# Cardiac Diffusion Tensor Biomarkers of Chronic Infarction Based on In Vivo Data
## 4 Discussion
RD is the average of e\({}_{2}\) and e\({}_{3}\) and represents the changes occurring in the radial direction due to the increase or decrease of ECV. In this study, we showed that RD increases significantly from the remote to the border (18% increase) and infarct (32.3% increase) regions. The results computed from experimental data concur with the findings of particle diffusion simulations. From the diffusion simulations, as ECV increases, e\({}_{1}\), e\({}_{2}\), e\({}_{3}\), andMD increase, and FA decreases. These trends agree with previous studies [42] and remain consistent regardless of the number of simulated water molecules (from four to thirty thousand water molecules per representative volume), length of adopted time step (from 10\({}^{-5}\) s to 10\({}^{-7}\) s), and cell structures (10 to 45 cell structures have been simulated). Additionally, as ECV increases, simulated e\({}_{2}\) and e\({}_{3}\) values increase at a higher rate with respect to e\({}_{1}\). Among T1-mapping, ECV and diffusion quantities, ECV demonstrated the highest change in the infarct (51.6% increase) and border (22.6% increase) regions compared to the remote myocardium. However, among the non-contrast-based methods, e\({}_{2}\), e\({}_{3}\), and RD exhibited the largest change. Moreover, the increases in e\({}_{2}\) (31.9% and 19.2% increases from remote to infarct and border regions, respectively), e\({}_{3}\) (33.4% and 16.1% increases from remote to infarct and border regions, respectively), and RD (32.3% and 18% increases from remote to infarct and border regions, respectively) were higher than native T1 (21.2% and 8.4% increases from remote to infarct and border regions, respectively). In our previous study [14], ex vivo cDTI swine data acquired six to ten weeks post-infarction was used to compare diffusion tensor invariants, diffusion eigenvalues, and radial diffusivity across the remote, border, and infarct regions. In terms of the increase or decrease of tensor invariants, eigenvalues, and radial diffusivity in the infarct and border regions, similar trends were observed as in the present study (cf. Figure 7). However, while the diffusion eigenvalues and mean diffusivity computed using in vivo cDTI were observed to be higher than the values obtained using ex vivo data across all regions, their percentage changes were lower than the percentage changes computed using ex vivo data. The median e\({}_{1}\), e\({}_{2}\), e\({}_{3}\), and RD values computed using ex vivo data (values computed using in vivo data in this study are in parenthesis) were, respectively: 1.16 (2.28) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{1}\), 0.88 (1.83) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{2}\), 0.72 (1.42) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{3}\), and 0.79 (1.62) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for RD, in the infarct region; 0.91 (2.14) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{1}\), 0.55 (1.65) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{2}\), 0.39 (1.24) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{3}\), and 0.47 (1.45) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for RD, in the border region; 0.70 (1.94) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{1}\), 0.41 (1.38) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{2}\), 0.28 (1.06) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for e\({}_{3}\), and 0.35 (1.22) \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s for RD, in the remote region. The observed discrepancy between results obtained using in vivo and ex vivo data could be due to several factors, among which the in vivo motion artifact and perfusion. Furthermore, the MRI sequence parameters were not identical in vivo and ex vivo. The ex vivo data were acquired at a higher resolution of 1.0 \(\times\) 1.0 \(\times\) 1.0 mm\({}^{3}\), higher SNR of \(\approx\)41 and higher b-value of 1000 s/mm\({}^{2}\) while the in vivo data were acquired at a resolution of 2.0 \(\times\) 2.0 \(\times\) 2.0 mm\({}^{3}\) with a SNR of \(\approx\)16 and b-value of 350 s/mm\({}^{2}\).