Three-dimensional micro-structurally informed in silico myocardium -- towards virtual imaging trials in cardiac diffusion weighted MRI

In silico tissue models enable evaluating quantitative models of magnetic resonance imaging. This includes validating and sensitivity analysis of imaging biomarkers and tissue microstructure parameters. We propose a novel method to generate a realistic numerical phantom of myocardial microstructure. We extend previous studies accounting for the cardiomyocyte shape variability, water exchange between the cardiomyocytes (intercalated discs), myocardial microstructure disarray, and four sheetlet orientations. In the first stage of the method, cardiomyocytes and sheetlets are generated by considering the shape variability and intercalated discs in cardiomyocyte-to-cardiomyocyte connections. Sheetlets are then aggregated and oriented in the directions of interest. Our morphometric study demonstrates no significant difference ($p>0.01$) between the distribution of volume, length, and primary and secondary axes of the numerical and real (literature) cardiomyocyte data. Structural correlation analysis validates that the in-silico tissue is in the same class of disorderliness as the real tissue. Additionally, the absolute angle differences between the simulated helical angle (HA) and input HA (reference value) of the cardiomyocytes ($4.3^\circ\pm 3.1^\circ$) demonstrate a good agreement with the absolute angle difference between the measured HA using experimental cardiac diffusion tensor imaging (cDTI) and histology (reference value) reported by (Holmes et al., 2000) ($3.7^\circ\pm6.4^\circ$) and (Scollan et al., 1998) ($4.9^\circ\pm 14.6^\circ$). The angular distance between eigenvectors and sheetlet angles of the input and simulated cDTI is smaller than those between measured angles using structural tensor imaging (gold standard) and experimental cDTI. These results confirm that the proposed method can generate richer numerical phantoms for the myocardium than previous studies.