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Explanation: Ther process by which the endometrium thickens and develops a richer blood supply around ovulation can be described in many ways but the technical word, and the only word which conveys any sense of Gefäss, is vascularization. I recommend you write "under the influence of oestrogen and progesterone, the lining of the uterus becomes highly vascularized in preparation for a possible pregnancy" (even though this is slightly incorrect: what is prepared for is the implantation of the fertilized egg; pregnancy is the result if this succeeds!).
You have to look at the context! of course -sprossen can mean to sprout (though I don't know any context where something could sprout INwards, as sprouting is by nature an expansive, upward growth), but how could you apply that to the growth of blood vessels in the uterine lining?