  We revisit the problem of proving the incompressible limit for the
compressible porous media equation with Newtonian drift and growth. The
question is motivated by models of living tissues development including
chemotaxis. We extend the problem, already treated by the authors and several
other contributions, in using a simplified approach, in treating dimensions two
or higher, and in incorporating the pressure driven growth term. We also
complete the analysis with stronger $L^4$ estimates on the pressure gradient.
The major difficulty is to prove the strong convergence of the pressure
gradient which is obtained here by a new observation on an algebraic relation
involving the pressure gradient for weak limits.
