Using a comparison operator on a value stored as a field in the same document

Question

I want to perform a $pull update operation on votes array in the following document

{ _id: 1, votes: [ 3, 5, 6, 7, 7, 8 ], threshold : 5 } 

for which I used the following query

db.values.update({_id:1},{$pull:{votes:{$lt:"$threshold"}}},{})

This query doesn't seem to work if try to access threshold dynamically. If I try to use {$lt:5}, it works, but that beats my purpose.

I expect this to return the following document

{ _id: 1, votes: [ 5, 6, 7, 7, 8 ], threshold : 5 }

Is there a way that this could be done without changing the structure of my json or creating any additional fields?