# Cardiac Diffusion Tensor Biomarkers of Chronic Infarction Based on In Vivo Data
## 2 Methods
### Regional Subdivision and Registration  
To quantitatively compare diffusion tensor quantities, Native T1, and ECV, the myocardium was subdivided into remote, border, and infarct regions. The regional subdivision process was based on late gadolinium enhanced (LGE) MR images. Following the regional subdivision technique described by [PERSON] et al. [22], regions of interest were drawn on the remote regions of each slice. Mean signal intensity (\(\mu_{\mathrm{remote}}\)) and standard deviation (\(\sigma_{\mathrm{remote}}\)) were computed for each subject using regions of interest across all slices. Voxels with signal intensity (SI) less than the sum of mean signal intensity  
Figure 1: Experimental procedure: infarct induction and MR imaging  
and two standard deviations were labeled as the remote zone (i.e., SI \(\leq\mu_{\text{remote}}+2\sigma_{\text{remote}}\)). To determine mean signal intensity (\(\mu_{\text{infarct}}\)) and standard deviation (\(\sigma_{\text{infarct}}\)) of the infarct zone, small regions of interest (ROIs) were outlined on the most hyper-enhanced region of the remaining unlabeled myocardium of each slice. The mean signal intensities of remote and infarct zones were averaged to compute an intermediate value. Voxels with signal intensity higher than the sum of mean signal intensity and two standard deviations of the remote zone, but below the computed intermediate value (i.e., \(\mu_{\text{remote}}+2\sigma_{\text{remote}}<\text{SI}<\frac{1}{2}(\mu_{ \text{remote}}+\mu_{\text{infarct}})\)) were labeled as border zone. The remaining voxels (i.e., voxels with SI \(\geq\frac{1}{2}(\mu_{\text{infarct}}+\mu_{\text{remote}})\)) were labeled as infarct zone. Based on this approach, label maps marking remote, border, and infarct regions were created for each slice. LGE data were acquired during diastole while cDTI, due to its motion-compensated approach, was acquired during systole. Moreover, the LGE and cDTI sequences had different resolutions and fields of view. Hence, both rigid and non-rigid registrations were necessary to superimpose the LGE-based remote, border, and infarct zones to the cDTI data. For this purpose, quaternions [23] computed from LGE and cDTI images were used to rigidly register LGE nodes (each node corresponded to a voxel in the image space) to the cDTI nodes in the cDTI image space. This step was carried out to ensure that the LGE and cDTI nodes were in the same image space (Figure 2a). To reflect the left ventricle (LV) longitudinal shortening during systole, spacing along the \(z\)-axis between LGE-based label map slices was reduced uniformly on a subject-specific basis. This was accomplished by matching the \(z\) coordinates of the most basal and apical LGE slices with the corresponding most basal and apical cDTI slices (Figure 2b). Figure 2: Diagram illustrating the registration process that was used to register LGE-based label maps to cDTI slices. (**a**) Quaternions were used to rigidly register LGE-based label maps to cDTI binary masks to ensure that both LGE and cDTI were in the same image space. (**b**) Since LGE was acquired during diastole and cDTI was acquired during systole, the longitudinal spacing between the LGE slices was reduced to reflect the contracted LV state during systole. This shortening was achieved by matching the basal and apical LGE and cDTI slices. (**c**) Although the basal and apical LGE and cDTI slices were aligned, the rest of the slices were not aligned. Hence, the cDTI slice masks at the \(z\)-axis location of the LGE slices were obtained via weighted average. (**d**) To obtain label maps at the cDTI location, aligned LGE-based label maps and weighted averaged cDTI slices were non-rigidly registered. (**e**) The cDTI label maps obtained in step (**d**) were at the \(z\)-axis location of the LGE slices. Hence, 3D interpolation was carried out to obtain label map values at the \(z\)-axis location of the original cDTI slices.