Stay on the Beat With Tensor-Valued Encoding: Time-Dependent Diffusion and Cell Size Estimation in ex vivo Heart

Samo Lasič*, Nadira Yuldasheva, Filip Szczepankiewicz, Markus Nilsson, Matthew Budde, Erica Dall’Armellina, Jürgen E. Schneider, Irvin Teh, Henrik Lundell

*Corresponding author for this work
3 Citations (Scopus)


Diffusion encoding with free gradient waveforms can provide increased microstructural specificity in heterogeneous tissues compared to conventional encoding approaches. This is achieved by considering specific aspects of encoding, such as b-tensor shape, sensitivity to bulk motion and to time-dependent diffusion (TDD). In tensor-valued encoding, different b-tensor shapes are used, such as in linear tensor encoding (LTE) or spherical tensor encoding (STE). STE can be employed for estimation of mean diffusivity (MD) or in combination with LTE to probe average microscopic anisotropy unconfounded by orientation dispersion. While tensor-valued encoding has been successfully applied in the brain and other organs, its potential and limitations have not yet been fully explored in cardiac applications. To avoid artefacts due to motion, which are particularly challenging in cardiac imaging, arbitrary b-tensors can be designed with motion compensation, i.e. gradient moment nulling, while also nulling the adverse effects of concomitant gradients. Encoding waveforms with varying degrees of motion compensation may however have significantly different sensitivities to TDD. This effect can be prominent in tissues with relatively large cell sizes such as in the heart and can be used advantageously to provide further tissue information. To account for TDD in tensor-valued encoding, the interplay between asynchronous gradients simultaneously applied along different directions needs to be considered. As the first step toward in vivo cardiac applications, our overarching goal was to explore the feasibility of acceleration compensated tensor-valued encoding on preclinical and clinical scanners ex vivo. We have demonstrated strong and predictable variation of MD due to TDD in mouse and pig hearts using a wide range of LTE and STE with progressively increasing degrees of motion compensation. Our preliminary data from acceleration compensated STE and LTE at high b-values, attainable on the preclinical scanner, indicate that TDD needs to be considered in experiments with varying b-tensor shapes. We have presented a novel theoretical framework, which enables cell size estimation, helps to elucidate limitations and provides a basis for further optimizations of experiments probing both mean diffusivity and microscopic anisotropy in the heart.

Original languageEnglish
Article number812115
JournalFrontiers in Physics
Pages (from-to)1-19
Number of pages19
Publication statusPublished - 25 Mar 2022


  • b-tensor
  • cardiac MRI
  • isotropic diffusion weighting
  • mean diffusivity
  • microscopic anisotropy
  • motion compensation
  • tensor-valued diffusion encoding
  • time-dependent restricted diffusion


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