Can Botox be injected in the tear trough ligament to relax it and cause some atrophy?

Hello and thank you for your question. It is always best to see you face to face for a consult and examination however in this case no this is not possible - botox works on muscle fibres not ligamentous tissue. You may find filler here is more beneficial. I hope that helps answer your question. Always seek an experienced and qualified medical professional for these treatments. Very best wishes

Botulinum toxin mainly works on muscle and not ligaments, if injected specifically to a ligament structure it is unlikely to have any effect, but of course if it spills over to surrounding muscle structure it may have unwanted effects.

Botox is used to affect the ability of a muscle to contract. This would not work on ligaments. There are many treatments available to improve the tear trough area. The most common is fillers. But there are other treatments to improve skin tone and texture such as Morpheus8. See an expert injector near you to learn more.