Using High-level API or plain OpenGL

I’m struggling with the following problem and need to decide what technology I should use to do that.
The problem is to create a 3D model of a vascular system. So, as you can figure out, the model is complicated and irregular. To be specific it should consist of generalized cylinders connected to each other. The junktions are also irregular. This forms a tree that should look more or less like this
I really don’t want to reinvent a circle :). I would like to work at a maximum high level of abstraction (if possible). So my question is: do I need to use plain OpenGL and draw cylinders (where top and down ellipes are not parallel, of course) and take care of everything on my own? Or can I use a already existing API that will help me with e.x. meshing such a cylinder? If yes, what API? I’d like to start a discussion here what is the best and easiest way to do that.

What is not clear in your post is whether you create the tree procedurally, or from a specific modeller, or measured from an actual vascular system.
This is important to help decide how to mesh it.

I want to create in, using a modification of a method described here:
The whole algorythm for meshing is described there. But, I want to make my work as simple as it can get so, e.x. would be convenient if I could use a function for drawing a generalized cylinder instead of writing such on my own.
As far as I know glut provides some of the functionality that I may use, but still, I don’t want to write everything from scratch (if that is possible, of course).