# Cardiac Diffusion Tensor Biomarkers of Chronic Infarction Based on In Vivo Data
###### Abstract  
In vivo cardiac diffusion tensor imaging (cDTI) data were acquired in swine subjects six to ten weeks post-myocardial infarction (MI) to identify microstructural-based biomarkers of MI. Diffusion tensor invariants, diffusion tensor eigenvalues, and radial diffusivity (RD) are evaluated in the infarct, border, and remote myocardium, and compared with extracellular volume fraction (ECV) and native T1 values. Additionally, to aid the interpretation of the experimental results, the diffusion of water molecules was numerically simulated as a function of ECV. Finally, findings based on in vivo measures were confirmed using higher-resolution and higher signal-to-noise data acquired ex vivo in the same subjects. Mean diffusivity, diffusion tensor eigenvalues, and RD increased in the infarct and border regions compared to remote myocardium, while fractional anisotropy decreased. Secondary (e\({}_{2}\)) and tertiary (e\({}_{3}\)) eigenvalues increased more significantly than the primary eigenvalue in the infarct and border regions. These findings were confirmed by the diffusion simulations. Although ECV presented the largest increase in infarct and border regions, e\({}_{2}\), e\({}_{3}\), and RD increased the most among non-contrast-based biomarkers. RD is of special interest as it summarizes the changes occurring in the radial direction and may be more robust than e\({}_{2}\) or e\({}_{3}\) alone. diffusion tensor imaging; in vivo cDTI; chronic infarction; cardiac microstructure; radial diffusivity; swine infarction model +
Footnote †: journal: Medical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA; tanjib@knights. Diffusion tensor invariants, such as mean diffusivity (MD) and fractional anisotropy (FA), can be used to detect and quantify the extent of MI with the additional benefit of providing insight into cardiac microstructure. In chronic infarcted tissue, previous studies [9; 10; 11] have reported an increase in MD and a decrease in FA, indicating overall microstructural changes post-MI. However, these overall microstructural changes have not carried over to specific changes in the preferential direction of the cardiomyocytes and along the sheetlets/cross-myofiber directions. Information regarding changes in these microstructural directions can be extracted from the diffusion tensor eigenvalues. Indeed, the primary eigenvalue (e\({}_{1}\)) corresponds to the diffusivity along the preferential direction of the cardiomyocytesocytes [12], while the secondary (e\({}_{2}\)) and tertiary (e\({}_{3}\)) eigenvalues correspond to the diffusivity along the sheetlet and cross-myofiber directions [13]. The main goal of this study is to refine the analysis of cardiac microstructural changes by studying the individual diffusion tensor eigenvalues and by computing radial diffusivity, a marker of both sheetlet and cross-myofiber diffusivity, using in vivo cDTI data (radial diffusivity is defined as the average of the secondary and tertiary eigenvalues). These quantities are then compared against diffusion tensor invariants (e.g., MD, FA), native-T1, and extracellular volume fraction (ECV) to establish their sensitivity in identifying the infarcted tissue and its microstructural changes. In the infarcted region, the extracellular volume fraction increases due to the death of cardiomyocytes. We hypothesize that this increased extracellular space will mainly occur in the radial direction of the remaining cardiomyocytes and replacement fibrosis, and will be reflected by a higher increase in e\({}_{2}\), e\({}_{3}\), and radial diffusivity compared to the increase in e\({}_{1}\) and MD. This hypothesis is also motivated by our previous work [14] based on ex vivo, high-resolution, and high signal-to-noise ratio (SNR) data. Moreover, to further understand the results computed from experimental data, we simulate numerically the diffusion of water molecules. The computed diffusion quantities are then compared with experimental results as a function of ECV.