Here is another video of how tysabri works. You will notice they say that tysabri inhibits Leukocytes (Amercian Spelling) Leucocytes (Britsh Spelling) but this means white blood cells T cells B cell monocytes, etc. so it is not just T cells
In the video you see the white blood cells by leaving the blood by pushing between the gap from blood vessel cells next to each other. I believe this is wrong, they actually go through the blood vessel cell and not the gap between cells of the blood vessel.