Check if point is inside of shape drawn by a complex Path2D

I want to check if a given point is inside of the space drawn inside of a irregular path – inside of the brain (the path is below).

I don’t seem to be able to use CanvasRenderingContext2D.isPointInPath(path, x, y) because it only returns true if the point is literally inside the path (the white outline).

I also don’t think I can use the odd polygon rule, given that it is possible for a point not to be in the edge and its line still hit the shape wall an even number of times…