Lifecycle of a Mushroom: Travelling through the Mushroom

I've been thinking of ways that I can show the transition from the outside of the mushroom into the microscopic level of the mushroom. Using a technique I developed a little while back, I think i've come up with an elegant solution to this problem. In my animatic the transition is an extremely ugly and cumbersome cross fade, which doesn't fit in with the overall editing and visual style. The aim here is to simulate the feeling of travelling up through the mushroom (the concentric circles) to discover the world within.