do osteophytes continue to grow?

[sahuaro]

I just had an appointment with a neurologist today who is convinced that my injuries are what they are and won't progress and therefore I should not have surgery. He is insisting that the osteophytes will not continue to grow. Is this true? Now I am really confused! I had envisioned them creeping along my damaged disk (sort of like a fungus) until they reached my spinal cord... Info and opinions would really help!! Thanks.