Whether sclerotherapy works or not depends on whether the whole vein wall is destroyed by the sclerosing agent or not.
If we compare a large vein - the sort that become varicose - with a thread vein, we can see that the normal/varicose vein is larger than the thread vein. But more importantly, the wall is far thicker - especially the media.
If you now look at the animation on the left of this page you cam see the effects of injecting sclerosing agent on each of these sorts of veins |