Which procedure involves “washing” to separate healthy sperm from the unhealthy ones, and then placing this concentration of healthy sperm into the uterus around the time of ovulation?

Intrauterine insemination

Explanation:

Intrauterine insemination is considered a low complexity assisted reproduction technique. Like programmed intercourse, a woman's menstrual cycle is followed by the doctor through serial transvaginal ultrasounds. However, the difference is that in this technique the patient returns to the clinic during her ovulatory period for the deposition of semen, her partner or the donor, in her uterine cavity. Semen is washed off and healthy sperm are placed directly into the woman's uterine cavity facilitating gamete encounter and natural fertilization.