A meniscectomy is the surgical procedure of removing a meniscus.
The meniscus of the knee acts as a shock absorber between the long bones of the knee, and the most effective part of the shock absorption is around the peripheral rim of the meniscus. Knee surgeons will do their best to keep this part of the meniscus intact, so a total meniscectomy is very seldom performed unless there has been total destruction of the meniscus during an injury. So if a meniscus tear is not amenable to suturing (sewing back together) and the damaged bit is causing problems like locking of the knee, then the surgeon may choose to remove the damaged bit - this is called a partial meniscectomy. The outer rim would be left intact. Sometimes the meniscus is just frayed on its free edge, and the surgeon may trim away this frayed edge, because the damaged tissues may be producing chemicals that lead to further inflammation within the knee.
The free edge of the meniscus has a poorer blood supply than the rim, and the bits removed in a partial meniscectomy are likely to be those bits that would not have healed on their own due to the poor blood supply.
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