Comparison of diffusion tensor imaging by cardiovascular magnetic resonance and gadolinium enhanced 3D image intensity approaches to investigation of structural anisotropy in explanted rat hearts

Table 2 Summary of the notation used for vectors and angles

e ₁ ^DTI, e ₂ ^DTI and e ₃ ^DTI	DTI eigenvector corresponding to the most, intermediate and least extended directions of diffusion
v ₁ ^ST, v ₂ ^ST, v ₃ ^ST	the vector of the most, intermediate and least extended orthogonal directions of FLASH signal, determined by structure-tensor analysis.
λ₁ ^ST	eigenvalue (λ) with the subscript indicating the eigenvalue number.
α'v ₁ ^ST and α'e ₁ ^DTI	vector helix angle, used for quantification of the putative myocyte orientation. The vector quantified is identified after α’. The angle is defined in Figure 2.
α''v ₁ ^ST and α''e ₁ ^DTI	vector transverse angle, used for quantification of the putative myocyte orientation.
β'v ₃ ^ST and β'e ₃ ^DTI	vector elevation angle, used for quantification of the putative sheetlet/sheetlet-normal orientation.
β”v ₃ ^ST and β''e ₃ ^DTI	vector transverse angle, used for quantification of the putative sheetlet/sheetlet-normal orientation.
m	the true myocyte orientation vector.
s	the true sheetlet (in-plane) vector.
n	the true sheetlet normal vector. The superscript FI is used in the case of n measured by FLASH/FI.

The angles, cardiac reference planes and cardiac coordinate system are defined in Figure 1 and Figure 2 Note: the putative myocyte helix-angle α’ is projected onto the wall-tangent plane whereas the β’ elevation angles associated with the putative sheetlet in-plane and normal vectors (s and n) are projected onto the long-axis plane. FLASH: fast low angle shot; ST: structure tensor of FLASH data; DTI: diffusion tensor magnetic resonance imaging.

ISSN: 1532-429X