Abstract—In this paper, a model-based approach to medical image analysis is presented. It is aimed at understanding the in-fluence of the physiological (related to tissue) and physical (related to image modality) processes underlying the image content. This methodology is exemplified by modeling first, the liver and its vas-cular network, and second, the standard computed tomography (CT) scan acquisition. After a brief survey on vascular modeling literature, a new method, aimed at the generation of growing three-dimensional vascular structures perfusing the tissue, is described. A solution is proposed in order to avoid intersections among vessels belonging to arterial and/or venous trees, which are physiologically con-nected. Then it is sho...