'with the insertion of' is a perfectly correct and usable phrase in written English.
You can use it when you need to describe a process of inserting something - for example, "The project involved adding new features, with the insertion of several scripts".
That didn't change much with the insertion of Alex Muyl.
Schmidt goes along with this, diversifying a generally chronological approach with the insertion of novelists from much later.
Fabric length is increased with the insertion of each succeeding weft yarn.
No femoral fractures occurred intraoperatively with the insertion of the prosthesis.
And the degradation rate of the backbone increased with the insertion of MA into the terpolymers.
With the insertion of the Magellan spacecraft in Venus orbit, systematic radar mapping of Earth's planetary neighbor began under the leadership of the Principal Investigator, Professor Gordon Pettengill.
All participants compared the insertion of the MIDCM device favorably with the insertion of a chest drain.
(Saltwater pearls begin with the insertion of a bead -- simulating a piece of sand -- but the freshwaters are cultured with a piece of mantle tissue taken from another mussel).
The Buccaneers saw the Giants' secondary as a weak spot in the defense, and that feeling only grew with the insertion of Webster, who had not started since the third game of the season.
Dr. Bird, as part of his continuing study of what the gene does, engineered a strain of mice whose MECP2 genes had been inactivated with the insertion of an extra block of DNA.
Copia elements showed relatively recent insertion during the period corresponding to substitution values of between 0 and 0.2, which coincides with the insertion of Gypsy and Copia elements in the tomato genome (Fig. 2e).
