How do you store a quadtree from jsts?

I’m using a quadtree from the jsts library. I am wondering what ways of storing the quadtree would preserve the properties of it so that when it is being read again I could access the methods in the jsts library?

So far I have tried saving the quadtree as a json and creating a new Quadtree and setting the _root to the json that is read, but when it is stringified using the JSON.toString() it changes the types of some of the properties, such as [Node] is changed to [object]. When I read it back again, I can’t use the quadtree methods such as size() returns an error of this._root.size is not a function.