Heart failure is a leading cause of premature death globally. A significant contributor is the impairment of myocardial blood flow due to microvascular dysfunction. Studies show that over one-third of patients with angina have microvascular disease [1]. Current clinical methods identify microvascular dysfunction only through invasive tests. To better understand these conditions, personalised patient-specific models that reflect the complexities and abnormalities of the microvasculature are essential. Existing computational models treat microvessel flow homogeneously and fail to account for specific microvessel defects. Some studies have used a constrained constructive algorithm (CCO) to generate micro blood vessels [2], but these are not patient-specific, and it does not account for the geometry of large blood vessels obtained from imaging. This study introduces a novel algorithm for creating patient-specific small and micro blood vessels connected to existing epicardial large vessels in the left ventricle myocardium, using a modified CCO algorithm that integrates statistical data from invasive measurements. Our method incrementally constructs blood vessels linked to terminal points distributed throughout the myocardium. Each new vessel connects to an existing one, with adjustments made to the bifurcation points and vessel radii in accordance with Murray’s law and Poiseuille’s law, aimed at minimising total blood flow resistance. Additional constraints are applied to regulate the radius ratio and length of the principal paths of the transmural vessels. Our findings demonstrate that, even within this simplified model, the branching angles and radius ratios of the microvessels align with the statistical characteristics observed in clinical data. As a result, the generated microvessels closely correspond to existing clinical observations.