The development of non-invasive methods for the accurate hemodynamic assessment of the coronary vasculature has become a non-trivial matter for the everyday clinical practice. Virtual Functional Assessment Index has already been suggested as a valid alternative to the invasively measured FFR but only on coronary arterial segments. In this work, we propose a novel method for the estimation of the severity of coronary lesions in arterial branches from CCTA derived images. Four left arterial branches were reconstructed in 3D using our in-house developed 3D reconstruction algorithm, and were subjected to computational blood flow simulations for the final calculation of the vFAI through the whole arterial branch. Strong correlation was found (r=0.82) between the two methods. A small relative error of 3.2% and a small trend of overestimation (0.023, SD=0.088) were also observed. All pathological cases presenting ischemia, were correctly discriminated by our method as hemodynamically significant lesions.