Susceptibility tensor imaging (STI) can probe tissue microstructure and cellular content^1,2, but is limited by incomplete or incorrect phase information. As a result, STI noticeably differs from DTI when used to map fiber orientations in the brain³ and heart⁴. By including R₂* information, one study showed that these differences can be mitigated to improve susceptibility-based fiber tractography in the heart using conjoint relaxation and susceptibility tensor imaging (CRSTI)⁴. This work presents a fast and effective CRSTI algorithm that improves STI tractography in not only the heart, but also the kidney and brain.

Organ specimens were excised from adult, male C57BL/6 mice. One mouse was perfusion fixed with 50 mM Gd-HP-DO3A in 10% buffered formalin⁴. The chambers of the heart were then perfused with agarose gel that solidified before the organ was excised. A second mouse was perfusion fixed with 10% buffered formalin⁵. The kidney was excised and immersed in formalin overnight. A third mouse was perfusion fixed with 50 mM of Gd-HP-DO3A in 10% buffered formalin following a procedure described by Johnson et al.⁶ The head was removed with the brain intact and immersed in formalin overnight. All three specimens were stored in a solution of 2.5 mM Gd-HP-DO3A in 10 mM phosphate-buffered saline prior to scanning. MRI data was acquired from each organ using the protocols in Table 1.

Normalized phase data were calculated from the multi-orientation GRE image data using iHARPERELLA⁷. Susceptibility and relaxation tensors were calculated using MATLAB’s LSQR algorithm with mean-value regularization⁸ and constraints on high spatial frequencies³. The susceptibility tensor ($$${\bfχ}$$$) was reconstructed by inverting the susceptibility-phase relationship². A second-order relaxation tensor ($$${\bf R}$$$) was fit to the apparent R₂* observed in each subject orientation⁴. R₂* is smallest in the direction parallel to the long axis of axons⁹, myofibers⁴, and renal tubules, so the orientation of these structures is indicated by the minor eigenvector of $$${\bf R}$$$. In $$${\bfχ}$$$, orientation is indicated by the major eigenvector in myofibers and axon fiber bundles^2,10, and by the minor eigenvector in the renal tubules⁵. To estimate a set of shared eigenvectors ($$${\bf Q}$$$), a CRSTI algorithm was implemented to eigendecompose a weighted combination of $$${\bfχ}$$$ and $$${\bf R}$$$: $${\ttν{\bfχ}–{\bf R}={\bf Q}(ν{\bfΛ_χ}–{\bfΛ_R}){\bf Q}^T}$$ Here, ν (Hz) attempts to assign equal weight to the susceptibility and relaxation tensors, and $$${\bfΛ_χ}$$$ and $$${\bfΛ_R}$$$ are diagonal matrices of the eigenvalues of $$${\bfχ}$$$ and $$${\bf R}$$$, respectively. Relaxation is defined as –$$${\bf R}$$$, and the sign of ν is selected to ensure that the major eigenvector of $$${\bf Q}$$$ aligns with the tissue structure orientation. Tractography was then performed on the STI, CRSTI, and DTI data using Diffusion Toolkit and TrackVis¹¹.

The proposed CRSTI algorithm improved susceptibility-based tractography in each organ. As similarly demonstrated in an earlier study⁴, the mouse heart tractography data (Fig. 1) show that CRSTI fiber orientations are more consistent with DTI compared to traditional STI. In the kidney tractography data (Fig. 2), CRSTI yielded improvements over STI that were most obvious in the medullary regions, where susceptibility and diffusion anisotropy were greatest. STI tractography exhibited the greatest differences from DTI in the mouse brain (Fig. 3). CRSTI corrected the orientation and improved the continuity of axon fiber tracts throughout the white matter regions of the brain, particularly in the corpus callosum, cerebellum, and anterior commissure.

CRSTI is able to compensate for inadequate phase information by including eigenvector data from $$${\bf R}$$$⁴. This is possible because R₂* in a set of parallel cylinders is positively correlated with the magnetic susceptibility difference between the objects and the surrounding medium¹². Hence, the anisotropy of $$${\bfχ}$$$ engenders anisotropy in $$${\bf R}$$$¹³, and the two tensors share an eigenvector corresponding to the orientation of the cylindrical tissue structure. Though not necessary for CRSTI, contrast agents can also be used to enhance the inherently anisotropic component of $$${\bf R}$$$ in organs with capillaries that align with the tissue structure¹⁴, such as the heart¹⁵ and kidney¹⁶.

Susceptibility-based tensor mapping is useful for studying the organized molecular sources of susceptibility contrast and anisotropy in the heart, kidney, and brain. This technique is made more robust by conjoint tensor estimation, which requires no additional scan time since phase and relaxation data can be acquired simultaneously. By simplifying the shared eigenvector optimization problem⁴, this particular CRSTI algorithm requires very little computational overhead. The efficiency and chemical sensitivity of this technique make CRSTI a potential tool for studying disease in a variety of magnetically anisotropic tissues throughout the body.