A few more things to add about K18 - It is primarily associated with the structural integrity of epithelial cells in the body. Note that this is not just the skin (epithelium) but includes linings of cavities of the body, muscle, connective tissue and nervous tissue.
So the rapid increase in all of these tissues will be associated with an increase of K18 need throughout the body to support the rapid growth.
Research also suggests that keratins are involved in signalling pathways that are involved in regulating cell death, cell growth, and movement of various simple epithelial cells (especially in relation to tumor formation). So increases in K-18 may not just be a by-product of the growth, but in an internal feedback loop help continue the growth of tissues in the body.