Introduction

Multiple sclerosis (MS) is a neurodegenerative disease that causes a lack of integrity in the myelin layer of the nerves. Although T₂-weighted imaging can diagnose most areas of the myelin damage^1,2, it is inherently qualitative and depends on hardware and acquisition parameters. In contrast, quantitative T₂ mapping could be more sensitive to identifying MS disease. While T₂ mapping is fairly common after an MS diagnosis, the generation of T₂ maps from T₂w images, routinely used for a wide range of neurological assessments, could allow for earlier diagnosis of MS disease. This abstract demonstrates the feasibility of obtaining an accurate T₂ map from a single Turbo Spin Echo (TSE) k-space of a product sequence.
Conventional quantitative T₂ mapping uses a series of images (Fig. 1a) acquired with different timings after excitation (echo-times, or TE) to fit a physics model across time for each pixel:
$$I_{TE}(x)=I_{0}(x)e^{\frac{-TE}{T_{2}(x)}},$$ where $$$I_{TE}(x) $$$ is the image brightness at a given $$$TE$$$, $$$=I_{0}(x)$$$ is the image brightness at $$$TE=0$$$, and $$$T_{2}(x)$$$ is a constant that reflects the tissue microstructure in that voxel.³
A novel method dubbed e-CAMP (Fig 1d,e) was recently proposed to computationally normalize (standardize) clinical MRI scans by computing a quantitative T₂ map from a single TSE k-space. Initial results showed that the method worked on simulations and retrospective undersampling of single echo images taken with different echo times. Here we compute T₂ maps directly from retrospectively undersampled multi-echo spin-echo (MESE) sequences and single image T₂w-TSE. These have been demonstrated in phantoms and the human brain, corresponding well to the fully sampled T₂ mapping experiments.

Methods

The images are related by a signal model characterized by one or several parameter maps, e.g., a T₂ map. As previously proposed, the e-CAMP algorithm alternates between optimizing the image series and the parameter map. However, it minimizes a single cost function that incorporates: (1) consistency between each parameter image and its k-space data and (2) adherence of the image series to the relaxometry model for each pixel. Thus, the algorithm's objective function $$$J=J_1+J_2+J_3$$$ where: $$$J_1$$$ is concerned with data fidelity, $$$J_2$$$ is regularization, and $$$J_3$$$ is imposing the model constraint.
The data fidelity term $$$J_1$$$ measures the error between the acquired data sets and our current estimate of the images.
$$$J_1=∑_{p=1}^P‖S_p-E_p m_p ‖^2= ∑_{p=1}^P(S_p-E_p m_p )^H (S_p-E_p m_p ),$$$ where $$$()^{H}$$$ refers to the complex conjugate transpose of a matrix.
The regularization term $$$J_2$$$ minimizes the effect of MR noise, and the solution is regularized by adding TV regularization. $$$J_2=τ∑_{p=1}^PTV(m_p) $$$, where $$$TV(m_p )=∑_{x=1}^N|∇m_p (x)|, |\Box|$$$ refers to the modulus, and $$$N$$$ is the number of pixels.
The constraint penalty is imposed using $$$J_3$$$, $$$J_3=λ∑_{x=1}^N∑_{p=1}^{P-1}‖m_{p+1} (x)-α(x) m_p (x)‖^2 $$$, where $$$λ>0$$$ scales the penalty.
Retrospective Human Brain Experiments
Cartesian spin-echo images were acquired on a 3T MRI scanner (TIM-Trio, Siemens Healthcare, Erlangen, Germany). Fully sampled k-space was acquired at each TE and retrospectively undersampled (Fig. 2a).
Cartesian 8-echo MESE images were acquired on a 3T MRI scanner (MAGNETOM Prisma^fit; Siemens Healthcare, Erlangen, Germany). These data were acquired with full k-space sampling at each echo, contrasts= 8. This dataset was retrospectively reconstructed with an echo spacing of 40 ms, as shown in Fig. 2b. The same dataset was retrospectively reconstructed with an echo spacing of 20 ms, as in Fig. 2c.
Prospective Human Brain Experiments
e-CAMP was used to reconstruct the T₂ map using a T2w image acquired using the TSE Siemens product sequence (ETL=9, echo spacing=20 ms). For validation, we acquired fully sampled MESE images and fully sampled spin echo images. To compare the TSE reconstructions to the SE reconstructions, we used the echo modulation curve (EMC)⁴ corrections to be applied to the T₂w images reconstructed using TSE image acquisitions, as shown in Fig. 3.
Phantom Experiments
A phantom was built in-house using six tubes filled with varying concentrations of MnCl₂ solutions immersed in an agar gel solution. In addition, during the same scanning exam, a set of fully sampled Cartesian 9-echo images were acquired using a TSE sequence. Finally, a T₂w image was acquired using a Siemens product sequence (ETL=9, echo spacing=20 ms). Once again, the echo modulation curve (EMC)⁴ corrections were applied to the T₂w images reconstructed using TSE image acquisitions, as shown in Fig. 4.

Results

Fig. 2a (previously reported) shows images from retrospectively undersampled single-echo data. Fig 2b-c shows experimentally acquired fully-sampled MESE sequences, where the k-space of each image was retrospectively undersampled to a T₂w-TSE k-space. Fig. 2d shows e-CAMP results using T₂w image data from a Siemens TSE product sequence (i.e., prospective undersampling). In addition, a separate scan acquired fully sampled echo train MESE images for reference. These results agree with the e-CAMP image series generated from the T₂w image data. This study also acquired a series of fully sampled spin echo images to generate a gold standard T₂ map, shown on the left panel of Fig. 3.
Fig. 4 shows T₂ maps generated from gold standard spin echo phantom experiments, a MESE, and a product T₂w imaging experiment reconstructed with e-CAMP.

Discussion and Conclusion

This abstract demonstrates the feasibility of reconstructing quantitative T₂ maps using only the data acquired in a standard T₂w acquisition.

Acknowledgements

No acknowledgement found.