The results described in this work are part of a larger project. The long term goal of this project is to help physicians predict the hemodynamic changes, and associated risks, caused by different treatment options for brain arteriovenous malformations. First, we need to build a model of the vascular architecture of each specific patient. Our approach to build these models is described in this work. Later we will use the model of the vascular architecture to simulate the velocity and pressure gradients of the blood flowing within the vessels, and the stresses on the blood vessel walls, before and after treatment. We are developing a computer program to describe each blood vessel as a parametric curve, where each point within this curve includes a normal vector that points in the opposite direction of the pressure gradient. The shape of the cross section of the vessel in each point is described as an ellipse. Our program is able to describe the geometry of a blood vessel using as an input a cloud of dots. The program allows us to model any blood vessel, and other tubular structures.