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Cardiovascular diseases (CVDs) are a major global health concern, re- responsible for more than a quarter of annual deaths (around 17.5 million). Non-invasive dMRI models, like apparent diffusion coefficient and diffusion tensor imaging, can assess changes in the myocardium due to CVDs. How- ever, these models lack biophysical interpretations preferred by clinicians. To address this, biophysical models are being developed to better under- stand the myocardium's microstructure. A virtual imaging framework is essential to validate these models and analyze dMRI sensitivity to micro-structural changes. In this thesis, we present a virtual imaging framework to simulate dMRI signals in cardiac microstructure and microvasculature. The framework in- includes a numerical phantom mimicking cardiac microstructure and a solver for the generalized Bloch-Torrey equation, termed SpinDoctor-IVIM. With the first objective, the morphometric study found no significant difference (p > 0.01) between the volume, length, and primary and secondary axes of the simulated and real cardiomyocyte data from the literature. Structural correlation analysis confirmed that the in-silico tissue shows a similar disorderliness as the real tissue. The absolute angle differences between the simulated helical angles (HA) and the input HA of the cardiomyocytes (4.3◦ ± 3.1◦) closely match the angle differences reported in previous studies using experimental cardiac diffusion tensor imaging (cDTI) and histology (3.7◦ ± 6.4◦) and (4.9◦ ± 14.6◦). With the second objective, the SpinDoctor-IVIM stands out for accounting for volumetric microvasculature during blood flow simulations, incorporating diffusion phenomena in the intravascular space, and considering permeability between the intravascular and extravascular spaces, providing more accurate and comprehensive results. Overall, this thesis contributes valuable insights into the microstructure and microvasculature of the myocardium, offering promising advancements in studying CVD using dMRI. The developed virtual imaging framework is a crucial step towards improving cardiac research based on dMRI.