Diels Alder - Why HOMO and LUMO?

[CrimpJiggler]

In diels alder reactions, why does the reaction always occur between the HOMO of the diene, and the LUMO of the dienophile? Well, what I'm really trying to figure out is how to determine which reactant donates the electrons, and which reactant receives them in cycloadditions.

 

[DrDu]

In the course of the reaction, the bond in the dienophile is broken, so it's LUMO has somehow to be populated. The other possibility, depopulation of the HOMO, would not leave electrons at all on the dienophile to form the new bonds.