Embeddings of disks into Euclidean space

Question

What are the smooth embeddings $D^n \hookrightarrow D^{2n}$ so that $\partial D^n \hookrightarrow \partial D^{2n}$, up to smooth isotopy (which can move the boundary of the disk)? This question might be too difficult in low-dimensions, $n = 2$, but maybe the answer is known in high-dimensions, $n \ge 3$. Let me know point out that Haefliger constructed different embeddings of $S^3 \hookrightarrow S^6$, which suggest that there are different embeddings $D^3 \hookrightarrow D^6$.