20 week scan amniotic band

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Had my scan today, all good but right at the end she said she'd found an amniotic band, showed me a thin white line, and said she'd refer for a growth scan. Didn't seem too fussed, said it was "tissue" and said no more.

But of course now I'm worried! Anyone else had this?

One of those things that can have a range of outcomes.

The majority found on scans resolve and don't cause issues. If there are no signs of any effects on the baby on the scan (normal movement, band not attached to baby) then they tend to have no consequences.

Definitely speak to your doctor to find out more. The more detailed scan will check there have been no issues, but talk to your doc for more info and peace of mind.

It's eight weeks until my next appt, I didn't really ask anything as I had no idea what it was

It's basically where the part of the amnion ruptures (they think) and you end up with loops of it in the amniotic sack. Most cause no issues at all and you'd never have known they were there. Some can get tangled round extremities (a bit like elastic bands) and cause issues as the baby grows, but I think if they're leaving you 8 weeks and didn't seem concerned then it's more likely you fall into the former camp.
I'd certainly call your midwife for a chat about it - she should be able to tell you what they picked up.