Low-Rank Tensor Models for Improved Multidimensional MRI: Application to Dynamic Cardiac $T_1$ Mapping

Multidimensional, multicontrast magnetic resonance imaging (MRI) has become increasingly available for comprehensive and time-efficient evaluation of various pathologies, providing large amounts of data and offering new opportunities for improved image reconstructions. Recently, a cardiac phase-resolved myocardial <inline-formula><tex-math notation="LaTeX">$T_1$</tex-math></inline-formula> mapping method has been introduced to provide dynamic information on tissue viability. Improved spatio-temporal resolution in clinically acceptable scan times is highly desirable but requires high acceleration factors. Tensors are well-suited to describe interdimensional hidden structures in such multi-dimensional datasets. In this study, we sought to utilize and compare different tensor decomposition methods, without the use of auxiliary navigator data. We explored multiple processing approaches in order to enable high-resolution cardiac phase-resolved myocardial <inline-formula><tex-math notation="LaTeX">$T_1$</tex-math></inline-formula> mapping. Eight different low-rank tensor approximation and processing approaches were evaluated using quantitative analysis of accuracy and precision in <inline-formula><tex-math notation="LaTeX">$T_1$</tex-math></inline-formula> maps acquired in six healthy volunteers. All methods provided comparable <inline-formula><tex-math notation="LaTeX">$T_1$</tex-math></inline-formula> values. However, the precision was significantly improved using local processing, as well as a direct tensor rank approximation. Low-rank tensor approximation approaches are well-suited to enable dynamic <inline-formula><tex-math notation="LaTeX">$T_1$</tex-math></inline-formula> mapping at high spatio-temporal resolutions.