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In this paper, a model-based approach to medical image analysis is presented. It is aimed at understanding the influence 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 vascular 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 connected. Then it is shown how the propagation of contrast material leads to simulate time-dependent sequences of enhanced liver CT slices.