 5c. While, PDFF and PDwF values are found as expected, the relationship between $$$R^*_{2w}$$$ and $$$R^*_{2f}$$$ is unexpected, which may be due to susceptibility effects dominating both relaxation rates.

Conclusion

A series of T1w, T2w and T2*w images and the corresponding parameter maps were concurrently reconstructed using the proposed framework. Tissue type maps, PDFF and PDwF within each tissue type computed from 18% k-space data showed good similarity with the fully-sampled ground truth values.

Acknowledgements


References

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Figures

Figure 1. k-space data obtained from the scanner is undersampled using the cartesian sampling mask. The Joint Reconstruction Algorithm is used to reconstruct the series of T1w images and their parameter maps. The process is repeated to reconstruct T2w/T2*w images and their parameter maps. Validation of the results is carried out by identifying the tissue types like muscle, fluid, tumor and adipose and using the rules on T1 and T2 maps. The T2*w images are subjected [1] to estimate PDFF, PDwF, & in the muscle, fluid, tumor and adipose tissue type.

Figure 2. T1w reconstructed images for 2 mouse slices with mask of ~27%, ~36% k-space data are shown.The sampling masks are shown in col 1. The results for the Repetition times (TR) 0.4s and 5s are shown in col 2 & 3 for mouse 1 and col 4 & 5 for mouse 2. The 5th & 6th column shows the detailed version of the region highlighted in the red box.The MI value is computed for 4 undersampling masks 18%, 27%, 36%, & 52% shown on x-axis. The y-axis shows the MI value when the ground truth |u| are compared to the reconstructed |u|. The mean MI and standard error of the mean (S.E.M) is calculated over n = 30 mouse slices.

Figure 3. a) T2w reconstructed images for 2 mouse slices with undersampled Cartesian mask of ~27%,~36% k-space data are shown and compared to the ground truth MR images. The results for the echo times 15.3ms and 46ms are shown in col 1 & 2 for mouse 1 and col 3 & 4 for mouse 2. b) The plots of MI value for different echo times TE1 to TE16 of the reconstructed image when compared to the ground truth T2w image. The y-axis is the MI value obtained by comparing fully-sampled |u| to reconstructed |u|. The x-axis is the MI for 4 acceleration rates. The mean MI and S.E.M are calculated over n = 30 mouse slices.

Figure 4. a) T1 b) T2 reconstructed maps for 2 different mouse slices. c) Threshold values for 4 tissue type average T1 & T2 map values are obtained over the hand drawn contours for 30 mouse slices. Here pink, yellow, blue and red segments signify the muscle, tumor, fat and water respectively. d, e) Mean and SD of T1 & T2 maps calculated for in different tissue types (n = 30). f) The Dice coefficient to measure the similarity between the ground truth clusters of 4 tissue types with the reconstructed clusters is shown. The y-axis is the mean and S.E.M. of Dice coefficient value calculated for n = 30.

Figure 5. a) PDFF, PDwF are obtained using [1] for 2 different mouse slices are obtained using [1] for undersampled Cartesian masks (~27%,~36% k-space data). b) R*2w & R*2f are shown and are compared to the ground truth (last row). c) The PDFF(1st col), PDwF(2nd col), R*2f (3rd col) and R*2w (4th col) values calculated using [1] in tissue types fluid (1st row), adipose (2nd row), muscle(3rd row) and tumor(4th row) are shown. The y-axis is the mean value calculated over all pixels in given tissue type for n = 30. The red bar denotes the SD calculated over all pixels in given tissue type.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)
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