Cardiovascular MR Multitasking Using Low-Rank Tensor Imaging


There are many sources of dynamics in body imaging: cardiac motion, respiratory motion, MR relaxation and more. Unfortunately, conventional MRI is subject to the “curse of dimensionality,” making imaging multiple dynamics at the same time extremely difficult. As a result, most cardiovascular MR (CMR) scans use inefficient and often-unreliable “freezing” mechanisms to isolate different sources of image dynamics: ECG triggering to freeze cardiac motion, breath-holding to freeze respiratory motion, steady-state imaging or limited acquisition windows to freeze image contrast, etc. With this project we are developing cardiovascular MR multitasking — simultaneous imaging of multiple overlapping sources of dynamics — accomplished using low-rank tensor imaging, a novel framework for cardiovascular MRI.

CMR multitasking allows us to image multiple time dimensions (or “tasks”) in a single, short scan. For example, we can obtain cardiac-resolved, respiratory-resolved images with multiple contrast weightings, enabling T1 mapping (or scout-free selective tissue nulling) without relying on ECG or breath-holds. Our framework is usable with many applications; here we highlight two of them: non-ECG, free-breathing myocardial native T1 mapping and non-ECG, dynamic T1 mapping of contrast agent dynamics for quantitative myocardial perfusion.


The low-rank tensor framework exploits the correlation along each time dimension of a multidimensional cardiovascular image. Many combinations of time dimensions are possible, but as an example, consider an image with four time dimensions indexing:

  • Cardiac phase = C
  • Respiratory phase = R
  • Sequence timing parameter = T
  • Heartbeat = H

The discretized image can be represented as a five-way tensor (or array) A, with the first dimension indexing all the voxels X and the other four indexing the different time dimensions. To capture the signal correlation, our framework models A as low-rank; i.e., as the product of a small core tensor B and five matrices X, C, R, T and H containing basis functions for describing each image dimension. All that is required to represent an image is to determine its core tensor and basis functions; because these model components have far fewer degrees of freedom than a full-rank A of the same size, this results in greatly reduced scan times.

Our demonstration of native T1 mapping used an inversion recovery (IR)-prepared FLASH sequence and our demonstration of myocardial perfusion T1 mapping used saturation recovery (SR)-prepared FLASH. Odd-numbered readouts collected radial spokes in golden-angle increments (for determining X); even-numbered readouts collected the 0° spoke (for determining B and the temporal bases). Data were collected for one minute for native T1 mapping and 30-45 seconds for myocardial perfusion.

There are multiple ways to determine the model components using our framework. In the included examples, the relaxation basis in T was pre-estimated from a dictionary of relaxation curves; the core tensor B and the temporal bases in C, R (for native T1 mapping only) and H (for myocardial perfusion only) were jointly estimated after low-rank tensor completion of the 0° spoke data constrained to the relaxation subspace described by T. The remaining un¬known, X, was estimated by fitting the core tensor and temporal bases to the golden-angle data. The model components were then combined to express the image at any combination of timings.


Figure 1 shows

  • The ability to retrospectively select any timing combination from the multidimensional IR-FLASH image
  • The resulting T1 map at every cardiac phase

A. timing in a multidimensional IR-FLASH image

B. T1 map at every cardiac phase

Figure 1: (A) Retrospective selection of timing combinations with three time dimensions.
(B) T1 cine calculated from the images in (A).

Figure 2 shows:

  • Cardiac motion, with retrospective selection of the heartbeat and saturation time, which maximizes blood-to-myocardial contrast
  • First-pass perfusion for end-diastole at a different saturation time, maximizing post- to pre-bolus myocardial contrast
  • Signal intensity surfaces for the left ventricle (LV) blood pool and myocardium at end-diastole and (D) end-diastolic R1 = 1\T1 curves for the myocardium and the arterial input function (AIF); i.e., the LV blood pool

A. Cine image     B. fp

C.2D signal intensity surfaces


Figure 2: (A) Cine images showing cardiac motion. (B) First-pass perfusion images showing contrast agent dynamics. (C) -2D signal intensity surfaces for the left ventricle (LV) and myocardium and (D) R1 curves for the myocardium and arterial input function (AIF); i.e., the LV blood pool.


Figure 1 demonstrates the utility of the IR-FLASH images for three different tasks: imaging cardiac motion, imaging respiratory motion and imaging multiple T1 weightings (multiple inversion times). The ability to retrospectively select any inversion time allows both bright- and dark-blood imaging without inversion time scouting. The ability to obtain a cardiac-resolved T1 map allows retrospective selection of any cardiac phase for analysis of T1 and may enable the study of T1 changes throughout the cardiac cycle.

Figure 2 demonstrates the utility of the SR-FLASH images for three different tasks as well: imaging cardiac motion, imaging contrast agent dynamics and imaging multiple T1 weightings (multiple saturation times). Retrospective timing selection allows maximal contrast for different tasks, with different saturation times providing better contrast for cine imaging and first-pass myocardial perfusion imaging. Since multiple time dimensions are available, signal intensity is represented as multidimensional surfaces rather than as curves. Time-resolved R1 curves can be computed, and have the important benefit of a linear response to contrast agent concentration, facilitating quantification by deconvolution of the input (AIF) and output (myocardial) R1 curves.


We have developed a novel framework exploiting the low-rank tensor structure of multidimensional cardiac images, demonstrating its use for two challenging applications. The framework enhances the practical utility of T1 mapping — using efficient, continual acquisition and advanced reconstruction techniques to overcome the practical limitations of ECG and breath-holds — and demonstrates time-resolved mapping during first-pass perfusion, which may allow direct quantification of tissue contrast agent concentration with a single bolus. Current work underway includes an extension to 3-D (expected to improve blood pool inflow properties), quantitative evaluation and validation of these applications, and exploration of other non-ECG, free-breathing multitasking applications.


  • Anthony G. Christodoulou, PhD
  • Jaime L. Shaw
  • Yibin Xie, PhD
  • Christopher T. Nguyen, PhD
  • Zhengwei Zhou
  • Nan Wang, PhD
  • Sen Ma
  • Debiao Li, PhD

Internal Collaborations

  • Cedars-Sinai Heart Institute

Representative Publications

Christodoulou, A.G., Shaw, J.L., Nguyen, C., Yang, Q., Xie, Y., Wang, N., and Li, D., “Magnetic resonance multitasking for motion-resolved quantitative cardiovascular imaging”, Nature Biomedical Engineering, doi:10.1038/s41551-018-0217-y.

Christodoulou AG, Shaw JL, Sharif B, Li D. A general low-rank tensor framework for high-dimensional cardiac imaging: application to time-resolved T1 mapping. 24th Annual ISMRM Scientific Meeting and Exhibition. Singapore. 2016:867.

Shaw JL, Christodoulou AG, Sharif B, Li D. Ungated, free-breathing native T1 mapping in multiple cardiac phases in under one minute: a proof of concept. 24th Annual ISMRM Scientific Meeting and Exhibition. Singapore. 2016:3149.