yes, i got it.
i don't have a7, only a6, i could open your fbx and mdl files, but not your level.
ok. your model does not have cuts, nor are the normals flipped, nor is it an alpha issue. the meshes are ok.
you said, "parts of the heart is cut". do you refer to ->this? the black lines?
that is because of your skin design.
you used Max' Render-To-Texture, i assume. it is a nice feature, but stops to render precisely on certain edges. that is where you see the black lines, MED's/Acknex's mipmapping and skinning process in not one-pixel-accurate. how to solve: if max allows it, render with a greater overdraw (if that's the right word, i mean render 2 or 3 px more on the borders than it is actually necessary), if not, choose a neutral background, not black, some kind of red/yellow would do for your heart i think.