GR Group Theory – Arbitrary distortion of cyclic subgroups of soluble groups

Accept $$G$$ is a finally generated solvable group, and $$H$$ an infinite cyclic subgroup of $$G$$, Which possible functions can occur as subgroup distortion? $$H$$ in the $$G$$?

For polycyclic groups Osin and others have investigated this question. However, I am particularly interested in finitely generated, finite-rank solvable non-polycyclic groups. If this is already known, any references would be very happy.

Thank you for possible answers.